**2. Ferroelectric liquid crystals**

 In 1974, Meyer suggested theoretically that LCs that form an LC phase with low symmetry should exhibit ferroelectricity [15]. Meyer instructed the synthesis of a liquid crystalline molecule that exhibits the smectic C (SmC) phase and also possesses chiral structure and permanent dipole moment. The structure of the LC molecule (DOBANBC) is shown in Figure 4. As Meyer had expected, DOBANBC was found to exhibit ferroelectricity. After the discovery of ferroelectricity in LCs, an intensive search for FLCs was conducted by many researchers, including LCD developers. As a result, it was determined that not only pure liquid crystalline compounds, but also mixtures of smectic LC compounds and chiral compounds exhibit ferroelectric phases. This was very advantageous for practical applications because clear, defect-free large-area panels could be realized using such mixtures and the properties of the mixtures could be adjusted by the selection of appropriate component compounds. In 1997, a fast FLC display panel was commercially released by Canon.

FLCs belong to the class of smectic LCs that have a layered structure [1, 2, 15]. A typical FLC molecule consists of a central core, a carbonyl group, and a chiral unit (Figure 4). The dipole moment of an FLC molecule is perpendicular to the long molecular axis. FLCs exhibit a chiral smectic C phase (SmC\*) that possesses a helical structure. It should be noted here that to observe ferroelectricity in these materials, the FLCs must be formed into thin films [1] with a thickness of a few micrometers. When an FLC is sandwiched between glass plates to form a film with a thickness of a few micrometers, the helical structure of the SmC\* phase uncoils and a surface-stabilized state (SS-state) is formed in which ferroelectricity appears (Figure 5). The thickness of the FLC film is typically 2 μm when it is used in display applications. The FLC molecules are restricted to only two directions in such thin films. The state is termed as SSstate. The direction of the alignment of FLC molecules is changed by the change in direction of the spontaneous polarization (Figure 6). When an alternating electric field is applied to the SS-FLC, the FLC molecules perform a continuous switching motion. The response time of the electrical switching in the FLCs is typically shorter than 1 ms. The direction of spontaneous polarization is governed by the applied electric field, which causes a change in the properties according to the direction of polarization. The mechanism for the photorefractive effect in FLCs is shown in Figure 7. When laser beams interfere in a mixture of an FLC and a photoconductive compound, internal electric fields are produced between the bright and dark positions of the interference fringe. The direction of spontaneous polarization in the area between the bright and dark positions of the interference fringes is changed by the internal electric field and a striped pattern of the FLC molecule orientations is induced. The process is different from those occur in other organic photorefractive materials. In a photorefractive FLC, the bulk polariza‐ tion responds to the internal electric field. That is the base of the fast switching of FLC molecules.

**Figure 4.** Molecular structures of FLCs.

FLCs belong to the class of smectic LCs that have a layered structure [1, 2, 15]. A typical FLC molecule consists of a central core, a carbonyl group, and a chiral unit (Figure 4). The dipole moment of an FLC molecule is perpendicular to the long molecular axis. FLCs exhibit a chiral smectic C phase (SmC\*) that possesses a helical structure. It should be noted here that to observe ferroelectricity in these materials, the FLCs must be formed into thin films [1] with a thickness of a few micrometers. When an FLC is sandwiched between glass plates to form a film with a thickness of a few micrometers, the helical structure of the SmC\* phase uncoils and a surface-stabilized state (SS-state) is formed in which ferroelectricity appears (Figure 5). The thickness of the FLC film is typically 2 μm when it is used in display applications. The FLC molecules are restricted to only two directions in such thin films. The state is termed as SSstate. The direction of the alignment of FLC molecules is changed by the change in direction of the spontaneous polarization (Figure 6). When an alternating electric field is applied to the SS-FLC, the FLC molecules perform a continuous switching motion. The response time of the

fast FLC display panel was commercially released by Canon.

In 1974, Meyer suggested theoretically that LCs that form an LC phase with low symmetry should exhibit ferroelectricity [15]. Meyer instructed the synthesis of a liquid crystalline molecule that exhibits the smectic C (SmC) phase and also possesses chiral structure and permanent dipole moment. The structure of the LC molecule (DOBANBC) is shown in Figure 4. As Meyer had expected, DOBANBC was found to exhibit ferroelectricity. After the discovery of ferroelectricity in LCs, an intensive search for FLCs was conducted by many researchers, including LCD developers. As a result, it was determined that not only pure liquid crystalline compounds, but also mixtures of smectic LC compounds and chiral compounds exhibit ferroelectric phases. This was very advantageous for practical applications because clear, defect-free large-area panels could be realized using such mixtures and the properties of the mixtures could be adjusted by the selection of appropriate component compounds. In 1997, a

**Figure 3.** Structures of the nematic and smectic phases.

128 Ferroelectric Materials – Synthesis and Characterization

**2. Ferroelectric liquid crystals**

**Figure 5.** Structures of the SmC phase and the SS-state of the SmC phase (SS-FLC).

 

 

**Figure 6.** Electro-optical switching in the SS-state of FLCs.

**Figure 7.** Schematic illustration of the mechanism for the photorefractive effect in FLCs. (a) Two laser beams interfere in the SS-state of the FLC/photoconductive compound mixture; (b) charge generation occurs at the light areas of the interference fringes; (c) electrons are trapped at the trap sites in the light areas, and holes migrate by diffusion or drift in the presence of an external electric field to generate an internal electric field between the light and dark positions; (d) the orientation of the spontaneous polarization vector (i.e., orientation of mesogens in the FLCs) is altered by the internal electric field.

#### - **3. Asymmetric energy exchange in photorefractive materials**

 

130 Ferroelectric Materials – Synthesis and Characterization

**Figure 5.** Structures of the SmC phase and the SS-state of the SmC phase (SS-FLC).

 

**Figure 6.** Electro-optical switching in the SS-state of FLCs.

 

 

 

 

The phase of the refractive index grating formed by photorefractive effect is shifted from the interference fringe because the change in refractive index is induced between the bright and the dark positions of the interference fringe. In an ideal case, the phase of the refractive index grating is shifted from the interference fringe by π/2.This is a distinctive feature of the photorefractive effect. When a refractive index grating is formed via a photochemical reaction or thermal change in density, the change in refractive index occurs at the bright areas and forms a refractive index grating with the same phase as that of the interference fringe (Figure 8(a)). The induced grating diffracts the interfering laser beams; however, the apparent transmitted intensities of the laser beams do not change because beam 1 is diffracted to the direction of beam 2, and beam 2 is diffracted in the direction of beam 1. However, when the phase of the refractive index grating is shifted from that of the interference fringe (photore‐ fractive grating), the apparent transmitted intensity of beam 1 increases and that of beam 2 decreases (Figure 8(b)). This phenomenon is known as the asymmetric energy exchange in the two-beam coupling [3]. The occurrence of the asymmetric energy exchange is the evidence for the photorefractive effect. Therefore, two-beam coupling measurement is the most straight‐ forward way to unambiguously distinguish between the photorefractive effect and other types of grating. In LCs and low-glass-transition temperature polymers, the sign of the electro-optic coefficient is determined by the direction of the applied electric field. A change in the electric field polarity reverses the sign of the gain coefficient due to the change in sign of the electrooptic coefficient. Thus, the amplification and attenuation of beam 1 and beam 2 switches when the polarity of the applied electric field is reversed.

**Figure 8.** Schematic illustrations of (a) photochromic and (b) photorefractive gratings.

A schematic illustration of the setup used for the two-beam coupling experiment is shown in Figure 9(a). Laser beams (p-polarized) are interfered in the sample. An electric field (external electric field) is applied to the sample to increase the efficiency of charge generation in the film. The transmitted intensities of the laser beams through the sample are monitored. If a material exhibits photorefractive effect, an asymmetric energy exchange is observed. The magnitude of photorefractive effect is evaluated by the magnitude of gain coefficient, which is obtained from the two-beam coupling experiment [3]. According to the standard theory of the photo‐ refractive effect with the limit of the ratio of beam intensities (pump/signal) >>1, the intensity of the transmitted signal beam is given by:

$$I = I\_0 \exp\{\Gamma l\},\tag{1}$$

where *I0* is the signal beam intensity, *l* is the interaction length in the sample, and Γ is the gain coefficient. In order to obtain the two-beam coupling gain coefficient, the diffraction condition must be clarified whether it is in the Bragg diffraction regime or in the Raman-Nath diffraction regime. The diffraction conditions are distinguished by a parameter *Q* [3]:

$$\mathbf{Q} = 2\pi\lambda\mathbf{L} / n\Lambda^2 \,\tag{2}$$

where *λ* is the wavelength of the laser, *L* is the interaction path length, *n* is the refractive index, and Λ is the grating spacing. If the *Q* value is larger than 1, the condition is classified to the Bragg regime of optical diffraction in which only one order of diffraction is allowed. If *Q* value is smaller than 1, the condition is classified to the Raman-Nath regime of optical diffraction in which many orders of diffraction are allowed. In order to guarantee the entire Bragg diffraction regime, *Q* > 10 is often required.

The two-beam coupling gain coefficient Γ (cm-1) for the Bragg diffraction condition is calculated according to the following equation [5]:

Dynamic Amplification of Optical Signals by Photorefractive Ferroelectric Liquid Crystals http://dx.doi.org/10.5772/60776 133

$$
\Gamma = \frac{1}{D} \text{ln} \left( \frac{\text{gm}}{1 + m - \text{g}} \right) \tag{3}
$$

where *D* = *L*/cos(*θ*) is the interaction path for the signal beam (*L* = sample thickness, *θ* = propagation angle of the signal beam in the sample), *g* is the ratio of the signal beam intensities behind the sample with and without a pump beam, and *m* is the ratio of the beam intensities (pump/signal) in front of the sample.

**Figure 9.** Schematic illustration of the experimental setup for the two-beam coupling experiment.
