**Temperature Effects on Liquid Crystal Nonlinearity**

DOI: 10.5772/intechopen.70414

Temperature Effects on Liquid Crystal Nonlinearity

Lamees Abdulkaeem Al-Qurainy and Kais A.M. Al Naimee Lamees Abdulkaeem Al-Qurainy and

Additional information is available at the end of the chapter Kais A.M. Al Naimee

http://dx.doi.org/10.5772/intechopen.70414 Additional information is available at the end of the chapter

#### Abstract

The effect of temperature variation on nonlinear refractive indices of several types of liquid crystal (LC) compounds has been reported. Five samples have been investigated: two pure components (E7, MLC 6241-000) and three mixtures are obtained by mixing the previous two in different proportions. Birefringence, the average refractive index and the temperature gradients of refractive indices of the LCs are determined. The variations in refractive indices and birefringence were fitted theoretically using the modified Vuks equation. Excellent agreement is obtained between the fitted values and experimental data. Finally, the bistability of nonlinear refractive indices with temperature of liquid crystal (LC) compounds has been studied. The bistability of liquid crystals based on temperature is clearly observed for all samples. Also, the extraordinary refractive index has larger bistability than the ordinary refractive index. The measurements are performed at 1550 nm wavelength using wedged cell refractometer method.

Keywords: extraordinary, refractive index, liquid crystal, birefringence, order parameter

### 1. Introduction

Liquid crystals exhibit optical anisotropy or birefringence (Δn). This is an essential physical property of liquid crystals and is a key element in how they are implemented in the display [1, 2], photonic devices [3], communications signal processing [4], and beam steering [5].

When light propagates through anisotropic media such as liquid crystals, it will be divided into two rays which travel through the material at different velocities, and therefore have different refractive indices, the ordinary index (no), and extraordinary index (ne), and the difference is called as birefringence or double refraction (Δn=ne � no). Depending on the values of ne and no, birefringence can be positive or negative [6, 7].

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

Temperature plays a fundamental role in affecting the refractive indices of LCs. As the temperature increases, ordinary (no) and extraordinary (ne) refractive indices of LCs behave differently from each other [8, 9].

For an isotropic LC, the ordinary and extraordinary refractive indices are determined by corresponding ordinary and extraordinary molecular polarizability α<sup>o</sup> and αe. Vuks modified the Lorentz-Lorenz equation by assuming that the internal field in a liquid crystal is equal in all directions, and therefore produce a semi-empirical equation correlating macroscopic refractive

The temperature-dependent LC refractive indices based on Vuks model can be expressed by

2 3

3

Tc <sup>B</sup>

> Tc <sup>β</sup>

〈n〉 ¼ A � BT (9)

ne ¼ 〈n〉 þ

no <sup>¼</sup> 〈n〉 � <sup>1</sup>

On the other hand, the LC birefringence is linearly proportional to the order parameter S. Through Haller's semi-empirical equation, the order parameter can be approximated as

<sup>S</sup> <sup>¼</sup> <sup>1</sup> � <sup>T</sup>

where T is the operating temperature, Tc is the clearing temperature of LC material, and B is the material constant, for many LC compounds and mixtures studied β = (0.2–0.25). Thus, the

<sup>Δ</sup>n Tð Þ¼ ð Þ <sup>Δ</sup><sup>n</sup> <sup>o</sup> <sup>1</sup> � <sup>T</sup>

where (Δn)o is the LC birefringence in the crystalline state at absolute zero (T = 0 K). From

<sup>S</sup> <sup>¼</sup> <sup>Δ</sup><sup>n</sup> ð Þ Δn <sup>o</sup>

Substituting Eqs. (7) and (9) back to Eqs. (4) and (5), the modified four-parameter model for

The average refractive index decreases linearly with increasing temperature as [16]:

describing the temperature effect on the LC refractive indices is obtained [17–19]:

<sup>3</sup> <sup>α</sup>e, <sup>o</sup> (3)

Temperature Effects on Liquid Crystal Nonlinearity http://dx.doi.org/10.5772/intechopen.70414

Δn (4)

Δn (5)

> is defined as <n2

> =

161

(6)

(7)

(8)

index with microscopic molecular polarizability [11, 15].

(ne <sup>2</sup> + 2no 2 )/3

n2 e, <sup>o</sup> � 1 〈n<sup>2</sup>〉 <sup>þ</sup> <sup>2</sup> <sup>¼</sup> <sup>4</sup>π<sup>N</sup>

ne and no are the extraordinary and ordinary refractive indices, <n<sup>2</sup>

the average refractive index <n> and birefringence Δn as [11, 16],

temperature-dependent Δn can be written as

Eqs. (6) and (7), the order parameter can be written as:

Several techniques have been studied to describe the temperature effect on LC refractive indices. Horn measured the refractive indices as a function of temperature throughout the nematic phase of 4-n pentyl-4-cyanobiphenyl (5CB) and the smectic A and nematic phases of 4-n-octyl-4-cyanobiphenyl (8CB) using the method of Pellet and Chatelain at the wavelength (589 and 632.8 nm) [10]. Wu developed a single-band model and a three-band model for understanding the refractive index dispersions of liquid crystals. The three- and twocoefficient Cauchy equations based on the three-band model for the wavelength- and temperature-dependent refractive indices of anisotropic liquid crystals were derived by Jun Li and Wu. For low birefringence liquid crystal mixtures, the two-coefficient Cauchy model works equally well as the three-coefficient model in the off-resonance spectral region [11]. A four-parameter model for describing the temperature effect on the refractive indices of LCs based on the Vuks equation was derived by Jun Li et al. Four different LC materials with different birefringence were used to validate these parameters. An excellent agreement between theory and experiment was obtained [12]. Jun Li et al. measured the refractive indices of E7 LC mixture at six visible and two infrared (λ = 1.55 and 10.6 μm) wavelengths at different temperatures using Abbe and wedged cell refractometer methods [13]. In the present chapter, the temperature effect on nonlinear refractive indices of several types of liquid crystal (LC) compounds has been studied. In the beginning, the mathematical models are discussed. Second, using the refractive indices data, other parameters can be determined, such as birefringence (Δn), average refractive indices, and the temperature gradient of refractive indices (dne/dT, dno/dT). Finally, the bistability of nonlinear refractive indices with temperature of LC is also reported. The measurements performed at 1550 nm wavelength using wedged cell refractometer method. The variation in refractive indices was fitted theoretically using the modified four-parameter model, which is based on the Vuks equation.

### 2. Modeling

The classical Clausius-Mossotti equation correlates the dielectric constant (ε) of an isotropic media with molecular packing density (N), which means the number of molecules per unit volume and molecular polarizability (α) are as follows [6, 14, 15]

$$\frac{\varepsilon - 1}{\varepsilon + 2} = \frac{4\pi}{3} \text{Na} \tag{1}$$

The Lorentz-Lorenz equation correlates the refraction index of anisotropic medium with molecular polarizability at optical frequencies and obtained the following equation [14, 15]

$$\frac{n^2 - 1}{n^2 + 2} = \frac{4\pi}{3} N \alpha \tag{2}$$

For an isotropic LC, the ordinary and extraordinary refractive indices are determined by corresponding ordinary and extraordinary molecular polarizability α<sup>o</sup> and αe. Vuks modified the Lorentz-Lorenz equation by assuming that the internal field in a liquid crystal is equal in all directions, and therefore produce a semi-empirical equation correlating macroscopic refractive index with microscopic molecular polarizability [11, 15].

Temperature plays a fundamental role in affecting the refractive indices of LCs. As the temperature increases, ordinary (no) and extraordinary (ne) refractive indices of LCs behave

Several techniques have been studied to describe the temperature effect on LC refractive indices. Horn measured the refractive indices as a function of temperature throughout the nematic phase of 4-n pentyl-4-cyanobiphenyl (5CB) and the smectic A and nematic phases of 4-n-octyl-4-cyanobiphenyl (8CB) using the method of Pellet and Chatelain at the wavelength (589 and 632.8 nm) [10]. Wu developed a single-band model and a three-band model for understanding the refractive index dispersions of liquid crystals. The three- and twocoefficient Cauchy equations based on the three-band model for the wavelength- and temperature-dependent refractive indices of anisotropic liquid crystals were derived by Jun Li and Wu. For low birefringence liquid crystal mixtures, the two-coefficient Cauchy model works equally well as the three-coefficient model in the off-resonance spectral region [11]. A four-parameter model for describing the temperature effect on the refractive indices of LCs based on the Vuks equation was derived by Jun Li et al. Four different LC materials with different birefringence were used to validate these parameters. An excellent agreement between theory and experiment was obtained [12]. Jun Li et al. measured the refractive indices of E7 LC mixture at six visible and two infrared (λ = 1.55 and 10.6 μm) wavelengths at different temperatures using Abbe and wedged cell refractometer methods [13]. In the present chapter, the temperature effect on nonlinear refractive indices of several types of liquid crystal (LC) compounds has been studied. In the beginning, the mathematical models are discussed. Second, using the refractive indices data, other parameters can be determined, such as birefringence (Δn), average refractive indices, and the temperature gradient of refractive indices (dne/dT, dno/dT). Finally, the bistability of nonlinear refractive indices with temperature of LC is also reported. The measurements performed at 1550 nm wavelength using wedged cell refractometer method. The variation in refractive indices was fitted theoretically using the modified four-parameter model, which is based on the Vuks equation.

The classical Clausius-Mossotti equation correlates the dielectric constant (ε) of an isotropic media with molecular packing density (N), which means the number of molecules per unit

The Lorentz-Lorenz equation correlates the refraction index of anisotropic medium with molecular polarizability at optical frequencies and obtained the following equation [14, 15]

<sup>3</sup> <sup>N</sup><sup>α</sup> (1)

<sup>3</sup> <sup>N</sup><sup>α</sup> (2)

ε � 1 <sup>ε</sup> <sup>þ</sup> <sup>2</sup> <sup>¼</sup> <sup>4</sup><sup>π</sup>

<sup>n</sup><sup>2</sup> � <sup>1</sup> <sup>n</sup><sup>2</sup> <sup>þ</sup> <sup>2</sup> <sup>¼</sup> <sup>4</sup><sup>π</sup>

volume and molecular polarizability (α) are as follows [6, 14, 15]

differently from each other [8, 9].

160 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

2. Modeling

$$\frac{m\_{e,o}^2 - 1}{\langle n^2 \rangle + 2} = \frac{4\pi N}{3} \alpha\_{e,o} \tag{3}$$

ne and no are the extraordinary and ordinary refractive indices, <n<sup>2</sup> > is defined as <n2 > = (ne <sup>2</sup> + 2no 2 )/3

The temperature-dependent LC refractive indices based on Vuks model can be expressed by the average refractive index <n> and birefringence Δn as [11, 16],

$$m\_e = \langle n \rangle + \frac{2}{3} \Delta n \tag{4}$$

$$m\_o = \langle n \rangle - \frac{1}{3} \Delta n \tag{5}$$

On the other hand, the LC birefringence is linearly proportional to the order parameter S. Through Haller's semi-empirical equation, the order parameter can be approximated as

$$S = \left(1 - \frac{T}{T\_c}\right)^B \tag{6}$$

where T is the operating temperature, Tc is the clearing temperature of LC material, and B is the material constant, for many LC compounds and mixtures studied β = (0.2–0.25). Thus, the temperature-dependent Δn can be written as

$$
\Delta n(T) = (\Delta n)\_o \left( 1 - \frac{T}{T\_c} \right)^{\beta} \tag{7}
$$

where (Δn)o is the LC birefringence in the crystalline state at absolute zero (T = 0 K). From Eqs. (6) and (7), the order parameter can be written as:

$$S = \frac{\Delta \mathbf{n}}{\left(\Delta \mathbf{n}\right)\_\mathbf{o}}\tag{8}$$

The average refractive index decreases linearly with increasing temperature as [16]:

$$
\langle n \rangle = A - BT \tag{9}
$$

Substituting Eqs. (7) and (9) back to Eqs. (4) and (5), the modified four-parameter model for describing the temperature effect on the LC refractive indices is obtained [17–19]:

$$m\_{\epsilon}(T) \approx A - BT + \frac{2(\Delta n)\_{o}}{3} \left(1 - \frac{T}{T\_{c}}\right)^{\beta} \tag{10}$$

where θ is the angle of the wedged formed by two plates, δ<sup>o</sup> and δ<sup>e</sup> are the angles formed by

P Q

Ө

Table 1. The angle's value formed by the two substrates of five samples.

Figure 2. The experimental setup for the measurement of the refractive indices of LC.

Sample Angle E7 0.036215581 25% E7 with 75% MLC 6241-000 0.036635508 50% E7 with 50% MLC 6241-000 0.049305551 75% E7 with 25% MLC 6241-000 0.032724923 MLC 6241-000 0.052359877

L

δo δe Xo

X

Temperature Effects on Liquid Crystal Nonlinearity http://dx.doi.org/10.5772/intechopen.70414 163

Ro

Rref O

Re

Xe

two beams Ro and Re.

Figure 1. The used liquid crystal wedged cell.

$$m\_o(T) \approx A - BT - \frac{(\Delta n)\_o}{3} \left(1 - \frac{T}{T\_c}\right)^{\beta} \tag{11}$$

Eqs. (10) and (11) contain four unknown parameters A, B, (Δn)o, and β. The parameters A and B can be obtained by fitting the temperature-dependent average refractive index using Eq. (9), while (Δn)o and β can be obtained by fitting the birefringence data Δn as a function of temperature using Eq. (7). By taking temperature derivatives of Eqs. (10) and (11), the temperature gradient for ne and no can be derived [9, 19–24].

$$\frac{dn\_{\epsilon}}{dT} = -B - \frac{2\beta(\Delta n)\_{o}}{3T\_{\epsilon}\left(1 - \frac{T}{T\_{\epsilon}}\right)^{1-\beta}}\tag{12}$$

$$\frac{dn\_o}{dT} = -B + \frac{\beta(\Delta n)\_o}{3T\_c \left(1 - \frac{T}{T\_c}\right)^{1-\beta}}\tag{13}$$

### 3. Experimental refractive index

Five samples have been investigated in this work; two of them are E7 and MLC 6241-000 samples, the clearing temperatures are 333 and 373.7 K, respectively. The other three have been obtained by mixing the previous two liquid crystals in different proportions (75% E7 with 25% MLC 6241-000, 50% E7 with 50% MLC 6241-000, and 25% E7 with 75% MLC 6241-000). The clearing temperature (Tc) of three mixture samples is measured using hot-stage optical microscope, and they are found to be 348, 353, and 368 K, respectively.

The effect of temperature variation on nonlinear refractive indices of these liquid crystal compounds has been reported using wedged cell refractometer method. The cell is made up of two glass substrates separated by two spacers that have different thickness as shown in Figure 1. The wedged angle was measured using an optical method [9], and the angle value of five samples is shown in Table 1.

The experimental setup used during this work is shown in Figure 2, and a more detailed description of this setup and the measurement method can be found in [9]. The laser beam is divided into two rays, when it passes through LC sample because of birefringence of LC, the values of two refractive indices (no and ne) of the liquid crystal can be calculated by these equations

$$m\_o = \frac{\sin\left(\theta + \delta\_o\right)}{\sin\theta} \tag{14}$$

$$m\_{\ell} = \frac{\sin\left(\theta + \delta\_{\ell}\right)}{\sin\theta} \tag{15}$$

where θ is the angle of the wedged formed by two plates, δ<sup>o</sup> and δ<sup>e</sup> are the angles formed by two beams Ro and Re.

Figure 1. The used liquid crystal wedged cell.

neð Þ T ≈ A � BT þ

ature gradient for ne and no can be derived [9, 19–24].

162 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

3. Experimental refractive index

five samples is shown in Table 1.

equations

dne

dno

scope, and they are found to be 348, 353, and 368 K, respectively.

noð Þ <sup>T</sup> <sup>≈</sup> <sup>A</sup> � BT � ð Þ <sup>Δ</sup><sup>n</sup> <sup>o</sup>

2ð Þ Δn <sup>o</sup>

Eqs. (10) and (11) contain four unknown parameters A, B, (Δn)o, and β. The parameters A and B can be obtained by fitting the temperature-dependent average refractive index using Eq. (9), while (Δn)o and β can be obtained by fitting the birefringence data Δn as a function of temperature using Eq. (7). By taking temperature derivatives of Eqs. (10) and (11), the temper-

dT ¼ �<sup>B</sup> � <sup>2</sup>βð Þ <sup>Δ</sup><sup>n</sup> <sup>o</sup>

dT ¼ �<sup>B</sup> <sup>þ</sup> <sup>β</sup>ð Þ <sup>Δ</sup><sup>n</sup> <sup>o</sup>

Five samples have been investigated in this work; two of them are E7 and MLC 6241-000 samples, the clearing temperatures are 333 and 373.7 K, respectively. The other three have been obtained by mixing the previous two liquid crystals in different proportions (75% E7 with 25% MLC 6241-000, 50% E7 with 50% MLC 6241-000, and 25% E7 with 75% MLC 6241-000). The clearing temperature (Tc) of three mixture samples is measured using hot-stage optical micro-

The effect of temperature variation on nonlinear refractive indices of these liquid crystal compounds has been reported using wedged cell refractometer method. The cell is made up of two glass substrates separated by two spacers that have different thickness as shown in Figure 1. The wedged angle was measured using an optical method [9], and the angle value of

The experimental setup used during this work is shown in Figure 2, and a more detailed description of this setup and the measurement method can be found in [9]. The laser beam is divided into two rays, when it passes through LC sample because of birefringence of LC, the values of two refractive indices (no and ne) of the liquid crystal can be calculated by these

no <sup>¼</sup> sin ð Þ <sup>θ</sup> <sup>þ</sup> <sup>δ</sup><sup>o</sup>

ne <sup>¼</sup> sin ð Þ <sup>θ</sup> <sup>þ</sup> <sup>δ</sup><sup>e</sup>

<sup>3</sup>Tc <sup>1</sup> � <sup>T</sup> Tc

<sup>3</sup>Tc <sup>1</sup> � <sup>T</sup> Tc

<sup>3</sup> <sup>1</sup> � <sup>T</sup>

<sup>3</sup> <sup>1</sup> � <sup>T</sup>

Tc <sup>β</sup>

Tc <sup>β</sup>

<sup>1</sup>�<sup>β</sup> (12)

<sup>1</sup>�<sup>β</sup> (13)

sin<sup>θ</sup> (14)

sin<sup>θ</sup> (15)

(10)

(11)


Table 1. The angle's value formed by the two substrates of five samples.

Figure 2. The experimental setup for the measurement of the refractive indices of LC.

$$
\delta\_\vartheta = \tan^{-1} \left( \frac{\chi\_\vartheta}{D} \right) \tag{16}
$$

$$
\delta\_{\varepsilon} = \tan^{-1} \left( \frac{\chi\_{\varepsilon}}{D} \right) \tag{17}
$$

So that

$$m\_o = \frac{\sin\left(\theta + \tan^{-1}(\mathbf{x}\_o/D)\right)}{\sin\theta} \tag{18}$$

$$m\_{\varepsilon} = \frac{\sin\left(\theta + \tan^{-1}(\mathbf{x}\_{\varepsilon}/D)\right)}{\sin\theta} \tag{19}$$

respectively, while solid lines are fitting results using Eq. (7). The fitting parameters for these samples are also listed in Table 2. Through fittings, we obtain parameters (Δn)o and β. As shown in Figures 3, 4, and 7, the four-parameter model fits the experimental data of samples

Table 2. Fitting parameters for the average refractive index <n> and birefringence Δn of five LCs at 1550 nm.

LC materials <n> Δn

Figure 3. Temperature dependent refractive indices of E7 and MLC 6241-000 at λ = 1550 nm. Red squares and blue circles represent the refractive indices ne and no of E7 and MLC 6241-000, respectively. The solid curves are the fitting using

280 290 300 310 320 330 340 350 360 370 380

**Temperature(K)**

ne

Temperature Effects on Liquid Crystal Nonlinearity http://dx.doi.org/10.5772/intechopen.70414 165

no

) (Δn)o β

A B (K<sup>1</sup>

ne

no

1.4 1.42 1.44 1.46 1.48 1.5 1.52 1.54 1.56 1.58 1.6 1.62 1.64 1.66 1.68 1.7 1.72

**Refractive Index**

E7 1.750172 5.88 <sup>10</sup><sup>4</sup> 0.301812 0.259542 25% E7 with 75% MLC 6241-000 1.61647 4.17 <sup>10</sup><sup>4</sup> 0.153497 0.246991 50% E7 with 50% MLC 6241-000 1.622715 4.18 <sup>10</sup><sup>4</sup> 0.189193 0.22493 75% E7 with 25% MLC 6241-000 1.650715 4.49 <sup>10</sup><sup>4</sup> 0.182306 0.204806 MLC 6241-000 1.6008 4.21 <sup>10</sup><sup>4</sup> 0.147301 0.248339

Figure 8 shows the temperature-dependent birefringence of three mixing samples. Blue triangles, green circles, and red squares, represent the birefringence LCs of (50% E7 with 50% MLC 6241-000, 25% E7 with 75% MLC 6241-000, and 75% E7 with 25% MLC 6241-000), respectively. The solid lines are fitting curves using Eq. (7). The LC mixture (50% E7 with 50%

E7 and MLC 6241-000 very well.

Eqs. (10) and (11).

MLC 6241-000) has higher birefringence.

These measurements have been repeated many times by changing the temperature of the LC sample to measure the refractive indices at different temperatures. Also, this experiment has been repeated by decreasing the temperature of LC sample to study the bistability of liquid crystal due to temperature.

### 4. Results and discussions

#### 4.1. Nonlinear refractive index

The refractive indices of the five liquid crystals were measured using wedged cell refractometer method at 1550 nm wavelength [9]. Figure 3 shows the temperature dependence of the refractive indices no and ne of E7 and MLC 6241-000. Red squares and blue circles are experimental data for refractive indices ne and no of E7 and MLC 6241-000, respectively. The solid curves are fittings using the four-parameter model Eqs. (10) and (11). The fitting parameters are listed in Table 2.

The temperature dependence of refractive indices of three LC mixtures is shown in Figure 4. Blue squares, green triangles, and red circles represent the refractive indices of (50% E7 with 50% MLC 6241-000, 25% E7 with 75% MLC 6241-000, and 75% E7 with 25% MLC 6241-000), respectively. The solid curves are fittings using Eqs. (10) and (11).

Brugioni et al. also studied the temperature effect on nonlinear refractive indices of E7 liquid crystal at mid-infrared region (10.6 μm) using a wedge cell refractometer method as shown in Figure 5 [13, 25].

Figure 6 shows the wavelength-dependent refractive indices of E7 at T = 25�C. Squares and circles represent the ne and no of E7 in the visible region, while the downward and upward triangles stand for the measured data at λ = 1.55 and 10.6 μm, respectively [25]. Figure 6 also indicates that the refractive indices will saturate in the far-infrared region, the agreement between experiment and theory is very good.

The temperature-dependent birefringence of E7 and MLC 6241-000 at 1550 nm is shown in Figure 7. Blue squares and red circles represent the birefringence of E7 and MLC 6241-000,

<sup>δ</sup><sup>o</sup> <sup>¼</sup> tan �<sup>1</sup> xo

164 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

<sup>δ</sup><sup>e</sup> <sup>¼</sup> tan �<sup>1</sup> xe

no <sup>¼</sup> sin <sup>θ</sup> <sup>þ</sup> tan �<sup>1</sup>ð Þ xo=<sup>D</sup>

ne <sup>¼</sup> sin <sup>θ</sup> <sup>þ</sup> tan �<sup>1</sup>ð Þ xe=<sup>D</sup>

These measurements have been repeated many times by changing the temperature of the LC sample to measure the refractive indices at different temperatures. Also, this experiment has been repeated by decreasing the temperature of LC sample to study the bistability of liquid

The refractive indices of the five liquid crystals were measured using wedged cell refractometer method at 1550 nm wavelength [9]. Figure 3 shows the temperature dependence of the refractive indices no and ne of E7 and MLC 6241-000. Red squares and blue circles are experimental data for refractive indices ne and no of E7 and MLC 6241-000, respectively. The solid curves are fittings using the four-parameter model Eqs. (10) and (11). The fitting parameters

The temperature dependence of refractive indices of three LC mixtures is shown in Figure 4. Blue squares, green triangles, and red circles represent the refractive indices of (50% E7 with 50% MLC 6241-000, 25% E7 with 75% MLC 6241-000, and 75% E7 with 25% MLC 6241-000),

Brugioni et al. also studied the temperature effect on nonlinear refractive indices of E7 liquid crystal at mid-infrared region (10.6 μm) using a wedge cell refractometer method as shown in

Figure 6 shows the wavelength-dependent refractive indices of E7 at T = 25�C. Squares and circles represent the ne and no of E7 in the visible region, while the downward and upward triangles stand for the measured data at λ = 1.55 and 10.6 μm, respectively [25]. Figure 6 also indicates that the refractive indices will saturate in the far-infrared region, the agreement

The temperature-dependent birefringence of E7 and MLC 6241-000 at 1550 nm is shown in Figure 7. Blue squares and red circles represent the birefringence of E7 and MLC 6241-000,

respectively. The solid curves are fittings using Eqs. (10) and (11).

between experiment and theory is very good.

So that

crystal due to temperature.

4. Results and discussions

4.1. Nonlinear refractive index

are listed in Table 2.

Figure 5 [13, 25].

D 

D 

sin<sup>θ</sup> (18)

sin<sup>θ</sup> (19)

(16)

(17)

Figure 3. Temperature dependent refractive indices of E7 and MLC 6241-000 at λ = 1550 nm. Red squares and blue circles represent the refractive indices ne and no of E7 and MLC 6241-000, respectively. The solid curves are the fitting using Eqs. (10) and (11).


Table 2. Fitting parameters for the average refractive index <n> and birefringence Δn of five LCs at 1550 nm.

respectively, while solid lines are fitting results using Eq. (7). The fitting parameters for these samples are also listed in Table 2. Through fittings, we obtain parameters (Δn)o and β. As shown in Figures 3, 4, and 7, the four-parameter model fits the experimental data of samples E7 and MLC 6241-000 very well.

Figure 8 shows the temperature-dependent birefringence of three mixing samples. Blue triangles, green circles, and red squares, represent the birefringence LCs of (50% E7 with 50% MLC 6241-000, 25% E7 with 75% MLC 6241-000, and 75% E7 with 25% MLC 6241-000), respectively. The solid lines are fitting curves using Eq. (7). The LC mixture (50% E7 with 50% MLC 6241-000) has higher birefringence.

Figure 4. Temperature-dependent refractive indices of three mixture samples at λ = 1550 nm. Red circles, blue squares, and green triangles represent the refractive indices ne and no of (75% E7 with 25% MLC 6241-000, 50% E7 with 50% MLC 6241-000, and 25% E7 with 75% MLC 6241-000), respectively. The solid curves are the fitting using Eqs. (10) and (11).

Figure 6. Wavelength-dependent refractive indices of E7 at T = 25�C. The open squares and circles are the ne and no of E7 measured at the visible spectrum. The solid curves are the fittings to the experimental data measured at the visible spectrum using the extended Cauchy model. The downward and upward triangles are ne and no of E7 measured at

Temperature Effects on Liquid Crystal Nonlinearity http://dx.doi.org/10.5772/intechopen.70414 167

280 290 300 310 320 330 340 350 360 370 380

**Temperature(K)**

Figure 7. Temperature-dependent birefringence of E7 and MLC 6241-000 at λ = 1550 nm, blue squares and red circles

represent the birefringence of E7 and MLC 6241-000, respectively. Solid lines are fitting results using Eq. (7).

T = 25�C and λ = 1.55 and 10.6 μm, respectively.

0

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

**Birefringence**

 **(Δn)**

0.2 0.18

Figure 5. Temperature-dependent refractive indices of E7 at 10.6 μm. The filled circles are the refractive indices measured by the wedged LCcell refractometer method. The filled triangles are the average refractive index calculated by the experimental data. The open circles represent no and ne extrapolated from the experimental data measured at visible spectrum using the extended Cauchy model. The open triangles are the average refractive index calculated by the extrapolated ne and no, respectively. The solid curves are the fitting using Eqs. (10) and (11).

Figure 6. Wavelength-dependent refractive indices of E7 at T = 25�C. The open squares and circles are the ne and no of E7 measured at the visible spectrum. The solid curves are the fittings to the experimental data measured at the visible spectrum using the extended Cauchy model. The downward and upward triangles are ne and no of E7 measured at T = 25�C and λ = 1.55 and 10.6 μm, respectively.

1.42 1.44 1.46 1.48 1.5 1.52 1.54 1.56 1.58 1.6 1.62

280 290 300 310 320 330 340 350 360 370

no

**Temperature(K)**

Figure 4. Temperature-dependent refractive indices of three mixture samples at λ = 1550 nm. Red circles, blue squares, and green triangles represent the refractive indices ne and no of (75% E7 with 25% MLC 6241-000, 50% E7 with 50% MLC 6241-000, and 25% E7 with 75% MLC 6241-000), respectively. The solid curves are the fitting using Eqs. (10) and (11).

Figure 5. Temperature-dependent refractive indices of E7 at 10.6 μm. The filled circles are the refractive indices measured by the wedged LCcell refractometer method. The filled triangles are the average refractive index calculated by the experimental data. The open circles represent no and ne extrapolated from the experimental data measured at visible spectrum using the extended Cauchy model. The open triangles are the average refractive index calculated by the

extrapolated ne and no, respectively. The solid curves are the fitting using Eqs. (10) and (11).

ne

**RefractiveIndex**

166 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

Figure 7. Temperature-dependent birefringence of E7 and MLC 6241-000 at λ = 1550 nm, blue squares and red circles represent the birefringence of E7 and MLC 6241-000, respectively. Solid lines are fitting results using Eq. (7).

Figure 8. Temperature-dependent birefringence of three mixture samples at λ = 1550 nm. Red squares, blue triangles, and green circles represent the birefringence LCs (75% E7 with 25% MLC 6241-000, 50% E7 with 50% MLC 6241-000, and 25% E7 with 75% MLC 6241-000), respectively. Solid lines are fitting results using Eq. (7).

The temperature-dependent average refractive index of five liquid crystal samples is shown in Figure 9. Green triangles, red squares, black circles, brown stars, and blue monoclinic represent the average refractive index LCs of E7, 75% E7 with 25% MLC 6241-000, 50% E7 with 50% MLC 6241-000, and 25% E7 with 75% MLC 6241-000, and MLC 6241-000), respectively, while solid lines are fitting results using the four-parameter model (Eq. (9)). The fitting parameters A and B for these five samples are listed in Table 2. Average refractive index decreases linearly as the temperature increases.

4.3. Studying bistability based on temperature

lines are fitting results using Eq. (9).

1.44

1.46

1.48

1.5

1.52

1.54

**AverageRefractiveIndex<n>**

1.56

1.58

1.6

1.62

equal until they reach to 291 K as shown in Figure 11e.

increasing temperature case after the intersect point at 310 K.

gence (increasing and decreasing). The measured areas are listed in Table 3.

The refractive indices of the five liquid crystal samples were measured at λ = 1550 nm in the temperature range from 290 to 330 K. Figure 11a–e shows the temperature-dependent extraordinary refractive index of E7, MLC 6241-000, and three mixture samples (25% E7 with 75% MLC 6241-000, 75% E7 with 25% MLC 6241-000, and 50% E7 with 50% MLC 6241-000), respectively. From these figures, the bistability of LCs due to temperature for extraordinary refractive index is clearly observed. In the case of mixture (50% E7 with 50% MLC 6241-000), the two curves of increasing and decreasing liquid crystal's temperature intersect at 310 K to be

280 290 300 310 320 330 340 350 360 370 380

Temperature Effects on Liquid Crystal Nonlinearity http://dx.doi.org/10.5772/intechopen.70414 169

**Temperature (K)**

Figure 9. Temperature-dependent average refractive index > n < of five LCs at 1550 nm. Green triangles, red squares, black circles, brown stars, and blue monoclinic represent the average refractive index LCs of E7, 75% E7 with 25% MLC 6241-000, 50% E7 with 50% MLC 6241-000, and 25% E7 with 75% MLC 6241-000, and MLC 6241-000), respectively. Solid

Figure 12a–e shows the temperature dependent ordinary refractive index of E7, MLC 6241- 000, and three mixture samples (25% E7 with 75% MLC 6241-000, 75% E7 with 25% MLC 6241- 000, and 50% E7 with 50% MLC 6241-000), respectively. Also, from these figures the bistability of LCs due to temperature is clearly observed for ordinary refractive index. As shown in Figure 12e, for mixture (50% E7 with 50% MLC 6241-000), the values of ordinary refractive index in the case of decreasing temperature become larger than its values in the case of

Figure 13a–e shows the birefringence bistability of the five liquid crystal samples. The bistability is represented by the area between the temperature refractive indices and birefrin-

#### 4.2. Temperature gradient of refractive index

For practical applications, it is necessary to operate the LC device at room temperature. So, LC should be designed with crossover temperature (To) lower than 300 K to obtain a positive dno/dT at room temperature. The temperature dependence of �dne/dt and dno/dt for liquid crystal can be found using Eqs. (12) and (13). These are shown in Figure 10a–e. The calculated values of crossover temperatures for LCs (E7, MLC 6241-000, 25% E7 with 75% MLC 6241-000, 50% E7 with 50% MLC 6241-000, and 75% E7 with 25% MLC 6241-000) are ~311.1, 360.54, 354.61, 335.8, and 333.56 K, respectively. Negative temperature gradient (�dne/dt) positive for all LC samples, that means the extraordinary refractive index decreases with increase in temperature, whereas the positive temperature gradient (dno/dt) changes its sign from negative to positive value. The dno/dt is negative when the temperature is below To, whereas it becomes positive when the temperature is above To. To achieve a high dno/dT, high birefringence and low clearing temperature are two important factors for this.

Figure 9. Temperature-dependent average refractive index > n < of five LCs at 1550 nm. Green triangles, red squares, black circles, brown stars, and blue monoclinic represent the average refractive index LCs of E7, 75% E7 with 25% MLC 6241-000, 50% E7 with 50% MLC 6241-000, and 25% E7 with 75% MLC 6241-000, and MLC 6241-000), respectively. Solid lines are fitting results using Eq. (9).

### 4.3. Studying bistability based on temperature

The temperature-dependent average refractive index of five liquid crystal samples is shown in Figure 9. Green triangles, red squares, black circles, brown stars, and blue monoclinic represent the average refractive index LCs of E7, 75% E7 with 25% MLC 6241-000, 50% E7 with 50% MLC 6241-000, and 25% E7 with 75% MLC 6241-000, and MLC 6241-000), respectively, while solid lines are fitting results using the four-parameter model (Eq. (9)). The fitting parameters A and B for these five samples are listed in Table 2. Average refractive index decreases linearly as

Figure 8. Temperature-dependent birefringence of three mixture samples at λ = 1550 nm. Red squares, blue triangles, and green circles represent the birefringence LCs (75% E7 with 25% MLC 6241-000, 50% E7 with 50% MLC 6241-000, and 25%

280 290 300 310 320 330 340 350 360 370 380 **Temperature(K)**

For practical applications, it is necessary to operate the LC device at room temperature. So, LC should be designed with crossover temperature (To) lower than 300 K to obtain a positive dno/dT at room temperature. The temperature dependence of �dne/dt and dno/dt for liquid crystal can be found using Eqs. (12) and (13). These are shown in Figure 10a–e. The calculated values of crossover temperatures for LCs (E7, MLC 6241-000, 25% E7 with 75% MLC 6241-000, 50% E7 with 50% MLC 6241-000, and 75% E7 with 25% MLC 6241-000) are ~311.1, 360.54, 354.61, 335.8, and 333.56 K, respectively. Negative temperature gradient (�dne/dt) positive for all LC samples, that means the extraordinary refractive index decreases with increase in temperature, whereas the positive temperature gradient (dno/dt) changes its sign from negative to positive value. The dno/dt is negative when the temperature is below To, whereas it becomes positive when the temperature is above To. To achieve a high dno/dT, high birefringence and low clearing temper-

the temperature increases.

4.2. Temperature gradient of refractive index

0.03

E7 with 75% MLC 6241-000), respectively. Solid lines are fitting results using Eq. (7).

0.05

0.07

0.09

**Birefringence Δn** 

0.11

0.13

0.15

168 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

ature are two important factors for this.

The refractive indices of the five liquid crystal samples were measured at λ = 1550 nm in the temperature range from 290 to 330 K. Figure 11a–e shows the temperature-dependent extraordinary refractive index of E7, MLC 6241-000, and three mixture samples (25% E7 with 75% MLC 6241-000, 75% E7 with 25% MLC 6241-000, and 50% E7 with 50% MLC 6241-000), respectively. From these figures, the bistability of LCs due to temperature for extraordinary refractive index is clearly observed. In the case of mixture (50% E7 with 50% MLC 6241-000), the two curves of increasing and decreasing liquid crystal's temperature intersect at 310 K to be equal until they reach to 291 K as shown in Figure 11e.

Figure 12a–e shows the temperature dependent ordinary refractive index of E7, MLC 6241- 000, and three mixture samples (25% E7 with 75% MLC 6241-000, 75% E7 with 25% MLC 6241- 000, and 50% E7 with 50% MLC 6241-000), respectively. Also, from these figures the bistability of LCs due to temperature is clearly observed for ordinary refractive index. As shown in Figure 12e, for mixture (50% E7 with 50% MLC 6241-000), the values of ordinary refractive index in the case of decreasing temperature become larger than its values in the case of increasing temperature case after the intersect point at 310 K.

Figure 13a–e shows the birefringence bistability of the five liquid crystal samples. The bistability is represented by the area between the temperature refractive indices and birefringence (increasing and decreasing). The measured areas are listed in Table 3.

1.63 1.64 1.65 1.66 1.67 1.68 1.69 1.7

1.535

respectively.

1.54

1.545

1.55

1.555

**Extraordinary R.I**

1.56

1.565

**Extraordinary**

 **R.I**

**Temperature(K)**

285 290 295 300 305 310 315 320 325 330 335

285 290 295 300 305 310 315 320 325 330 **Temperature(K)**

**(c)** 

1.55 1.555 1.56 1.565 1.57 1.575 1.58 1.585

**Extrardinary R.I**

1.52

1.575

**Temperature(K)**

285 290 295 300 305 310 315 320 325 330 335

**(e)** 

Figure 11. Temperature dependent extraordinary refractive index of (a) E7, (b) MLC 6241-000, (c) 25% E7 with 75% MLC 6241-000, (d) 75% E7 with 25% MLC 6241-000, and (e) 50% E7 with 50% MLC 6241-000, at 1550 nm. Squares and circles represent extraordinary refractive index for increasing (red line) and decreasing (blue line) temperature,

1.58

1.585

1.59

**Extraordinary R.I**

1.595

1.6

1.605

285 290 295 300 305 310 315 320 325 330 **Temperature(K)**

Temperature Effects on Liquid Crystal Nonlinearity http://dx.doi.org/10.5772/intechopen.70414 171

285 290 295 300 305 310 315 320 325 330

**Temperature(K) (d)** 

1.525

1.53

1.535

**Extraordinary**

**(a) (b)** 

 **R.I**

1.54

1.545

1.55

Figure 10. Temperature gradient for ne and no of LC samples (a) E7, (b) MLC 6241-000, (c) 25% E7 with 75% MLC 6241- 000, (d) 50% E7 with 50% MLC 6241-000, and (e) 75% E7 with 25% MLC 6241-000 at 1550 nm. Blue and red solid lines represent the calculated dno/dT and �dne/dT, respectively. The crossover temperature for these samples are around 311.2, 360.6, 354.7, 335.9, and 333.6 K for E7, MLC 6241-000, 25% E7 with 75% MLC 6241-000, 50% E7 with 50% MLC 6241-000, and 75% E7 with 25% MLC 6241-000, respectively.

Figure 11. Temperature dependent extraordinary refractive index of (a) E7, (b) MLC 6241-000, (c) 25% E7 with 75% MLC 6241-000, (d) 75% E7 with 25% MLC 6241-000, and (e) 50% E7 with 50% MLC 6241-000, at 1550 nm. Squares and circles represent extraordinary refractive index for increasing (red line) and decreasing (blue line) temperature, respectively.

Figure 10. Temperature gradient for ne and no of LC samples (a) E7, (b) MLC 6241-000, (c) 25% E7 with 75% MLC 6241- 000, (d) 50% E7 with 50% MLC 6241-000, and (e) 75% E7 with 25% MLC 6241-000 at 1550 nm. Blue and red solid lines represent the calculated dno/dT and �dne/dT, respectively. The crossover temperature for these samples are around 311.2, 360.6, 354.7, 335.9, and 333.6 K for E7, MLC 6241-000, 25% E7 with 75% MLC 6241-000, 50% E7 with 50% MLC 6241-000,

and 75% E7 with 25% MLC 6241-000, respectively.

170 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

0.115

0.086 0.088 0.09 0.092 0.094 0.096 0.098 0.1 0.102 0.104 0.106

**Birefringence Δn**

285 290 295 300 305 310 315 320 325 330 335 340 **Temperature(K)**

**dfd** dfd

290 295 300 305 310 315 320 325 330 **Temperature(K)**

0.102

birefringence refractive index for increasing and decreasing temperature.

0.107

0.112

**Birefringence Δn**

0.117

0.122

0.127

0.086 0.088 0.09 0.092 0.094 0.096 0.098 0.1 0.102

**Birefringence Δn**

0.11 0.112 0.114 0.116 0.118 0.12 0.122 0.124 0.126

**(c) (d)**

285 290 295 300 305 310 315 320 325 330 335 340 **Temperature(K)**

**(e)**

Figure 13. Temperature-dependent birefringence (Δn) of (a) E7, (b) MLC 6241-000, (c) 25% E7 with 75% MLC 6241-000, (d) 75% E7 with 25% MLC 6241-000, and (e) 50% E7 with 50% MLC 6241-000 at 1550 nm. Squares and circles represent

**Birefringence Δn**

**(a) (b)**

285 290 295 300 305 310 315 320 325 330 **Temperature(K)**

Temperature Effects on Liquid Crystal Nonlinearity http://dx.doi.org/10.5772/intechopen.70414 173

290 295 300 305 310 315 320 325 330 335 **Temperature(K)**

0.125

0.135

0.145

**Birefringence Δn**

0.155

0.165

0.175

Figure 12. Temperature-dependent ordinary refractive index of (a) E7, (b) MLC 6241-000, (c) 25% E7 with 75% MLC 6241- 000, (d) 75% E7 with 25% MLC 6241-000 and (e) 50% E7 with 50% MLC 6241-000 at 1550 nm. Squares and circles represent ordinary refractive index for increasing (red line) and decreasing (blue line) temperature respectively.

1.514 1.515 1.516 1.517 1.518 1.519 1.52 1.521

**Ordinary Refractive index**

1.449

1.451

1.453

1.455

**Ordinary Refractive index**

1.457

1.459

1.461

285 290 295 300 305 310 315 320 325 330 335 **Temperature(K)**

172 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

285 290 295 300 305 310 315 320 325 330 335 **Temperature(K)**

**(c)**

**Ordinary Refractive index**

1.446 1.448 1.45 1.452 1.454 1.456 1.458 1.46 1.432 1.434 1.436 1.438 1.44 1.442 1.444 1.446

**(a) (b)**

**Ordinary Refractive index**

**Ordinary Refractive index**

1.464 1.466 1.468 1.47 1.472 1.474 1.476 1.478

285 290 295 300 305 310 315 320 325 330 335

**Temperature(K)**

**(e)**

Figure 12. Temperature-dependent ordinary refractive index of (a) E7, (b) MLC 6241-000, (c) 25% E7 with 75% MLC 6241- 000, (d) 75% E7 with 25% MLC 6241-000 and (e) 50% E7 with 50% MLC 6241-000 at 1550 nm. Squares and circles represent

ordinary refractive index for increasing (red line) and decreasing (blue line) temperature respectively.

285 290 295 300 305 310 315 320 325 330 **Temperature(K)**

290 295 300 305 310 315 320 325 330 335

**Temperature(K) (d)**

Figure 13. Temperature-dependent birefringence (Δn) of (a) E7, (b) MLC 6241-000, (c) 25% E7 with 75% MLC 6241-000, (d) 75% E7 with 25% MLC 6241-000, and (e) 50% E7 with 50% MLC 6241-000 at 1550 nm. Squares and circles represent birefringence refractive index for increasing and decreasing temperature.


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Table 3. The area between increasing and decreasing temperature curves of liquid crystal samples.

From these measurements, the extraordinary refractive index has larger bistability than the ordinary refractive index.

### 5. Conclusions

The ordinary and extraordinary refractive indices of five types of liquid crystals were measured at near-infrared region (1550 nm) and in temperature range from 290 to 330 K, using a wedged cell refractometer method. The variation in refractive indices, and average refractive index were fitted theoretically using a modified four-parameter model. Excellent agreement between the experimental data and fitted values by using four-parameter model is obtained. In addition, the birefringence of liquid crystal as a function of the temperature is calculated; high birefringence is obtained when the mixing is 50% E7 with 50% MLC 6241-000. The temperature gradients of liquid crystal refractive indices are presented; high birefringence and low clearing temperature are two important factors to achieve large dno/dT. The bistability of LCs due to temperature is also studied. The liquid crystal bistability based on the temperature is clearly observed for all samples. Also, the extraordinary refractive index has larger bistability than the ordinary refractive index.

### Author details

Lamees Abdulkaeem Al-Qurainy<sup>1</sup> \* and Kais A.M. Al Naimee1,2

\*Address all correspondence to: lamees.alqurainy@ino.it


### References

From these measurements, the extraordinary refractive index has larger bistability than the

Sample Area

174 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

Extraordinary R.I

E7 0.16882 0.01577 0.15304 25% E7 with 75% MLC 6241-000 0.06328 0.05379 0.00599 50% E7 with 50% MLC 6241-000 0.03333 0.00693 0.0264 75% E7 with 25% MLC 6241-000 0.05007 0.02704 0.02303 MLC 6241-000 0.05643 0.0337 0.02272

Table 3. The area between increasing and decreasing temperature curves of liquid crystal samples.

Ordinary R.I

Birefringence

The ordinary and extraordinary refractive indices of five types of liquid crystals were measured at near-infrared region (1550 nm) and in temperature range from 290 to 330 K, using a wedged cell refractometer method. The variation in refractive indices, and average refractive index were fitted theoretically using a modified four-parameter model. Excellent agreement between the experimental data and fitted values by using four-parameter model is obtained. In addition, the birefringence of liquid crystal as a function of the temperature is calculated; high birefringence is obtained when the mixing is 50% E7 with 50% MLC 6241-000. The temperature gradients of liquid crystal refractive indices are presented; high birefringence and low clearing temperature are two important factors to achieve large dno/dT. The bistability of LCs due to temperature is also studied. The liquid crystal bistability based on the temperature is clearly observed for all samples. Also, the extraordinary refractive index has larger bistability than the

\* and Kais A.M. Al Naimee1,2

1 Physics Department, College of Science, University of Baghdad, Bagdad, Iraq

ordinary refractive index.

ordinary refractive index.

Lamees Abdulkaeem Al-Qurainy<sup>1</sup>

\*Address all correspondence to: lamees.alqurainy@ino.it

2 C.N.R. Istituto Nazionale di Ottica Applicata, Firenze, Italy

Author details

5. Conclusions


[17] Thingujam KD, Sarkar SD, Choudhury B, Bhattacharjee A. Effect of temperature on the refractive indices of liquid crystals and validation of a modified four- parameter model. Acta Physica Polonica A. 2012;122:754-757

**Chapter 9**

**Provisional chapter**

**Micro/Nano Liquid Crystal Layer–Based Tunable**

DOI: 10.5772/intechopen.70413

**Micro/Nano Liquid Crystal Layer–Based Tunable Optical** 

Miniaturization and integration are the main trends in modern photonic technology. In this chapter, two kinds of micro-/nano liquid crystal (LC) layer–based tunable optical fiber interferometers are proposed. One fiber interferometer is the optical fiber gratings (LPGs), and the other one is the locally bent microfiber taper (LBMT). The working principles of the devices are theoretically analyzed. The preparation process and the func-

**Keywords:** liquid crystal device, fiber gratings, microfiber taper, interferometry, mode

As optical materials that exhibit very large anisotropic properties, liquid crystal (LC) has been used in a variety of photonic applications with an eye toward enabling tunable optical responses, with stimuli including thermal [1], electrical [2], magnetic [3], and optical fields [4]. Miniaturization and integration are the main trends in modern photonic technology. With the help of micro-/nanofabrication technology, people can design and prepare various optical fiber micro-/nanostructures and devices, which exhibit significant difference in characteristics when the functional structure size decreases to micrometers and/or nanometers. These special physical properties have wide theoretical research prospects and practical applications. In this chapter, two kinds of novel micro-/nano LC layer–based tunable optical fiber interferometers are theoretically analyzed and experimentally studied, including the mode coupling properties and relevant micro-/nanofabrication technologies. The operation principle, preparation process, and functional properties of the proposed optical fiber devices are studied in detail. By comparison

tional properties of the devices are experimentally investigated as well.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

**Optical Fiber Interferometers**

Haimei Luo, Changjing Wang, Yinghua Ji

**Fiber Interferometers**

Wen Yuan

and Wen Yuan

**Abstract**

**1. Introduction**

Haimei Luo, Changjing Wang, Yinghua Ji and

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.70413


**Provisional chapter**

### **Micro/Nano Liquid Crystal Layer–Based Tunable Optical Fiber Interferometers Fiber Interferometers**

DOI: 10.5772/intechopen.70413

**Micro/Nano Liquid Crystal Layer–Based Tunable Optical** 

Haimei Luo, Changjing Wang, Yinghua Ji and Wen Yuan and Wen Yuan Additional information is available at the end of the chapter

Haimei Luo, Changjing Wang, Yinghua Ji

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.70413

#### **Abstract**

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and near-IR regions. Opticheskii Zhurnal. 2006;73:15-17

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2006;453:355-370

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2004;12

2007;112

2014;199:275-286

Miniaturization and integration are the main trends in modern photonic technology. In this chapter, two kinds of micro-/nano liquid crystal (LC) layer–based tunable optical fiber interferometers are proposed. One fiber interferometer is the optical fiber gratings (LPGs), and the other one is the locally bent microfiber taper (LBMT). The working principles of the devices are theoretically analyzed. The preparation process and the functional properties of the devices are experimentally investigated as well.

**Keywords:** liquid crystal device, fiber gratings, microfiber taper, interferometry, mode

### **1. Introduction**

As optical materials that exhibit very large anisotropic properties, liquid crystal (LC) has been used in a variety of photonic applications with an eye toward enabling tunable optical responses, with stimuli including thermal [1], electrical [2], magnetic [3], and optical fields [4]. Miniaturization and integration are the main trends in modern photonic technology. With the help of micro-/nanofabrication technology, people can design and prepare various optical fiber micro-/nanostructures and devices, which exhibit significant difference in characteristics when the functional structure size decreases to micrometers and/or nanometers. These special physical properties have wide theoretical research prospects and practical applications. In this chapter, two kinds of novel micro-/nano LC layer–based tunable optical fiber interferometers are theoretically analyzed and experimentally studied, including the mode coupling properties and relevant micro-/nanofabrication technologies. The operation principle, preparation process, and functional properties of the proposed optical fiber devices are studied in detail. By comparison

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

with that of the traditional sized optical fiber devices, the advantages in performance of the micro-/nano LC layer based ones are verified. The main contents of this chapter are as follows.

Up to date, most of the studies have concentrated on the analysis of the LPG response to the surrounding medium refractive index (SRI) smaller than that of silica [6]. The idea of coated LPG with a thin HRI layer was first put forward by Rees et al. [7]. Then, Wang et al. presented a detailed study to investigate the sensitivity of LPG to SRI when they are coated with a nanosized HRI film [8]. In the same year, a comprehensive investigation of mode transition in HRI layer–coated LPG was reported by Cusano et al. [9]. Their analysis indicated that the cladding modes reorganization occurred for a fixed overlay thickness and refractive index by increasing the SRI. In fact, changing the HRI could also result in cladding modes reorganization. The theoretical and experimental study proposed by Del Villar et al. showed that by selecting an appropriate overlay thickness, the highest sensitivity of the resonance wavelengths to HRI

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Fiber tapers, which have a variety of functions including filtering, light coupling, and sensing, consist of a waist between two tapered sections fabricated by heating and pulling technology [12, 13]. Different length and shape of the first tapered section have different effects on the

Recently, we reported a compact fiber interferometer named LBMT interferometer [14–16]. This kind of interferometer has unique features of low insertion loss and ultrathin taper waist, so it is promising for high-sensitivity sensing. It is interesting to integrating a LBMT interferometer and functional material due to physical effect of functional material and the high

Based on the phase-matching condition between the core and the cladding modes, the center

**Figure 1** shows the structure of HRI-coated LPG with four layers. Using the transfer matrix method proposed by Anemogiannis et al., the cladding mode effective index can be calculated

The analysis used the standard Corning SMF-28 optical fiber parameters: numerical aperture 0.14, refractive index difference 0.36% [9], cladding, and core diameter 125 and 8.2 μm, respectively. The HRI-LC overlay is with refractive index of 1.47–1.55 close to the experimental testing

*i*

)*Λ* (1)

is the effective refractive

*i*

of the *j*th attenuation band can be expressed as [17]

change of the overlay can be obtained [10, 11].

sensitivity of the microfiber to the surroundings.

*λ<sup>i</sup>* = (*nco* - *ncl*

*2.2.2. Numerical analysis of HRI overlay–coated LPG*

**2.2. Mode transition in the nanosized HRI overlay–coated LPG**

where *nco* is the effective refractive index of the core mode and *ncl*

index of the *i*th cladding mode. *Λ* is the grating period [5].

[19] and with different thickness changing from 600 to 900 nm.

*2.1.2. Tapered optical fiber interferometer*

input mode [13].

*2.2.1. Theory background*

wavelength *λ<sup>i</sup>*

[18].

Two kinds of typical optical fiber–based modal interference devices and the relevant micro-/ nanofabrication technology are proposed in Section 2.1. One typical fiber modal interference device is the optical fiber grating. The other typical device is the tapered optical fiber. Adopting optic fiber surface micro-/nanostructure technology, two kinds of micro-/nano liquid crystal layer–based wide range tunable optical fiber devices are achieved. The properties of the cladding modes in LPG coated with a high refractive index (HRI) micro-/nanometer overlay are theoretically studied in Section 2.2. The resonant wavelength and spectral characteristics of the four layer model long period grating are also analyzed based on the coupled-mode theory. Besides, the transmission spectra of LPG with different overlay thickness and refractive indices are numerically calculated. The tuning characteristics of locally bent microfiber taper (LBMT) covered with a nanosized HRI layer under different temperatures and electric field intensities have been theoretically analyzed in Section 2.3. The mathematical model for LBMT is established. The mode coupling and interference characteristics in a LBMT are described. In Section 2.4, a new structure LPG coated with nanosized HRI-LC layer is experimentally realized. The refractive indices of LC at different temperatures are measured. Using the sample brush coating technology, LC layers with different thicknesses are deposited on the surface of LPG. The sensitivity of the resonance wavelength to the change of the nanoscale overlay refractive index is experimentally observed. Experimental results show that the phenomenon of cladding mode reorganization in HRI-LC–coated LPG occurs when the high refractive index (HRI) of the nanosized LC overlay is changed from 1.477 to 1.515 resulting from temperature increasing from 20 to 65°C. The electro-optic tuning ability of LPG coated with the HRI-LC layer is also demonstrated. By choosing an appropriate operating point, the maximum tuning range can reach approximately 10 nm. The experimental results are in good agreement with the theoretical analysis in Section 2.2. The transmission characteristics of the nanosized HRI-LC layer– coated LBMT in response to the environmental temperature, and external electric fields have been experimentally investigated in Section 2.5. A microfiber taper with a diameter of ~3.72 μm is fabricated using the flame brushing technique. By bending the transition region of the taper and later by placing a ~200-nm LC layer over the uniform taper waist region, a high-efficiency thermal and electric tunable LC-coated LBMT interferometer is achieved. This suggests a potential application of this device as tunable all-fiber photonic devices, such as filters, modulators, and sensing elements. Finally, conclusions are drawn in section 3.

### **2. Micro-/nano LC layer–based tunable optical fiber interferometers**

#### **2.1. Two kinds of typical optical modal interferometers**

#### *2.1.1. Long period gratings (LPG)*

In-fiber long period gratings (LPG), which have the ability to couple energy from the code mode to different cladding modes with the same propagation direction, have been widely investigated in the field of optical sensing and communication [5].

Up to date, most of the studies have concentrated on the analysis of the LPG response to the surrounding medium refractive index (SRI) smaller than that of silica [6]. The idea of coated LPG with a thin HRI layer was first put forward by Rees et al. [7]. Then, Wang et al. presented a detailed study to investigate the sensitivity of LPG to SRI when they are coated with a nanosized HRI film [8]. In the same year, a comprehensive investigation of mode transition in HRI layer–coated LPG was reported by Cusano et al. [9]. Their analysis indicated that the cladding modes reorganization occurred for a fixed overlay thickness and refractive index by increasing the SRI. In fact, changing the HRI could also result in cladding modes reorganization. The theoretical and experimental study proposed by Del Villar et al. showed that by selecting an appropriate overlay thickness, the highest sensitivity of the resonance wavelengths to HRI change of the overlay can be obtained [10, 11].

### *2.1.2. Tapered optical fiber interferometer*

with that of the traditional sized optical fiber devices, the advantages in performance of the micro-/nano LC layer based ones are verified. The main contents of this chapter are as follows. Two kinds of typical optical fiber–based modal interference devices and the relevant micro-/ nanofabrication technology are proposed in Section 2.1. One typical fiber modal interference device is the optical fiber grating. The other typical device is the tapered optical fiber. Adopting optic fiber surface micro-/nanostructure technology, two kinds of micro-/nano liquid crystal layer–based wide range tunable optical fiber devices are achieved. The properties of the cladding modes in LPG coated with a high refractive index (HRI) micro-/nanometer overlay are theoretically studied in Section 2.2. The resonant wavelength and spectral characteristics of the four layer model long period grating are also analyzed based on the coupled-mode theory. Besides, the transmission spectra of LPG with different overlay thickness and refractive indices are numerically calculated. The tuning characteristics of locally bent microfiber taper (LBMT) covered with a nanosized HRI layer under different temperatures and electric field intensities have been theoretically analyzed in Section 2.3. The mathematical model for LBMT is established. The mode coupling and interference characteristics in a LBMT are described. In Section 2.4, a new structure LPG coated with nanosized HRI-LC layer is experimentally realized. The refractive indices of LC at different temperatures are measured. Using the sample brush coating technology, LC layers with different thicknesses are deposited on the surface of LPG. The sensitivity of the resonance wavelength to the change of the nanoscale overlay refractive index is experimentally observed. Experimental results show that the phenomenon of cladding mode reorganization in HRI-LC–coated LPG occurs when the high refractive index (HRI) of the nanosized LC overlay is changed from 1.477 to 1.515 resulting from temperature increasing from 20 to 65°C. The electro-optic tuning ability of LPG coated with the HRI-LC layer is also demonstrated. By choosing an appropriate operating point, the maximum tuning range can reach approximately 10 nm. The experimental results are in good agreement with the theoretical analysis in Section 2.2. The transmission characteristics of the nanosized HRI-LC layer– coated LBMT in response to the environmental temperature, and external electric fields have been experimentally investigated in Section 2.5. A microfiber taper with a diameter of ~3.72 μm is fabricated using the flame brushing technique. By bending the transition region of the taper and later by placing a ~200-nm LC layer over the uniform taper waist region, a high-efficiency thermal and electric tunable LC-coated LBMT interferometer is achieved. This suggests a potential application of this device as tunable all-fiber photonic devices, such as filters, modulators,

178 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

and sensing elements. Finally, conclusions are drawn in section 3.

investigated in the field of optical sensing and communication [5].

**2.1. Two kinds of typical optical modal interferometers**

*2.1.1. Long period gratings (LPG)*

**2. Micro-/nano LC layer–based tunable optical fiber interferometers**

In-fiber long period gratings (LPG), which have the ability to couple energy from the code mode to different cladding modes with the same propagation direction, have been widely Fiber tapers, which have a variety of functions including filtering, light coupling, and sensing, consist of a waist between two tapered sections fabricated by heating and pulling technology [12, 13]. Different length and shape of the first tapered section have different effects on the input mode [13].

Recently, we reported a compact fiber interferometer named LBMT interferometer [14–16]. This kind of interferometer has unique features of low insertion loss and ultrathin taper waist, so it is promising for high-sensitivity sensing. It is interesting to integrating a LBMT interferometer and functional material due to physical effect of functional material and the high sensitivity of the microfiber to the surroundings.

### **2.2. Mode transition in the nanosized HRI overlay–coated LPG**

### *2.2.1. Theory background*

Based on the phase-matching condition between the core and the cladding modes, the center wavelength *λ<sup>i</sup>* of the *j*th attenuation band can be expressed as [17]

$$\Lambda\_i = \{\mathfrak{n}\_{ao} \text{ - } \mathfrak{n}\_{ab}^i\} \Lambda \tag{1}$$

where *nco* is the effective refractive index of the core mode and *ncl i* is the effective refractive index of the *i*th cladding mode. *Λ* is the grating period [5].

**Figure 1** shows the structure of HRI-coated LPG with four layers. Using the transfer matrix method proposed by Anemogiannis et al., the cladding mode effective index can be calculated [18].

#### *2.2.2. Numerical analysis of HRI overlay–coated LPG*

The analysis used the standard Corning SMF-28 optical fiber parameters: numerical aperture 0.14, refractive index difference 0.36% [9], cladding, and core diameter 125 and 8.2 μm, respectively. The HRI-LC overlay is with refractive index of 1.47–1.55 close to the experimental testing [19] and with different thickness changing from 600 to 900 nm.

**Figure 1.** (a) Illustrative schematic of LPG with an nm-thick thin-film coating. (b) Index profile of the thin-film coated LPG.

Each effective refractive index of the first six cladding modes as a function of the HRI is represented in **Figure 2(a)** for a 600-nm HRI overlay. From the figure, we know that each effective refractive index of the first six cladding modes goes up as the HRI increases, until a critical point is reached, when a significant shift in the effective refractive index occurs. There is a specific value of HRI that makes the lowest order cladding mode to be guided within the overlay for a fixed overlay thickness.

**Figures 2(b)–(d)** show the effective refractive index for a HRI overlay of 700, 800, and 900 nm, respectively. It can be seen that the transition point moves to a lower HRI as the overlay thickness increases.

#### **2.3. Tuning effect of nanosized HRI-LC overlay–coated LBMTs**

#### *2.3.1. Mode coupling and interference in LBMTs*

The fiber taper can be divided into two zones: (1) the taper waist with a constant diameter *d*<sup>0</sup> and (2) the transition region with a diameter continuously varying from *d*<sup>0</sup> to 125 μm. A LBMT is fabricated by bending the transition regions of the taper to form a modal interferometer.

*Lt* = 3 mm at *λ* = 1.550 μm. Each bent transition region was divided into 100 steps with the

**Figure 2.** Effective refractive index of the *LP*<sup>02</sup> − *LP*07 cladding modes versus HRI-coated fiber with (a) 600, (b) 700, (c)

the modal shown in **Figure 3(b)** [15], we can calculate the appropriate values of the angle *θ* in the bent transition region. **Figure 4** shows the evolution of the first four modes (LP01, LP11, LP21, and LP02). As we can see that there is no power transfer from the fundamental mode to other high-order modes when the bending curvature 1/*R* = 0. As the bending curvature goes up, the LP11, LP21, and LP02 modes are successively excited with their energy originated from the LP01 mode. The power of each mode remains almost constant in the central uniform taper waist. When 1/*R* increases, the coupling between the fundamental mode and the first higher order mode, the decisive factor in the interference extinction ratio is strengthened. The optimized status can be obtained at a certain bending curvature (e.g. 0.455 mm−1) with the

We calculated Poynting vectors of 200-nm LC layer–coated silica microfiber with different diameters ranging from 1 to 5 μm operating at 1.55 μm wavelength by solving Maxwell's equations of a three-layer structured cylindrical wavelength numerically (see **Figure 5(a)**–**(c)**)

maximum extinction ratio and the relatively low loss.

*2.3.2. Spectral tuning characteristics of a LBMT with a nanosized HRI-LC overlay*

/M). The 6-mm long uniform waist region has been considered as a step. From

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same length (*L*<sup>t</sup>

800, and (d) 900 nm film.

To study the modal characteristics in the bent transition region, we assume the bent fiber taper as a sequence of straight segments of the same length *l* with an angle of *θ* [20] (see **Figure 3(a)**) [15]. The complex amplitude, *a pq* (*i*+1) , of the modes in the (*i*+1)th region is given by [20]

$$a\_{pq}^{(t+1)} = \sum\_{\nu=0} \sum\_{m=0} \int\_0^\nu \int\_0^{2\pi} \Psi\_{nm}^\dagger \exp\left(-j\left[\beta\_{nn}^\dagger l\right]\right) \times \exp\left(j\left[\beta\_{nn}^\dagger \Theta r \cos\bigotimes\right] \Psi\_{nn}^{t+1\dagger} r dr d\bigotimes\right) \mathbf{i} = 1, 2, \dots \tag{2}$$

where *l i* is the length of the *i*th region, *βnm <sup>i</sup>* and *ψnm <sup>i</sup>* are the propagation constant and the normal field of the LP*mn* mode in the *i*th region, respectively [15]. *ψpq* (*i*+1)∗ is the complex conjugate of the mode field of the LP*pq* mode in the (*i*+1)th region [15].

The local-mode power evolution along the LBMT under various bending curvatures was theoretically examined. The LBMT parameters are as follows: *d*<sup>0</sup> = 3.7 μm, *L*<sup>0</sup> = 6 mm, and

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Each effective refractive index of the first six cladding modes as a function of the HRI is represented in **Figure 2(a)** for a 600-nm HRI overlay. From the figure, we know that each effective refractive index of the first six cladding modes goes up as the HRI increases, until a critical point is reached, when a significant shift in the effective refractive index occurs. There is a specific value of HRI that makes the lowest order cladding mode to be guided within the overlay

**Figure 1.** (a) Illustrative schematic of LPG with an nm-thick thin-film coating. (b) Index profile of the thin-film coated

**Figures 2(b)–(d)** show the effective refractive index for a HRI overlay of 700, 800, and 900 nm, respectively. It can be seen that the transition point moves to a lower HRI as the overlay

The fiber taper can be divided into two zones: (1) the taper waist with a constant diameter *d*<sup>0</sup>

To study the modal characteristics in the bent transition region, we assume the bent fiber taper as a sequence of straight segments of the same length *l* with an angle of *θ* [20] (see **Figure 3(a)**)

) × exp(*j βn<sup>m</sup>*

The local-mode power evolution along the LBMT under various bending curvatures was theoretically examined. The LBMT parameters are as follows: *d*<sup>0</sup> = 3.7 μm, *L*<sup>0</sup> = 6 mm, and

*<sup>i</sup>* and *ψnm*

, of the modes in the (*i*+1)th region is given by [20]

*<sup>i</sup> θr* cos  ∅)*Ψn<sup>m</sup>*

(*i*+1)∗

is fabricated by bending the transition regions of the taper to form a modal interferometer.

to 125 μm. A LBMT

(*i*+1)\* *rdrd* ∅ ,i = 1, 2, … (2)

is the complex conjugate of the

*<sup>i</sup>* are the propagation constant and the normal

**2.3. Tuning effect of nanosized HRI-LC overlay–coated LBMTs**

180 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

*pq* (*i*+1)

field of the LP*mn* mode in the *i*th region, respectively [15]. *ψpq*

mode field of the LP*pq* mode in the (*i*+1)th region [15].

*<sup>i</sup>* exp(−*j βn<sup>m</sup>*

*i l i*

and (2) the transition region with a diameter continuously varying from *d*<sup>0</sup>

*2.3.1. Mode coupling and interference in LBMTs*

is the length of the *i*th region, *βnm*

for a fixed overlay thickness.

[15]. The complex amplitude, *a*

(*i*+1) = ∑ *n*=0 ∑ *m*=0 ∫0 <sup>∞</sup> ∫<sup>0</sup> *<sup>2</sup><sup>π</sup> Ψn<sup>m</sup>*

*apq*

where *l i*

thickness increases.

LPG.

**Figure 2.** Effective refractive index of the *LP*<sup>02</sup> − *LP*07 cladding modes versus HRI-coated fiber with (a) 600, (b) 700, (c) 800, and (d) 900 nm film.

*Lt* = 3 mm at *λ* = 1.550 μm. Each bent transition region was divided into 100 steps with the same length (*L*<sup>t</sup> /M). The 6-mm long uniform waist region has been considered as a step. From the modal shown in **Figure 3(b)** [15], we can calculate the appropriate values of the angle *θ* in the bent transition region. **Figure 4** shows the evolution of the first four modes (LP01, LP11, LP21, and LP02). As we can see that there is no power transfer from the fundamental mode to other high-order modes when the bending curvature 1/*R* = 0. As the bending curvature goes up, the LP11, LP21, and LP02 modes are successively excited with their energy originated from the LP01 mode. The power of each mode remains almost constant in the central uniform taper waist. When 1/*R* increases, the coupling between the fundamental mode and the first higher order mode, the decisive factor in the interference extinction ratio is strengthened. The optimized status can be obtained at a certain bending curvature (e.g. 0.455 mm−1) with the maximum extinction ratio and the relatively low loss.

#### *2.3.2. Spectral tuning characteristics of a LBMT with a nanosized HRI-LC overlay*

We calculated Poynting vectors of 200-nm LC layer–coated silica microfiber with different diameters ranging from 1 to 5 μm operating at 1.55 μm wavelength by solving Maxwell's equations of a three-layer structured cylindrical wavelength numerically (see **Figure 5(a)**–**(c)**)

[16, 21]. In our calculation, the refractive indices of LC and silica microfiber are 1.50 and 1.44, respectively. We also calculated the amount of optical power guided in the LC layer and the air as a function of microfiber diameter in **Figure 5(d)** and **(e)**, respectively [16]. When the diameter of microfiber goes up from 1 to 5 μm, the amount of optical power is changed from 18.4 to 0.98% in the LC layer and from 10.5 to 0.31% in the air, respectively, which results in

High-order modes are excited successively from the fundamental mode after the light injects into the uniform taper waist from a locally bent transmission region. In the output bent transition region, these modes will couple back into the fundamental mode and the wavelength-

> \_ *I m I*

*<sup>m</sup>* is the amplitude of the propagation mode, Δ*neff* is the effective index difference, and

is the length of the taper waist. The attenuation peak wavelength *λN* of the interferometer

**Figure 5.** Calculated Poynting vector of a 200-nm thick LC-coated microfiber with diameter being (a) 1, (b) 3, and (c) 5 μm.

The amount of optical power guided in (d) LC overlay, and (e) air as a function of microfiber diameter [16].

*<sup>n</sup>* cos(2*πΔneff L*0/*λ*) (3)

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(2*N* + 1) (4)

smaller tuning efficiency and lower transmission loss.

*λ<sup>N</sup>* = 2*Δneff L*0/

*I* = ∑

can be expressed as [16]

where *I*

*L*0

dependent transmission spectrum could be expressed as [16]

*m I <sup>m</sup>* + 2∑ *m*>*n* ∑√

**Figure 3.** (a) Two adjacent sections of a fiber before and after bending. (b) Geometry used for the theoretical analysis of the bending effect on the fiber taper [15].

**Figure 4.** LPnm local-mode power longitudinal evolution of the LBMT with *d*<sup>0</sup> = 3.7 μm and *L*<sup>0</sup> = 6 mm under bending curvature 1/*R* being (a) 0, (b) 0.2, (c) 0.445, and (d) 0.526 mm−1 at *λ* = 1.555 μm.

[16, 21]. In our calculation, the refractive indices of LC and silica microfiber are 1.50 and 1.44, respectively. We also calculated the amount of optical power guided in the LC layer and the air as a function of microfiber diameter in **Figure 5(d)** and **(e)**, respectively [16]. When the diameter of microfiber goes up from 1 to 5 μm, the amount of optical power is changed from 18.4 to 0.98% in the LC layer and from 10.5 to 0.31% in the air, respectively, which results in smaller tuning efficiency and lower transmission loss.

High-order modes are excited successively from the fundamental mode after the light injects into the uniform taper waist from a locally bent transmission region. In the output bent transition region, these modes will couple back into the fundamental mode and the wavelengthdependent transmission spectrum could be expressed as [16]

$$I = \sum\_{m} I\_{m} + 2 \sum\_{m \gg n} \sum\_{l} \overline{I\_{m} I\_{n}} \cos \left(2 \pi \Delta n\_{eff} L\_{0} l\right) \tag{3}$$

where *I <sup>m</sup>* is the amplitude of the propagation mode, Δ*neff* is the effective index difference, and *L*0 is the length of the taper waist. The attenuation peak wavelength *λN* of the interferometer can be expressed as [16]

$$
\lambda\_{\infty} = 2\Delta n\_{eg} L\_d \text{(2N+1)}\tag{4}
$$

**Figure 5.** Calculated Poynting vector of a 200-nm thick LC-coated microfiber with diameter being (a) 1, (b) 3, and (c) 5 μm. The amount of optical power guided in (d) LC overlay, and (e) air as a function of microfiber diameter [16].

**Figure 4.** LPnm local-mode power longitudinal evolution of the LBMT with *d*<sup>0</sup>

182 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

the bending effect on the fiber taper [15].

**Figure 3.** (a) Two adjacent sections of a fiber before and after bending. (b) Geometry used for the theoretical analysis of

curvature 1/*R* being (a) 0, (b) 0.2, (c) 0.445, and (d) 0.526 mm−1 at *λ* = 1.555 μm.

= 3.7 μm and *L*<sup>0</sup>

= 6 mm under bending

where *N* is the interference order. According to Eq. (4), ∆*neff* changes when the effective index of the propagation mode of the microfiber taper waist is altered by the surrounding refractive index, and as a result, a wavelength shift is obtained. **Figure 6** shows the calculated Poynting vectors of a 3.72-μm diameter silica microfiber coated with different thickness HRI-LC overlay when wavelength is at 1.55 μm. As we can see, thicker LC films assure more optical power guided in the overlay for the fundamental mode and the first high-order mode. More optical power is converted to the radiation mode when the overlay thickness increases, which will result in a higher transmission loss.

The calculated transversal mode distributions for the first two modes with different 200-nm LC overlay HRIs are plotted in **Figure 7**. **Figure 8** depicts the effective index difference ∆*neff* of the fundamental mode and the first high-order mode as a function of the refractive index of LC, when the overlay thickness being 200, 400, and 600 nm. We can see that more light energy concentrates in the outside LC layer with higher refractive index of the LC overlay, leading to an increased tuning range. The microfiber taper interferometer with higher overlay refractive index or thicker overlay thickness exhibits higher sensitivity. The higher the refractive index of the overlay, the smaller the effective index difference ∆*neff*.

**Figure 7.** Transversal electric field distributions of the fundamental mode and the first high-order mode guided in the microfiber taper waist coated with a 200 nm LC overlay. (a) The fundamental mode and (b) the first high-order mode.

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**Figure 8.** Calculated dependence of ∆*neff* on the refractive index and the thickness of the LC overlay at the wavelength

of 1559 nm.

**Figure 6.** Distribution of the fundamental mode and the first high-order mode for three LC overlay thickness values: (a) 0, (b) 200, (c) 400, and (d) 600 nm.

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where *N* is the interference order. According to Eq. (4), ∆*neff* changes when the effective index of the propagation mode of the microfiber taper waist is altered by the surrounding refractive index, and as a result, a wavelength shift is obtained. **Figure 6** shows the calculated Poynting vectors of a 3.72-μm diameter silica microfiber coated with different thickness HRI-LC overlay when wavelength is at 1.55 μm. As we can see, thicker LC films assure more optical power guided in the overlay for the fundamental mode and the first high-order mode. More optical power is converted to the radiation mode when the overlay thickness increases, which will

The calculated transversal mode distributions for the first two modes with different 200-nm LC overlay HRIs are plotted in **Figure 7**. **Figure 8** depicts the effective index difference ∆*neff* of the fundamental mode and the first high-order mode as a function of the refractive index of LC, when the overlay thickness being 200, 400, and 600 nm. We can see that more light energy concentrates in the outside LC layer with higher refractive index of the LC overlay, leading to an increased tuning range. The microfiber taper interferometer with higher overlay refractive index or thicker overlay thickness exhibits higher sensitivity. The higher the refractive index

**Figure 6.** Distribution of the fundamental mode and the first high-order mode for three LC overlay thickness values: (a) 0,

result in a higher transmission loss.

(b) 200, (c) 400, and (d) 600 nm.

of the overlay, the smaller the effective index difference ∆*neff*.

184 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

**Figure 7.** Transversal electric field distributions of the fundamental mode and the first high-order mode guided in the microfiber taper waist coated with a 200 nm LC overlay. (a) The fundamental mode and (b) the first high-order mode.

**Figure 8.** Calculated dependence of ∆*neff* on the refractive index and the thickness of the LC overlay at the wavelength of 1559 nm.

### **2.4. Experimental study of nanosized HRI-LC layer–coated LPG**

### *2.4.1. Temperature-dependent mode transition in HRI-LC–coated LPG*

The LPG was fabricated on Corning SMF-28 fibers through CO<sup>2</sup> irradiation. The grating period is 620 μm, and the grating region is 50 mm. A white light source and an optical spectrum analyzer are used to record the spectral response. Attention bands were focus on the LP02 and LP03 modes in the range of 1400–1700 nm.

**Figure 11** shows the transmission spectrum of the ultrathin LC-coated LPG for different temperatures between 20 and 65°C. From the figure, we know that when temperature is increased from 20 to 58°C, wavelength blueshifts slightly (the LP0i mode has been marked with *i*). A large wavelength shift is obtained in the attenuation band of LP03 mode when the temperature goes up to about 59°C. The phenomenon of cladding modes reconfiguration appears when

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**Figure 12** shows a clearer wavelength shift. As we can see, outside the transition region, the center wavelength of the LP02 mode shifts from 1579.7 to 1579.2 nm, and the LP03 mode shifts from 1687.5 to 1665.7 nm. However, only LP03 mode can be observed within the transition region with its center wavelength changing from 1665.7 to 1583.7 nm, which shifts ~82 nm.

**Figure 11.** Transmission spectra of an ultrathin HRI-LC–coated LPG for different temperatures in the 20–65°C range.

To clarify the experimental observations, the temperature dependent refractive index of the LC overlay was also measured. The methods for measuring the refractive index of liquids can be classified into refraction technique and reflection techniques including total reflection [22]. **Figure 13** shows the schematic diagram of the experiment setup with an efficient method

We immerse a detecting tip into air, water, and LC under different magnetic fields. The reflected light power under every condition is measured. **Figure 14** shows the thermo-depen-

*2.4.2. Measurement of the refractive index of LC at different temperatures*

dent HRI of LC in the infrared light region based on the experimental data.

developed by Pu et al. [23].

temperature in changed from 58 to 60°C.

LC material MDA-98-3699 is from Merck. The refractive index of LC is higher than that of silica. The coating process is simple. We dipped a tampon with the liquid crystal, and daubed it on the fiber grating evenly. The surface tension of the slimy liquid crystal makes itself uniformly coated. **Figure 9** shows the CCD photographs of the bare and LC-coated LPG taken by

**Figure 9.** CCD photographs of bare and LC-coated LPG.

OLYMPUS STM6 measuring microscope. The thickness of the LC layer is controlled by the times of daubing. **Figure 10** shows the CCD photographs of overlay thickness of about (a) 400 and (b) 800 nm. A heater box was used to change the temperature of the liquid crystal from 20 to 65°C.

**Figure 10.** CCD photographs reveal approximate overlay thicknesses of (a) 400 and (b) 800 nm.

**Figure 11** shows the transmission spectrum of the ultrathin LC-coated LPG for different temperatures between 20 and 65°C. From the figure, we know that when temperature is increased from 20 to 58°C, wavelength blueshifts slightly (the LP0i mode has been marked with *i*). A large wavelength shift is obtained in the attenuation band of LP03 mode when the temperature goes up to about 59°C. The phenomenon of cladding modes reconfiguration appears when temperature in changed from 58 to 60°C.

**2.4. Experimental study of nanosized HRI-LC layer–coated LPG**

186 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

*2.4.1. Temperature-dependent mode transition in HRI-LC–coated LPG*

LP02 and LP03 modes in the range of 1400–1700 nm.

**Figure 9.** CCD photographs of bare and LC-coated LPG.

to 65°C.

The LPG was fabricated on Corning SMF-28 fibers through CO<sup>2</sup>

period is 620 μm, and the grating region is 50 mm. A white light source and an optical spectrum analyzer are used to record the spectral response. Attention bands were focus on the

LC material MDA-98-3699 is from Merck. The refractive index of LC is higher than that of silica. The coating process is simple. We dipped a tampon with the liquid crystal, and daubed it on the fiber grating evenly. The surface tension of the slimy liquid crystal makes itself uniformly coated. **Figure 9** shows the CCD photographs of the bare and LC-coated LPG taken by

OLYMPUS STM6 measuring microscope. The thickness of the LC layer is controlled by the times of daubing. **Figure 10** shows the CCD photographs of overlay thickness of about (a) 400 and (b) 800 nm. A heater box was used to change the temperature of the liquid crystal from 20

**Figure 10.** CCD photographs reveal approximate overlay thicknesses of (a) 400 and (b) 800 nm.

irradiation. The grating

**Figure 11.** Transmission spectra of an ultrathin HRI-LC–coated LPG for different temperatures in the 20–65°C range.

**Figure 12** shows a clearer wavelength shift. As we can see, outside the transition region, the center wavelength of the LP02 mode shifts from 1579.7 to 1579.2 nm, and the LP03 mode shifts from 1687.5 to 1665.7 nm. However, only LP03 mode can be observed within the transition region with its center wavelength changing from 1665.7 to 1583.7 nm, which shifts ~82 nm.

### *2.4.2. Measurement of the refractive index of LC at different temperatures*

To clarify the experimental observations, the temperature dependent refractive index of the LC overlay was also measured. The methods for measuring the refractive index of liquids can be classified into refraction technique and reflection techniques including total reflection [22]. **Figure 13** shows the schematic diagram of the experiment setup with an efficient method developed by Pu et al. [23].

We immerse a detecting tip into air, water, and LC under different magnetic fields. The reflected light power under every condition is measured. **Figure 14** shows the thermo-dependent HRI of LC in the infrared light region based on the experimental data.

**Figure 12.** Wavelength shift of LP02 and LP03 cladding modes for the LPG coated with a HRI layer versus temperature.

**2.5. Experimental investigation of nanosized LC-coated LBMT interferometer**

file parameters of the microfiber taper are as follows: the waist diameter *d*<sup>0</sup>

**Figure 18(c)** shows the SEM image of the taper waist.

**Figure 14.** Refractive index versus temperature (°C) of LC MDA-98-3699.

transmission loss peak of ∼2 dB can be observed.

1.4794 to 1.4845 when the temperature goes up from 25 to 35°C.

temperature response is only 0.026 nm/°C.

length *L*<sup>0</sup>

**Figure 18** shows the experimental setup. The microfiber taper integrated with the nanosized LC layer was pulled straightly first, and then, the transition regions of the microfiber taper were locally bent to form a fiber interferometer. Two pieces of strip electrodes parallel to each other were pressed against the microfiber with a 4-μm gap maintained by spacers. The pro-

in **Figure 18(b)** together with the critical diameter corresponding to the bent transition region.

The LC material MDA-98-3699 is from Merck [16, 24]. CCD photographs of the bare and LC-coated microfiber taper waist are shown in **Figure 19**. By rubbing the strip electrodes directly on both sides of the microfiber, the planar anchoring of the LC can be obtained.

A comparison of transmitted spectra of a bare and LC-coated LBMT interferometer at 25°C is given in **Figure 20**. Compared with the bare one, a redshift of ∼4.9 nm and a decrease of the

We first measured the transmission spectra of the bare microfiber interferometer at temperatures ranging from 25 to 50°C, and the temperature responses for the attenuation peak at the wavelength of 1529.3 nm are shown in **Figure 21**. Here, we can see from **Figure 21** that the

As to thermal tuning, we use the temperature dependence of the ordinary effective index of LC. We measured the ordinary refractive indices of the LC under different temperatures at a wavelength of 1.55 μm [25]. The ordinary refractive index of the LC increases linearly from

≈ 6.3 mm, and bent transition region length *L*t ≈ 3 mm. These parameters are given

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≈ 3.72 μm, waist

**Figure 15** shows the theoretically calculated center wavelength shifts with the measured HRI data. The experimental results are in good agreement with the theoretical analysis. For LP<sup>03</sup> mode, the sensitivity to HRI in the transition region was approximately six times the sensitivity outside the transition region, which means that we can choose this region as high-sensitivity operating region for sensing application.

#### *2.4.3. Electrical spectral tuning of LC-coated LPG at the highly sensitive operating point*

A simple scheme for active electrically controlled tunable fiber gratings is illustrated schematically in **Figure 16**. Two parallel substrates are used to fix the LC-coated LPG separated by two 125-μm spacers. The external electric fields are applied through a pair of electrodes under stabilized temperature at 20, 55, 58, 59, 60, and 65°C. The electrical spectra tunability of the LC-coated LPG under different temperatures is shown in **Figure 17**. As we can see that the most sensitive operating point for the device is at 60°C, the maximum tuning range is about 10 nm.

**Figure 13.** Schematic diagram of experimental setup for measuring the refractive index of the LC.

**Figure 14.** Refractive index versus temperature (°C) of LC MDA-98-3699.

**Figure 15** shows the theoretically calculated center wavelength shifts with the measured HRI data. The experimental results are in good agreement with the theoretical analysis. For LP<sup>03</sup> mode, the sensitivity to HRI in the transition region was approximately six times the sensitivity outside the transition region, which means that we can choose this region as high-sensitiv-

**Figure 12.** Wavelength shift of LP02 and LP03 cladding modes for the LPG coated with a HRI layer versus temperature.

A simple scheme for active electrically controlled tunable fiber gratings is illustrated schematically in **Figure 16**. Two parallel substrates are used to fix the LC-coated LPG separated by two 125-μm spacers. The external electric fields are applied through a pair of electrodes under stabilized temperature at 20, 55, 58, 59, 60, and 65°C. The electrical spectra tunability of the LC-coated LPG under different temperatures is shown in **Figure 17**. As we can see that the most sensitive operating point for the device is at 60°C, the maximum tuning range is about 10 nm.

*2.4.3. Electrical spectral tuning of LC-coated LPG at the highly sensitive operating point*

**Figure 13.** Schematic diagram of experimental setup for measuring the refractive index of the LC.

ity operating region for sensing application.

188 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

### **2.5. Experimental investigation of nanosized LC-coated LBMT interferometer**

**Figure 18** shows the experimental setup. The microfiber taper integrated with the nanosized LC layer was pulled straightly first, and then, the transition regions of the microfiber taper were locally bent to form a fiber interferometer. Two pieces of strip electrodes parallel to each other were pressed against the microfiber with a 4-μm gap maintained by spacers. The profile parameters of the microfiber taper are as follows: the waist diameter *d*<sup>0</sup> ≈ 3.72 μm, waist length *L*<sup>0</sup> ≈ 6.3 mm, and bent transition region length *L*t ≈ 3 mm. These parameters are given in **Figure 18(b)** together with the critical diameter corresponding to the bent transition region. **Figure 18(c)** shows the SEM image of the taper waist.

The LC material MDA-98-3699 is from Merck [16, 24]. CCD photographs of the bare and LC-coated microfiber taper waist are shown in **Figure 19**. By rubbing the strip electrodes directly on both sides of the microfiber, the planar anchoring of the LC can be obtained.

A comparison of transmitted spectra of a bare and LC-coated LBMT interferometer at 25°C is given in **Figure 20**. Compared with the bare one, a redshift of ∼4.9 nm and a decrease of the transmission loss peak of ∼2 dB can be observed.

We first measured the transmission spectra of the bare microfiber interferometer at temperatures ranging from 25 to 50°C, and the temperature responses for the attenuation peak at the wavelength of 1529.3 nm are shown in **Figure 21**. Here, we can see from **Figure 21** that the temperature response is only 0.026 nm/°C.

As to thermal tuning, we use the temperature dependence of the ordinary effective index of LC. We measured the ordinary refractive indices of the LC under different temperatures at a wavelength of 1.55 μm [25]. The ordinary refractive index of the LC increases linearly from 1.4794 to 1.4845 when the temperature goes up from 25 to 35°C.

**Figure 17.** Electrical spectra tenability of the LC cladding LPG at different temperatures.

**Figure 18.** (a) Schematic diagram of the experimental setup for magnetic field tenability test; (b) measured profile of the

≈ 6.3 mm with *d*A and *d*B corresponding to the bent transition region; (c) SEM image of the

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LBMT having *d*<sup>0</sup>

≈ 3.72 μm, *L*<sup>0</sup>

microfiber taper waist with a diameter of ∼3.72 μm.

**Figure 15.** Theoretical and experimental center wavelength of (a) LP02 and (b) LP03 shift dependence on HRI.

**Figure 16.** Experimental setup and schematic representation of the LC cladding LPG.

Micro/Nano Liquid Crystal Layer–Based Tunable Optical Fiber Interferometers http://dx.doi.org/10.5772/intechopen.70413 191

**Figure 17.** Electrical spectra tenability of the LC cladding LPG at different temperatures.

**Figure 18.** (a) Schematic diagram of the experimental setup for magnetic field tenability test; (b) measured profile of the LBMT having *d*<sup>0</sup> ≈ 3.72 μm, *L*<sup>0</sup> ≈ 6.3 mm with *d*A and *d*B corresponding to the bent transition region; (c) SEM image of the microfiber taper waist with a diameter of ∼3.72 μm.

**Figure 16.** Experimental setup and schematic representation of the LC cladding LPG.

190 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

**Figure 15.** Theoretical and experimental center wavelength of (a) LP02 and (b) LP03 shift dependence on HRI.

A redshift of 10.5 nm for the attenuation peak wavelength of 1534.2 nm was achieved as temperature increased from 25 to 35°C, as shown in **Figure 22**. The tuning efficiency is ~1.05 nm/°C, which is approximately 40 times higher than that of the bare locally bent microfiber interferometer.

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As to electric tuning, electric fields of 1.25, 2.50, and 3.75 V/μm were applied to the electrodes in our experiment by adjusting the tunable voltage source with the temperature stabilized at 25°C [16]. **Figure 23(a)** is the measured transmission spectra of the same attenuation peak under different electric fields. **Figure 23(b)** is the wavelength of attenuation peak as a function

**Figure 23.** (a) Transmission spectra of LC-coated LBMT interferometer according to the external electric field and (b)

wavelength shift of the transmission spectrum with the variation of the electric field intensity.

**Figure 22.** Measured wavelength shifts of a certain attenuation peak of the interferometer at different temperatures.

**Figure 19.** CCD photographs of bare and LC-coated microfiber taper waist.

**Figure 20.** Comparison of the transmission spectra of a bare and an approximate 200 nm LC-coated LBMT interferometer.

**Figure 21.** Temperature responses of bare microfiber interferometer for the attenuation peak at the wavelength of 1529.3 nm.

A redshift of 10.5 nm for the attenuation peak wavelength of 1534.2 nm was achieved as temperature increased from 25 to 35°C, as shown in **Figure 22**. The tuning efficiency is ~1.05 nm/°C, which is approximately 40 times higher than that of the bare locally bent microfiber interferometer.

**Figure 19.** CCD photographs of bare and LC-coated microfiber taper waist.

192 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

**Figure 20.** Comparison of the transmission spectra of a bare and an approximate 200 nm LC-coated LBMT interferometer.

**Figure 21.** Temperature responses of bare microfiber interferometer for the attenuation peak at the wavelength of

1529.3 nm.

**Figure 22.** Measured wavelength shifts of a certain attenuation peak of the interferometer at different temperatures.

As to electric tuning, electric fields of 1.25, 2.50, and 3.75 V/μm were applied to the electrodes in our experiment by adjusting the tunable voltage source with the temperature stabilized at 25°C [16]. **Figure 23(a)** is the measured transmission spectra of the same attenuation peak under different electric fields. **Figure 23(b)** is the wavelength of attenuation peak as a function

**Figure 23.** (a) Transmission spectra of LC-coated LBMT interferometer according to the external electric field and (b) wavelength shift of the transmission spectrum with the variation of the electric field intensity.

of the electric field. From the figures, we can see that the wavelength dip experiences some redshift by ~5.8 nm, when the electric field changes from 1.25 to 3.75 V/μm. Due to the uniaxial birefringent properties, the optic axis of nematic LC can be realigned by electric field. The effective refractive index is given by *n*eff = 1/√ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ (cos2 *θ*/*n*<sup>0</sup> 2 )<sup>2</sup> + (sin2 *θ*/*ne* 2 )2, when the light polarization direction has an angle *θ* with respect to the average alignment of the molecules [19]. These experimental results are in good accordance with the above theoretical analysis.

[2] Song L, Lee WK, Wang XS. AC electric field assisted photo-induced high efficiency orientational diffractive grating in nematic liquid crystals. Optics Express. 2006;**14**(6):2197-

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### **3. Conclusions**

In this chapter, two kinds of micro/nano LC layer based tunable optical fiber interferometers are reported. For interferometer 1, experimental results show that shifts of greater than 80 nm in the attenuation bands of the transmission spectrum of LPG can be obtained by changing the refractive index of the LC overlay through the thermo-optic effect. For interferometer 2, due to the high sensitivity of the microfiber taper waist to the LC overlay refractive index, the thermal sensitivity as high as 1.05 nm/°C has been achieved, and the electrical tuning range is ~ 5.8 nm when the external electric field is applied up to 3.75 V/μm. The results suggest that the potential application of the micro/nano LC layer based fiber interferometers as tunable all-fiber photonic devices, such as filter and all-optical switch.

### **Acknowledgements**

This work was supported in part by National Science Foundation of China (NSFC) (51567011, 11264016, 61505073, 61363012); China Scholarship Council (CSC) (201608360081); Science and Technology Project of Jiangxi Province (20151BDH80060, 20151BBG70062, 20161ACB21011, 20161BAB212045); Project of Jiangxi Province Department (160273, 150313).

### **Author details**

Haimei Luo\*, Changjing Wang, Yinghua Ji and Wen Yuan \*Address all correspondence to: nclhm2002@hotmail.com Jiangxi Normal University, Nanchang, Jiangxi, China

### **References**

[1] Hu DJJ, Shum P, Lu C, Sun X, Ren GB, Yu X, Wang GH. Design and analysis of thermally tunable liquid crystal filled hybrid photonic crystal fiber coupler. Optics Communications. 2009;**282**(12):2343-2347. DOI: 10.1016/j.optcom.2009.03.023

[2] Song L, Lee WK, Wang XS. AC electric field assisted photo-induced high efficiency orientational diffractive grating in nematic liquid crystals. Optics Express. 2006;**14**(6):2197- 2202. DOI: 10.1364/OE.14.002197

of the electric field. From the figures, we can see that the wavelength dip experiences some redshift by ~5.8 nm, when the electric field changes from 1.25 to 3.75 V/μm. Due to the uniaxial birefringent properties, the optic axis of nematic LC can be realigned by electric field. The effec-

> (cos2 *θ*/*n*<sup>0</sup> 2

experimental results are in good accordance with the above theoretical analysis.

tunable all-fiber photonic devices, such as filter and all-optical switch.

20161BAB212045); Project of Jiangxi Province Department (160273, 150313).

Haimei Luo\*, Changjing Wang, Yinghua Ji and Wen Yuan \*Address all correspondence to: nclhm2002@hotmail.com

2009;**282**(12):2343-2347. DOI: 10.1016/j.optcom.2009.03.023

Jiangxi Normal University, Nanchang, Jiangxi, China

direction has an angle *θ* with respect to the average alignment of the molecules [19]. These

In this chapter, two kinds of micro/nano LC layer based tunable optical fiber interferometers are reported. For interferometer 1, experimental results show that shifts of greater than 80 nm in the attenuation bands of the transmission spectrum of LPG can be obtained by changing the refractive index of the LC overlay through the thermo-optic effect. For interferometer 2, due to the high sensitivity of the microfiber taper waist to the LC overlay refractive index, the thermal sensitivity as high as 1.05 nm/°C has been achieved, and the electrical tuning range is ~ 5.8 nm when the external electric field is applied up to 3.75 V/μm. The results suggest that the potential application of the micro/nano LC layer based fiber interferometers as

This work was supported in part by National Science Foundation of China (NSFC) (51567011, 11264016, 61505073, 61363012); China Scholarship Council (CSC) (201608360081); Science and Technology Project of Jiangxi Province (20151BDH80060, 20151BBG70062, 20161ACB21011,

[1] Hu DJJ, Shum P, Lu C, Sun X, Ren GB, Yu X, Wang GH. Design and analysis of thermally tunable liquid crystal filled hybrid photonic crystal fiber coupler. Optics Communications.

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

)<sup>2</sup> + (sin2 *θ*/*ne*

2

)2, when the light polarization

tive refractive index is given by *n*eff = 1/√

194 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

**3. Conclusions**

**Acknowledgements**

**Author details**

**References**


[15] Luo HM, Li XW, Zou WW, Jiang WN, Chen JP. Modal interferometer based on a C-shaped ultrathin fiber taper for high-sensitivity refractive index measurement. Applied Physics Express. 2012;**5**:012502. DOI: 10.1143/APEX.5.012502

**Chapter 10**

Provisional chapter

**Liquid-Crystal-Based Phase Gratings and Beam Steerers**

DOI: 10.5772/intechopen.70449

Liquid-Crystal-Based Phase Gratings and Beam Steerers

We review our theoretical and experimental studies on a class of liquid crystal (LC) photonic devices, i.e., terahertz (THz) phase gratings and beam steerers by using LCs. Such gratings can function as a THz polarizer and tunable THz beam splitters. The beam splitting ratio of the zeroth-order diffraction to the first-order diffraction by the grating can be tuned from 10:1 to 3:5. Gratings with two different base dimensions were prepared. The insertion loss is lower by approximately 2.5 dB for the one with the smaller base. The response times of the gratings were also studied and were long (tens of seconds) as expected because of the thick LC layer used. Accordingly, the devices are not suitable for applications that require fast modulation. However, they are suitable for instrumentation or apparatuses that require precise control, e.g., an apparatus requiring a fixed beam splitting ratio with occasional fine tuning. Schemes for speeding up the device responses were proposed. Based on the grating structure, we also achieved an electrically tunable THz beam steerer. Broadband THz radiation can be steered by 8.5 with respect to the incident beam by varying the driving voltages to yield the designed phase gradient.

Keywords: liquid crystals, liquid crystal devices, diffraction, phase grating, grating arrays, polarizer, beam splitter, submillimeter wave, THz radiation, tunable circuits and

Terahertz (THz) science and technology have advanced significantly over the last 3 decades. Applications are abundant in topics such as material characterization, data communication, biomedicine, 3D imaging, and environmental surveillance [1–5]. These developments were hampered as crucial quasi-optic components such as phase shifters [6–9], phase gratings [10–12],

> © The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**for Terahertz Waves**

for Terahertz Waves

Wei-Ta Wu and Ru-Pin Pan

Wei-Ta Wu and Ru-Pin Pan

Abstract

1. Introduction

http://dx.doi.org/10.5772/intechopen.70449

devices, ultrafast optics, beam steering

Ci-Ling Pan, Chia-Jen Lin, Chan-Shan Yang,

Ci-Ling Pan, Chia-Jen Lin, Chan-Shan Yang,

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter


Provisional chapter

### **Liquid-Crystal-Based Phase Gratings and Beam Steerers for Terahertz Waves** Liquid-Crystal-Based Phase Gratings and Beam Steerers

DOI: 10.5772/intechopen.70449

Ci-Ling Pan, Chia-Jen Lin, Chan-Shan Yang, Wei-Ta Wu and Ru-Pin Pan Ci-Ling Pan, Chia-Jen Lin, Chan-Shan Yang,

Additional information is available at the end of the chapter Wei-Ta Wu and Ru-Pin Pan

http://dx.doi.org/10.5772/intechopen.70449 Additional information is available at the end of the chapter

for Terahertz Waves

#### Abstract

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[21] Lou JY, Tong LM, Ye ZZ. Dispersion shifts in optical nanowires with thin dielectric coat-

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[23] Pu S, Chen X, Chen Y, Liao W, Chen L, Xia Y. Measurement of the refractive index of a magnetic fluid by the retroreflection on the fiber-optic end face. Applied Physics Letters.

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(5-6):301-305. DOI: 10.1016/S0030-4018(00)01172-X

Lightwave Technology. 2003;**21**(1):218-227. DOI: 10.1109/JLT.2003.808637

Express. 2012;**5**:012502. DOI: 10.1143/APEX.5.012502

196 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

DOI: 10.1109/50.476137

50.85782

Applied Optics. 2016;**55**(26):7393-7397. DOI: 10.1364/AO.55.007393

We review our theoretical and experimental studies on a class of liquid crystal (LC) photonic devices, i.e., terahertz (THz) phase gratings and beam steerers by using LCs. Such gratings can function as a THz polarizer and tunable THz beam splitters. The beam splitting ratio of the zeroth-order diffraction to the first-order diffraction by the grating can be tuned from 10:1 to 3:5. Gratings with two different base dimensions were prepared. The insertion loss is lower by approximately 2.5 dB for the one with the smaller base. The response times of the gratings were also studied and were long (tens of seconds) as expected because of the thick LC layer used. Accordingly, the devices are not suitable for applications that require fast modulation. However, they are suitable for instrumentation or apparatuses that require precise control, e.g., an apparatus requiring a fixed beam splitting ratio with occasional fine tuning. Schemes for speeding up the device responses were proposed. Based on the grating structure, we also achieved an electrically tunable THz beam steerer. Broadband THz radiation can be steered by 8.5 with respect to the incident beam by varying the driving voltages to yield the designed phase gradient.

Keywords: liquid crystals, liquid crystal devices, diffraction, phase grating, grating arrays, polarizer, beam splitter, submillimeter wave, THz radiation, tunable circuits and devices, ultrafast optics, beam steering

### 1. Introduction

Terahertz (THz) science and technology have advanced significantly over the last 3 decades. Applications are abundant in topics such as material characterization, data communication, biomedicine, 3D imaging, and environmental surveillance [1–5]. These developments were hampered as crucial quasi-optic components such as phase shifters [6–9], phase gratings [10–12],

© 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

modulators [13, 14], attenuators [15], polarizers [16, 17], and beam splitters [18–21] in the THz range are still relatively underdeveloped.

To control the properties of electromagnetic waves at all wavelengths, periodic structures such as gratings are frequently employed. In the THz frequency range, gratings with various periods have been used for tailoring few-cycle pulses [22]. Gratings have also been used as couplers and filters [23]. Tunable THz devices based on an optically and electrically controlled carrier concentration in quantum-well structures have been demonstrated. However, these devices have a limited range of tunability and must be operated at cryogenic temperatures far below room temperature [24–26]. The potential of gratings with liquid-crystal-enabled functionalities was recognized 2 decades ago [27]. Recently, the focus has been on various tunable THz devices, such as phase shifters, filters, and switches that are controlled electrically or magnetically, employing liquid crystals, primarily nematic liquid crystals (NLCs) [6–10, 15, 16, 18, 27–33]. Previously, we demonstrated a magnetically controlled phase grating for manipulating THz waves [10]. This is based on magnetic-field-induced birefringence of the NLCs employed [34]. Nonetheless, electrically controlled phase gratings are generally regarded as desirable for many applications. Therefore, we also proposed and demonstrated an electrically controlled phase grating involving NLCs for THz waves [11]. However, the theoretical analysis was not described in detail and the issue of insertion loss was not touched upon in the previous communication.

binary phase grating. The grating is periodic along the x-direction. The THz wave is assumed to be polarized along the x-axis and propagates along the y-direction. Each section of the grating can be considered a retarder that introduces a phase shift. The Jones matrix [40]

Figure 1. Schematic of a generic binary phase grating consisting alternating sections with refractive indices of n<sup>1</sup> and n2. The width and height of each section of the phase element is respectively, l and d. P is the polarization direction of the THz

> <sup>R</sup><sup>b</sup> <sup>¼</sup> <sup>e</sup><sup>i</sup>δ<sup>x</sup> <sup>0</sup> 0 e<sup>i</sup>δ<sup>y</sup>

where δ is the phase retardation and a function of x. The Jones vector associated with the

Ei <sup>¼</sup> <sup>E</sup> <sup>1</sup> 0

where E is a constant amplitude factor. The transmitted field Et emerging from the retarder is then

<sup>c</sup> � Ei <sup>¼</sup> <sup>E</sup> <sup>e</sup><sup>i</sup>δ<sup>x</sup>

For our design, we set δ<sup>x</sup> = nNkd, where n<sup>N</sup> = n1 + κ<sup>1</sup> or n2 + κ<sup>2</sup> is the complex refractive index of the corresponding section, k is the wave number, and d is the thickness of the binary phase grating. The total transmitted field ET is then the superposition of the field transmitted through

E0e

E0e

iky sin<sup>φ</sup>e

iky sin<sup>φ</sup>e

i nð Þ <sup>1</sup>þκ<sup>1</sup> kddy

i nð Þ <sup>2</sup>þκ<sup>2</sup> kddy:

0

Et ¼ W

all the alternating phase elements. We further write E = E0eikysin<sup>ϕ</sup>

ETð Þ¼ <sup>φ</sup> <sup>X</sup>even

m¼0

þ<sup>X</sup> odd

m¼1

ðð Þ <sup>m</sup>þ<sup>1</sup> <sup>l</sup> ml

> ðð Þ <sup>m</sup>þ<sup>1</sup> <sup>l</sup> ml

angle. Therefore, the total transmitted field can be written as

� �, (1)

Liquid-Crystal-Based Phase Gratings and Beam Steerers for Terahertz Waves

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199

� �, (2)

� �: (3)

, where ϕ is the diffraction

(4)

associated with a particular retarder can be written as

incident THz field is given by

wave.

Besides, there is an urgent need for THz beam steering devices for scanning the THz beam over the surface of targets to get full topological and spectral information, a metamaterialbased beam steerer has been demonstrated and achieved a maximal deflection angle of 6 [35]. Other groups employed highly-doped semiconductors, such as Indium antimonide (InSb) [36] and GaAs [37], so that the propagation properties of surface plasmons mode in highly-doped semiconductor slits can be tailored by changing the carrier density there [36]. On the other hand, the development of a reconfigurable THz antenna [38], which can electrically steer the THz beam or vary the beam shapes, are useful for applications, such as adaptive wireless, satellite communication networks, and automobile radar systems. The use of LC to construct a phase array for beam steering in millimeter wave range has also been reported recently [39].

In this chapter, we report our comprehensive experimental studies on a phase grating for THz waves. In particular, we analyzed the insertion loss in such gratings and devised an approach for improving the loss by 2.5 dB over existing designs. Further, we demonstrated an electrically tunable phase shifter array to modulate the phase of THz beam. By applying different voltages on each part of the phase array, we can achieve a gradient in phase shift. Finally, it is shown that the incident THz wave can be steered toward a selected direction.

### 2. Theoretical and experimental methods

#### 2.1. Operation principles of the phase grating

We designed a binary phase grating consisting of alternating sections of two materials (fused silica and LCs) with different refractive indices. Figure 1 shows the schematic of a generic

modulators [13, 14], attenuators [15], polarizers [16, 17], and beam splitters [18–21] in the THz

To control the properties of electromagnetic waves at all wavelengths, periodic structures such as gratings are frequently employed. In the THz frequency range, gratings with various periods have been used for tailoring few-cycle pulses [22]. Gratings have also been used as couplers and filters [23]. Tunable THz devices based on an optically and electrically controlled carrier concentration in quantum-well structures have been demonstrated. However, these devices have a limited range of tunability and must be operated at cryogenic temperatures far below room temperature [24–26]. The potential of gratings with liquid-crystal-enabled functionalities was recognized 2 decades ago [27]. Recently, the focus has been on various tunable THz devices, such as phase shifters, filters, and switches that are controlled electrically or magnetically, employing liquid crystals, primarily nematic liquid crystals (NLCs) [6–10, 15, 16, 18, 27–33]. Previously, we demonstrated a magnetically controlled phase grating for manipulating THz waves [10]. This is based on magnetic-field-induced birefringence of the NLCs employed [34]. Nonetheless, electrically controlled phase gratings are generally regarded as desirable for many applications. Therefore, we also proposed and demonstrated an electrically controlled phase grating involving NLCs for THz waves [11]. However, the theoretical analysis was not described in detail and the issue of insertion loss was not touched upon in the

Besides, there is an urgent need for THz beam steering devices for scanning the THz beam over the surface of targets to get full topological and spectral information, a metamaterialbased beam steerer has been demonstrated and achieved a maximal deflection angle of 6 [35]. Other groups employed highly-doped semiconductors, such as Indium antimonide (InSb) [36] and GaAs [37], so that the propagation properties of surface plasmons mode in highly-doped semiconductor slits can be tailored by changing the carrier density there [36]. On the other hand, the development of a reconfigurable THz antenna [38], which can electrically steer the THz beam or vary the beam shapes, are useful for applications, such as adaptive wireless, satellite communication networks, and automobile radar systems. The use of LC to construct a phase array for beam steering in millimeter wave range has also been reported recently [39]. In this chapter, we report our comprehensive experimental studies on a phase grating for THz waves. In particular, we analyzed the insertion loss in such gratings and devised an approach for improving the loss by 2.5 dB over existing designs. Further, we demonstrated an electrically tunable phase shifter array to modulate the phase of THz beam. By applying different voltages on each part of the phase array, we can achieve a gradient in phase shift. Finally, it is

shown that the incident THz wave can be steered toward a selected direction.

We designed a binary phase grating consisting of alternating sections of two materials (fused silica and LCs) with different refractive indices. Figure 1 shows the schematic of a generic

2. Theoretical and experimental methods

2.1. Operation principles of the phase grating

range are still relatively underdeveloped.

198 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

previous communication.

Figure 1. Schematic of a generic binary phase grating consisting alternating sections with refractive indices of n<sup>1</sup> and n2. The width and height of each section of the phase element is respectively, l and d. P is the polarization direction of the THz wave.

binary phase grating. The grating is periodic along the x-direction. The THz wave is assumed to be polarized along the x-axis and propagates along the y-direction. Each section of the grating can be considered a retarder that introduces a phase shift. The Jones matrix [40] associated with a particular retarder can be written as

$$
\widehat{R} = \begin{bmatrix}
\varepsilon^{i\delta\_x} & 0 \\
0 & \varepsilon^{i\delta\_y}
\end{bmatrix}' \tag{1}
$$

where δ is the phase retardation and a function of x. The Jones vector associated with the incident THz field is given by

$$E\_i = E\begin{pmatrix} 1\\ 0 \end{pmatrix} . \tag{2}$$

where E is a constant amplitude factor. The transmitted field Et emerging from the retarder is then

$$E\_t = \widehat{\boldsymbol{W}} \cdot \boldsymbol{E}\_i = \boldsymbol{E} \begin{pmatrix} \boldsymbol{e}^{i\delta\_x} \\ \boldsymbol{0} \end{pmatrix}. \tag{3}$$

For our design, we set δ<sup>x</sup> = nNkd, where n<sup>N</sup> = n1 + κ<sup>1</sup> or n2 + κ<sup>2</sup> is the complex refractive index of the corresponding section, k is the wave number, and d is the thickness of the binary phase grating. The total transmitted field ET is then the superposition of the field transmitted through all the alternating phase elements. We further write E = E0eikysin<sup>ϕ</sup> , where ϕ is the diffraction angle. Therefore, the total transmitted field can be written as

$$\begin{split} E\_T(q) &= \sum\_{m=0}^{even} \int\_{ml}^{(m+1)l} E\_0 e^{iky \sin \psi} e^{i(n\_1 + \kappa\_1)kd} dy \\ &+ \sum\_{m=1}^{odd} \int\_{ml}^{(m+1)l} E\_0 e^{iky \sin \psi} e^{i(n\_2 + \kappa\_2)kd} dy. \end{split} \tag{4}$$

In Eq. (4), l is the width of each section (all sections are assumed to have identical widths) of the grating. The diffraction intensity I(ϕ) can then be expressed as

$$I(\varphi) = E\_T(\varphi) \cdot E\_T^\*(\varphi). \tag{5}$$

For an ideal binary phase grating, the diffraction efficiency η<sup>m</sup> of the mth-order diffracted wave, defined as the intensity ratio of the diffracted beam to that of the incident beam, is given by

$$\eta\_m = \frac{1}{\Lambda^2} \left| \int\_{-\Lambda/2}^{\Lambda/2} e^{i\delta} e^{-i(2\pi my/\Lambda)} dy \right|^2,\tag{6}$$

where δ is the x-dependent phase shift of the grating with grating period Λ [18, 41]. Following [41], we can write

$$\eta\_m = \begin{cases} \cos^2(\Delta \Gamma/2) & \text{if } m = 0 \\ \left[ (2/m\pi) \sin \left( m\pi/2 \right) \right]^2 \sin^2(\Delta \Gamma/2) & \text{if } m \neq 0 \end{cases} \tag{7}$$

where ΔΓ is the relative phase difference between two adjacent sections in the phase grating. For ΔΓ = (2 N + 1)π (where N is an integer), the diffraction efficiencies of the odd orders (m = �1, �3, �5, …) are maximal. Eq. (7) reveals that the diffraction efficiency of the third order η�<sup>3</sup> (4.5%) is nine times smaller than that of the first-order η�<sup>1</sup> (40.5%). Therefore, in this study, we considered only the zeroth and the first orders of the diffracted beam. Eqs. (6) and (7) were used as guides for designing the parameters of the grating. In practice, insertion loss causes the experimentally observed efficiencies to be lower than expected.

Because of the THz wavelength and THz beam size, the grating can have only a finite number of grooves. Further, the number of grooves N affects the angular resolution of the diffracted beam [42]. The angular width Δϕ is given by

$$
\Delta \varphi = \frac{\lambda}{N \Lambda \cos \varphi}.\tag{8}
$$

concentrated in the zeroth order, and η<sup>0</sup> ≈ 1. These predictions are valid provided the insertion

Figure 3. Diffraction efficiencies of a 10-period phase grating are plotted as a function of the diffraction angle for relative

**0 10 20 30 40 50**

**(deg.)**

**1 st-order**

**0 10 20 30 40 50**

Figure 2. The diffraction efficiency of a phase grating with 10 (black dashed curve) and 40 periods (red solid line) is

**(deg.)**

**1**

**st-order**

**10 periods 40 periods**

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201

Liquid-Crystal-Based Phase Gratings and Beam Steerers for Terahertz Waves

The design of the grating was based on the structure of the electrically controlled THz phase grating reported in our previous study [11]. This is shown schematically in Figure 4. The incident THz wave was assumed to be polarized in the y-direction. Orientations of the LC molecules for two possible configurations are shown (See Figure 4). The device was designed

losses can be ignored.

phase differences of π and 2π.

2.2. Construction of the grating

**0.0**

plotted as a function of the diffraction angle (for the first order).

**0.0**

**0.2**

**0.4**

**0.6**

**0 th-order**

**0.8**

**1.0**

**0.2**

**0.4**

**0.6**

**0.8**

**1.0**

Let the frequency of the THz be centered at 0.3 THz or a wavelength of 1 mm, we designed Λ to be 2 mm in our devices. The relative phase difference between adjacent sections is designed to be π. Therefore, the diffraction angle for the first order is 30�. Figure 2 shows a plot of the diffraction efficiency as a function of the diffraction angle (for the first order). It illustrates clearly the angular resolution achievable for a grating with 10 periods and a grating with 40 periods. According to Eq. (8), the angular widths for the first-order diffracted wave for 10 and 40 periods are 3.3 and 0.8�, respectively.

When the relative phase difference between adjacent groves is tuned between π and 2π, the diffracted signals between the zeroth order and the first order have the maximal tunable range. This is illustrated in Figure 3 for a grating with 10 periods. For ΔΓ = π, the diffracted signal lies mainly in the first-order, and η�<sup>1</sup> ≈ 0.4. By contrast, for ΔΓ = 2π, the diffracted signal mostly

Figure 2. The diffraction efficiency of a phase grating with 10 (black dashed curve) and 40 periods (red solid line) is plotted as a function of the diffraction angle (for the first order).

Figure 3. Diffraction efficiencies of a 10-period phase grating are plotted as a function of the diffraction angle for relative phase differences of π and 2π.

concentrated in the zeroth order, and η<sup>0</sup> ≈ 1. These predictions are valid provided the insertion losses can be ignored.

#### 2.2. Construction of the grating

In Eq. (4), l is the width of each section (all sections are assumed to have identical widths) of the

For an ideal binary phase grating, the diffraction efficiency η<sup>m</sup> of the mth-order diffracted wave, defined as the intensity ratio of the diffracted beam to that of the incident beam, is given by

where δ is the x-dependent phase shift of the grating with grating period Λ [18, 41]. Following

where ΔΓ is the relative phase difference between two adjacent sections in the phase grating. For ΔΓ = (2 N + 1)π (where N is an integer), the diffraction efficiencies of the odd orders (m = �1, �3, �5, …) are maximal. Eq. (7) reveals that the diffraction efficiency of the third order η�<sup>3</sup> (4.5%) is nine times smaller than that of the first-order η�<sup>1</sup> (40.5%). Therefore, in this study, we considered only the zeroth and the first orders of the diffracted beam. Eqs. (6) and (7) were used as guides for designing the parameters of the grating. In practice, insertion loss causes the experimentally observed efficiencies to be lower than

Because of the THz wavelength and THz beam size, the grating can have only a finite number of grooves. Further, the number of grooves N affects the angular resolution of the diffracted

<sup>Δ</sup><sup>φ</sup> <sup>¼</sup> <sup>λ</sup>

Let the frequency of the THz be centered at 0.3 THz or a wavelength of 1 mm, we designed Λ to be 2 mm in our devices. The relative phase difference between adjacent sections is designed to be π. Therefore, the diffraction angle for the first order is 30�. Figure 2 shows a plot of the diffraction efficiency as a function of the diffraction angle (for the first order). It illustrates clearly the angular resolution achievable for a grating with 10 periods and a grating with 40 periods. According to Eq. (8), the angular widths for the first-order diffracted wave for 10 and

When the relative phase difference between adjacent groves is tuned between π and 2π, the diffracted signals between the zeroth order and the first order have the maximal tunable range. This is illustrated in Figure 3 for a grating with 10 periods. For ΔΓ = π, the diffracted signal lies mainly in the first-order, and η�<sup>1</sup> ≈ 0.4. By contrast, for ΔΓ = 2π, the diffracted signal mostly

½ � ð Þ <sup>2</sup>=m<sup>π</sup> sin ð Þ <sup>m</sup>π=<sup>2</sup> <sup>2</sup> sin <sup>2</sup>ð Þ ΔΓ=<sup>2</sup> if <sup>m</sup> 6¼ <sup>0</sup>

∗

�ið Þ <sup>2</sup>πmy=<sup>Λ</sup> dy

� � � � �

2

ð Þ φ : (5)

,

<sup>N</sup><sup>Λ</sup> cosφ: (8)

, (6)

(7)

Ið Þ¼ φ ETð Þ� φ ET

ð<sup>Λ</sup>=<sup>2</sup> �Λ=2 e iδ e

� � � � �

grating. The diffraction intensity I(ϕ) can then be expressed as

200 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

<sup>η</sup><sup>m</sup> <sup>¼</sup> <sup>1</sup> Λ2

<sup>η</sup><sup>m</sup> <sup>¼</sup> cos <sup>2</sup>ð Þ ΔΓ=<sup>2</sup> if <sup>m</sup> <sup>¼</sup> <sup>0</sup>

(

beam [42]. The angular width Δϕ is given by

40 periods are 3.3 and 0.8�, respectively.

[41], we can write

expected.

The design of the grating was based on the structure of the electrically controlled THz phase grating reported in our previous study [11]. This is shown schematically in Figure 4. The incident THz wave was assumed to be polarized in the y-direction. Orientations of the LC molecules for two possible configurations are shown (See Figure 4). The device was designed

In the second set of experiments, the broadband THz signal was filtered by using a metallic hole array to obtain a quasi-monochromatic wave centered at 0.3 THz and with a line width of 0.03 THz [45]. The diffraction pattern of this beam produced by a grating with various nematic LC orientations was detected and mapped by a liquid-helium-cooled Si bolometer, which was at a distance of 20 cm from the device and located on a rotating arm that could be swung with respect to the fixed grating. The bolometer had an aperture with a diameter of approximately

To estimate the insertion loss of the THz grating, we regarded the device as a stack of parallelplate waveguides. The ITO conductive film was not an ideal conductor. We recently showed

for n and 20�70 for κ in the THz range [46]. On the basis of the manner of waveguide excitation, we can assume the mode of the propagating THz wave is transverse. The cutoff frequency of the parallel-plate waveguides can be written as fc = c/2 nl, where c is the velocity of light, l is the distance between two conductive layers, and n is the refractive index of the dielectric material within a waveguide. The attenuation constants α<sup>c</sup> and α<sup>d</sup> corresponding to

2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>f</sup> <sup>c</sup>=<sup>f</sup> � � <sup>1</sup> � <sup>f</sup> <sup>c</sup>=<sup>f</sup> � �<sup>2</sup>

> εr p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

, the complex refractive indices of ITO are 20�70

Liquid-Crystal-Based Phase Gratings and Beam Steerers for Terahertz Waves

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203

<sup>r</sup> h i , (9)

<sup>1</sup> � <sup>f</sup> <sup>c</sup>=<sup>f</sup> � �<sup>2</sup> <sup>q</sup> , (10)

�cm�<sup>1</sup>

conductor loss and dielectric loss, respectively, are given by [47, 48]

ffiffiffiffiffiffiffi πfε σc

l

<sup>α</sup><sup>d</sup> <sup>¼</sup> <sup>π</sup><sup>f</sup> tan <sup>δ</sup> ffiffiffiffi

where f is the frequency, ε is the permittivity of the dielectric material, σ<sup>c</sup> is the conductivity of the electrode, tanδ is the loss tangent, and ε<sup>r</sup> is the relative permittivity of the dielectric material. In practical applications, the insertion loss of the THz grating should be minimal.

We have also designed an electrically tunable phase shifter array which can function as the THz beam steerer. Figure 5 shows the structure of the phase shifter array, which is constructed by alternately stacking a number of NLC layers and electrodes. Voltage sources are connected to the electrodes to apply control voltages to each NLC layer. The effective refractive index, neff (V), of each NLC layer can be electrically tuned by applying appropriate voltages. The polarization of the THz wave was assumed to be along the z-direction while the wave was

The device was designed such that, when no voltage was applied, the NLC molecules are aligned along the y-direction. In this case, the effective refractive index equals to that of the

c

s

α<sup>c</sup> ¼

2.5. Electrically controlled steering of the THz beam

normally incident to the device.

2.5 cm.

and

2.4. Insertion loss

that for a conductivity of 1500–2200 Ω�<sup>1</sup>

Figure 4. Structure of the electrically controlled THz phase grating using nematic liquid crystals. ITO: Indium tin oxide; PI: Polyimide; LC: Liquid crystal molecules; no: Ordinary index of refraction; ne: Extraordinary index of refraction; Vth: Threshold voltage.

such that the frequency band of 0.3–0.5 THz would exhibit the highest zeroth-order diffraction efficiency.

Parallel grooves with a period of 2.0 mm, width of 1.0 mm, and groove depth of 2.5 mm were formed by stacking indium tin oxide (ITO)-coated fused silica substrates; the refractive index of these substrates is 1.95 in the sub-THz frequency region (0.2–0.8 THz). The surfaces of the fused silica substrates were coated with polyimide (SE-130B, Nissan) and then rubbed for homogenous alignment. The grooves were filled with NLCs (E7, Merck) and sealed with a sheet of fused silica coated with N,N-dimethyl-N-octadecyl-3-aminopropyltrimethoxysilyl chloride. At room temperature, E7 is a birefringent material with positive dielectric anisotropy. The LC molecules tend to be aligned parallel to the direction of the applied electric field when the applied voltage is greater than a threshold voltage. The effective refractive index of E7 [43], neff can be tuned from the refractive index for ordinary waves (no = 1.58) to that for extraordinary waves (ne = 1.71) by varying the applied voltage. A stack of ITO-coated fused silica plates with dimensions identical to those of the grating was prepared as a reference. Bases of the phase grating with two different dimensions (h<sup>1</sup> = 17.5 mm and h<sup>2</sup> = 7.5 mm) were fabricated for analyzing the effect of dimension of the base on insertion losses of the phase grating.

#### 2.3. Transmission measurements

A photoconductive (PC) antenna-based THz time-domain spectrometer (THz-TDS) [32, 44], was used for measuring the zeroth-order diffraction spectra of the device. Briefly, the pump beam from a femtosecond mode-locked Ti:sapphire laser was focused on a dipole antenna fabricated on LT-GaAs for generating a broadband THz signal, which was collimated and collected through the THz phase grating by using off-axis parabolic gold mirrors. A pair of parallel wire-grid polarizers (GS57204, Specac) was placed before and after the device under test. The zeroth-order diffraction of THz radiation was coherently detected by another PC antenna of the same type as that of the THz-TDS and grated by ultrafast pulses from the same laser.

In the second set of experiments, the broadband THz signal was filtered by using a metallic hole array to obtain a quasi-monochromatic wave centered at 0.3 THz and with a line width of 0.03 THz [45]. The diffraction pattern of this beam produced by a grating with various nematic LC orientations was detected and mapped by a liquid-helium-cooled Si bolometer, which was at a distance of 20 cm from the device and located on a rotating arm that could be swung with respect to the fixed grating. The bolometer had an aperture with a diameter of approximately 2.5 cm.

#### 2.4. Insertion loss

To estimate the insertion loss of the THz grating, we regarded the device as a stack of parallelplate waveguides. The ITO conductive film was not an ideal conductor. We recently showed that for a conductivity of 1500–2200 Ω�<sup>1</sup> �cm�<sup>1</sup> , the complex refractive indices of ITO are 20�70 for n and 20�70 for κ in the THz range [46]. On the basis of the manner of waveguide excitation, we can assume the mode of the propagating THz wave is transverse. The cutoff frequency of the parallel-plate waveguides can be written as fc = c/2 nl, where c is the velocity of light, l is the distance between two conductive layers, and n is the refractive index of the dielectric material within a waveguide. The attenuation constants α<sup>c</sup> and α<sup>d</sup> corresponding to conductor loss and dielectric loss, respectively, are given by [47, 48]

$$\alpha\_c = \sqrt{\frac{\pi f \varepsilon}{\sigma\_c}} \frac{2}{l \sqrt{\left(f\_c/f\right) \left[1 - \left(f\_c/f\right)^2\right]}},\tag{9}$$

and

such that the frequency band of 0.3–0.5 THz would exhibit the highest zeroth-order diffraction

Figure 4. Structure of the electrically controlled THz phase grating using nematic liquid crystals. ITO: Indium tin oxide; PI: Polyimide; LC: Liquid crystal molecules; no: Ordinary index of refraction; ne: Extraordinary index of refraction; Vth:

202 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

Parallel grooves with a period of 2.0 mm, width of 1.0 mm, and groove depth of 2.5 mm were formed by stacking indium tin oxide (ITO)-coated fused silica substrates; the refractive index of these substrates is 1.95 in the sub-THz frequency region (0.2–0.8 THz). The surfaces of the fused silica substrates were coated with polyimide (SE-130B, Nissan) and then rubbed for homogenous alignment. The grooves were filled with NLCs (E7, Merck) and sealed with a sheet of fused silica coated with N,N-dimethyl-N-octadecyl-3-aminopropyltrimethoxysilyl chloride. At room temperature, E7 is a birefringent material with positive dielectric anisotropy. The LC molecules tend to be aligned parallel to the direction of the applied electric field when the applied voltage is greater than a threshold voltage. The effective refractive index of E7 [43], neff can be tuned from the refractive index for ordinary waves (no = 1.58) to that for extraordinary waves (ne = 1.71) by varying the applied voltage. A stack of ITO-coated fused silica plates with dimensions identical to those of the grating was prepared as a reference. Bases of the phase grating with two different dimensions (h<sup>1</sup> = 17.5 mm and h<sup>2</sup> = 7.5 mm) were fabricated for analyzing the effect of dimension of the base on insertion losses of the phase grating.

A photoconductive (PC) antenna-based THz time-domain spectrometer (THz-TDS) [32, 44], was used for measuring the zeroth-order diffraction spectra of the device. Briefly, the pump beam from a femtosecond mode-locked Ti:sapphire laser was focused on a dipole antenna fabricated on LT-GaAs for generating a broadband THz signal, which was collimated and collected through the THz phase grating by using off-axis parabolic gold mirrors. A pair of parallel wire-grid polarizers (GS57204, Specac) was placed before and after the device under test. The zeroth-order diffraction of THz radiation was coherently detected by another PC antenna of the same type as that of the THz-TDS and grated by ultrafast pulses from the same

efficiency.

Threshold voltage.

laser.

2.3. Transmission measurements

$$\alpha\_d = \frac{\pi f \tan \delta \sqrt{\varepsilon\_r}}{c \sqrt{1 - \left(f\_c/f\right)^2}},\tag{10}$$

where f is the frequency, ε is the permittivity of the dielectric material, σ<sup>c</sup> is the conductivity of the electrode, tanδ is the loss tangent, and ε<sup>r</sup> is the relative permittivity of the dielectric material. In practical applications, the insertion loss of the THz grating should be minimal.

#### 2.5. Electrically controlled steering of the THz beam

We have also designed an electrically tunable phase shifter array which can function as the THz beam steerer. Figure 5 shows the structure of the phase shifter array, which is constructed by alternately stacking a number of NLC layers and electrodes. Voltage sources are connected to the electrodes to apply control voltages to each NLC layer. The effective refractive index, neff (V), of each NLC layer can be electrically tuned by applying appropriate voltages. The polarization of the THz wave was assumed to be along the z-direction while the wave was normally incident to the device.

The device was designed such that, when no voltage was applied, the NLC molecules are aligned along the y-direction. In this case, the effective refractive index equals to that of the

Figure 5. Schematic structure of the electrically controlled THz phase shifter array for beam steering. (a) Set-up of the beam steering experiment. The relationship between the steering angle, θ, optical delay length, Δd, and aperture, A, are shown. (b) Structure of the device with arrangement for voltage applied to each layer. Dimensions of the structure are also shown.

ordinary component of light in the LC, no. If sufficient control voltage is applied, the NLC molecules will orientate toward the direction parallel to the polarization direction of the THz wave (z-direction). The effective refractive index then equals to that of the extraordinary component of light in the LC, ne. The traversing time, which the THz wave takes to pass through the NLC layers, can be changed by applying voltages. The corresponding phase shift Δϕ(V) in the applying voltage V is given by

$$
\Delta\phi(V) = kd \left( n\_o - n\_{\rm eff}(V) \right),
\tag{11}
$$

<sup>Δ</sup><sup>d</sup> <sup>¼</sup> Δϕmax 2π

NLC block includes two NLC layers and two electrodes.

trodes provided 1 kHz-sinusoidal waves to the NLC layers.

The threshold voltage Vc can be estimated by Vc = π (k/ε0Δε)

be written as,

<sup>λ</sup>, and tan <sup>θ</sup> <sup>¼</sup> <sup>Δ</sup><sup>d</sup>

Δϕ<sup>i</sup> ¼ ð Þ i � 1 kð Þ 2h tan θ, (13)

Liquid-Crystal-Based Phase Gratings and Beam Steerers for Terahertz Waves

where λ is the corresponding wavelength of THz wave. Accordingly, the THz wave can be steered by the control voltage. The phase shift Δϕ<sup>i</sup> in the certain ith NLC block, in our case can

where 2h was the thickness of the ith NLC block and θ was the steering angle against the normal of the aperture. We can see the construction of the device in Figure 5(b), in which each

In this work, we used the 550-μm-thick Teflon sheet as the spacer and the 100-μm-thick copper foil as the electrode. The copper foil was coated with PI Nissan SE-130B on both sides and rubbed for homogeneous alignment along y-direction before applying the voltage. The 18 NLC layers and 19 electrodes were stacked up alternately. The total thickness of the device was 12.1 mm, which corresponded to the size of the aperture, A, along z-direction. The size of the aperture along x-direction was designed to be 20.0 mm, and the propagation length, d, of the THz wave was designed to be 10.0 mm. Control voltage sources connected to the elec-

refractive indices of NLC MDA-00-3461 for ordinary and extraordinary in THz range are no = 1.54, ne = 1.72, κ<sup>o</sup> = 0.03, and κ<sup>e</sup> = 0.01, respectively [49]. At a frequency of 0.3 THz, the

Figure 6. Improved THz-TDS. Probe beam is guided with a 1 m long optical fiber directly to the antenna. The detection

assembly is located on a rotatable arm and can be moved without changing the optical path.

<sup>A</sup> , (12)

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205

1/2 = 1.20 Vrms. The complex

where k is the wave number in free space and d is the propagation length of the NLC layer. When a certain phase gradient was created across the aperture of the device by adjusting the phase shift in each NLC layer, the wavefront of the transmitted wave was inclined against the aperture. According to the limited voltage source channels, we divided two NLC layers as a block. The steering angle θ can be determined by the aperture size A and the optical length delay Δd between the top NLC block and the bottom NLC block. The optical length delay Δd was according to the phase shift between the top and bottom NLC blocks Δϕmax. Therefore, the relationship between steering angle θ, optical length delay Δd, and the phase shift Δϕmax, was shown in Figure 5(a), and can be written as,

$$
\Delta d = \frac{\Delta \phi\_{\text{max}}}{2\pi} \lambda, \text{ and } \tan \theta = \frac{\Delta d}{A}, \tag{12}
$$

where λ is the corresponding wavelength of THz wave. Accordingly, the THz wave can be steered by the control voltage. The phase shift Δϕ<sup>i</sup> in the certain ith NLC block, in our case can be written as,

$$
\Delta \phi\_i = (i - 1)k(2h) \tan \theta\_i \tag{13}
$$

where 2h was the thickness of the ith NLC block and θ was the steering angle against the normal of the aperture. We can see the construction of the device in Figure 5(b), in which each NLC block includes two NLC layers and two electrodes.

In this work, we used the 550-μm-thick Teflon sheet as the spacer and the 100-μm-thick copper foil as the electrode. The copper foil was coated with PI Nissan SE-130B on both sides and rubbed for homogeneous alignment along y-direction before applying the voltage. The 18 NLC layers and 19 electrodes were stacked up alternately. The total thickness of the device was 12.1 mm, which corresponded to the size of the aperture, A, along z-direction. The size of the aperture along x-direction was designed to be 20.0 mm, and the propagation length, d, of the THz wave was designed to be 10.0 mm. Control voltage sources connected to the electrodes provided 1 kHz-sinusoidal waves to the NLC layers.

The threshold voltage Vc can be estimated by Vc = π (k/ε0Δε) 1/2 = 1.20 Vrms. The complex refractive indices of NLC MDA-00-3461 for ordinary and extraordinary in THz range are no = 1.54, ne = 1.72, κ<sup>o</sup> = 0.03, and κ<sup>e</sup> = 0.01, respectively [49]. At a frequency of 0.3 THz, the

ordinary component of light in the LC, no. If sufficient control voltage is applied, the NLC molecules will orientate toward the direction parallel to the polarization direction of the THz wave (z-direction). The effective refractive index then equals to that of the extraordinary component of light in the LC, ne. The traversing time, which the THz wave takes to pass through the NLC layers, can be changed by applying voltages. The corresponding phase shift

Figure 5. Schematic structure of the electrically controlled THz phase shifter array for beam steering. (a) Set-up of the beam steering experiment. The relationship between the steering angle, θ, optical delay length, Δd, and aperture, A, are shown. (b) Structure of the device with arrangement for voltage applied to each layer. Dimensions of the structure are also

where k is the wave number in free space and d is the propagation length of the NLC layer. When a certain phase gradient was created across the aperture of the device by adjusting the phase shift in each NLC layer, the wavefront of the transmitted wave was inclined against the aperture. According to the limited voltage source channels, we divided two NLC layers as a block. The steering angle θ can be determined by the aperture size A and the optical length delay Δd between the top NLC block and the bottom NLC block. The optical length delay Δd was according to the phase shift between the top and bottom NLC blocks Δϕmax. Therefore, the relationship between steering angle θ, optical length delay Δd, and the phase shift Δϕmax,

<sup>Δ</sup>ϕð Þ¼ <sup>V</sup> kd no � neffð Þ <sup>V</sup> , (11)

Δϕ(V) in the applying voltage V is given by

204 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

shown.

was shown in Figure 5(a), and can be written as,

Figure 6. Improved THz-TDS. Probe beam is guided with a 1 m long optical fiber directly to the antenna. The detection assembly is located on a rotatable arm and can be moved without changing the optical path.

estimated maximum phase shift applied to a propagation wave passing through NLC layer would be 11.31 rad, which is calculated by Eq. (11) and the refractive indices of NLC MDA-00- 3461. The maximum steering angle was estimated to be approximately 9� from Eq. (13) taking the maximum phase shift and aperture size into account.

The two types of waveguides were made to alternate (black and yellow sections in Figure 4) in the structure. The grating device extended from z = 0 to z = 2500 μm. The incident wave was set to have a Gaussian shape, and the beam size was 19.0 mm, as large as the device aperture. The wave was normally incident in the z-direction from a source at z < 0 and was polarized in the x-direction. The dimensions of the grid in the FTD analysis were 10 μm 10 μm in the xy-plane, while the time step was 1.67 <sup>10</sup><sup>14</sup> s. Figure 7 shows the simulation results for an incident THz wave that is yet to enter the device (a), THz waves at two positions in the grating (b and c), and a THz wave that has emerged from the grating. The false color (in 256 levels) indicates the strength of the electric field at a given spatial point. In Figure 7(b, c), we show THz waves transmitted through the grating with different velocities at different x-positions because of the difference in the refractive indices. After the THz signal emerged from the device (Figure 7(d)), we set the time

Liquid-Crystal-Based Phase Gratings and Beam Steerers for Terahertz Waves

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207

To illustrate performance of the grating, experimental and FDTD simulation results of the zeroth-order diffraction efficiencies of the phase grating operated at four values of applied voltage are plotted as a function of frequency in Figure 8 (reproduced from [11] with permission). Note that the experimentally measured diffraction efficiency was the highest near 0.3 THz, in agreement with the designed frequency. For an ordinary wave at 0.3 THz, the phase difference between fused silica and E7 was close to 2π. Therefore, the transmission of the

**(a) (b)**

**(c) (d)**

positions in the grating, and (d) a THz wave that has emerged from the grating.

Figure 7. Simulation results for (a) an incident THz wave that is yet to enter the device, (b) and (c) THz waves at two

monitor to obtain the superposition signal.

For studying THz beam steering, we modified the THz-TDS by employing a 1 m-long single mode fiber (F-SF-C-1FC, from Newport Corp.) to guide the femtosecond laser directly to the detecting antenna. This way, the optical path remained fixed when the detecting arm was moved as the THz beam was steered. The schematic diagram of the setup is shown in Figure 6. The detection assembly was 20 cm away from the device and located on a rotation arm that can be swung with respect to the fixed device. This system was much more stable and convenient to use than the one employing the bolometer.

### 3. Results and discussions

#### 3.1. Phase grating

We studied zeroth-order diffracted THz pulses by the phase grating for both ordinary and extraordinary waves were described in Ref. [11].

Experimentally, the diffraction efficiency of diffracted signals, η, in the frequency domain was determined by normalizing the diffracted signals in the frequency domain to the diffracted signals of the reference phase grating. To compare, a finite-difference time-domain (FDTD) algorithm (RSoft Design Group, Inc.) was used for simulating the diffraction of THz waves by a phase grating.

In the FDTD simulation, we analyzed the grating structure as a stack of rectangular-shaped waveguides. Neglecting conductive and magnetic loss of the materials involved, the Maxwell-Faraday and Maxwell-Ampere equations can be expanded in the Cartesian coordinates as

$$\begin{split} \frac{\partial H\_x}{\partial t} &= \frac{1}{\mu\_0} \left( \frac{\partial E\_y}{\partial z} - \frac{\partial E\_z}{\partial y} \right), \\ \frac{\partial H\_y}{\partial t} &= \frac{1}{\mu\_0} \left( \frac{\partial E\_z}{\partial x} - \frac{\partial E\_x}{\partial z} \right), \\ \frac{\partial H\_z}{\partial t} &= \frac{1}{\mu\_0} \left( \frac{\partial E\_x}{\partial y} - \frac{\partial E\_y}{\partial x} \right), \end{split} \tag{14}$$
 
$$\begin{split} \frac{\partial E\_x}{\partial t} &= \frac{1}{\varepsilon\_0} \left( \frac{\partial H\_z}{\partial y} - \frac{\partial H\_y}{\partial z} \right), \\ \frac{\partial E\_y}{\partial t} &= \frac{1}{\varepsilon\_0} \left( \frac{\partial H\_x}{\partial z} - \frac{\partial H\_z}{\partial x} \right), \\ \frac{\partial E\_z}{\partial t} &= \frac{1}{\varepsilon\_0} \left( \frac{\partial H\_y}{\partial x} - \frac{\partial H\_x}{\partial y} \right), \end{split} \tag{15}$$

where Hx, Hy, Hz, Ex, Ey, and Ez are components of the magnetic field and electric field, respectively. We set the refractive indices of the waveguides as those of fused silica and LCs. The two types of waveguides were made to alternate (black and yellow sections in Figure 4) in the structure. The grating device extended from z = 0 to z = 2500 μm. The incident wave was set to have a Gaussian shape, and the beam size was 19.0 mm, as large as the device aperture. The wave was normally incident in the z-direction from a source at z < 0 and was polarized in the x-direction. The dimensions of the grid in the FTD analysis were 10 μm 10 μm in the xy-plane, while the time step was 1.67 <sup>10</sup><sup>14</sup> s. Figure 7 shows the simulation results for an incident THz wave that is yet to enter the device (a), THz waves at two positions in the grating (b and c), and a THz wave that has emerged from the grating. The false color (in 256 levels) indicates the strength of the electric field at a given spatial point. In Figure 7(b, c), we show THz waves transmitted through the grating with different velocities at different x-positions because of the difference in the refractive indices. After the THz signal emerged from the device (Figure 7(d)), we set the time monitor to obtain the superposition signal.

estimated maximum phase shift applied to a propagation wave passing through NLC layer would be 11.31 rad, which is calculated by Eq. (11) and the refractive indices of NLC MDA-00- 3461. The maximum steering angle was estimated to be approximately 9� from Eq. (13) taking

For studying THz beam steering, we modified the THz-TDS by employing a 1 m-long single mode fiber (F-SF-C-1FC, from Newport Corp.) to guide the femtosecond laser directly to the detecting antenna. This way, the optical path remained fixed when the detecting arm was moved as the THz beam was steered. The schematic diagram of the setup is shown in Figure 6. The detection assembly was 20 cm away from the device and located on a rotation arm that can be swung with respect to the fixed device. This system was much more stable and convenient

We studied zeroth-order diffracted THz pulses by the phase grating for both ordinary and

Experimentally, the diffraction efficiency of diffracted signals, η, in the frequency domain was determined by normalizing the diffracted signals in the frequency domain to the diffracted signals of the reference phase grating. To compare, a finite-difference time-domain (FDTD) algorithm (RSoft Design Group, Inc.) was used for simulating the diffraction of THz waves by a phase grating. In the FDTD simulation, we analyzed the grating structure as a stack of rectangular-shaped waveguides. Neglecting conductive and magnetic loss of the materials involved, the Maxwell-Faraday and Maxwell-Ampere equations can be expanded in the Cartesian coordinates as

> ∂Ey <sup>∂</sup><sup>z</sup> � <sup>∂</sup>Ez ∂y

> ∂Ez <sup>∂</sup><sup>x</sup> � <sup>∂</sup>Ex ∂z

> ∂Ex <sup>∂</sup><sup>y</sup> � <sup>∂</sup>Ey ∂x

∂Hz <sup>∂</sup><sup>y</sup> � <sup>∂</sup>Hy ∂z

∂Hx <sup>∂</sup><sup>z</sup> � <sup>∂</sup>Hz ∂x

∂Hy <sup>∂</sup><sup>x</sup> � <sup>∂</sup>Hx ∂y

where Hx, Hy, Hz, Ex, Ey, and Ez are components of the magnetic field and electric field, respectively. We set the refractive indices of the waveguides as those of fused silica and LCs.

,

,

(14)

(15)

,

,

,

,

∂Hx <sup>∂</sup><sup>t</sup> <sup>¼</sup> <sup>1</sup> μ0

∂Hy <sup>∂</sup><sup>t</sup> <sup>¼</sup> <sup>1</sup> μ0

∂Hz <sup>∂</sup><sup>t</sup> <sup>¼</sup> <sup>1</sup> μ0

∂Ex <sup>∂</sup><sup>t</sup> <sup>¼</sup> <sup>1</sup> ε0

∂Ey <sup>∂</sup><sup>t</sup> <sup>¼</sup> <sup>1</sup> ε0

∂Ez <sup>∂</sup><sup>t</sup> <sup>¼</sup> <sup>1</sup> ε0

the maximum phase shift and aperture size into account.

206 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

to use than the one employing the bolometer.

extraordinary waves were described in Ref. [11].

3. Results and discussions

3.1. Phase grating

To illustrate performance of the grating, experimental and FDTD simulation results of the zeroth-order diffraction efficiencies of the phase grating operated at four values of applied voltage are plotted as a function of frequency in Figure 8 (reproduced from [11] with permission). Note that the experimentally measured diffraction efficiency was the highest near 0.3 THz, in agreement with the designed frequency. For an ordinary wave at 0.3 THz, the phase difference between fused silica and E7 was close to 2π. Therefore, the transmission of the

Figure 7. Simulation results for (a) an incident THz wave that is yet to enter the device, (b) and (c) THz waves at two positions in the grating, and (d) a THz wave that has emerged from the grating.

grating was higher. The THz wave was mainly concentrated in the zeroth order. By contrast, for extraordinary waves, the phase difference was close to π. Furthermore, the diffraction efficiency was lower for the zeroth order because the THz wave was mostly diffracted into the first order.

FDTD software for the o-ray and e-ray, respectively. Further, a structure with random arrangement of sections with deviations of 0.1 mm centered around 2.5 mm was also studied. The results are shown in Figure 9. Clear shifts are observed in the curves. Therefore, we inferred

Because of the periodically arranged ITO films in the grating, our device could be considered a wire-grid polarizer for the THz wave. Only a THz wave polarized perpendicular to the grooves could pass through the electrically tuned phase grating. The measurement result is shown in Figure 10. The extinction ratio of the device shows the ratio of the transmitted THz signals polarized parallel and perpendicular to the grooves is better than

**0.0**

Figure 9. FDTD simulation result showing the diffraction efficiency as a function of the frequency for the phase grating of

**0.1 0.2 0.3 0.4 0.5 0.6 0.7**

Figure 10. Extinction ratio of a sample. The data curve shows the proportion of THz-polarized transmitted signals

**Frequency (THz)**

**0.2**

**0.4**

**0.6**

**0.8**

**1.0**

**(b)**

Liquid-Crystal-Based Phase Gratings and Beam Steerers for Terahertz Waves

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209

**0.2 0.3 0.4 0.5 0.6 0.7**

**Frequency (THz)**

*ne* **(***d***=2.5mm)** *ne* **(***d***=2.4mm)** *ne* **(***d***=2.6mm)** *ne* **(***d***=random)**

that the experimental results are reliable.

**0.2 0.3 0.4 0.5 0.6 0.7**

different thicknesses (see text): (a) o-wave and (b) e-wave.

**Frequency (THz)**

**1E-3**

**0.01**

**Extintion ratio**

parallel and perpendicular to the grooves.

**0.1**

**1**

*no*

*no*

*no*

*no*

 **(***d***=2.5mm)**

 **(***d***=2.4mm)**

 **(***d***=2.6mm)**

 **(***d***=random)**

1:100 at ~ 0.3 THz.

**(a)**

**0.0**

**0.2**

**0.4**

**0.6**

**0.8**

**1.0**

The experimental and FDTD simulation results are in general agreement. In Figure 8(a, b), there are, however, some discrepancies in efficiencies and peak positions. This is expected as the thickness of the fused silica plates in the grating assembly varies by 0.1 mm. To check, we calculated diffraction efficiencies of gratings with dimensions of 2.4, 2.5, and 2.6 mm using the

Figure 8. (a) FDTD simulation and (b) experimental results of the frequency dependence of the zeroth-order diffraction efficiencies of the phase grating operated at four values of applied voltages. (Figure 3 of Ref. [11], reproduced by permission of the authors and IEEE).

FDTD software for the o-ray and e-ray, respectively. Further, a structure with random arrangement of sections with deviations of 0.1 mm centered around 2.5 mm was also studied. The results are shown in Figure 9. Clear shifts are observed in the curves. Therefore, we inferred that the experimental results are reliable.

grating was higher. The THz wave was mainly concentrated in the zeroth order. By contrast, for extraordinary waves, the phase difference was close to π. Furthermore, the diffraction efficiency was lower for the zeroth order because the THz wave was mostly diffracted into

The experimental and FDTD simulation results are in general agreement. In Figure 8(a, b), there are, however, some discrepancies in efficiencies and peak positions. This is expected as the thickness of the fused silica plates in the grating assembly varies by 0.1 mm. To check, we calculated diffraction efficiencies of gratings with dimensions of 2.4, 2.5, and 2.6 mm using the

**0.2 0.3 0.4 0.5 0.6 0.7**

**Frequency (THz)**

Figure 8. (a) FDTD simulation and (b) experimental results of the frequency dependence of the zeroth-order diffraction efficiencies of the phase grating operated at four values of applied voltages. (Figure 3 of Ref. [11], reproduced by

**0.7** *no* **(0V)**

**Experimental result**

**FDTD simulation (a)**

208 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

*no***=1.58** *neff***=1.62** *neff***=1.65** *ne***=1.71**

*neff* **(15V)** *neff* **(30V)** *ne* **(90V)**

the first order.

**0.0**

**(b)**

**0.0**

permission of the authors and IEEE).

**0.1**

**0.2**

**0.3**

**0.4**

**0.5**

**0.6**

**0.1**

**0.2**

**0.3**

**0.4**

**0.5**

**0.6**

**0.7**

Because of the periodically arranged ITO films in the grating, our device could be considered a wire-grid polarizer for the THz wave. Only a THz wave polarized perpendicular to the grooves could pass through the electrically tuned phase grating. The measurement result is shown in Figure 10. The extinction ratio of the device shows the ratio of the transmitted THz signals polarized parallel and perpendicular to the grooves is better than 1:100 at ~ 0.3 THz.

Figure 9. FDTD simulation result showing the diffraction efficiency as a function of the frequency for the phase grating of different thicknesses (see text): (a) o-wave and (b) e-wave.

Figure 10. Extinction ratio of a sample. The data curve shows the proportion of THz-polarized transmitted signals parallel and perpendicular to the grooves.

#### 3.2. Bolometer measurement results

In Figure 11, we present the intensity profiles of the diffracted 0.3 THz beam polarized in the y-direction. Data are shown for the grating biased from 0 to 90 V. The corresponding effective indices of refraction vary from 1.58 to 1.71. A diffraction maximum was detected at ϕ = 30, which corresponds to the first-order diffracted beam predicted by the grating equation Λsinϕ = mλ, where Λ is 2.0 mm and the wavelength λ is 1.0 mm for the 0.3 THz wave. The measured diffraction efficiencies for the zeroth and first orders are in accord with the predictions of Eq. (5), considering the finite dimensions of the grating and the acceptance angle of the bolometer (3).

When the E7 molecules were aligned such that the refractive index was no, the phase difference was close to 2π. Most of the THz signal propagated in the direction of the zeroth-order diffraction. Experimentally, the diffraction efficiencies were determined to be 0.62 and 0.06 for the zeroth and first orders, respectively. The diffraction efficiencies were tuned by increasing the applied voltage (Vappl) gradually. When the refractive index of E7 was varied from 1.58 to 1.71, the diffraction efficiency of the zeroth order decreased; by contrast, the diffraction efficiency of the first order increased. When the E7 molecules were aligned such that the refractive index was ne, the phase difference was close to π. The THz wave propagated mostly as a first-order diffracted beam. The diffraction efficiencies were 0.16 and 0.26 for the zeroth and first orders, respectively.

Figure 12(a, b) show the diffraction efficiencies of the zeroth and first orders as a function of the refractive index of E7 and Vappl. The experimental results, shown by dot symbols, are in good agreement with the theoretical predictions. Such results indicate that the grating functions as a variable beam splitter. The beam splitting ratio of the zeroth order to the first order can be tuned by varying the applied voltage.

Alternatively, these results indicate that the beam splitting ratio can be tuned and varied as a function of the refractive index of the nematic liquid crystal, E7. This is illustrated in Figure 13.

The theoretical calculation results and the experimental results are shown by the curve and dot symbols, respectively in Figure 13. The results indicate that the beam splitting ratio of the

Figure 13. Beam splitting ratio as a function of the refractive index of E7. The theoretical calculation results and

**1.56 1.58 1.60 1.62 1.64 1.66 1.68 1.70 1.72**

*n*

**15V 0V**

**30V**

Insertion loss is a critical parameter for THz devices. We have experimentally and theoretically studied the insertion loss of two classes of devices. Figure 14(a) shows the diffraction efficiency

zeroth order to the first order can be tuned from 10:1 to 3:5.

**0.0**

experimental results are shown by the curve and dots, respectively.

**0.5**

**1.0**

**Beam splitting ratio (**

**1st / 0th)**

**1.5**

**2.0**

**2.5**

**3.0**

**1.56 1.58 1.60 1.62 1.64 1.66 1.68 1.70 1.72**

*n*

**15V**

 (**0 th-order) 0V**

**30V**

**60V 90V**

**0.0**

Figure 12. Diffraction efficiency as a function of the refractive index of E7 and the applied voltage for the (a) zeroth order and (b) first order. The theoretical calculation results and experimental results are shown by the curves and dots,

**Theoretical calculation**

**0V**

**0.1**

**0.2**

**0.3**

**0.4**

**1.56 1.58 1.60 1.62 1.64 1.66 1.68 1.70 1.72**

**(1st-order) (b)**

Liquid-Crystal-Based Phase Gratings and Beam Steerers for Terahertz Waves

*n*

**15V**

**60V 90V**

**30V**

**Theoretical**

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**90V**

211

**60V**

**Theoretical calculation**

**0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8**

respectively.

**(a)**

3.3. Insertion loss

Figure 11. Diffraction efficiencies of the grating biased at several values of applied voltages are plotted as a function of the diffraction angle for the 0.3 THz beam. Solid lines are theoretical curves.

Figure 12. Diffraction efficiency as a function of the refractive index of E7 and the applied voltage for the (a) zeroth order and (b) first order. The theoretical calculation results and experimental results are shown by the curves and dots, respectively.

Figure 13. Beam splitting ratio as a function of the refractive index of E7. The theoretical calculation results and experimental results are shown by the curve and dots, respectively.

The theoretical calculation results and the experimental results are shown by the curve and dot symbols, respectively in Figure 13. The results indicate that the beam splitting ratio of the zeroth order to the first order can be tuned from 10:1 to 3:5.

#### 3.3. Insertion loss

3.2. Bolometer measurement results

210 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

can be tuned by varying the applied voltage.

**0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8**

**<sup>0</sup> <sup>10</sup> <sup>20</sup> <sup>30</sup> <sup>40</sup> <sup>50</sup>**

**(de**

the diffraction angle for the 0.3 THz beam. Solid lines are theoretical curves.

**g.)**

**0th-order**

respectively.

In Figure 11, we present the intensity profiles of the diffracted 0.3 THz beam polarized in the y-direction. Data are shown for the grating biased from 0 to 90 V. The corresponding effective indices of refraction vary from 1.58 to 1.71. A diffraction maximum was detected at ϕ = 30, which corresponds to the first-order diffracted beam predicted by the grating equation Λsinϕ = mλ, where Λ is 2.0 mm and the wavelength λ is 1.0 mm for the 0.3 THz wave. The measured diffraction efficiencies for the zeroth and first orders are in accord with the predictions of Eq. (5), considering

When the E7 molecules were aligned such that the refractive index was no, the phase difference was close to 2π. Most of the THz signal propagated in the direction of the zeroth-order diffraction. Experimentally, the diffraction efficiencies were determined to be 0.62 and 0.06 for the zeroth and first orders, respectively. The diffraction efficiencies were tuned by increasing the applied voltage (Vappl) gradually. When the refractive index of E7 was varied from 1.58 to 1.71, the diffraction efficiency of the zeroth order decreased; by contrast, the diffraction efficiency of the first order increased. When the E7 molecules were aligned such that the refractive index was ne, the phase difference was close to π. The THz wave propagated mostly as a first-order diffracted beam. The diffraction efficiencies were 0.16 and 0.26 for the zeroth and first orders,

Figure 12(a, b) show the diffraction efficiencies of the zeroth and first orders as a function of the refractive index of E7 and Vappl. The experimental results, shown by dot symbols, are in good agreement with the theoretical predictions. Such results indicate that the grating functions as a variable beam splitter. The beam splitting ratio of the zeroth order to the first order

Alternatively, these results indicate that the beam splitting ratio can be tuned and varied as a function of the refractive index of the nematic liquid crystal, E7. This is illustrated in Figure 13.

> **1st -order**

Figure 11. Diffraction efficiencies of the grating biased at several values of applied voltages are plotted as a function of

**1.56 1.59 1.62 1.65 1.68 1.71**

*n*

*n***=1.58 V***appl* **= 0V** *n***=1.62 V***appl* **= 15V** *n***=1.65 V***appl* **= 30V** *n***=1.68 V***appl* **= 60V** *n***=1.71 V***appl* **= 90V**

the finite dimensions of the grating and the acceptance angle of the bolometer (3).

Insertion loss is a critical parameter for THz devices. We have experimentally and theoretically studied the insertion loss of two classes of devices. Figure 14(a) shows the diffraction efficiency

0.5 THz were estimated to be 5.5 and 6.9 dB, respectively. Table 2 shows the estimated and measured values of the two devices. The discrepancy between the estimated insertion loss and measured data could be due to the finite collection efficiency of the detection system and nonideal assembly of the grating. The experimental results indicate that by reducing the thickness of the thick fused silica plates in the base of the device by10 mm, the insertion loss

Driving voltage 0 V (no) at 0.3 THz 90 V (ne) at 0.5 THz 0 V (no) at 0.3 THz 90 V (ne) at 0.5 THz

2.3 dB 3.2 dB 5.5 dB

Liquid-Crystal-Based Phase Gratings and Beam Steerers for Terahertz Waves

3.8 dB 3.1 dB 6.9 dB 213

http://dx.doi.org/10.5772/intechopen.70449

**0 100 200 300 400 500 600 700**

**63%**

**Fall time=288.8 s**

**Voltage-off**

**Time (s)**

7.8 dB 4.9 dB 13 dB

Measured value 8.0 dB 10 dB 6.1 dB 7.4 dB

Phase grating h = 17.5 mm h = 7.5 mm

4.7 dB 4.3 dB 9.0 dB

Therefore, if a grating device without a base (h = 2.5 mm) can be fabricated, the insertion loss can be as low as 2.5 dB. Such a device would be more attractive for practical use. Furthermore, the performance of the grating can be improved by using electrodes with higher conductivity. The thickness of the electrodes affects the conductor loss, as detailed in Ref. [50].

For gratings using LCs, the response time of the device is a concern. The voltage-on and voltage-off times were measured by subjecting the device to a pulse signal. Figure 15(a, b) shows the normalized power as a function of the driving voltage in the voltage-on and voltage-off states, respectively. We defined the rise time as the duration for which the driving voltage was turned on for reducing the power to 37% of the maximum. The fall time was defined as the duration for which the driving voltage was turned off for increasing the power

**0.0**

**0.2**

**off**

**(b)**

**0.4**

**0.6**

**Power (a.u.)** 

**0.8**

**1.0**

can be reduced by approximately 2.5 dB.

**0 10 20 30 40 50 60 70 80 90**

**Rising time=22.8 s**

**on 37%**

 **Voltage-on**

Figure 15. Response times of a phase grating: (a) voltage-on state and (b) voltage-off state.

**Time (s )**

**(Driving voltage=90V)**

Table 2. Insertion loss of phase gratings.

3.4. Device response times

**0.0**

**0.2**

**0.4**

**0.6**

**Power (a.u.)** 

**0.8**

**1.0**

**(a)**

(Estimated insertion loss) Conductor loss Dielectric loss Total

Figure 14. Diffraction efficiency of the devices with bases of (a) h = 17.5 mm and (b) h = 7.5 mm.

of a grating with a thicker base (h = 17.5 mm), obtained by normalizing the diffracted signals for the o-ray and e-ray to the reference THz signal for which the grating was removed. The experimentally measured diffraction efficiency for the o-ray at 0.3 THz is approximately 0.07. The diffraction efficiency for the o-ray at 0.3 THz predicted by the classic diffraction theory or evaluated by performing an FDTD simulation was approximately 0.45. The loss of the device was thus 8.0 dB for the o-ray at 0.3 THz. Similarly, the diffraction efficiency for the e-ray at 0.5 THz was approximately 0.046, whereas the theoretical prediction was approximately 0.45. The loss value of the grating for the e-ray at 0.5 THz was therefore 10 dB. A grating device with a smaller base component (h = 7.5 mm) was prepared to compare the insertion loss (Figure 14(b)). The experimentally measured diffraction efficiency for the o-ray at 0.3 THz was approximately 0.11, and the loss was 6.1 dB. The diffraction efficiency for the eray at 0.5 THz was approximately 0.083 and the loss value was 7.4 dB. The diffraction efficiency of the device with a smaller base is obviously higher than that of the device with a larger base.

The thickness of the ITO film we used was approximately 200 nm. According to [46], the conductivity <sup>σ</sup> of the film was 1.5 <sup>10</sup><sup>3</sup> <sup>Ω</sup><sup>1</sup> cm<sup>1</sup> . The parameters of fused silica and LC with different refractive indices in the frequency range of 0.20.8 THz are used for the insertion loss calculations shown in Table 1.

The estimated loss value was obtained from Eqs. (9) and (10). For the grating with a larger base component (h = 17.5 mm), the total loss for the o-wave at 0.3 THz and for the e-wave at 0.5 THz were estimated to be 9.0 and 13 dB, respectively. Similarly, for the grating with a smaller base component (h = 7.5 mm), the total loss for the o-wave at 0.3 THz and for the e-wave at


Table 1. Parameters of fused silica and the NLC E7.


Table 2. Insertion loss of phase gratings.

0.5 THz were estimated to be 5.5 and 6.9 dB, respectively. Table 2 shows the estimated and measured values of the two devices. The discrepancy between the estimated insertion loss and measured data could be due to the finite collection efficiency of the detection system and nonideal assembly of the grating. The experimental results indicate that by reducing the thickness of the thick fused silica plates in the base of the device by10 mm, the insertion loss can be reduced by approximately 2.5 dB.

Therefore, if a grating device without a base (h = 2.5 mm) can be fabricated, the insertion loss can be as low as 2.5 dB. Such a device would be more attractive for practical use. Furthermore, the performance of the grating can be improved by using electrodes with higher conductivity. The thickness of the electrodes affects the conductor loss, as detailed in Ref. [50].

#### 3.4. Device response times

of a grating with a thicker base (h = 17.5 mm), obtained by normalizing the diffracted signals for the o-ray and e-ray to the reference THz signal for which the grating was removed. The experimentally measured diffraction efficiency for the o-ray at 0.3 THz is approximately 0.07. The diffraction efficiency for the o-ray at 0.3 THz predicted by the classic diffraction theory or evaluated by performing an FDTD simulation was approximately 0.45. The loss of the device was thus 8.0 dB for the o-ray at 0.3 THz. Similarly, the diffraction efficiency for the e-ray at 0.5 THz was approximately 0.046, whereas the theoretical prediction was approximately 0.45. The loss value of the grating for the e-ray at 0.5 THz was therefore 10 dB. A grating device with a smaller base component (h = 7.5 mm) was prepared to compare the insertion loss (Figure 14(b)). The experimentally measured diffraction efficiency for the o-ray at 0.3 THz was approximately 0.11, and the loss was 6.1 dB. The diffraction efficiency for the eray at 0.5 THz was approximately 0.083 and the loss value was 7.4 dB. The diffraction efficiency of the device with a smaller base is obviously higher than that of the device with a larger base. The thickness of the ITO film we used was approximately 200 nm. According to [46], the

**0.00 0.02 0.04 0.06 0.08 0.10 0.12**

**(b)**

**0V (n o**

**h = 17.5mm**

212 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

Figure 14. Diffraction efficiency of the devices with bases of (a) h = 17.5 mm and (b) h = 7.5 mm.

**) 90V (n e**

**)**

cm<sup>1</sup>

different refractive indices in the frequency range of 0.20.8 THz are used for the insertion loss

The estimated loss value was obtained from Eqs. (9) and (10). For the grating with a larger base component (h = 17.5 mm), the total loss for the o-wave at 0.3 THz and for the e-wave at 0.5 THz were estimated to be 9.0 and 13 dB, respectively. Similarly, for the grating with a smaller base component (h = 7.5 mm), the total loss for the o-wave at 0.3 THz and for the e-wave at

Material Fused silica E7 (no) E7 (ne) ε<sup>r</sup> 3.80 2.50 2.92 ε<sup>i</sup> 0.008 0.095 0.041 tanδ 0.0021 0.038 0.014

. The parameters of fused silica and LC with

**0.2 0.3 0.4 0.5 0.6 0.7**

**Frequency (THz)**

**h = 7.5mm**

> **0V (n o**

**) 90V (n e**

**)**

conductivity <sup>σ</sup> of the film was 1.5 <sup>10</sup><sup>3</sup> <sup>Ω</sup><sup>1</sup>

Table 1. Parameters of fused silica and the NLC E7.

**0.2 0.3 0.4 0.5 0.6 0.7**

**Frequency (THz)**

**0.00**

**0.02**

**0.04**

**0.06**

**0.08**

**0.10**

**0.12**

**(a)**

calculations shown in Table 1.

For gratings using LCs, the response time of the device is a concern. The voltage-on and voltage-off times were measured by subjecting the device to a pulse signal. Figure 15(a, b) shows the normalized power as a function of the driving voltage in the voltage-on and voltage-off states, respectively. We defined the rise time as the duration for which the driving voltage was turned on for reducing the power to 37% of the maximum. The fall time was defined as the duration for which the driving voltage was turned off for increasing the power

Figure 15. Response times of a phase grating: (a) voltage-on state and (b) voltage-off state.

to 63% of the maximum. The rise and fall times of the grating were found to be approximately 23 and 290 s, respectively. The phase grating responded slowly because of the thick LC layer used. Consequently, the present device is not suitable for applications that require fast modulation. However, the device is appropriate for instrumentation or apparatuses that require, for example, a fixed beam splitting ratio with occasional fine tuning.

The response time of the voltage-off state depended only on the material properties and cell thickness. Therefore, it cannot be shortened by applying a higher electric field. To shorten the response time, LCs with birefringence than E7 can be used. Alternatively, dual-frequency LCs can be employed; the use of dual-frequency LCs has been discussed in previous papers [51–54]. Dual-frequency LCs show high dielectric dispersion, and their dielectric anisotropy is frequency dependent, resulting in a change in sign at the crossover frequency. Dual-frequency materials in which the crossover frequency is a few kilohertz and changes markedly over the range are commercially available. Dual-frequency LCs would enable the operation of phase gratings in a nonzero applied voltage state.

#### 3.5. Phase shifting and beam steering

We have studied the phase shift experienced by the THz wave propagating through the grating in which the control voltages were applied equally to all NLC layers. Figure 16 shows the measured THz waveforms for biasing voltages varied from 0 to 28.8 Vrms. It is obviously that the pulses delay increase as applying voltages increased, as the NLC molecules re-orientate gradually from ordinary to extraordinary refractive index.

By applying Fourier transform on the waveforms in Figure 16, we obtained the phase shift as a function of frequency. This is shown in Figure 17. The phase shift increased with increasing

applying voltages as expected. Figure 18 is a plot the phase shift at 0.3 THz as a function of the control voltage. Above the threshold voltage, 1.20 Vrms, the phase shift rapidly increases with the applying voltage. The maximum phase shift reached approximately 11.24 rad. This value is

**0 5 10 15 20 25 30**

**Phase shift at 0.3 THz**

**Voltage (Vrms)**

**0.1 0.2 0.3 0.4 0.5 0.6 0.7**

**0.8**

http://dx.doi.org/10.5772/intechopen.70449

215

Liquid-Crystal-Based Phase Gratings and Beam Steerers for Terahertz Waves

We measured the beam steering characteristics of the phase-shifting array with the modified THz-TDS shown in Figure 6. Although the applying voltage should be adjusted layer-by layer for beam steering, only nine values of control voltages were available to be applied to each NLC block consisting two NLC layers. As the phase shift Δϕ<sup>i</sup> in each NLC block needed for beam steering is given by Eq. (12), the control voltage corresponding to phase shift can be

determined from the experimental results in Figure 18, and are tabulated in Table 3.

in close agreement with the calculated value.

**0**

Figure 18. Phase shift at 0.3 THz as a function of the control voltage.

**2**

**4**

**6**

**Phase (rad)**

**8**

**10**

**12**

**0**

**5**

**10**

**15**

**Phase (rad)**

**20**

**25**

**30**

**35**

**1.20Vrms 1.50Vrms 1.95Vrms 3.60Vrms 28.80Vrms**

Figure 17. Spectra of phase shift of THz signal. Phase increases as applying voltage increases.

Figure 16. THz signal delay in time domain. Delay time increases as applying voltage increases.

Figure 17. Spectra of phase shift of THz signal. Phase increases as applying voltage increases.

Figure 18. Phase shift at 0.3 THz as a function of the control voltage.

to 63% of the maximum. The rise and fall times of the grating were found to be approximately 23 and 290 s, respectively. The phase grating responded slowly because of the thick LC layer used. Consequently, the present device is not suitable for applications that require fast modulation. However, the device is appropriate for instrumentation or apparatuses that require, for

The response time of the voltage-off state depended only on the material properties and cell thickness. Therefore, it cannot be shortened by applying a higher electric field. To shorten the response time, LCs with birefringence than E7 can be used. Alternatively, dual-frequency LCs can be employed; the use of dual-frequency LCs has been discussed in previous papers [51–54]. Dual-frequency LCs show high dielectric dispersion, and their dielectric anisotropy is frequency dependent, resulting in a change in sign at the crossover frequency. Dual-frequency materials in which the crossover frequency is a few kilohertz and changes markedly over the range are commercially available. Dual-frequency LCs would enable the operation of phase

We have studied the phase shift experienced by the THz wave propagating through the grating in which the control voltages were applied equally to all NLC layers. Figure 16 shows the measured THz waveforms for biasing voltages varied from 0 to 28.8 Vrms. It is obviously that the pulses delay increase as applying voltages increased, as the NLC molecules re-orientate

By applying Fourier transform on the waveforms in Figure 16, we obtained the phase shift as a function of frequency. This is shown in Figure 17. The phase shift increased with increasing

**50 52 54 56 58 60**

**DelayTime (ps)**

example, a fixed beam splitting ratio with occasional fine tuning.

214 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

gratings in a nonzero applied voltage state.

gradually from ordinary to extraordinary refractive index.

**0Vrms 1.20Vrms 1.50Vrms 1.95Vrms 3.60Vrms 28.80Vrms**

Figure 16. THz signal delay in time domain. Delay time increases as applying voltage increases.

3.5. Phase shifting and beam steering

**-0.0003 -0.0002 -0.0001 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005**

**THz field (a.u.)**

applying voltages as expected. Figure 18 is a plot the phase shift at 0.3 THz as a function of the control voltage. Above the threshold voltage, 1.20 Vrms, the phase shift rapidly increases with the applying voltage. The maximum phase shift reached approximately 11.24 rad. This value is in close agreement with the calculated value.

We measured the beam steering characteristics of the phase-shifting array with the modified THz-TDS shown in Figure 6. Although the applying voltage should be adjusted layer-by layer for beam steering, only nine values of control voltages were available to be applied to each NLC block consisting two NLC layers. As the phase shift Δϕ<sup>i</sup> in each NLC block needed for beam steering is given by Eq. (12), the control voltage corresponding to phase shift can be determined from the experimental results in Figure 18, and are tabulated in Table 3.


Table 3. Control voltage and corresponding phase shift at 0.3 THz.

The experimental results demonstrating beam steering are shown in Figure 19.

In the above figure, (a) shows the THz signal before transmitted to the device, and (b) and (c) show the THz signal transmitted through the device with ordinary and extraordinary refractive indices at θ = 0, respectively. The main beam was steered in the direction of θ = 8.5 as the control voltages were varied to yield the phase gradient as shown in (d). The signal vanishes as we removed the device as shown in (e). Applying FFT analysis, the corresponding THz spectra

in frequency domain are shown in Figure 20. According to the results, the device can steer the

Figure 20. Spectra of THz signals before steered at θ = 0: (a) without sample; with sample (b) at no-state, (c) at ne-state;

steered signals at θ = 8.5: (d) sample applied voltage to yield gradient phase, (e) without sample.

**0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0**

**Frequency (THz)**

 **= 8.5 o without sample**

**(e)**

**(d)**

**(c)**

**(b)**

**(a)**

217

 **= 8.5 <sup>o</sup> gradient phase)**

 **= 0<sup>o</sup> without sample)**

http://dx.doi.org/10.5772/intechopen.70449

 **= 0<sup>o</sup> (***ne* **)**

 **= 0<sup>o</sup> (***no* **)**

Liquid-Crystal-Based Phase Gratings and Beam Steerers for Terahertz Waves

In this work, we review our theoretical and experimental studies on electrically controlled LCbased phase gratings for manipulating THz waves. This device can be used as a tunable THz beam splitter, and the beam splitting ratio of the zeroth-order diffraction to the first-order diffraction can be tuned from 10:1 to 3:5. An FDTD simulation was performed to investigate the diffraction effect of the phase grating. The experimental and simulation results were in general agreement. The signal losses of the device were discussed. It was observed that the insertion loss could be reduced by reducing the thickness of the fused silica plates in the base component of the device. The rise and fall times of the grating are approximately 23 and 290 s, respectively. The slow response could be accounted for because of the thick LC layer employed. Consequently, it is not suitable for applications that require fast modulation. However, the device is appropriate for instrumentation or apparatuses that require, for example, a fixed beam splitting ratio with occasional fine tuning. The use of highly-birefringent NLCs or dual-frequency LCs could alleviate the problem somewhat. Besides, we demonstrated a

broadband THz signal up to about 0.5 THz.

4. Summary

**10-3 10-1 10<sup>1</sup> 10<sup>3</sup> 10-3 10-1 10<sup>1</sup> 10<sup>3</sup> 10-3 10-1 10<sup>1</sup> 10<sup>3</sup> 10-3 10-1 10<sup>1</sup> 10<sup>3</sup> 10-3 10-1 10<sup>1</sup> 10<sup>3</sup>**

**Power (a.u.)**

Figure 19. THz signals before steered at θ = 0: (a) without sample; with sample (b) at no-state, (c) at ne-state; steered signals at θ = 8.5: (d) sample applied voltage to yield gradient phase, (e) without sample.

Figure 20. Spectra of THz signals before steered at θ = 0: (a) without sample; with sample (b) at no-state, (c) at ne-state; steered signals at θ = 8.5: (d) sample applied voltage to yield gradient phase, (e) without sample.

in frequency domain are shown in Figure 20. According to the results, the device can steer the broadband THz signal up to about 0.5 THz.

### 4. Summary

The experimental results demonstrating beam steering are shown in Figure 19.

Table 3. Control voltage and corresponding phase shift at 0.3 THz.

**0**

**30**

**(e)**

**(d)**

**(c)**

**(b)**

**0**

**30**

**0**

**THz Field (a.u.)**

**30**

**0**

V<sup>1</sup> 0 0 V<sup>2</sup> 1.32 1.41 V<sup>3</sup> 1.44 2.81 V<sup>4</sup> 1.57 4.22 V<sup>5</sup> 1.77 5.62 V<sup>6</sup> 2.18 7.03 V<sup>7</sup> 2.96 8.43 V<sup>8</sup> 4.88 9.84 V<sup>9</sup> 28.80 11.24

216 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

In the above figure, (a) shows the THz signal before transmitted to the device, and (b) and (c) show the THz signal transmitted through the device with ordinary and extraordinary refractive indices at θ = 0, respectively. The main beam was steered in the direction of θ = 8.5 as the control voltages were varied to yield the phase gradient as shown in (d). The signal vanishes as we removed the device as shown in (e). Applying FFT analysis, the corresponding THz spectra

 **= 0<sup>o</sup> without sample) (a)**

**0 20 40 60 80**

 **= 8.5 o without sample**

 **= 8.5 <sup>o</sup> gradient phase)**

 **= 0<sup>o</sup>** *ne* **)**

 **= 0<sup>o</sup>** *no* **)**

**Delay time (ps)**

Figure 19. THz signals before steered at θ = 0: (a) without sample; with sample (b) at no-state, (c) at ne-state; steered

signals at θ = 8.5: (d) sample applied voltage to yield gradient phase, (e) without sample.

Applied voltage (Vrms) Phase shift (rad) at 0.3 THz

In this work, we review our theoretical and experimental studies on electrically controlled LCbased phase gratings for manipulating THz waves. This device can be used as a tunable THz beam splitter, and the beam splitting ratio of the zeroth-order diffraction to the first-order diffraction can be tuned from 10:1 to 3:5. An FDTD simulation was performed to investigate the diffraction effect of the phase grating. The experimental and simulation results were in general agreement. The signal losses of the device were discussed. It was observed that the insertion loss could be reduced by reducing the thickness of the fused silica plates in the base component of the device. The rise and fall times of the grating are approximately 23 and 290 s, respectively. The slow response could be accounted for because of the thick LC layer employed. Consequently, it is not suitable for applications that require fast modulation. However, the device is appropriate for instrumentation or apparatuses that require, for example, a fixed beam splitting ratio with occasional fine tuning. The use of highly-birefringent NLCs or dual-frequency LCs could alleviate the problem somewhat. Besides, we demonstrated a grating-structured phase shifter array that can be used as the THz shifter and THz beam steerer. A phase shift as large as 11.24 rad was achieved. Using a designed voltage gradient biasing on the grating structure, broadband THz signal below 0.5 THz can be steered by as much as 8.5. The experimental results are in good agreement with theoretical predictions.

[7] Yang C-S, Tang T-T, Pan R-P, Yu P, Pan C-L. Liquid crystal terahertz phase shifter s with functional indium-tin-oxide nanostructures for biasing and alignment. Applied Physics

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### Acknowledgements

This work was partly supported by the National Science Council of Taiwan (104–2221-E-007- 093-MY3), the Academic Top University Program of the Taiwan Ministry of Education, and the U.S. Air Force Office of Scientific Research (FA2386–13–1-4086). Chia-Jen Lin is now with Taiwan Semiconductor Manufacturing Company. Contributions by Mr. Chuan-Hsien Lin are gratefully acknowledged.

### Author details

Ci-Ling Pan1 \*, Chia-Jen Lin<sup>2</sup> , Chan-Shan Yang<sup>1</sup> , Wei-Ta Wu<sup>2</sup> and Ru-Pin Pan2

\*Address all correspondence to: clpan@phys.nthu.edu.tw


### References


[7] Yang C-S, Tang T-T, Pan R-P, Yu P, Pan C-L. Liquid crystal terahertz phase shifter s with functional indium-tin-oxide nanostructures for biasing and alignment. Applied Physics Letters. 2014;104:141106

grating-structured phase shifter array that can be used as the THz shifter and THz beam steerer. A phase shift as large as 11.24 rad was achieved. Using a designed voltage gradient biasing on the grating structure, broadband THz signal below 0.5 THz can be steered by as much as 8.5. The experimental results are in good agreement with theoretical predictions.

This work was partly supported by the National Science Council of Taiwan (104–2221-E-007- 093-MY3), the Academic Top University Program of the Taiwan Ministry of Education, and the U.S. Air Force Office of Scientific Research (FA2386–13–1-4086). Chia-Jen Lin is now with Taiwan Semiconductor Manufacturing Company. Contributions by Mr. Chuan-Hsien Lin are

, Wei-Ta Wu<sup>2</sup> and Ru-Pin Pan2

, Chan-Shan Yang<sup>1</sup>

1 Department of Physics, National Tsing Hua University, Hsinchu, Taiwan

erated by photonics. Nature Photonics. 2016;10:371-379

Optics Letters. 2014;39(8):2511-2513

2 Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan

[1] Ferguson B, Zhang X-C. Materials for terahertz science and technology. Nature Materials.

[4] Nagatsuma T, Ducournau G, Renaud CC. Advances in terahertz communications accel-

[5] Alonso-González P, Nikitin AY, Gao Y, Woessner A, Lundeberg MB, Principi A, Forcellini N, Yan W, Vélez S, Huber AJ, Watanabe K, Taniguchi T, Casanova F, Hueso LE, Polini M, Hone J, Koppens FHL, Hillenbrand R. Acoustic terahertz graphene plasmons revealed by photocurrent nanoscopy. Nature Nanotechnology. 2017;12:31-35 [6] Yang C-S, Tang T-T, Chen P-H, Pan R-P, Yu P, Pan C-L. Voltage-controlled liquid-crystal terahertz phase shifter with indium-tin-oxide nanowhiskers as transparent electrodes.

[2] Tonouchi M. Cutting-edge terahertz technology. Nature Photonics. 2007;1:97-105 [3] Zhang X-C, Xu J. Introduction to THz Wave Photonics. New York: Springer; 2010

Acknowledgements

gratefully acknowledged.

\*, Chia-Jen Lin<sup>2</sup>

\*Address all correspondence to: clpan@phys.nthu.edu.tw

218 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

Author details

Ci-Ling Pan1

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2002;1:26-33


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[43] Yang C-S, Lin C-J, Pan R-P, Que CT, Yamamoto K, Tani M, Pan C-L. The complex refractive indices of the liquid crystal mixture E7 in the terahertz frequency range. Journal

[44] Yang C-S, Lin M-H, Chang C-H, Yu P, Shieh J-M, Shen C-H, Wada O, Pan C-L. Non-Drude behavior in indium-tin-oxide nanowhiskers and thin films by transmission and reflection THz time-domain spectroscopy. IEEE Journal of Quantum Electronics.

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[46] Chen C-W, Lin Y-C, Chang C-H, Yu P, Shieh J-M, Pan C-L. Frequency-dependent complex conductivities and dielectric responses of indium tin oxide thin films from the visible

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[50] Kamoda H, Kuki T, Nomoto T. Conductor loss reduction for liquid crystal millimeter-

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[24] Kersting R, Strasser G, Unterrainer K. Terahertz phase modulator. Electronics Letters.

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[27] Chen J, Bos PJ, Vithana H, Johnson DL. An electro-optically controlled liquid crystal

[28] Chen CY, Hsieh CF, Lin YF, Pan RP, Pan CL. Magnetically tunable room-temperature 2π

[29] Wu HY, Hsieh CF, Tang TT, Pan RP, Pan CL. Electrically tunable room-temperature 2π liquid crystal terahertz phase shifter. IEEE Photonics Technology Letters. 2006;18:1488-1490

[30] Chen C-Y, Hsieh C-F, Lin Y-F, Pan C-L, Pan R-P. Liquid- crystal-based terahertz tunable

[31] Ho I-C, Pan C-L, Hsieh C-F, Pan R-P. Liquid- crystal- based terahertz tunable Solc filter.

[32] Ghattan Z, Hasek T, Wilk R, Shahabadi M, Koch M. Sub- terahertz on–off switch based on a two-dimensional photonic crystal infiltrated by liquid crystals. Optics Communica-

[33] Jewell1 SA, Hendry E, Isaac TH, Sambles JR. Tuneable Fabry–Perot etalon for terahertz

[34] Pan R-P, Hsieh C-F, Chen C-Y, Pan C-L. Temperature- dependent optical constants and birefringence of nematic liquid crystal 5CB in the terahertz frequency range. Journal of

[35] Neu J, Beiggang R, Rahm M. Metamaterial-based gradient index beam steerers for

[36] Xu B, Hu H, Liu J, Wei X, Wang Q, Song G, Xu Y. Terahertz light deflection in doped

diffraction grating. Applied Physics Letters. 1995;67:2588-2590

Lyot filter. Applied Physics Letters. Mar. 2006;88:101107

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semiconductor slit arrays. Optics Communication. 2013;308:74-77

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[52] Golovin AB, Shiyanovskii SV, Lavrentovich OD. Fast switching dual-frequency liquid crystal optical retarder, driven by an amplitude and frequency modulated voltage. SID 03 Digest. 2003;2(1472):55

**Chapter 11**

**Provisional chapter**

**Design and Fabrication of Ultra-Short Throw Ratio**

One of applications for liquid crystal on silicon (LCoS) could be an emitted light panel for display and projection. Among optical projectors, the most challenging work is to design ultra-short throw projection systems for LCoS projector for home cinema, virtual reality (VR), head-up display (HUD) in automobile. The chapter discloses the design and fabrication of such kind of projector. In fact, such design is not only to design wide angle projection optics but also to optimize illumination for LCoS in order to have high-quality image. The projector optical system is simply with a telecentric field lens and inlet optics of symmetric double gauss or a large angle eyepiece, with a conic aspheric mirror, thus the full projection angle large than 155°. Applying Koehler illumination, the resolution of image is increased; thus, the modulation transfer function of image in high spatial frequency is increased to form the high-quality illuminated image. Based on telecentric lens type of projection systems and Koehler illumination, optical parameters are provided. The partial coherence analysis has verified that the design is reached to 2.5 lps/mm within 2 × 1.5 m. The best performance of systems has been achieved. The throw ratio is

**Keywords:** LCoS, Koehler illumination, telecentric, ultra-short throw ratio

**Design and Fabrication of Ultra-Short Throw Ratio** 

DOI: 10.5772/intechopen.72670

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

The mass requirement for display as viewing accessory has been applied toward the smart phone, HUD, and computers, home games, and home cinema. Projector has been one of the display tools for classrooms, family rooms or theaters, while the LCD display cannot be fully replaced due to its unique characteristics of adjustable view angle and size, and environmental

**Projector Based on Liquid Crystal on Silicon**

**Projector Based on Liquid Crystal on Silicon**

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.72670

less than 0.25 with HD format.

Jiun-Woei Huang

**Abstract**

**1. Introduction**

protection issue.

Jiun-Woei Huang


**Provisional chapter**

### **Design and Fabrication of Ultra-Short Throw Ratio Projector Based on Liquid Crystal on Silicon Design and Fabrication of Ultra-Short Throw Ratio Projector Based on Liquid Crystal on Silicon**

DOI: 10.5772/intechopen.72670

Jiun-Woei Huang Jiun-Woei Huang

[52] Golovin AB, Shiyanovskii SV, Lavrentovich OD. Fast switching dual-frequency liquid crystal optical retarder, driven by an amplitude and frequency modulated voltage. SID

[53] Hsieh CT, Huang CY, Lin CH. In-plane switching dual-frequency liquid crystal cell.

[54] Chen C-C, Chiang W-F, Tsai M-C, Jiang S-A, Chang T-H, Wang S-H, Huang C-Y. Continuously tunable and fast-response terahertz metamaterials using in-plane-switching dual-

frequency liquid crystal cells. Optics Letters. 2015;40:2021-2024

03 Digest. 2003;2(1472):55

Optics Express. 2007;15:11685-11690

222 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.72670

### **Abstract**

One of applications for liquid crystal on silicon (LCoS) could be an emitted light panel for display and projection. Among optical projectors, the most challenging work is to design ultra-short throw projection systems for LCoS projector for home cinema, virtual reality (VR), head-up display (HUD) in automobile. The chapter discloses the design and fabrication of such kind of projector. In fact, such design is not only to design wide angle projection optics but also to optimize illumination for LCoS in order to have high-quality image. The projector optical system is simply with a telecentric field lens and inlet optics of symmetric double gauss or a large angle eyepiece, with a conic aspheric mirror, thus the full projection angle large than 155°. Applying Koehler illumination, the resolution of image is increased; thus, the modulation transfer function of image in high spatial frequency is increased to form the high-quality illuminated image. Based on telecentric lens type of projection systems and Koehler illumination, optical parameters are provided. The partial coherence analysis has verified that the design is reached to 2.5 lps/mm within 2 × 1.5 m. The best performance of systems has been achieved. The throw ratio is less than 0.25 with HD format.

**Keywords:** LCoS, Koehler illumination, telecentric, ultra-short throw ratio

### **1. Introduction**

The mass requirement for display as viewing accessory has been applied toward the smart phone, HUD, and computers, home games, and home cinema. Projector has been one of the display tools for classrooms, family rooms or theaters, while the LCD display cannot be fully replaced due to its unique characteristics of adjustable view angle and size, and environmental protection issue.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Since two decades ago, rear projection TV has been used the projection in the back to image in the back of screen then formed in the front screen, to the forward projection LCoS refractive projection systems, the throw ratio is 1.4 to 1.6, recently, Sony short throw projection LSPX-W1 has announced the throw ratio to less than 0.5 [2].

In the past decade, several companies [3] had announced reflective-type projectors could provide the short ratio projection under 0.5, and Sony [4] has announced the throw ratio to less than 0.2, even it is posted in **Figure 1**, yet it is still no unique solution for such kind design disclosure. Thales [5, 7] reports that several reflective design are suggested by using optical deviated and tilted method, yet the engineering is enable to be carried.

### **1.1. The advantage of LCoS applicable in show throw ratio projector**

Digital light processing (DLP) has been a display device based on optical micro-electromechanical structures. In DLP projectors, the image is created by microscopically small mirrors laid out in a matrix on a semiconductor chip, known as a digital micro-mirror. In addition, it has been popularly used in the projectors, and due to each element in DLP mechanical driving, it has limited to drive in high-speed image display. However, LCoS display modulates the emitted liquid crystal, which is much faster than mechanical driving panel. The other evaluating factor is color contrast and duration. Based on reflective coating in silicon, the efficiency of true color and duration is superior to DLP. The typical LCoS is shown in **Figure 2**.

throw ratio and compact. Especially, for LCoS projector, the emitted panel, such as liquid crystal on silicon chip (LCoS), has to be emitted by light. The three panels of LCoS projector are shown in **Figure 3**. Emitted RGB panels, carrying modulated LCD video information, pass through di-chloic filters and polarized beam splitters into lens system to form image on screen. Obviously, the lens for delivering image is crucial part in the projector. Because reflective can reduce the size, enlarge the projection angle, and make system packed, it is the best for short throw projector. The image has to be delivered out from LCoS, the optical system, thus, it is proper to design projector by a reflective mirror to project a wide screen with very

Design and Fabrication of Ultra-Short Throw Ratio Projector Based on Liquid Crystal on Silicon

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225

To classify the projectors' format, the standard video format for ultra-high definition television is shown in **Table 1**. In this case, the image format DCI 4K: 4096 × 2160 is applied.

Usually, the definition of throw ratio is D/W, but for the short throw projector, the throw ratio is defined W/D'. D' is the distance between the bottom side of screen to the last lens or mirror.

short distance and wide angle system.

**Figure 2.** Typical LCoS panel and output circuit.

**1.4. The definition of throw ratio**

**Figure 3.** Three-panel LCoS projection diagrams.

**1.3. The HD format and the short throw ratio**

### **1.2. Short throw ratio projection optics**

For those forward-projecting diffractive lens are quite popular, yet the throw ratios almost is above 1, thus, the project is especially to design and fabricate a lens for throw ratio under 0.5 or less and is hard to achieve. To design short throw ratio of projection lens which is different from other projection lens with refractive lens, the performance of system is short

**Figure 1.** Sony short throw ratio projector for home theater.

**Figure 2.** Typical LCoS panel and output circuit.

Since two decades ago, rear projection TV has been used the projection in the back to image in the back of screen then formed in the front screen, to the forward projection LCoS refractive projection systems, the throw ratio is 1.4 to 1.6, recently, Sony short throw projection

In the past decade, several companies [3] had announced reflective-type projectors could provide the short ratio projection under 0.5, and Sony [4] has announced the throw ratio to less than 0.2, even it is posted in **Figure 1**, yet it is still no unique solution for such kind design disclosure. Thales [5, 7] reports that several reflective design are suggested by using optical

Digital light processing (DLP) has been a display device based on optical micro-electromechanical structures. In DLP projectors, the image is created by microscopically small mirrors laid out in a matrix on a semiconductor chip, known as a digital micro-mirror. In addition, it has been popularly used in the projectors, and due to each element in DLP mechanical driving, it has limited to drive in high-speed image display. However, LCoS display modulates the emitted liquid crystal, which is much faster than mechanical driving panel. The other evaluating factor is color contrast and duration. Based on reflective coating in silicon, the efficiency of true color and duration is superior to DLP. The typical LCoS is shown in **Figure 2**.

For those forward-projecting diffractive lens are quite popular, yet the throw ratios almost is above 1, thus, the project is especially to design and fabricate a lens for throw ratio under 0.5 or less and is hard to achieve. To design short throw ratio of projection lens which is different from other projection lens with refractive lens, the performance of system is short

LSPX-W1 has announced the throw ratio to less than 0.5 [2].

224 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

**1.2. Short throw ratio projection optics**

**Figure 1.** Sony short throw ratio projector for home theater.

deviated and tilted method, yet the engineering is enable to be carried.

**1.1. The advantage of LCoS applicable in show throw ratio projector**

throw ratio and compact. Especially, for LCoS projector, the emitted panel, such as liquid crystal on silicon chip (LCoS), has to be emitted by light. The three panels of LCoS projector are shown in **Figure 3**. Emitted RGB panels, carrying modulated LCD video information, pass through di-chloic filters and polarized beam splitters into lens system to form image on screen. Obviously, the lens for delivering image is crucial part in the projector. Because reflective can reduce the size, enlarge the projection angle, and make system packed, it is the best for short throw projector. The image has to be delivered out from LCoS, the optical system, thus, it is proper to design projector by a reflective mirror to project a wide screen with very short distance and wide angle system.

### **1.3. The HD format and the short throw ratio**

To classify the projectors' format, the standard video format for ultra-high definition television is shown in **Table 1**. In this case, the image format DCI 4K: 4096 × 2160 is applied.

### **1.4. The definition of throw ratio**

Usually, the definition of throw ratio is D/W, but for the short throw projector, the throw ratio is defined W/D'. D' is the distance between the bottom side of screen to the last lens or mirror.

**Figure 3.** Three-panel LCoS projection diagrams.


**Table 1.** The format for ultra-high-definition television.

In **Figure 4**, the throw ratio is the ratio of the distance from the lens to the screen (throw) to the screen width. A larger throw ratio corresponds to a more tightly focused optical system.

**1.5. The projection system**

**Figure 5.** Projection system with illumination and optics.

**2. Theory**

*2.1.1. Telecentric system*

*2.1.2. Koehler illumination*

To design and fabrication of projection system has included two parts: one is imaging, and the other is illumination, [1] and it is desirable that the deterministic optical parameters to optimize the contrast of image requirement must be considered with full consideration of illumination and imaging. **Figure 5** is an illustration of projection system with illumination and optics.

Design and Fabrication of Ultra-Short Throw Ratio Projector Based on Liquid Crystal on Silicon

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227

To design projection system has considered two aspects: one is imaging, and the other is illu-

The liquid crystal on silicon (LCoS) projector includes a cube formed RGB panel with collimated source and projection lens. The illumination requires a cube formed RGB collimated source to introduce the light into pattern by the LCoS module. By a projection lens, the meaningful video information in LCoS is projected into a wall or screen with large field of view, up to throw ratio less than 0.4. In the design, illumination and image require the optimized parameters to form highly demanded images. In order to optimize these systems, the theory

The telecentric is best fitted for short throw projection system because telecentric in the object side can separate the central object rays and margin rays with different optical path and increase the contrast of image plane [10, 12, 14]. Moreover, the telecentric system can provide the nondistorted image or object along optical axis, and the projection system is easy to be optimized.

Koehler illumination [1] is the light source imaged in aperture, while the rays are collimated in LCoS panel. Due to the panels requiring uniform intensity in optical axis in order to keep polarization and coherence, the high performance platform often selects Koehler illumination.

mination, [1] and the theories are explained in the following [6].

of Koehler illumination and telecentric optical system are chosen.

**2.1. Koehler illumination and telecentric**

This projection lens is to reimage of each pixel of LCoS to the projected screen truly, the performance is emphasized the image of LCoS elements, and the size of the object less one LCoS element becomes less important. In three pieces LCoS Panels system, the pixel is 4 μm, and the minimum size is for 2048 × 1080 mm DCI 4K2K projected screen.

**Figure 4.** The view to show throw ratio.

Design and Fabrication of Ultra-Short Throw Ratio Projector Based on Liquid Crystal on Silicon http://dx.doi.org/10.5772/intechopen.72670 227

**Figure 5.** Projection system with illumination and optics.

### **1.5. The projection system**

To design and fabrication of projection system has included two parts: one is imaging, and the other is illumination, [1] and it is desirable that the deterministic optical parameters to optimize the contrast of image requirement must be considered with full consideration of illumination and imaging. **Figure 5** is an illustration of projection system with illumination and optics.

### **2. Theory**

In **Figure 4**, the throw ratio is the ratio of the distance from the lens to the screen (throw) to the screen width. A larger throw ratio corresponds to a more tightly focused optical

This projection lens is to reimage of each pixel of LCoS to the projected screen truly, the performance is emphasized the image of LCoS elements, and the size of the object less one LCoS element becomes less important. In three pieces LCoS Panels system, the pixel is 4 μm, and

the minimum size is for 2048 × 1080 mm DCI 4K2K projected screen.

**Table 1.** The format for ultra-high-definition television.

226 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

system.

**Figure 4.** The view to show throw ratio.

To design projection system has considered two aspects: one is imaging, and the other is illumination, [1] and the theories are explained in the following [6].

### **2.1. Koehler illumination and telecentric**

The liquid crystal on silicon (LCoS) projector includes a cube formed RGB panel with collimated source and projection lens. The illumination requires a cube formed RGB collimated source to introduce the light into pattern by the LCoS module. By a projection lens, the meaningful video information in LCoS is projected into a wall or screen with large field of view, up to throw ratio less than 0.4. In the design, illumination and image require the optimized parameters to form highly demanded images. In order to optimize these systems, the theory of Koehler illumination and telecentric optical system are chosen.

### *2.1.1. Telecentric system*

The telecentric is best fitted for short throw projection system because telecentric in the object side can separate the central object rays and margin rays with different optical path and increase the contrast of image plane [10, 12, 14]. Moreover, the telecentric system can provide the nondistorted image or object along optical axis, and the projection system is easy to be optimized.

#### *2.1.2. Koehler illumination*

Koehler illumination [1] is the light source imaged in aperture, while the rays are collimated in LCoS panel. Due to the panels requiring uniform intensity in optical axis in order to keep polarization and coherence, the high performance platform often selects Koehler illumination.

Being designed by telecentric and Koehler illumination, the best performance of systems, having the optimized optical parameters, could be achieved.

similar method by adjusting the conic curvature of reflective mirror. The image on screen can be expanded and optimized by adjusting the conic value and radius of reflective mirror. In a typical case, the design has passed through three stages, which are given as follows.

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229

The initial stage is setup delivering optics. The lens, such as double gauss or eyepiece types in **Figure 8**, will pull instant image of emitted panel out to pass through common aperture and spread out to form an intermediate image and to broad the field of view, as shown in **Figure 9**.

In **Figure 10**, each principal rays formed common aperture due to telecentric effect. Light passing through the aperture and convergent, the projection angle can be enlarged. Because

*2.3.1. Initial stage*

*2.3.2. Middle stage*

**Figure 7.** The common aperture and intermediate image.

**Figure 8.** Symmetric double gauss and wide eye-piece types.

**Figure 9.** The wide-angle eyepiece to broad the field of view.

### **2.2. Model of components build up**

First, the emitted panel is stimulated by using a paralleled light bundle of mercury light source to hit LCoS panel. Rays, spreading as an emitted object, are shown in **Figure 4**. In the system, three LCoS panels are combined paths as one object, which is pseudo Lambertian distribution in ray field. It acts as telecentric source, shown in **Figure 6**.

#### **2.3. Optical design**

The optical system requirement is listed in **Table 2**. In order to enlarge the projection angle, the optical system of the short throw projection includes two parts, one is refractive lens system, and the other is reflective mirror. In **Figure 7**, a telecentric system is defined, and the principal rays from three fields as parallel rays, from the object, will be focused in one position as common aperture, while the other rays form image. Thus, the image will be formed with reduction value greater than 1. The intermediate image is relayed to the final screen with a

**Figure 6.** The common aperture and intermediate image.


**Table 2.** The specification for theater short throw factor lens.

similar method by adjusting the conic curvature of reflective mirror. The image on screen can be expanded and optimized by adjusting the conic value and radius of reflective mirror.

In a typical case, the design has passed through three stages, which are given as follows.

#### *2.3.1. Initial stage*

Being designed by telecentric and Koehler illumination, the best performance of systems,

First, the emitted panel is stimulated by using a paralleled light bundle of mercury light source to hit LCoS panel. Rays, spreading as an emitted object, are shown in **Figure 4**. In the system, three LCoS panels are combined paths as one object, which is pseudo Lambertian

The optical system requirement is listed in **Table 2**. In order to enlarge the projection angle, the optical system of the short throw projection includes two parts, one is refractive lens system, and the other is reflective mirror. In **Figure 7**, a telecentric system is defined, and the principal rays from three fields as parallel rays, from the object, will be focused in one position as common aperture, while the other rays form image. Thus, the image will be formed with reduction value greater than 1. The intermediate image is relayed to the final screen with a

having the optimized optical parameters, could be achieved.

228 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

distribution in ray field. It acts as telecentric source, shown in **Figure 6**.

**Items Specification** Projected screen 2500 mm in diagonal

Lens type Refractive and reflective

LCoS size 1 inch Pixels size 4 μ2 Video format 4K2K

Short distance to project between last mirror and screen 666 mm

**Table 2.** The specification for theater short throw factor lens.

**2.2. Model of components build up**

**2.3. Optical design**

**Specification for short throw factor lens**

**Figure 6.** The common aperture and intermediate image.

The initial stage is setup delivering optics. The lens, such as double gauss or eyepiece types in **Figure 8**, will pull instant image of emitted panel out to pass through common aperture and spread out to form an intermediate image and to broad the field of view, as shown in **Figure 9**.

### *2.3.2. Middle stage*

In **Figure 10**, each principal rays formed common aperture due to telecentric effect. Light passing through the aperture and convergent, the projection angle can be enlarged. Because

**Figure 7.** The common aperture and intermediate image.

**Figure 9.** The wide-angle eyepiece to broad the field of view.

of image formation, each emitted element in LCoS, two vicinities will not be correlated according to the calculation. If the polarization is considered, two coherence sources may just be passing through, and two bundles of coherent photo will never be interfered. In practical condition, this always happens, that is, once the two bundle groups of photo are partially coherent, the partial

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The system has been verified in a projector, without lens, by a 3-panel LCoS system. The

LCoS reflective-type projection system is shown in **Figure 12**. The illumination requires a cube formed RGB collimated source to introduce the light into pattern by LCoS module.

The emitted LCoS panel as modulate image reflector, while the collimated rays propagate through the open-state liquid crystal and reflecting back to lens system, thus it can be modified

optics system totally replaces the previous lens to demo the function.

coherence should be calculated.

**Figure 11.** Design in the final stage.

Simulation is mentioned below [3, 5, 6].

**3.1. LCoS projection structure**

**2.6. Fabrication**

**3. Simulation**

**Figure 10.** Design in middle stage.

the final image has to be formed in plane, the previous intermediated image has to be a conic trajectory. By mirror theory, the object forms a conic trajectory to broaden the field angle, as in **Figure 10**. Thus, the final image will be placed through the reflective mirror.

### *2.3.3. Final stage*

In the final stage, the intermediate image, coupling with a mirror, forms a broad view image on the screen. The intermediate image relays on the final screen with a similar method by a reflective mirror, shown in **Figure 11**. The whole system has to be optimized in the constraint optical parameters. The optimized condition can be reached [8].

#### **2.4. Image evaluation**

Image evaluation has been carried out by evaluation of spot diagrams, image distortion diagram, to instant adjust the lens size, space and material in order to reach the small and less aberration spot. The third aberration for each lens provides the instant information to adjust lens shape and other parameters to the final stage.

#### **2.5. Partial coherence**

Illumination could be calculated by illumination program. The condenser and collimated lens could be designed by optimizing the uniformity of illumination of LCoS. For detailed calculation Design and Fabrication of Ultra-Short Throw Ratio Projector Based on Liquid Crystal on Silicon http://dx.doi.org/10.5772/intechopen.72670 231

**Figure 11.** Design in the final stage.

of image formation, each emitted element in LCoS, two vicinities will not be correlated according to the calculation. If the polarization is considered, two coherence sources may just be passing through, and two bundles of coherent photo will never be interfered. In practical condition, this always happens, that is, once the two bundle groups of photo are partially coherent, the partial coherence should be calculated.

### **2.6. Fabrication**

the final image has to be formed in plane, the previous intermediated image has to be a conic trajectory. By mirror theory, the object forms a conic trajectory to broaden the field angle, as

In the final stage, the intermediate image, coupling with a mirror, forms a broad view image on the screen. The intermediate image relays on the final screen with a similar method by a reflective mirror, shown in **Figure 11**. The whole system has to be optimized in the constraint

Image evaluation has been carried out by evaluation of spot diagrams, image distortion diagram, to instant adjust the lens size, space and material in order to reach the small and less aberration spot. The third aberration for each lens provides the instant information to adjust

Illumination could be calculated by illumination program. The condenser and collimated lens could be designed by optimizing the uniformity of illumination of LCoS. For detailed calculation

in **Figure 10**. Thus, the final image will be placed through the reflective mirror.

optical parameters. The optimized condition can be reached [8].

230 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

lens shape and other parameters to the final stage.

*2.3.3. Final stage*

**Figure 10.** Design in middle stage.

**2.4. Image evaluation**

**2.5. Partial coherence**

The system has been verified in a projector, without lens, by a 3-panel LCoS system. The optics system totally replaces the previous lens to demo the function.

### **3. Simulation**

Simulation is mentioned below [3, 5, 6].

### **3.1. LCoS projection structure**

LCoS reflective-type projection system is shown in **Figure 12**. The illumination requires a cube formed RGB collimated source to introduce the light into pattern by LCoS module.

The emitted LCoS panel as modulate image reflector, while the collimated rays propagate through the open-state liquid crystal and reflecting back to lens system, thus it can be modified type Koehler illumination. By a projection lens, the meaningful video information in LCoS is projected on a wall or screen with large field of view, up to throw ratio less than 0.3 [9, 11, 13].

### **3.2. Numerical calculation**

codeV (an optical design software) is used in the study [5]. codeV provides MTF, wave-front, coupling efficiency and longitudinal aberration methods to reach the optimized solution. The program-constrained conditions are defined, and at least 100 runs of optimization are performed. The result for requirement of specification is reached. The tolerance of tilted optics has also performed by tilting different elements. The results are expressed in MTF graphs. codeV almost can trace each point in the space through the lens system to target.

### **3.3. Image quality**

The design is shown in **Figure 13**. The refractive lens is to apply double gauss delivering the emitted to spread out due to the symmetric structure and less aberration induced. **Figure 14** shows the comparison between input object and output image, and the output image could truly describe the object with slight pincushion distortion. **Figure 15** shows

**Figure 13.** The optical design for short throw ratio projector.

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**Figure 14.** The simulated object and image.

**Figure 15.** The relative illumination between before and after tuning the lens shapes.

**Figure 12.** The short throw ratio LCoS projection system with Koehler illumination and telecentric optics.

Design and Fabrication of Ultra-Short Throw Ratio Projector Based on Liquid Crystal on Silicon http://dx.doi.org/10.5772/intechopen.72670 233

**Figure 13.** The optical design for short throw ratio projector.

type Koehler illumination. By a projection lens, the meaningful video information in LCoS is projected on a wall or screen with large field of view, up to throw ratio less than 0.3 [9, 11, 13].

codeV (an optical design software) is used in the study [5]. codeV provides MTF, wave-front, coupling efficiency and longitudinal aberration methods to reach the optimized solution. The program-constrained conditions are defined, and at least 100 runs of optimization are performed. The result for requirement of specification is reached. The tolerance of tilted optics has also performed by tilting different elements. The results are expressed in MTF graphs.

The design is shown in **Figure 13**. The refractive lens is to apply double gauss delivering the emitted to spread out due to the symmetric structure and less aberration induced. **Figure 14** shows the comparison between input object and output image, and the output image could truly describe the object with slight pincushion distortion. **Figure 15** shows

codeV almost can trace each point in the space through the lens system to target.

**Figure 12.** The short throw ratio LCoS projection system with Koehler illumination and telecentric optics.

**3.2. Numerical calculation**

232 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

**3.3. Image quality**

**Figure 14.** The simulated object and image.

**Figure 15.** The relative illumination between before and after tuning the lens shapes.

the relative illumination between before and after optimization. Optimize illumination shows that the full screen is above 70%, for the the full field of view is fitted for human eyes.

plane. The MTF is shown in **Figure 18**. It shows the corresponded spatial frequency for

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The conic aspheric mirror is used to relay the intermediate image on screen. The conic constant keeps in 1.55–1.8 to form image and distortion is less than 1%. The optical system for 2048 mm × 1080 m DCI 4K2K projected screen with projecting distance 670 mm with throw ratio 0.33 is designed, and the minimum size 500 μm for the corresponded 4 μm pixel of LCoS

the LCoS is still above 0.25.

is reached, except for the bottom of the screen.

**Figure 17.** The third-order aberration for each surface.

**Figure 18.** The MTF of short throw ratio projector.

**3.5. Optical evaluation**

### **3.4. Aberration**

**Figure 16** shows the field distortion between before and after optimization. Initially, the distortion was high, and after adjusting the conic constant of reflective mirror, the distortion in the margin becomes straight and less distorted. **Figure 17** shows the third-order aberration of surfaces. The image aberration is almost reduced to the least in the image

**Figure 16.** The distortion before and after tuning the optical parameter.

plane. The MTF is shown in **Figure 18**. It shows the corresponded spatial frequency for the LCoS is still above 0.25.

### **3.5. Optical evaluation**

the relative illumination between before and after optimization. Optimize illumination shows that the full screen is above 70%, for the the full field of view is fitted for human

234 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

**Figure 16** shows the field distortion between before and after optimization. Initially, the distortion was high, and after adjusting the conic constant of reflective mirror, the distortion in the margin becomes straight and less distorted. **Figure 17** shows the third-order aberration of surfaces. The image aberration is almost reduced to the least in the image

**Figure 16.** The distortion before and after tuning the optical parameter.

eyes.

**3.4. Aberration**

The conic aspheric mirror is used to relay the intermediate image on screen. The conic constant keeps in 1.55–1.8 to form image and distortion is less than 1%. The optical system for 2048 mm × 1080 m DCI 4K2K projected screen with projecting distance 670 mm with throw ratio 0.33 is designed, and the minimum size 500 μm for the corresponded 4 μm pixel of LCoS is reached, except for the bottom of the screen.

**Figure 17.** The third-order aberration for each surface.

**Figure 18.** The MTF of short throw ratio projector.

### **4. Prototype and analysis**

### **4.1. Fabrication for demonstration**

In **Figure 19**, the utmost Co LCoS projector with the lens is adapted as emitted panel or effective light source. The opto-mechatronic mount between LCoS engine and short throw ratio projection are built. The performance is ready to be verified at room light on and at room light off, as shown in **Figures 20** and **21**, respectively.

In this case, 2048 mm × 1080 m DCI 4K2K projected screen with projecting distance 670 mm with throw ratio 0.3 is designed, and the minimum size 500 μm for the corresponded 4 μm pixel of LCoS is reached, except for the bottom of the screen.

In **Table 3**, the analysis of the system is explained as follows:


### **4.2. The throw factor ratio**

The short throw and wide-angle projection lens is different from other lens systems. According Eq. (1), D′ is the distance between the bottom side of screen to the last lens or mirror.

$$\text{Throw ratio} = \text{W/D}'\tag{1}$$

present pixels of LCoS in each field to fulfill the requirement of 4K2K. A 4-bar pattern with the pitch of 0.004 μ corresponded to one pixel of LCoS is projected in each field respect to each field. The width of pitch projected on screen is 0.5 mm, and with the full screen, it is

filled 4K2K, beside the field 0°. By setting relative numerical aperture (RNA) 0.6, the partial coherence analysis is shown in **Figure 22**. All the fields are resolvable except blur bottom of

The F/# for the short throw and wide-angle projection, different from other lens systems, has considered two f/#; one is optical system and the other is illumination. Here, the LCoS as light source projects onto the screen to form image, as the source of the Koehler model. The F/# of projection lens is 3 and F/# of each pixel of as effective light source is 40, thus the

. For each pair, the resolution has reached 2.5 lps/mm, and has 5K2.5K ful-

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2000 × 1000 mm2

**Figure 20.** At room light on (day).

**4.4. The number aperture and F/#**

relative numerical aperture is applied.

the screen.

In this case, the throw ratio 666/2000 mm = 0.333.

#### **4.3. Illumination and partial coherence analysis**

The partial coherence analysis has been applied to this case. Because MTF cannot provide the full view to verify the requirement of 4K2K, the partial coherence distribution can fully

**Figure 19.** Utmost Co. LCoS projection engine with the self-designed optics and opto-mechatronic mount.

Design and Fabrication of Ultra-Short Throw Ratio Projector Based on Liquid Crystal on Silicon http://dx.doi.org/10.5772/intechopen.72670 237

**Figure 20.** At room light on (day).

**4. Prototype and analysis**

contrast will be viewed.

**4.2. The throw factor ratio**

**4.1. Fabrication for demonstration**

off, as shown in **Figures 20** and **21**, respectively.

In this case, the throw ratio 666/2000 mm = 0.333.

**4.3. Illumination and partial coherence analysis**

pixel of LCoS is reached, except for the bottom of the screen. In **Table 3**, the analysis of the system is explained as follows:

236 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

**1.** The throw ratio of projection is less than 0.3 and reaches the requirement.

**2.** The contrast of projected image can be enhanced by using telecentric system.

In **Figure 19**, the utmost Co LCoS projector with the lens is adapted as emitted panel or effective light source. The opto-mechatronic mount between LCoS engine and short throw ratio projection are built. The performance is ready to be verified at room light on and at room light

In this case, 2048 mm × 1080 m DCI 4K2K projected screen with projecting distance 670 mm with throw ratio 0.3 is designed, and the minimum size 500 μm for the corresponded 4 μm

**3.** By modifying Koehler illumination in reflective LCoS panel, the clear image with high

The short throw and wide-angle projection lens is different from other lens systems. According

Throw ratio = W/D′ (1)

The partial coherence analysis has been applied to this case. Because MTF cannot provide the full view to verify the requirement of 4K2K, the partial coherence distribution can fully

**Figure 19.** Utmost Co. LCoS projection engine with the self-designed optics and opto-mechatronic mount.

Eq. (1), D′ is the distance between the bottom side of screen to the last lens or mirror.

present pixels of LCoS in each field to fulfill the requirement of 4K2K. A 4-bar pattern with the pitch of 0.004 μ corresponded to one pixel of LCoS is projected in each field respect to each field. The width of pitch projected on screen is 0.5 mm, and with the full screen, it is 2000 × 1000 mm2 . For each pair, the resolution has reached 2.5 lps/mm, and has 5K2.5K fulfilled 4K2K, beside the field 0°. By setting relative numerical aperture (RNA) 0.6, the partial coherence analysis is shown in **Figure 22**. All the fields are resolvable except blur bottom of the screen.

#### **4.4. The number aperture and F/#**

The F/# for the short throw and wide-angle projection, different from other lens systems, has considered two f/#; one is optical system and the other is illumination. Here, the LCoS as light source projects onto the screen to form image, as the source of the Koehler model. The F/# of projection lens is 3 and F/# of each pixel of as effective light source is 40, thus the relative numerical aperture is applied.

**5. Conclusion**

reaching 4K2K.

presented.

be formed.

**5.1. Very short projecting distance optical system**

**Figure 22.** 4-bar pattern with the pitch of 0.004 μ is projected in each field.

Being designed by Koehler illumination and telecentric optics, the systems, having the optimized optical parameters, could be achieved. The results for two system requirement are promising, better than other structures. As the systems are built, the optimized performance should be expected. The partial coherence analysis has been applied to verify the system

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The chapter presents the design of a short throw projector optical system, and the throw ratio is 0.3, with a single aspheric mirror and the least number of spherical lens. It provides a wide angle projection lens system with partial coherence source parameter provided. The throw ratio is less than 0.3. The procedures of the optical design and illumination are

With regard to throw ratio that can be less than 0.2, the design has also been carried out. While tilting the mirror at 8°, the throw ratio is 0.186663, as shown in **Figure 23**. However, the image may be keystone, and it can be corrected by the Scheimpflug effect. The image may be corrected by slightly tilting the object, and the corrected nondistorted image may

**Figure 21.** At room light on (night).


**Table 3.** The comparison between design specification and actual value.

The result and analysis are mentioned as follows: The design has fulfilled the requirement as shown in **Table 2**. Two configurations of short throw ratio projection lens are fabricated and under test.

Design and Fabrication of Ultra-Short Throw Ratio Projector Based on Liquid Crystal on Silicon http://dx.doi.org/10.5772/intechopen.72670 239

**Figure 22.** 4-bar pattern with the pitch of 0.004 μ is projected in each field.

### **5. Conclusion**

The result and analysis are mentioned as follows: The design has fulfilled the requirement as shown in **Table 2**. Two configurations of short throw ratio projection lens are fabricated and

*Item Design specification Actual* 1 Pixels size in 1 m 1 mm <0.5 mm

3 Short throw ratio <0.4 <0.3

**Table 3.** The comparison between design specification and actual value.

238 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

2 Lens type Refractive and reflective Refractive and reflective

under test.

**Figure 21.** At room light on (night).

**No. Specification for short throw factor lens**

Being designed by Koehler illumination and telecentric optics, the systems, having the optimized optical parameters, could be achieved. The results for two system requirement are promising, better than other structures. As the systems are built, the optimized performance should be expected. The partial coherence analysis has been applied to verify the system reaching 4K2K.

The chapter presents the design of a short throw projector optical system, and the throw ratio is 0.3, with a single aspheric mirror and the least number of spherical lens. It provides a wide angle projection lens system with partial coherence source parameter provided. The throw ratio is less than 0.3. The procedures of the optical design and illumination are presented.

### **5.1. Very short projecting distance optical system**

With regard to throw ratio that can be less than 0.2, the design has also been carried out. While tilting the mirror at 8°, the throw ratio is 0.186663, as shown in **Figure 23**. However, the image may be keystone, and it can be corrected by the Scheimpflug effect. The image may be corrected by slightly tilting the object, and the corrected nondistorted image may be formed.

**References**

[1] Chung F-C, Ho F-C, Wu Y-L. High-resolution 60-in liquid crystal rear-projection TV. In:

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[3] Matsumoto S, Amano R, Okuda M, Adachi T, Okuno S. Ultra-short Throw Distance Front Projector with Mirror-Lens Hybrid Projection Optical System. 9.4-2 Consumer Electronics, 2008. ICCE 2008. Digest of Technical Papers. In: International Conference on

[4] Abe T, Mashitani K, Kanayama H. Floor-Projected 3D system by 3D ready Ultra Short Throw Distance Projector. In: IEEE International Conference on Consumer Electronics

[6] Sidney F. Ray, Applied Photograpic Optics, Ch.64. London: Focal Press; 1988. pp. 453-468

[9] Huang J-W. The optical design of ultrashort throw system for panel emitted theater video system. In: International Conference on Optical and Photonic Engineering (icO-

[10] Huang J-W. The design and fabrication of common optical components lithography lens. In: International Conference on Optical and Photonic Engineering (icOPEN 2015)

[11] Huang J-W. Optical design of ultra-short throw LCoS projection system. In: ODF2016 International Conference on Optics-Photonics Design & Fabrication 2S3-05. Weigarten

[12] Huang J-W. Optical design of a 1-to-1lithography projection. Optical Review. 2016;**23**(5):

[13] Huang J-W. Optical design of ultrashort throw liquid crystal on silicon projection sys-

[14] Huang J-W. Chap.15.7.2 and Chap. 38. Design and fabrication of optro-mechatronics system. Taipei, Taiwan, R.O.C.: Wunan Bookstore Co. http://www.wunan.com.tw/book-

Projection Displays 2000: Sixth in a Series", Proc. SPIE 3954. 2000

[2] http://www.sony.net/Products/4k-ultra-short-throw/

[5] DLP, https://en.wikipedia.org/wiki/Digital\_Light\_Processing

[7] Charbonneau M. Short throw projector system. Thales Co; 2012

[8] Code V 11. Optimization: Synopsys Co; 2017

PEN 2015), Proc. SPIE 9524-134; 2015

tem. Optical Engineering. 2017;**56**(5):051408

Date 9-13 January 2008

(ICCE); 2011. pp. 757-758

Proc. SPIE 9524-69; 2015

Germany; 2016

detail.asp?no=11702

870-877

**Figure 23.** The tilt-mirror projector.

#### **5.2. Other issues**

The zoom system can be done. It could be zoomed by various distance of first lens, and the 1 to 1.33, by replacing with zoom optics of relay lens.

In conclusion, the optical system has been fabricated and installed in a three-panel forward looking projector system. It has been demonstrated and reached to 4K2K format. The application can be used for other projections such as automobile HUD, VR, glass-type display, smart phone external display, and others can be easily applied.

### **Acknowledgements**

The study is supported by the grants from Ministry of Science and Technology, Taiwan, Republic of China (MOST 104-2221-E-492-040-)and(MOST-2622-E-492\_029-CC3). We thank the cooperation of Professor C.H. Chen, and Mr. Wei-Cheng Lin. We deeply thank Dr. Shih-Feng Tseng for his sincerely instruction and encouragement.

### **Author details**

Jiun-Woei Huang1,2\*

\*Address all correspondence to: jwhuang@narlabs.org.tw

1 National Applied Laboratories, Instrument Technology Research Center, Hsin Chu, Taiwan, R.O.C

2 Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan, R.O.C

### **References**

**5.2. Other issues**

**Figure 23.** The tilt-mirror projector.

**Acknowledgements**

**Author details**

Jiun-Woei Huang1,2\*

Chu, Taiwan, R.O.C

to 1.33, by replacing with zoom optics of relay lens.

240 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

phone external display, and others can be easily applied.

Feng Tseng for his sincerely instruction and encouragement.

\*Address all correspondence to: jwhuang@narlabs.org.tw

1 National Applied Laboratories, Instrument Technology Research Center, Hsin

2 Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan, R.O.C

The zoom system can be done. It could be zoomed by various distance of first lens, and the 1

In conclusion, the optical system has been fabricated and installed in a three-panel forward looking projector system. It has been demonstrated and reached to 4K2K format. The application can be used for other projections such as automobile HUD, VR, glass-type display, smart

The study is supported by the grants from Ministry of Science and Technology, Taiwan, Republic of China (MOST 104-2221-E-492-040-)and(MOST-2622-E-492\_029-CC3). We thank the cooperation of Professor C.H. Chen, and Mr. Wei-Cheng Lin. We deeply thank Dr. Shih-


**Chapter 12**

**Provisional chapter**

**Recent Dispersion Technology Using Liquid Crystal**

Lyotropic liquid crystals have prospective potentials for several industrial applications and also being a key technology in terms of the quality assurance of a product, drug carrier, as well as interpretation of biological phenomena. This chapter will provide the recent topics on several applications of liquid crystals in the cosmetic and pharmaceutical fields and review how to generate the lyotropic liquid crystals in the amphiphilic material system on the basis of the phase behavior and why the liquid crystal structure can

**Keywords:** liquid crystal-based emulsification, nanoemulsion, vesicle, cubosome,

In a few decades, formulation technology in the fields of cosmetics and pharmaceutics has evolved owing to the advanced nanotechnologies involving theory, computational simulation, and analytical devices, and nowadays, various forms such as a capsule, tablet, poultice, and liquid emulsion can be designed in consideration of usability, quality assurance, as well as efficacy of an active ingredient. Colloid science is a very strong tool to understand and control these points and eventually most of formulations regardless of soft and hard matters. In addition, the stuff we are made of, blood, organ, and bone, contains colloidal particles. Since the industrial era, new kinds of colloid-containing products, including paint, foam, pastes,

The colloidal system is referred to be a system in which one phase is homogeneously dispersed in another phase. It seems to be the similar relation of solute and solvent, while this dispersion system should be little soluble mutually. Both the dispersed phase and continuous phase are

**Recent Dispersion Technology Using Liquid Crystal**

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

DOI: 10.5772/intechopen.74156

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.74156

impact the respective application.

hexosome, drug delivery vehicle

Yuji Yamashita

**Abstract**

**1. Introduction**

and so on, have been developed.

Yuji Yamashita

#### **Recent Dispersion Technology Using Liquid Crystal Recent Dispersion Technology Using Liquid Crystal**

DOI: 10.5772/intechopen.74156

#### Yuji Yamashita Yuji Yamashita

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.74156

**Abstract**

Lyotropic liquid crystals have prospective potentials for several industrial applications and also being a key technology in terms of the quality assurance of a product, drug carrier, as well as interpretation of biological phenomena. This chapter will provide the recent topics on several applications of liquid crystals in the cosmetic and pharmaceutical fields and review how to generate the lyotropic liquid crystals in the amphiphilic material system on the basis of the phase behavior and why the liquid crystal structure can impact the respective application.

**Keywords:** liquid crystal-based emulsification, nanoemulsion, vesicle, cubosome, hexosome, drug delivery vehicle

### **1. Introduction**

In a few decades, formulation technology in the fields of cosmetics and pharmaceutics has evolved owing to the advanced nanotechnologies involving theory, computational simulation, and analytical devices, and nowadays, various forms such as a capsule, tablet, poultice, and liquid emulsion can be designed in consideration of usability, quality assurance, as well as efficacy of an active ingredient. Colloid science is a very strong tool to understand and control these points and eventually most of formulations regardless of soft and hard matters. In addition, the stuff we are made of, blood, organ, and bone, contains colloidal particles. Since the industrial era, new kinds of colloid-containing products, including paint, foam, pastes, and so on, have been developed.

The colloidal system is referred to be a system in which one phase is homogeneously dispersed in another phase. It seems to be the similar relation of solute and solvent, while this dispersion system should be little soluble mutually. Both the dispersed phase and continuous phase are

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

in gas, liquid, solid states, and may be in liquid crystal (LC) state, and generally many industrial products can be categorized by these phase states (**Figure 1**) [1]. Typically, the emulsified products such as milk consist of oil (oil phase) and water (aqueous phase), namely being a liquid-liquid dispersion system. When one liquid is dispersed in another liquid, the dispersion system would be called "lotion" for a transparent solution or "emulsion" for a turbid solution. Thus, the colloid dispersion system can be classified into two types, in which one is "molecular colloid" or "association colloid," and the other "dispersed colloid." The molecular colloids are known to be formed in polymer solutions such as starch and protein, and the association colloids are micellar solution consisting of surfactant molecules. These two colloid systems are thermodynamically stable and spontaneously formed in a solvent, generally called "solubilizing system." This system has been utilized for cleansing, the targeting drug delivery of a poorly soluble compound encapsulated in micelle, and so on. On the other hand, the dispersed colloid is unstable and separated into two phases sooner or later, and many of formulations, such as liquid-liquid emulsion and liquid-solid suspension, are concerned.

The first topic will explain emulsion systems stabilized by LCs and the unique properties, and note that LC can be used as a stabilizer for emulsion. The second topic may be more common for the recent researchers of LCs and will review various LC dispersions that are prospective

First, LC used for cosmetics and pharmaceutics is explained in brief. As known well, the LC can be classified into "lyotropic" and "thermotropic" LCs, which may be defined by their dependent parameters, concentration and temperature, respectively. In some cases, they cannot be definitively distinguished by their features, for example, the nematic phase is often observed in the thermotropic LC, but a peculiar surfactant solution system forms it at certain temperature [2]. In addition, the identical LC structure may be termed independently, for example, hexagonal LC for lyotropic system and columnar LC for thermotropic one. The principal difference between two LCs is constituent; the representative compound to form the lyotropic LC is surfactant, and the thermotropic LC is formed by anisotropic molecules with a mesogen group. Some surfactants have mesogen groups in the molecule as well, whereas the important interactions in the lyotropic LC system should be solvation and hydrophobic interaction rather than molecular interactions via the mesogen group that can provide the translational order and optical anisotropy. Therefore, most of the surfactant cannot work in the absence of solvent and

The surfactant is paraphrased by amphiphiles which have the dual character, hydrophilicity and lipophilicity, derived from hydrophilic and lipophilic groups. The thermodynamic properties of amphiphiles in aqueous solution are controlled by the hydrophilic group to avoid contact with water, referring to "hydrophobic effect" [3]. This leads to spontaneous formation of micelle at lower concentration of surfactant (above critical micellar concentration, CMC) and generally liquid crystals at higher concentration. The formation of self-assembled bodies is predominantly determined by an entropic contribution which arises from the local structur-

At high concentrations, surfactants can self-assemble into lyotropic LCs and their structures depend on the concentration. **Figure 2** shows schematic structures of the series of typical lyotropic LCs formed in a surfactant system. Cubic LC is very stiff and optically isotropic,

cubic LCs are furthermore classified into 230 kinds of the crystal lattice with symmetries called space group. The space group can be assigned by the characteristic reflection plane

infinitely elongated rod-like micelles are packed in the hexagonal array and shows optical anisotropy. Lamellar LC (Lα) consists of one-dimensionally stacked bilayers and also shows optical anisotropy. The reverse-type micelle and LCs except for Lα are formed in the surfac-

), reverse discontinuous (I<sup>2</sup>

) and bicontinuous cubic LC (V<sup>1</sup>

Recent Dispersion Technology Using Liquid Crystal http://dx.doi.org/10.5772/intechopen.74156 245

) has the two-dimensional structure that the

) and bicontinuous cubic LC (V<sup>2</sup>

). These

),

**2. Lyotropic liquid crystal formed in surfactant system**

vehicles for the drug delivery system.

rarely forms LC by itself.

ing of water, known as iceberg structure.

basically divided into two types: discontinuous (I1

).

relevant to Miller indices. Hexagonal LC (H<sup>1</sup>

tant solution; reverse micelle (L<sup>2</sup>

and reverse hexagonal LC (H<sup>2</sup>

This chapter will introduce unstable colloid dispersion systems using LC. One may have doubt on the relation between the colloid dispersion and LC. However, this intermediate state has a potential to generate new value and some liquid crystals have been already contributed to the formulation technology. Here, the following two topics will be separately mentioned because LCs are applied in different manners.


**Figure 1.** Various colloidal dispersion systems [1].

The first topic will explain emulsion systems stabilized by LCs and the unique properties, and note that LC can be used as a stabilizer for emulsion. The second topic may be more common for the recent researchers of LCs and will review various LC dispersions that are prospective vehicles for the drug delivery system.

### **2. Lyotropic liquid crystal formed in surfactant system**

in gas, liquid, solid states, and may be in liquid crystal (LC) state, and generally many industrial products can be categorized by these phase states (**Figure 1**) [1]. Typically, the emulsified products such as milk consist of oil (oil phase) and water (aqueous phase), namely being a liquid-liquid dispersion system. When one liquid is dispersed in another liquid, the dispersion system would be called "lotion" for a transparent solution or "emulsion" for a turbid solution. Thus, the colloid dispersion system can be classified into two types, in which one is "molecular colloid" or "association colloid," and the other "dispersed colloid." The molecular colloids are known to be formed in polymer solutions such as starch and protein, and the association colloids are micellar solution consisting of surfactant molecules. These two colloid systems are thermodynamically stable and spontaneously formed in a solvent, generally called "solubilizing system." This system has been utilized for cleansing, the targeting drug delivery of a poorly soluble compound encapsulated in micelle, and so on. On the other hand, the dispersed colloid is unstable and separated into two phases sooner or later, and many of formulations,

This chapter will introduce unstable colloid dispersion systems using LC. One may have doubt on the relation between the colloid dispersion and LC. However, this intermediate state has a potential to generate new value and some liquid crystals have been already contributed to the formulation technology. Here, the following two topics will be separately mentioned

such as liquid-liquid emulsion and liquid-solid suspension, are concerned.

because LCs are applied in different manners.

**Figure 1.** Various colloidal dispersion systems [1].

(2) LC dispersions

(1) Emulsification technology using self-assemblies

244 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

First, LC used for cosmetics and pharmaceutics is explained in brief. As known well, the LC can be classified into "lyotropic" and "thermotropic" LCs, which may be defined by their dependent parameters, concentration and temperature, respectively. In some cases, they cannot be definitively distinguished by their features, for example, the nematic phase is often observed in the thermotropic LC, but a peculiar surfactant solution system forms it at certain temperature [2]. In addition, the identical LC structure may be termed independently, for example, hexagonal LC for lyotropic system and columnar LC for thermotropic one. The principal difference between two LCs is constituent; the representative compound to form the lyotropic LC is surfactant, and the thermotropic LC is formed by anisotropic molecules with a mesogen group. Some surfactants have mesogen groups in the molecule as well, whereas the important interactions in the lyotropic LC system should be solvation and hydrophobic interaction rather than molecular interactions via the mesogen group that can provide the translational order and optical anisotropy. Therefore, most of the surfactant cannot work in the absence of solvent and rarely forms LC by itself.

The surfactant is paraphrased by amphiphiles which have the dual character, hydrophilicity and lipophilicity, derived from hydrophilic and lipophilic groups. The thermodynamic properties of amphiphiles in aqueous solution are controlled by the hydrophilic group to avoid contact with water, referring to "hydrophobic effect" [3]. This leads to spontaneous formation of micelle at lower concentration of surfactant (above critical micellar concentration, CMC) and generally liquid crystals at higher concentration. The formation of self-assembled bodies is predominantly determined by an entropic contribution which arises from the local structuring of water, known as iceberg structure.

At high concentrations, surfactants can self-assemble into lyotropic LCs and their structures depend on the concentration. **Figure 2** shows schematic structures of the series of typical lyotropic LCs formed in a surfactant system. Cubic LC is very stiff and optically isotropic, basically divided into two types: discontinuous (I1 ) and bicontinuous cubic LC (V<sup>1</sup> ). These cubic LCs are furthermore classified into 230 kinds of the crystal lattice with symmetries called space group. The space group can be assigned by the characteristic reflection plane relevant to Miller indices. Hexagonal LC (H<sup>1</sup> ) has the two-dimensional structure that the infinitely elongated rod-like micelles are packed in the hexagonal array and shows optical anisotropy. Lamellar LC (Lα) consists of one-dimensionally stacked bilayers and also shows optical anisotropy. The reverse-type micelle and LCs except for Lα are formed in the surfactant solution; reverse micelle (L<sup>2</sup> ), reverse discontinuous (I<sup>2</sup> ) and bicontinuous cubic LC (V<sup>2</sup> ), and reverse hexagonal LC (H<sup>2</sup> ).


**Figure 2.** Summary of self-assembly structures formed in surfactant systems, and relationship between the structure and three parameters, critical packing parameter (CPP), hydrophilic-lipophilic balance (HLB), and interfacial curvature.

Mean curvature: *H* = \_\_1

solution, H<sup>1</sup>

: hexagonal LC, V<sup>1</sup>

mean curvature corresponds to *H* = 1/R (R = R<sup>1</sup> = R<sup>2</sup>

to small in the order corresponding to L1

interfacial free energy per surfactant molecule (*μN*

**2.2. Critical packing parameter (CPP)**

Gaussian curvature: *G* = \_\_1

2( \_\_1 *R*1 + \_\_1

: bicontinuous LC, La: lamellar LC, S: surfactant solid, and II: two phase.

, Lα, V<sup>2</sup>

, H<sup>2</sup> , I2 , L2

) can be written as follows [4]:

In the case of a spherical micelle, which is formed at the low surfactant concentration, the

[2] because of its isotropic structure. On the other hand, anisotropic structures, such as

for the cylindrical structure, *H* ~ 0 and *G* ~ 0 for the bilayer structure. In general, the positive curvature indicates convex toward the water phase, and contrarily the negative one is concave. Thus, the curvature continuously changes from positive to negative or from large

The LC structures are governed geometrically by the volume fraction of the self-assembly occupied in space of the solution and the molecular structure of surfactant composed in the system. The surfactant molecules can be arranged in a self-assembly under a given condition so that the interfacial area per molecule will be minimized in order to avoid the contact of the alkyl chain and water. The morphology of the self-assembly is determined by the balance of two opposing forces, hydrophobic attraction at the alkyl chain-water interface, and repulsive force between the head groups of surfactants (ionic repulsion, hydration force, steric hindrance, etc.). The

0

, I1 , H<sup>1</sup> , V1

cylindrical micelle and bilayer structure, give different curvatures; *H* = 1/(2R<sup>1</sup>

**Figure 3.** Schematic phase diagram of a binary surfactant/water system. W: monodispersed solution, L<sup>1</sup>

*R*1 × \_\_1 *R*2

*<sup>R</sup>*2) (1)

) and the Gaussian curvature is *G* = 1/R

Recent Dispersion Technology Using Liquid Crystal http://dx.doi.org/10.5772/intechopen.74156

(2)

: micellar

247

) and *G* ~ 0

as shown in **Figure 2**.

A schematic phase diagram in a binary surfactant/water system is demonstrated in **Figure 3**, indicating that all LCs not always appear over the concentration range. The type of LC formed in the system depends on the kind of surfactant, added oil, and additive as well as surfactant concentration. Temperature is also a factor to determine the micelle and LC structure. The temperature-dependent phase transitions can be observed in **Figure 3**, for example, micellar solution (L1 ) → two phase (II), and hexagonal LC (H<sup>1</sup> ) → L1 . Any phase transitions in a surfactant system are always relevant to interaction between surfactant and solvent, and three important parameters, interfacial curvature, critical packing parameter (CPP), hydrophile-lipophile balance (HLB) number, prevailing in the academic and industrial fields are applied to understanding and controlling the self-assembly structures and the phase transition phenomena. The concentration-dependent LC structures can also be interpreted by these parameters.

#### **2.1. Interfacial curvature**

The LC structure is characterized by the interfacial curvature (main curvature). In principle, overall area on the interface can be defined as the mean curvature (*H*) and Gaussian curvature (*G*) using the radii of the main curvatures, R<sup>1</sup> and R<sup>2</sup>

**Figure 3.** Schematic phase diagram of a binary surfactant/water system. W: monodispersed solution, L<sup>1</sup> : micellar solution, H<sup>1</sup> : hexagonal LC, V<sup>1</sup> : bicontinuous LC, La: lamellar LC, S: surfactant solid, and II: two phase.

$$\text{Mean curvature:} \qquad H = \frac{1}{2} \left( \frac{1}{R\_1} + \frac{1}{R\_2} \right) \tag{1}$$

$$\text{Gaussian curvature:} \qquad G = \frac{1}{R\_1} \times \frac{1}{R\_2} \tag{2}$$

In the case of a spherical micelle, which is formed at the low surfactant concentration, the mean curvature corresponds to *H* = 1/R (R = R<sup>1</sup> = R<sup>2</sup> ) and the Gaussian curvature is *G* = 1/R [2] because of its isotropic structure. On the other hand, anisotropic structures, such as cylindrical micelle and bilayer structure, give different curvatures; *H* = 1/(2R<sup>1</sup> ) and *G* ~ 0 for the cylindrical structure, *H* ~ 0 and *G* ~ 0 for the bilayer structure. In general, the positive curvature indicates convex toward the water phase, and contrarily the negative one is concave. Thus, the curvature continuously changes from positive to negative or from large to small in the order corresponding to L1 , I1 , H<sup>1</sup> , V1 , Lα, V<sup>2</sup> , H<sup>2</sup> , I2 , L2 as shown in **Figure 2**.

#### **2.2. Critical packing parameter (CPP)**

A schematic phase diagram in a binary surfactant/water system is demonstrated in **Figure 3**, indicating that all LCs not always appear over the concentration range. The type of LC formed in the system depends on the kind of surfactant, added oil, and additive as well as surfactant concentration. Temperature is also a factor to determine the micelle and LC structure. The temperature-dependent phase transitions can be observed in **Figure 3**, for example, micellar solu-

**Figure 2.** Summary of self-assembly structures formed in surfactant systems, and relationship between the structure and three parameters, critical packing parameter (CPP), hydrophilic-lipophilic balance (HLB), and interfacial curvature.

system are always relevant to interaction between surfactant and solvent, and three important parameters, interfacial curvature, critical packing parameter (CPP), hydrophile-lipophile balance (HLB) number, prevailing in the academic and industrial fields are applied to understanding and controlling the self-assembly structures and the phase transition phenomena. The concentration-dependent LC structures can also be interpreted by these parameters.

The LC structure is characterized by the interfacial curvature (main curvature). In principle, overall area on the interface can be defined as the mean curvature (*H*) and Gaussian curvature

and R<sup>2</sup>

) → L1

. Any phase transitions in a surfactant

) → two phase (II), and hexagonal LC (H<sup>1</sup>

246 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

tion (L1

**2.1. Interfacial curvature**

(*G*) using the radii of the main curvatures, R<sup>1</sup>

The LC structures are governed geometrically by the volume fraction of the self-assembly occupied in space of the solution and the molecular structure of surfactant composed in the system. The surfactant molecules can be arranged in a self-assembly under a given condition so that the interfacial area per molecule will be minimized in order to avoid the contact of the alkyl chain and water. The morphology of the self-assembly is determined by the balance of two opposing forces, hydrophobic attraction at the alkyl chain-water interface, and repulsive force between the head groups of surfactants (ionic repulsion, hydration force, steric hindrance, etc.). The interfacial free energy per surfactant molecule (*μN* 0 ) can be written as follows [4]:

$$
\mu\_N^0 = \gamma a + \frac{K}{a} \tag{3}
$$

methods such as the phase inversion temperature (PIT) method [15], D-phase emulsification [16], quenching method [17], and liquid crystal (LC) emulsification [18], which are attributed to stability at the oil-water interface accumulated by surfactant molecules or self-assemblies. The LC emulsification method was discovered by Suzuki et al. and referred to the process that an oil phase was added directly to a lamellar liquid crystal (Lα) phase, and then dispersed by agitation to produce an emulsion (**Figure 4**) [18]. The key to LC method is to select an appropriate surfactant that preferentially forms Lα phase, as well as constituents of aqueous phase. According to CPP, the surfactant with a balanced HLB number, in general, a two tails surfactant tends to form Lα. This emulsification method is achieved in two steps corresponding to the arrows in **Figure 4**. In the first step, the oil phase is added and dispersed into the Lα phase composed of surfactant/glycerol/water. In the second step, water is poured into the oil in Lα (O/LC) to form an O/W emulsion. This LC method can form a stable emulsion because the LC phase is present as "third phase" surrounding the dispersed oil phase and physically prohibits coalescence of emulsion droplets. The stabilization mechanism of emulsion can be referred to the other emulsification technologies such as Pickering emulsification [19] and three-phase emulsification [20], collectively named "Active Interfacial Modifier

Recent Dispersion Technology Using Liquid Crystal http://dx.doi.org/10.5772/intechopen.74156 249

**Figure 4.** Procedure of LC emulsification in the ternary phase diagram of b-branched L-arginine hexyldecyl phosphate

which oil is added then in order to form the two phase LC+O (O/LC) (first step). Finally, O/W emulsion (LC+O+W) is obtained by adding water to the O/LC solution (second step). W: water phase, O: oil phase, and LC: liquid crystal phase.

R10MP-1Arg/glycerol/water forms the lamellar LC, in

R10MP-1Arg)/glycerol/oil/water system [18]. Premixture of R<sup>6</sup>

(AIM)" [21, 22].

(R<sup>6</sup>

where *K* is the constant, γ is the interfacial tension, and *a* is the cross-sectional area of the surfactant head group at the interface. The first and second terms in the equation represent attraction and repulsion, respectively. Assuming that these interactions would operate within the same interfacial area, the optimized effective cross-sectional area per molecule (*aS* ) is estimated from the minimum *μN* 0 .

Israelachivili proposed "critical packing parameter (CPP)," which allows one to predict the morphology of the self-assembly [4]. CPP has the non-dimensional unit and can be calculated using the volume of alkyl chain (*VL* ), the length of the extended alkyl chain (*l*), and *aS*

$$\text{CPP} = \frac{V\_1}{a\_s l} \tag{4}$$

CPP gives a geometric characterization of a surfactant molecule and will be seen to be very useful when discussing the type of self-organized structure formed by a given amphiphile. Considering what surfactants fall into the different categories of the self-assembly structures shown in **Figure 2**, we note that CPP characterizes the self-assembly structure, for example, the CPP < 1/3 for the spherical micelles (L<sup>1</sup> , I1 ), 1/3 ~ 1/2 for the cylindrical micelles (H<sup>1</sup> ), ~1 for the bilayer structure (Lα). For the nonionic surfactant, CPP becomes smaller with increasing the polymerization degree of the hydrophilic group [5–7], indicating that curvature changes toward positive.

#### **2.3. Hydrophile-lipophile balance (HLB) number**

The HLB number has been utilized as a parameter which characterizes the surfactant and would be widely spreading in the industrial field because of the chain length distribution of the commercial surfactants.

HLB denotes the nature of surfactant in terms of hydrophilicity and lipophilicity. Griffin [8, 9] codified the HLB numbers for nonionic surfactants. Till now, several equations have been proposed to calculate the HLB number for different surfactants including ionic surfactants [10–14]. Generally, the HLB number can be calculated from the hydrophilic and lipophilic portions of the molecule. The HLB number is a useful parameter for selection of surfactants suitable for various applications (e.g., emulsifier, solubilizer, wetting agent, and antifoamer).

### **3. Formulation utilizing self-assembly**

#### **3.1. Liquid crystal emulsification**

Since an emulsion is a thermodynamically unstable system, the state and stability are greatly influenced by the preparation process. This can be understood from the several emulsification methods such as the phase inversion temperature (PIT) method [15], D-phase emulsification [16], quenching method [17], and liquid crystal (LC) emulsification [18], which are attributed to stability at the oil-water interface accumulated by surfactant molecules or self-assemblies.

*μN*

248 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

0 .

CPP <sup>=</sup> *<sup>V</sup>*\_\_\_*<sup>L</sup>*

example, the CPP < 1/3 for the spherical micelles (L<sup>1</sup>

**2.3. Hydrophile-lipophile balance (HLB) number**

**3. Formulation utilizing self-assembly**

**3.1. Liquid crystal emulsification**

using the volume of alkyl chain (*VL*

curvature changes toward positive.

the commercial surfactants.

from the minimum *μN*

(H<sup>1</sup>

<sup>0</sup> = γ*a* + \_\_ *K*

where *K* is the constant, γ is the interfacial tension, and *a* is the cross-sectional area of the surfactant head group at the interface. The first and second terms in the equation represent attraction and repulsion, respectively. Assuming that these interactions would operate within the

Israelachivili proposed "critical packing parameter (CPP)," which allows one to predict the morphology of the self-assembly [4]. CPP has the non-dimensional unit and can be calculated

CPP gives a geometric characterization of a surfactant molecule and will be seen to be very useful when discussing the type of self-organized structure formed by a given amphiphile. Considering what surfactants fall into the different categories of the self-assembly structures shown in **Figure 2**, we note that CPP characterizes the self-assembly structure, for

), ~1 for the bilayer structure (Lα). For the nonionic surfactant, CPP becomes smaller with increasing the polymerization degree of the hydrophilic group [5–7], indicating that

The HLB number has been utilized as a parameter which characterizes the surfactant and would be widely spreading in the industrial field because of the chain length distribution of

HLB denotes the nature of surfactant in terms of hydrophilicity and lipophilicity. Griffin [8, 9] codified the HLB numbers for nonionic surfactants. Till now, several equations have been proposed to calculate the HLB number for different surfactants including ionic surfactants [10–14]. Generally, the HLB number can be calculated from the hydrophilic and lipophilic portions of the molecule. The HLB number is a useful parameter for selection of surfactants suitable for

Since an emulsion is a thermodynamically unstable system, the state and stability are greatly influenced by the preparation process. This can be understood from the several emulsification

various applications (e.g., emulsifier, solubilizer, wetting agent, and antifoamer).

, I1

), the length of the extended alkyl chain (*l*), and *aS*

same interfacial area, the optimized effective cross-sectional area per molecule (*aS*

*<sup>a</sup>* (3)

*aS <sup>l</sup>* (4)

), 1/3 ~ 1/2 for the cylindrical micelles

) is estimated

The LC emulsification method was discovered by Suzuki et al. and referred to the process that an oil phase was added directly to a lamellar liquid crystal (Lα) phase, and then dispersed by agitation to produce an emulsion (**Figure 4**) [18]. The key to LC method is to select an appropriate surfactant that preferentially forms Lα phase, as well as constituents of aqueous phase. According to CPP, the surfactant with a balanced HLB number, in general, a two tails surfactant tends to form Lα. This emulsification method is achieved in two steps corresponding to the arrows in **Figure 4**. In the first step, the oil phase is added and dispersed into the Lα phase composed of surfactant/glycerol/water. In the second step, water is poured into the oil in Lα (O/LC) to form an O/W emulsion. This LC method can form a stable emulsion because the LC phase is present as "third phase" surrounding the dispersed oil phase and physically prohibits coalescence of emulsion droplets. The stabilization mechanism of emulsion can be referred to the other emulsification technologies such as Pickering emulsification [19] and three-phase emulsification [20], collectively named "Active Interfacial Modifier (AIM)" [21, 22].

**Figure 4.** Procedure of LC emulsification in the ternary phase diagram of b-branched L-arginine hexyldecyl phosphate (R<sup>6</sup> R10MP-1Arg)/glycerol/oil/water system [18]. Premixture of R<sup>6</sup> R10MP-1Arg/glycerol/water forms the lamellar LC, in which oil is added then in order to form the two phase LC+O (O/LC) (first step). Finally, O/W emulsion (LC+O+W) is obtained by adding water to the O/LC solution (second step). W: water phase, O: oil phase, and LC: liquid crystal phase.

#### **3.2. Nanoemulsion prepared by cubic liquid crystal**

Nanoemulsions are nanosized emulsions, typically, a size of tens to hundreds nanometer, which can be expected to improve the stability of emulsion and the delivery of active ingredients. The term "nanoemulsion" also refers to a mini-emulsion which is fine oil/water or water/oil dispersion stabilized by an interfacial surfactant film. According to the droplet size, the nanoemulsions are apparently transparent or translucent [23–25]. Contrary to the microemulsions, the nanoemulsions are thermodynamically unstable, yet they may have high kinetic stability. Disruption of the nanoemulsions would be processing within hours, days, or weeks through general flocculation, coalescence, and Ostwald ripening. These characteristic properties have put the nanoemulsions to practical use, such as cosmetics [26–28], pharmaceutics [29–34], reaction media for polymerization [35, 36], and agrochemicals [37].

This method, however, is not preferable from the point of environmental view because of a large amount of energy loss. On the other hand, the low-energy methods utilize unique properties of surfactant and in particular the phase transitions that take place during the emulsification process as a result of a change in the spontaneous curvature of the surfactant. The phase transition with the drastic curvature change can be driven by the phase inversion temperature (PIT) method [15, 38] and the phase inversion composition (PIC) method [39]. The preparation methods of nanoemulsions have been widely reported in the nonionic and ionic surfactant systems, by using both of the high- and low-energy methods [23, 24]. Solans et al. had thoroughly investigated low-energy input methods using PIT and PIC and successfully produced finely dispersed nanoemulsions [40–45]. It was also demonstrated that a liquid crystal formation would play an essential role in forming a fine

Yamashita et al. proposed a unique nanoemulsion using a discontinuous cubic LC (I<sup>1</sup>

the semi-stable structure of the nanoemulsion is breaking down gradually by applying a

emulsion. Such a new type of emulsion would be applicable for cosmetics and pharmaceutics as an external application. Since the solution transforms from nanoemulsion to emulsion when shearing force is applied, the solubility of active agent loaded in the hydrophobic compartment of the nanoemulsion should be varied. This can also modulate partition between the formulation and the skin surface (stratum corneum), which is a key factor for transdermal drug delivery

**Figure 6.** Change in transmittance of the nanoemulsion formed in the polyoxyethylene octyldodecyl ether (C12C<sup>8</sup>

water/glycerol/squalane system as a function of time under different shearing rates; 3000 rpm (■), 4000 rpm (○), and 5000 rpm (●) [46]. The transmittance measurements were carried out using the monochromatic light source (l = 550 nm)

and V1

) [46].

251

EOn)/

without any high-energy input (**Figure 5**).

Recent Dispersion Technology Using Liquid Crystal http://dx.doi.org/10.5772/intechopen.74156

do not form such transparent nano-


nanoemulsion [44].

systems [47, 48].

This nanoemulsion is simply obtained by diluting I1

mechanical energy (**Figure 6**). On the other hand, H<sup>1</sup>

at room temperature. The surfactant concentration is 1.4 wt.%.

Contrary to the common emulsions, the I<sup>1</sup>

In industrial fields, it has been paid attention to how to formulate and prepare a stable emulsion. Two major methods for the preparation of fine emulsions are well known: dispersion or high-energy methods, and condensation or low-energy methods [23]. The high-energy method is the most popular procedures to produce a fine emulsion using specific equipment, such as high-shear stirring, high-pressure homogenization, and ultrasonication [24].

**Figure 5.** Quasi-ternary equilibrated phase diagram in the polyoxyethylene octyldodecyl ether (C12C<sup>8</sup> EOn)/water/ glycerol/squalane system at 25°C (top) [46]. The weight ratio of water/glycerol is fixed at 31/69. The arrow in the phase diagram indicates the preparation route of the novel emulsion. Bottom pictures show sample appearances of the solutions prepared by (a) simple mixing and (b) dilution method utilizing the cubic liquid crystal (I<sup>1</sup> ). L<sup>1</sup> : micellar solution, I1 : discontinuous cubic LC, and O: excess oil (O).

This method, however, is not preferable from the point of environmental view because of a large amount of energy loss. On the other hand, the low-energy methods utilize unique properties of surfactant and in particular the phase transitions that take place during the emulsification process as a result of a change in the spontaneous curvature of the surfactant. The phase transition with the drastic curvature change can be driven by the phase inversion temperature (PIT) method [15, 38] and the phase inversion composition (PIC) method [39]. The preparation methods of nanoemulsions have been widely reported in the nonionic and ionic surfactant systems, by using both of the high- and low-energy methods [23, 24]. Solans et al. had thoroughly investigated low-energy input methods using PIT and PIC and successfully produced finely dispersed nanoemulsions [40–45]. It was also demonstrated that a liquid crystal formation would play an essential role in forming a fine nanoemulsion [44].

Yamashita et al. proposed a unique nanoemulsion using a discontinuous cubic LC (I<sup>1</sup> ) [46]. This nanoemulsion is simply obtained by diluting I1 without any high-energy input (**Figure 5**). Contrary to the common emulsions, the I<sup>1</sup> -based nanoemulsion has an abnormal shear-response: the semi-stable structure of the nanoemulsion is breaking down gradually by applying a mechanical energy (**Figure 6**). On the other hand, H<sup>1</sup> and V1 do not form such transparent nanoemulsion. Such a new type of emulsion would be applicable for cosmetics and pharmaceutics as an external application. Since the solution transforms from nanoemulsion to emulsion when shearing force is applied, the solubility of active agent loaded in the hydrophobic compartment of the nanoemulsion should be varied. This can also modulate partition between the formulation and the skin surface (stratum corneum), which is a key factor for transdermal drug delivery systems [47, 48].

**Figure 6.** Change in transmittance of the nanoemulsion formed in the polyoxyethylene octyldodecyl ether (C12C<sup>8</sup> EOn)/ water/glycerol/squalane system as a function of time under different shearing rates; 3000 rpm (■), 4000 rpm (○), and 5000 rpm (●) [46]. The transmittance measurements were carried out using the monochromatic light source (l = 550 nm) at room temperature. The surfactant concentration is 1.4 wt.%.

**Figure 5.** Quasi-ternary equilibrated phase diagram in the polyoxyethylene octyldodecyl ether (C12C<sup>8</sup>

the solutions prepared by (a) simple mixing and (b) dilution method utilizing the cubic liquid crystal (I<sup>1</sup>

: discontinuous cubic LC, and O: excess oil (O).

**3.2. Nanoemulsion prepared by cubic liquid crystal**

250 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

Nanoemulsions are nanosized emulsions, typically, a size of tens to hundreds nanometer, which can be expected to improve the stability of emulsion and the delivery of active ingredients. The term "nanoemulsion" also refers to a mini-emulsion which is fine oil/water or water/oil dispersion stabilized by an interfacial surfactant film. According to the droplet size, the nanoemulsions are apparently transparent or translucent [23–25]. Contrary to the microemulsions, the nanoemulsions are thermodynamically unstable, yet they may have high kinetic stability. Disruption of the nanoemulsions would be processing within hours, days, or weeks through general flocculation, coalescence, and Ostwald ripening. These characteristic properties have put the nanoemulsions to practical use, such as cosmetics [26–28], pharmaceutics [29–34], reaction media for polymerization [35, 36], and agrochemi-

In industrial fields, it has been paid attention to how to formulate and prepare a stable emulsion. Two major methods for the preparation of fine emulsions are well known: dispersion or high-energy methods, and condensation or low-energy methods [23]. The high-energy method is the most popular procedures to produce a fine emulsion using specific equipment, such as high-shear stirring, high-pressure homogenization, and ultrasonication [24].

solution, I1

cals [37].

glycerol/squalane system at 25°C (top) [46]. The weight ratio of water/glycerol is fixed at 31/69. The arrow in the phase diagram indicates the preparation route of the novel emulsion. Bottom pictures show sample appearances of

EOn)/water/

: micellar

). L<sup>1</sup>

### **4. Liquid crystal dispersion**

Liquid crystal dispersions are promising drug carriers and typically referred to vesicle (liposome), cubosome, and hexosome that have two domains to accumulate both hydrophilic and lipophilic ingredients, although the micelle or reverse micelle has either compartment.

#### **4.1. Vesicle and liposome**

A vesicle is a hollow aggregate with a shell made from one or more amphiphilic bilayers. According to the number of bilayer shell, vesicles can be roughly categorized: a vesicle with a single bilayer is called "unilamellar vesicle" and the one with a shell of several bilayers is "multilamellar vesicle (MLV)." MLV is sometimes called "onion vesicle." **Figure 7** exhibits a unilamellar vesicle. Vesicles formed by lipids are termed "liposomes," which are of great interest and have been widely studied because they are simple membrane models for cell. Vesicles or liposomes have no biological functionality, while vesicle formation and fusion should be important in many physiological processes. Liposomes are also important technology in cosmetics and for drug delivery. In both cases, the liposome acts as a delivery vehicle for active material contained inside. The aims of encapsulating the active materials (or drugs) in the liposome are mainly targeting and release control, whereby not only effective delivery but reduction of side-effect can be attained. However, this targeting technology has not been established yet, although gradually developed by recent studies such as protein recognition and stealth vehicle.

Vesicles (or liposomes) are usually not in thermodynamic equilibrium, while they can be kinetically stable for quite long period. As seen in **Figure 8** [49], vesicles are formed in a twophase region, Lα + W, where excess water is separated from the Lα phase. In such systems, the constituent molecules cannot transform to another LC when diluted with water because of their packing restriction of lipophilic chain, and instead vesicles are formed to minimize the energy loss of lamellar membrane edge (*Eedge*) [50, 51].

$$E\_{edge} = \text{Tr} \mathbf{R} \,\gamma\_L \tag{5}$$

depending on the size. General unilamellar vesicles are listed in **Table 1**, where one can compare to various cell sizes [53, 54]. Regarding the topological effect of the vesicle, the surface

**Figure 8.** Phase diagram of the binary DPPC/water system [49]. La: lamellar LC, H: reverse-type hexagonal LC, Q:

: non-flat ripple phase, L<sup>b</sup>

: gel phase, and W: excess water.

Recent Dispersion Technology Using Liquid Crystal http://dx.doi.org/10.5772/intechopen.74156 253

: flat ripple phase, P<sup>b</sup>

reverse-type bicontinuous cubic LC, P<sup>b</sup>

energy depends on the curvature as expressed by Laplace equation

**Figure 7.** Schematic representation of unilamellar vesicle.

*R* is the radius of lamellar sheet (disk) and γ*<sup>L</sup>* is the line tension. On the other hand, the bending energy (*Ebend*) should be required to form the vesicles, expressed by the following equation [52]:

$$E\_{load} = 8\pi\kappa\tag{6}$$

where *k* is the bending modulus. When *Ebend* is smaller than *Eedge*, vesicles are preferentially formed. The unit structure of vesicle is same with Lα and CPPs of both morphologies are assigned to be nearly unity. According to the morphological similarities, the concentric Lαphase can be reversibly transformed to a multi-lamellar vesicle (MLV) by applying a certain shearing force (**Figure 9**) [39].

Practically, unilamellar vesicles with different sizes are used for the drug delivery carrier and cell model, while the bilayers of these vesicles may have different physicochemical properties

**Figure 7.** Schematic representation of unilamellar vesicle.

**4. Liquid crystal dispersion**

252 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

**4.1. Vesicle and liposome**

Liquid crystal dispersions are promising drug carriers and typically referred to vesicle (liposome), cubosome, and hexosome that have two domains to accumulate both hydrophilic and lipophilic ingredients, although the micelle or reverse micelle has either compartment.

A vesicle is a hollow aggregate with a shell made from one or more amphiphilic bilayers. According to the number of bilayer shell, vesicles can be roughly categorized: a vesicle with a single bilayer is called "unilamellar vesicle" and the one with a shell of several bilayers is "multilamellar vesicle (MLV)." MLV is sometimes called "onion vesicle." **Figure 7** exhibits a unilamellar vesicle. Vesicles formed by lipids are termed "liposomes," which are of great interest and have been widely studied because they are simple membrane models for cell. Vesicles or liposomes have no biological functionality, while vesicle formation and fusion should be important in many physiological processes. Liposomes are also important technology in cosmetics and for drug delivery. In both cases, the liposome acts as a delivery vehicle for active material contained inside. The aims of encapsulating the active materials (or drugs) in the liposome are mainly targeting and release control, whereby not only effective delivery but reduction of side-effect can be attained. However, this targeting technology has not been established yet, although gradually

Vesicles (or liposomes) are usually not in thermodynamic equilibrium, while they can be kinetically stable for quite long period. As seen in **Figure 8** [49], vesicles are formed in a twophase region, Lα + W, where excess water is separated from the Lα phase. In such systems, the constituent molecules cannot transform to another LC when diluted with water because of their packing restriction of lipophilic chain, and instead vesicles are formed to minimize the

*Eedge* = 2*R γ<sup>L</sup>* (5)

energy (*Ebend*) should be required to form the vesicles, expressed by the following equation [52]:

*Ebend* = 8 (6)

where *k* is the bending modulus. When *Ebend* is smaller than *Eedge*, vesicles are preferentially formed. The unit structure of vesicle is same with Lα and CPPs of both morphologies are assigned to be nearly unity. According to the morphological similarities, the concentric Lαphase can be reversibly transformed to a multi-lamellar vesicle (MLV) by applying a cer-

Practically, unilamellar vesicles with different sizes are used for the drug delivery carrier and cell model, while the bilayers of these vesicles may have different physicochemical properties

is the line tension. On the other hand, the bending

developed by recent studies such as protein recognition and stealth vehicle.

energy loss of lamellar membrane edge (*Eedge*) [50, 51].

*R* is the radius of lamellar sheet (disk) and γ*<sup>L</sup>*

tain shearing force (**Figure 9**) [39].

depending on the size. General unilamellar vesicles are listed in **Table 1**, where one can compare to various cell sizes [53, 54]. Regarding the topological effect of the vesicle, the surface energy depends on the curvature as expressed by Laplace equation

**Figure 8.** Phase diagram of the binary DPPC/water system [49]. La: lamellar LC, H: reverse-type hexagonal LC, Q: reverse-type bicontinuous cubic LC, P<sup>b</sup> : flat ripple phase, P<sup>b</sup> : non-flat ripple phase, L<sup>b</sup> : gel phase, and W: excess water.

$$P\_{lu} = P\_{out} + \frac{2\gamma}{r} \tag{7}$$

**4.2. Cubosome and hexosome**

Thickness of cell membrane *ca.* 5 nm Small virus 30 nm

Lysosomes 200–500 nm

*E. coli*—a bacterium 2 mm Human red blood cell 9 mm

Human egg 100 mm

Small unilamellar vesicle (SUV) ~ 40 nm 1

Large unilamellar vesicle (LUV) ~200 nm 50

Giant unilamellar vesicle (GUV) 10 mm 250

Cubosome and hexosome are aqueous dispersions of inverted-type bicontinuous cubic [58–62] and hexagonal LCs [63, 64], respectively. Such nanostructured aqueous dispersions with internal hierarchical self-assemblies have received much attention because of their potential applications such as functional food and drug carriers [65–68]. **Figure 10** shows one example of phase diagram in the monoolein/water system [69], where bicontinuous cubic LC (Ia3d, Pn3m) are observed in the composition and temperature ranges. In addition, likely vesicles, two phase, Pn3m + water, is present in the water-rich region where cubosome can be formed. The fully hydrated inverted-type LCs with distinctive nanostructures are internally confined in the

**Figure 10.** Phase diagram of monoolein/water system [69]. FI: fluid isotropic phase, La: lamellar LC, HII: reverse-type

hexagonal LC, Ia3d and Pn3m (space group): reverse-type bicontinuous cubic LC.

**Table 1.** Classification of vesicles by size and relative pressure difference by Laplace equation [53, 54].

**Size Relative pressure difference**

*Pin − Pout = 2γ/r*

Recent Dispersion Technology Using Liquid Crystal http://dx.doi.org/10.5772/intechopen.74156 255

where *Pin* and *Pout* are the inside and outside pressure, *γ* is the interfacial tension, and *r* is the radius of curvature. As shown in **Table 1**, *Pin* for large unilamellar vesicle (LUV) and small unilamellar vesicle (SUV) are 25 and 250 times larger than giant unilamellar vesicle (GUV), respectively. In other words, *Ebend* of the membrane becomes larger with decreasing the vesicle size and then the molecules are less mobile and more ordered. Sakamoto suggested that the bilayer curvature had a significant effect on not only stiffness, but also function of the bilayer membrane [55].

Many methods can be applied to prepare various vesicles, which result in different types of vesicles and size distributions [56, 57]. First of all, it should be noted that vesicles are formed in a specific composition range depending on the kind of surfactant and phospholipid used in the system, and generally in the diluted lamellar phase which refers to the region coexisting the lamellar LC (Lα) and excess water (W) in the phase diagram. In this region, vesicles can be easily prepared by simple shaking, but many of them are MLV. Sonication is typical treatment to form vesicles with single bilayer; the high-frequency sound waves can break up the inhomogeneous stacked bilayers, inducing reassembly of bilayer. Such rough preparation produces SUV with a broad size distribution since the mechanical action is very uneven. Instead, an alternative procedure can be taken to form in particular LUV and GUV, referring to the thin film method: (1) the amphiphile is dispersed in an organic solvent, (2) the organic solvent is distilled away under vacuum to form a thin film of the amphiphile, and then (3) an excess of water is added to the thin film. In addition, dialysis and filtration (extrusion) are often utilized to fractionate the different sizes of vesicles. However, these methods deliver only formation of vesicles with a desirable size and membrane structure, and further technical methods are required to attain the prospective functions of uniform vesicles such as targeting and a large encapsulating ratio.

**Figure 9.** Dynamic phase diagram of SDS/pentanol/water/dodecane system as functions of the volume fraction of bilayer (*f*) and shear rate (*γ* ̇) [77]. I region: defected lamellar LC, II region: multilamellar vesicle (MLV), and III region: nondefected lamellar LC.


**Table 1.** Classification of vesicles by size and relative pressure difference by Laplace equation [53, 54].

#### **4.2. Cubosome and hexosome**

*Pin* = *Pout* +

254 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

and a large encapsulating ratio.

defected lamellar LC.

2*γ*\_\_\_

where *Pin* and *Pout* are the inside and outside pressure, *γ* is the interfacial tension, and *r* is the radius of curvature. As shown in **Table 1**, *Pin* for large unilamellar vesicle (LUV) and small unilamellar vesicle (SUV) are 25 and 250 times larger than giant unilamellar vesicle (GUV), respectively. In other words, *Ebend* of the membrane becomes larger with decreasing the vesicle size and then the molecules are less mobile and more ordered. Sakamoto suggested that the bilayer curvature had a significant effect on not only stiffness, but also function of the bilayer membrane [55]. Many methods can be applied to prepare various vesicles, which result in different types of vesicles and size distributions [56, 57]. First of all, it should be noted that vesicles are formed in a specific composition range depending on the kind of surfactant and phospholipid used in the system, and generally in the diluted lamellar phase which refers to the region coexisting the lamellar LC (Lα) and excess water (W) in the phase diagram. In this region, vesicles can be easily prepared by simple shaking, but many of them are MLV. Sonication is typical treatment to form vesicles with single bilayer; the high-frequency sound waves can break up the inhomogeneous stacked bilayers, inducing reassembly of bilayer. Such rough preparation produces SUV with a broad size distribution since the mechanical action is very uneven. Instead, an alternative procedure can be taken to form in particular LUV and GUV, referring to the thin film method: (1) the amphiphile is dispersed in an organic solvent, (2) the organic solvent is distilled away under vacuum to form a thin film of the amphiphile, and then (3) an excess of water is added to the thin film. In addition, dialysis and filtration (extrusion) are often utilized to fractionate the different sizes of vesicles. However, these methods deliver only formation of vesicles with a desirable size and membrane structure, and further technical methods are required to attain the prospective functions of uniform vesicles such as targeting

**Figure 9.** Dynamic phase diagram of SDS/pentanol/water/dodecane system as functions of the volume fraction of bilayer (*f*) and shear rate (*γ* ̇) [77]. I region: defected lamellar LC, II region: multilamellar vesicle (MLV), and III region: non-

*<sup>r</sup>* (7)

Cubosome and hexosome are aqueous dispersions of inverted-type bicontinuous cubic [58–62] and hexagonal LCs [63, 64], respectively. Such nanostructured aqueous dispersions with internal hierarchical self-assemblies have received much attention because of their potential applications such as functional food and drug carriers [65–68]. **Figure 10** shows one example of phase diagram in the monoolein/water system [69], where bicontinuous cubic LC (Ia3d, Pn3m) are observed in the composition and temperature ranges. In addition, likely vesicles, two phase, Pn3m + water, is present in the water-rich region where cubosome can be formed. The fully hydrated inverted-type LCs with distinctive nanostructures are internally confined in the

**Figure 10.** Phase diagram of monoolein/water system [69]. FI: fluid isotropic phase, La: lamellar LC, HII: reverse-type hexagonal LC, Ia3d and Pn3m (space group): reverse-type bicontinuous cubic LC.

**Author details**

Address all correspondence to: yyamashita@cis.ac.jp

Faculty of Pharmacy, Chiba Institute of Science, Chōshi, Chiba, Japan

[3] Tanford C. The Hydrophobic Effect. New York: Wiley; 1980

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Yuji Yamashita

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**Figure 11.** Cryo-TEM micrograph of cubosome [70]. The bar corresponds to 100 nm.

kinetically dispersed particles upon application of high-energy input in the presence of a suitable stabilizer like surfactant [58, 59, 68]. The internal nanostructures are controlled by CPP of amphiphilic molecule and have specific curvatures *H* and *G*. These aqueous dispersions, cubosome and hexosome, are often characterized by small-angle X-ray scattering (SAXS) and cryo-TEM. As seen in **Figure 11**, the cryo-TEM micrograph clearly demonstrates the internal nanostructures in the dispersions [70].

The feasibility of the nanostructured aqueous dispersions as drug carrier has been investigated since the 2000s, and the advantages of utilizing these dispersions have been reported, for example, solubilization of drug, bioavailability, efficient delivery, reduction of side effects, percutaneous penetration, protection of drug degradation, and release control [71– 76]. However, the number of studies on drug delivery system utilizing these dispersions is still limited regardless of the unique properties so far, and further investigations will be required to understand their potentials for drug carries and also to reveal the interaction of bioactive materials and LC carries while taking the phase behavior of LC into consideration.

### **5. Conclusion**

Beyond expectation, lyotropic liquid crystals are the soft matter familiar to our life, even managing biological functions such as homeostasis in the living system. Recently, we intend to learn or mimic many things from nature to construct artificial products with some function; on the other hand, the scientific technologies that we have ever accumulated would be applicable to reveal a new mechanism of biofunction by integrating several academic fields.

The formulations utilizing the liquid crystals have been contributed to the development of industry and supported our life. This may be a reason why the liquid crystals are constructed by self-assembling of numerous molecules and possess the properties of both liquid and solid. Still, there are many questions on the several applications utilizing the liquid crystals, and thus further investigations of the liquid crystals will clarify and find out unknown phenomena leading to novel functions of the liquid crystals.

### **Author details**

Yuji Yamashita

Address all correspondence to: yyamashita@cis.ac.jp

Faculty of Pharmacy, Chiba Institute of Science, Chōshi, Chiba, Japan

### **References**

**Figure 11.** Cryo-TEM micrograph of cubosome [70]. The bar corresponds to 100 nm.

256 Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

nanostructures in the dispersions [70].

consideration.

**5. Conclusion**

kinetically dispersed particles upon application of high-energy input in the presence of a suitable stabilizer like surfactant [58, 59, 68]. The internal nanostructures are controlled by CPP of amphiphilic molecule and have specific curvatures *H* and *G*. These aqueous dispersions, cubosome and hexosome, are often characterized by small-angle X-ray scattering (SAXS) and cryo-TEM. As seen in **Figure 11**, the cryo-TEM micrograph clearly demonstrates the internal

The feasibility of the nanostructured aqueous dispersions as drug carrier has been investigated since the 2000s, and the advantages of utilizing these dispersions have been reported, for example, solubilization of drug, bioavailability, efficient delivery, reduction of side effects, percutaneous penetration, protection of drug degradation, and release control [71– 76]. However, the number of studies on drug delivery system utilizing these dispersions is still limited regardless of the unique properties so far, and further investigations will be required to understand their potentials for drug carries and also to reveal the interaction of bioactive materials and LC carries while taking the phase behavior of LC into

Beyond expectation, lyotropic liquid crystals are the soft matter familiar to our life, even managing biological functions such as homeostasis in the living system. Recently, we intend to learn or mimic many things from nature to construct artificial products with some function; on the other hand, the scientific technologies that we have ever accumulated would be applicable to reveal a new mechanism of biofunction by integrating several academic fields.

The formulations utilizing the liquid crystals have been contributed to the development of industry and supported our life. This may be a reason why the liquid crystals are constructed by self-assembling of numerous molecules and possess the properties of both liquid and solid. Still, there are many questions on the several applications utilizing the liquid crystals, and thus further investigations of the liquid crystals will clarify and find out unknown phe-

nomena leading to novel functions of the liquid crystals.


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## *Edited by Pankaj Kumar Choudhury*

Liquid crystals exhibit amazingly interesting properties that make them indispensable for several technological applications. The book *Liquid Crystals - Recent Advancements in Fundamental and Device Technologies* is aimed to focus on various aspects of research and development that liquid crystal mediums have come across in recent years. This would be ranging from the physical and chemical properties to the important applications that the liquid crystals have in our everyday life. It is expected that the book will make the expert researchers to be abreast of recent research advancements, whereas the novice researchers will benefit from both the conceptual understanding and the recent developments in the area. Multitudes of research themes and directions pivoted to liquid crystals remain the essence, which the readers would get the glimpse of and move ahead for further investigations.

Photo by prill / iStock

Liquid Crystals - Recent Advancements in Fundamental and Device Technologies

Liquid Crystals

Recent Advancements in Fundamental

and Device Technologies

*Edited by Pankaj Kumar Choudhury*