**Three-Dimensional Vector Holograms in Photoreactive Anisotropic Media**

Tomoyuki Sasaki1, Akira Emoto2, Kenta Miura1,

Osamu Hanaizumi1, Nobuhiro Kawatsuki3 and Hiroshi Ono2 *1Department of Electronic Engineering, Graduate School of Engineering, Gunma University, 2Department of Electric Engineering, Nagaoka University of Technology, 3Department of Materials Science and Chemistry, Graduate School of Engineering, University of Hyogo, Japan* 

#### **1. Introduction**

178 Holograms – Recording Materials and Applications

lower environmental demand and higher storage density. The storage density of 2×108 bits/cm2 was obtained in the Fourier-transform holographic data storage by using orthogonal polarization holographic recording, which had a greatly improved signal-to-

Different kinds of multiplexing holographic storage, like polarization multiplexing, circumrotation multiplexing and angle multiplexing, were also realized in fulgide film, where 2 images, 5 images and 18 images were stored at the same position of the film, and diffracted without crosstalk with each other. And the application of the fulgide films in

[1] Yokoyama, Y. (2000). Fulgides for Memories and Switches. Chem. Rev., Vol.100, No.5,

[2] Fan, M. (1997). Photon Storage Principles and Photochromic Materials. Progress in

[3] Bouas-Laurent, H. & Dürr H. (2001). Organic Photochromism. Pure and Applied

[4] Menke, N.; Yao, B.; Wang, Y.; Zheng, Y.; Lei, M.; Chen, G.; Chen, Y.; Fan, M. & Li, T.

[5] Menke, N.; Yao, B.; Wang, Y.; Dong, W.; Lei, M.; Chen, Y.; Fan, M. & Li, T. (2008).

[7] Menke, N.; Yao, B.; Wang, Y. & Chen, Y. (2011). Polarization holography in 3-indoly-

[8] Cheng, M.; Menke, N.; Yao, B.; Wang, Y. & Chen, Y. (2011). Improvement of the

[9] Menke, N.; Yao, B.; Wang, Y.; Zheng, Y.; Lei, M.; Chen, G.; Chen, Y.; Fan, M.; Han, Y.

[10] Tao., S. (December 1998). Optical Holographic Storage (First Edition). Beijing University

[11] Ji, K.; Menke, N.; Menke, N.; Yao, B.; Wang, Y. & Chen, Y. (2011). Holographic

Volume 3, pp.V3-276-V3-280 (July 29-31, 2011, Dalian, China)

Volume2011, ArticleID509507, doi:10.1155/2011/509507, pp.1-20

7, pp.6047-6052 (June 24-26, 2011, Nanjing, China)

Fulgide Films, Journal of Modern Optic, Vol.55, No.6, pp. 1003-1011 [6] Du, J.; Menke, N.; Yao, B.; Wang, Y. & Chen, Y. (2011). Photoreaction constants of fulgide

(2006). Optical Image Processing Using The Photoinduced Anisotropy of

Spectral Relationship of Photoinduced Refractive Index and Absorption Changes in

films at different wavelengths, Proceedings of International Conference on Remote Sensing, Environment and Transportation Engineering 2011, IEEE Catalog Number: CFP1104M-PRT Volume 7, pp.6148-6154 (June 24-26, 2011, Nanjing,

benzylfulgimide/PMMA film. Journal of Atomic, Molecular, and Optical Physics

diffraction efficiency of holographic gratings in Fulgide films by auxiliary light, Proceedings of International Conference on Remote Sensing, Environment and Transportation Engineering 2011, IEEE Catalog Number: CFP1104M-PRT, Volume

& Meng, X. (2003). Holographic Recording Characteristics of a Rewritable Fulgide/PMMA Film, Acta Photonica Sinica, Vol.32, No.7, pp. 819-822 (in

interfermetry based on fulgide film, Proceedings of International Conference on Electronics and Optoelectroonics2011, IEEE Catalog Number: CFP1137N-PRT,

noise ratio of the diffraction image.

pp. 1717-1739

China)

Chinese)

Press, Beijing, pp.267-278

**6. References** 

holographic interferometry was also studied initially.

Chemistry. Vol.73, pp. 639–665

Chemistry, Vol.9, No.2, pp. 170-178 (in Chinese)

Pyrrylfulgide, J. Opt. Soc. Am. A, Vol.23, No.2, pp. 267-271

Polarization gratings, in which optical anisotropy is periodically modulated, are very attractive from the point of view of their interesting optical properties, including polarization selectivity of the diffraction efficiency and polarization conversion in the diffraction process (Nikolova et al., 1984). These properties make polarization gratings useful for numerous optical applications related to polarization discrimination (Davis et al., 2001; Asatryan et al., 2004), control (Nikolova et al., 1997; Hasman et al., 2002), and measurement (Gori, 1999; Provenzano et al., 2006). Polarization gratings can be fabricated by holographic exposure with polarized interference light in photoanisotropic media such as azobenzene-containing polymer (azopolymer) films (Todorov et al., 1984; Ebralidze et al., 1992; Huang and Wagner, 1993; Samui, 2008). Since azobenzene molecules reorient in accordance with polarization of light resulting from trans-cis-trans photoisomerization reactions, periodic structures are formed as spatial distribution of the molecular orientation by holographic recording using vectrial light (i.e., by vector holography). In addition, surface relief gratings are obtained by holographic recording in azopolymers (Rochon et al., 1995; Kim et al., 1995; Ramanujam et al., 1996; Naydenova et al., 1998; Labarthet et al., 1998, 1999). Nikolova et al. have investigated the diffraction properties of various types of vector holograms recorded in side-chain azobenzene polyesters (Nikolova et al., 1996). Birabassov and Galstian have analyzed the relationship of polarization states between holographic recording and reconstruction beams with the use of azopolymers (Birabassov et al., 2001). It has been also demonstrated that vector holograms realize recording and reconstruction of polarized optical images (Ono et al., 2009a, 2009b). In a previous paper, we presented three-dimensional (3D) vector holography, which is a novel concept for holographic recording using vectrial light (Sasaki et al., 2008). Common

vector holograms are recorded in initially isotropic media such as amorphous azopolymers. In contrast, 3D vector holograms are recoded in initially anisotropic media. Since the propagation velocity of light in anisotropic media varies in accordance with the polarization state, standing waves with a multidimensionally varying state of polarization were obtained in the region of overlap. We recorded anisotropic gratings in a liquid crystalline medium by

Three-Dimensional Vector Holograms in Photoreactive Anisotropic Media 181

*m m mm*

( )

*ik z*

*m*

*zz zz*

1

εε

ε

ε ε*xy yx* ==− *n n*

ε ε*xz zx* == − *n n*

ε ε

ε

 ε

2

2

ε

ε

*c*

2 2 2

0 is the angle between the *xy* -plane and 0 **c** , and

*c*

θ

1

exp 0 0 exp *z*

<sup>=</sup>

2 o e e o 2 2

( ) ( ) ( )

*k k kk kk*

1 22 2

ε ε

ε ε

*xx* =+ − *n nn*

−+ + <sup>=</sup>

ε

1 cos sin *z xz m <sup>m</sup> zz*

<sup>−</sup> =− + − −

[ ][ ]

ε

[ ][ ] [ ][ ] [ ][ ] *m zz xy m z xz zy z xx m zz m z zx m z xz*

Here, *m* = 1, 2 , *d* is the film thickness, *n*o and *n*e are the ordinary and extraordinary indexes,

*xx xy xz yx yy yz zx zy zz*

εεε

εεε

<sup>=</sup>

εεε

( ) 2 22 2 2 o eo 0 0 cos cos

( ) 22 2

( ) 2 2

( ) 2 2

θ

eo 0 0 0 cos sin cos

eo 0 0 0 sin cos cos

 θ

eo 0 0 0

θ

θ

( ) 2 22 2 2 o eo 0 0

*yy* =+ − *n nn* cos sin

*yz zy* ==− *n n* sin cos sin

 φ

φ

φ

φ

θφφ

 θ

 θ

*m zz yx m z zx yz z m yy m zz yz zy*

+ − −−

− −− + +

φ

*k k nn n n k k k n k*

( ) ( )( )

−+ + <sup>=</sup>

*k k k kk k*

[ ][ ]

( ) ( )( ) ( ) ( ) ( )( ) ( )( )

projection of 0 **c** onto the *xy* -plane. The dielectric tensor of the medium can be written as

*k k k kk k*

2 2 2

*k k k k k kk k k kk k*

where

1

( )

*ik z*

*z*

2

( ) <sup>2</sup> <sup>2</sup>

e

*c*

1 1 1 *<sup>m</sup>*

*c* <sup>=</sup>

2

**G** ,( ) 0 ≤ ≤*z d* , (3)

<sup>−</sup> **J SGS** = , (2)

**S** , (4)

*z m* 1 o *k k n kk* = − , (5)

 φ , (6)

. (8)

, (7)

 ε

0 is the angle between the *x* -axis and the

, (10)

, (11)

, (12)

, (13)

, (14)

2 2 2

ε ε

ε ε

 εε

**ε** , (9)

2 0 0

1

2

θ

ε

 ε

the 3D vector holography, and investigated their diffraction properties. As a result, it was demonstrated that the 3D vector holography enables formation of higher-order periodical modulation of optical anisotropy. In addition, we observed that the multidimensional distribution exhibited interesting diffraction properties.

The present chapter reported the principle of 3D vector holography in detail, and investigated optical characteristics of 3D vector holograms recorded in a photoreactive anisotropic medium. Interference of two polarized light in anisotropic media was described by employing the extended Jones matrix method. Diffraction properties of the holograms, recorded in the model medium, were observed and the obtained results were analyzed through the use of the finite-difference time-domain (FDTD) method. By comparing the experimental and calculated results, we discussed the adequacy of the formation mechanism of the 3D vector holograms. In addition, the diffraction efficiency was simulated for various recording conditions to reveal the relationship between the multidimensional structure and the optical behaviour.

#### **2. Principle of three-dimensional vector holography**

We consider interference of mutually coherent polarized light in uniaxial anisotropic media. As illustrated in Fig. 1, the *xz* -plane is the incident plane and the *z* -axis is taken normal to the film plane. Assuming that the two recording beams are plane waves and that the amplitude of their incident angles is small, the electric field of interference light is described using the Jones vector as

$$\mathbf{E}(\mathbf{x}, z) = \mathbf{J}\_1(z)\mathbf{E}\_1\exp(ik\_1\mathbf{x}) + \mathbf{J}\_2(z)\mathbf{E}\_2\exp(ik\_2\mathbf{x}),\tag{1}$$

where 1**J** and 2**J** are the extended Jones matrixes of the medium for the two beams, **E**1 and **E**2 are the Jones vectors of the two beams, *k k* 1 11 = ≡ ( ) 2 sin sin πλ θ θ , 2 2 *k k* = sinθ , θ1 and θ 2 are the incident angles of the two beams, and λ is the wavelength in a vacuum. Here, to simplify the analysis, reflection at the air-medium boundaries is neglected. When the ordinary and extraordinary indexes and the direction of the optical axis 0 **c** are homogeneous in the medium, the extended Jones matrix is given by (Lien, 1990, 1997)

Fig. 1. Schematic illustration of arrangement for holographic recording and reconstruction. **E**in is the electric field vector of reconstruction light

$$\mathbf{J}\_m = \mathbf{S}\_m \mathbf{G}\_m \mathbf{S}\_m^{-1} \tag{2}$$

where

180 Holograms – Recording Materials and Applications

the 3D vector holography, and investigated their diffraction properties. As a result, it was demonstrated that the 3D vector holography enables formation of higher-order periodical modulation of optical anisotropy. In addition, we observed that the multidimensional

The present chapter reported the principle of 3D vector holography in detail, and investigated optical characteristics of 3D vector holograms recorded in a photoreactive anisotropic medium. Interference of two polarized light in anisotropic media was described by employing the extended Jones matrix method. Diffraction properties of the holograms, recorded in the model medium, were observed and the obtained results were analyzed through the use of the finite-difference time-domain (FDTD) method. By comparing the experimental and calculated results, we discussed the adequacy of the formation mechanism of the 3D vector holograms. In addition, the diffraction efficiency was simulated for various recording conditions to reveal the

We consider interference of mutually coherent polarized light in uniaxial anisotropic media. As illustrated in Fig. 1, the *xz* -plane is the incident plane and the *z* -axis is taken normal to the film plane. Assuming that the two recording beams are plane waves and that the amplitude of their incident angles is small, the electric field of interference light is described

where 1**J** and 2**J** are the extended Jones matrixes of the medium for the two beams, **E**1 and

simplify the analysis, reflection at the air-medium boundaries is neglected. When the ordinary and extraordinary indexes and the direction of the optical axis 0 **c** are homogeneous in the medium, the extended Jones matrix is given by (Lien, 1990, 1997)

*z*

*y*

θ2 θF θ1

θin

**E**2

**E**in

**E**in is the electric field vector of reconstruction light

**E**1

Fig. 1. Schematic illustration of arrangement for holographic recording and reconstruction.

( ) () ( ) () ( ) 11 1 22 2 **E JE JE** *x z z ik x z ik x* , exp = + exp , (1)

 θ  θ

, 2 2 *k k* = sin

is the wavelength in a vacuum. Here, to

*x*

θ , θ1 and

πλ

0th

−1st

λ

+1st

relationship between the multidimensional structure and the optical behaviour.

**2. Principle of three-dimensional vector holography** 

**E**2 are the Jones vectors of the two beams, *k k* 1 11 = ≡ ( ) 2 sin sin

2 are the incident angles of the two beams, and

using the Jones vector as

θ

distribution exhibited interesting diffraction properties.

$$\mathbf{G}\_m = \begin{bmatrix} \exp\left(ik\_{z1}z\right) & 0\\ 0 & \exp\left(ik\_{z2}z\right) \end{bmatrix}, \left(0 \le z \le d\right), \tag{3}$$

$$\mathbf{S}\_m = \begin{bmatrix} 1 & c\_2 \\ c\_1 & 1 \end{bmatrix} \tag{4}$$

$$k\_{z1} \slash k = \sqrt{n\_{\diamond}^2 - \left(k\_m / k\right)^2} \,, \tag{5}$$

$$\frac{k\_{z2}}{k} = -\frac{\varepsilon\_{xz}}{\varepsilon\_{zz}} \frac{k\_m}{k} + \frac{n\_o n\_e}{\varepsilon\_{zz}} \sqrt{\varepsilon\_{zz} - \left(1 - \frac{n\_e^2 - n\_o^2}{n\_e^2} \cos^2 \theta\_0 \sin^2 \phi\_0 \right) \left(\frac{k\_m}{k}\right)^2},\tag{6}$$

$$\varepsilon\_{1} = \frac{[\left(k\_{m}/k\right)^{2} - \varepsilon\_{zz}]\varepsilon\_{yx} + [\left(k\_{m}/k\right)\left(k\_{z1}/k\right) + \varepsilon\_{zx}]\varepsilon\_{yz}}{[\left(k\_{z1}/k\right)^{2} + \left(k\_{m}/k\right)^{2} - \varepsilon\_{yy}][\left(k\_{m}/k\right)^{2} - \varepsilon\_{zz}] - \varepsilon\_{yz}\varepsilon\_{zy}}\,\tag{7}$$

$$\varepsilon\_{2} = \frac{[\left(k\_{m}/k\right)^{2} - \varepsilon\_{zz}]\varepsilon\_{xy} + [\left(k\_{m}/k\right)\left(k\_{z2}/k\right) + \varepsilon\_{xz}]\varepsilon\_{zy}}{[\left(k\_{z2}/k\right)^{2} - \varepsilon\_{xx}][\left(k\_{m}/k\right)^{2} - \varepsilon\_{zz}] - [\left(k\_{m}/k\right)\left(k\_{z2}/k\right) + \varepsilon\_{xz}][\left(k\_{m}/k\right)\left(k\_{z2}/k\right) + \varepsilon\_{xz}]}} \tag{8}$$

Here, *m* = 1, 2 , *d* is the film thickness, *n*o and *n*e are the ordinary and extraordinary indexes, θ0 is the angle between the *xy* -plane and 0 **c** , and φ0 is the angle between the *x* -axis and the projection of 0 **c** onto the *xy* -plane. The dielectric tensor of the medium can be written as

$$\mathbf{c} = \begin{bmatrix} \mathcal{E}\_{xx} & \mathcal{E}\_{xy} & \mathcal{E}\_{xz} \\ \mathcal{E}\_{yx} & \mathcal{E}\_{yy} & \mathcal{E}\_{yz} \\ \mathcal{E}\_{zx} & \mathcal{E}\_{zy} & \mathcal{E}\_{zz} \end{bmatrix} \tag{9}$$

$$\mathcal{E}\_{\text{xx}} = n\_{\text{o}}^2 + \left(n\_{\text{e}}^2 - n\_{\text{o}}^2\right) \cos^2 \theta\_0 \cos^2 \phi\_0 \,\tag{10}$$

$$\mathcal{E}\_{xy} = \mathcal{E}\_{yx} = \left(\eta\_{\text{e}}^2 - \eta\_{\text{o}}^2\right) \cos^2\theta\_0 \sin\phi\_0 \cos\phi\_{\text{o}} \,\tag{11}$$

$$\mathcal{E}\_{xz} = \mathcal{E}\_{zx} = \left(n\_{\rm e}^2 - n\_{\rm o}^2\right) \sin\theta\_0 \cos\theta\_0 \cos\phi\_0 \,\tag{12}$$

$$
\varepsilon\_{yy} = n\_{\rm o}^2 + \left(n\_{\rm e}^2 - n\_{\rm o}^2\right) \cos^2 \theta\_0 \sin^2 \phi\_{0\prime} \tag{13}
$$

$$\mathcal{E}\_{yz} = \mathcal{E}\_{zy} = \left(n\_{\text{e}}^2 - n\_{\text{o}}^2\right) \sin\theta\_0 \cos\theta\_0 \sin\phi\_0 \,\tag{14}$$

Three-Dimensional Vector Holograms in Photoreactive Anisotropic Media 183

*S*1

−1 1

Fig. 2. Spatial distribution of the Stokes parameters in interference light calculated by

<sup>0</sup> . This fact suggests that the periodic structure, recorded by the

*S*2

*S*3

−1 1

−1 1

pattern also depended on

*n*o*, n*<sup>e</sup>

1.60, 1.60

1.55, 1.65

1.50, 1.70

varying the refractive indexes

φ

*S*0

0 1

0 Λ*<sup>x</sup>*

*z d*

*x*

3D vector holography, is affected by the initial alignment of the medium.

$$
\varepsilon\_{\rm zx} = n\_{\rm o}^2 + \left(n\_{\rm e}^2 - n\_{\rm o}^2\right) \sin^2 \theta\_0 \,. \tag{15}
$$

By setting

$$\mathbf{E}(x,\ z) \equiv \begin{bmatrix} A\_x \exp\left(i\delta\_x\right) \\ A\_y \exp\left(i\delta\_y\right) \end{bmatrix} \equiv \begin{bmatrix} E\_x' \\ E\_y' \end{bmatrix} \tag{16}$$

we obtain the polarization distribution in interference light with the use of the Stokes parameters as (Kliger, 1990)

$$\begin{bmatrix} S\_0 \\ S\_1 \\ S\_2 \\ S\_3 \end{bmatrix} = \begin{bmatrix} A\_x^2 + A\_y^2 \\ A\_x^2 - A\_y^2 \\ 2A\_x A\_y \cos\left(\delta\_y - \delta\_x\right) \\ 2A\_x A\_y \sin\left(\delta\_y - \delta\_x\right) \end{bmatrix}.\tag{17}$$

Figure 2 illustrates the polarization distribution in the interference light calculated by varying *n*o and *n*<sup>e</sup> . The paremeters used in this calculation are as follows: *d* = 10 μm , 0 θ = 0 , 0 φ = π 2 , 532 nm λ = , 1 2 θ θ =− = ° 1.5 (i.e., ( ) θθ θ 12 F + ≡= /2 0 ), **E**<sup>1</sup> = ( ) 0, 1 (i.e., **E**<sup>1</sup> is *s*-polarized light), and **E**<sup>2</sup> = ( ) 1, 0 (i.e., **E**<sup>2</sup> is *p*-polarized light). The one cycle of the interference pattern for the *x* -direction is given as 1 2 Λ= − ≅ *<sup>x</sup>* λθ θ sin sin 10 μm . As seen in Fig. 2, the polarization distribution of the interference light varies depending on values of *n*o and *n*<sup>e</sup> . When e o *nn n* − ≡Δ = 0 , namely, the medium is isotorpic, the polarization state is modulated only for the *x* -direction. However, that is modulated for the *x* - and *z* -dirctions in the case of 0 Δ ≠ *n* . This is because the refractive indexes for the *s*- and *p*-polarized components differ in the anisotorpic medium since the optical axis is parallel to the incident plane. These calculated results clearly indicate that multidimensional periodic distribution of optical anisotorpy can be formed by the holographic recording. Therefore, we call these holograms, recorded in anisotropic media by vectrical light, 3D vector holograms.

Figure 3 illustrates interference patterns calculated by varing polarization states of the two beams in the case of o *n* = 1.52 and e *n* = 1.75 . The other paremeters used in this calculation are the same as those mentioned above. In this chapter, linearly polarized (LP) light with the azimuth angle of 45 ± ° for the *x* -axis are described as *q*<sup>±</sup> -polarized, respectively. In addition, right- and left-handed circularly polarized light are denoted by *r* and *l*, respectively. The results shown in Fig. 3 demonstrate that various interference patterns are formed depending on polarization states of the two beams. When both the beams are *s*polarized, the intensity was modulated one-dimensionally and the polarization state was remained in the medium. In contrast, the polarization state was two-dimensionally modulated when both the beams are *q*<sup>+</sup> - or *r*-polarized. This is because *s*-polarized light propagates with no change of polarization state since the electric field vector is parallel to the optical axis 0 **c** . Figure 4 shows interference patterns calculated by varying φ0 (i.e., the azimuth angle of 0 **c** ). In this calculation, the two beams are *s*- and *p*-polarized and the other parameters are the same as those mentioned above. As seen in Fig. 4, the interference

( ) 2 22 2 o eo 0

( )

( ) ( )

θθ

λθ

 θ

δ δ

δ δ

δ

*A i E* δ

2 2

*x y x y xy y x xy y x*

*A A*

′ ≡ ≡ ′

*x x x y y y A i E*

( ) ( )

<sup>0</sup> 2 2

*S A A*

*S A A <sup>S</sup> A A*

> θ

interference pattern for the *x* -direction is given as 1 2 Λ= − ≅ *<sup>x</sup>*

holograms, recorded in anisotropic media by vectrical light, 3D vector holograms.

the optical axis 0 **c** . Figure 4 shows interference patterns calculated by varying

azimuth angle of 0 **c** ). In this calculation, the two beams are *s*- and *p*-polarized and the other parameters are the same as those mentioned above. As seen in Fig. 4, the interference

2 cos 2 sin

<sup>+</sup> <sup>−</sup> <sup>=</sup> <sup>−</sup> <sup>−</sup>

Figure 2 illustrates the polarization distribution in the interference light calculated by varying *n*o and *n*<sup>e</sup> . The paremeters used in this calculation are as follows: *d* = 10 μm ,

**E**<sup>1</sup> is *s*-polarized light), and **E**<sup>2</sup> = ( ) 1, 0 (i.e., **E**<sup>2</sup> is *p*-polarized light). The one cycle of the

in Fig. 2, the polarization distribution of the interference light varies depending on values of *n*o and *n*<sup>e</sup> . When e o *nn n* − ≡Δ = 0 , namely, the medium is isotorpic, the polarization state is modulated only for the *x* -direction. However, that is modulated for the *x* - and *z* -dirctions in the case of 0 Δ ≠ *n* . This is because the refractive indexes for the *s*- and *p*-polarized components differ in the anisotorpic medium since the optical axis is parallel to the incident plane. These calculated results clearly indicate that multidimensional periodic distribution of optical anisotorpy can be formed by the holographic recording. Therefore, we call these

Figure 3 illustrates interference patterns calculated by varing polarization states of the two beams in the case of o *n* = 1.52 and e *n* = 1.75 . The other paremeters used in this calculation are the same as those mentioned above. In this chapter, linearly polarized (LP) light with the azimuth angle of 45 ± ° for the *x* -axis are described as *q*<sup>±</sup> -polarized, respectively. In addition, right- and left-handed circularly polarized light are denoted by *r* and *l*, respectively. The results shown in Fig. 3 demonstrate that various interference patterns are formed depending on polarization states of the two beams. When both the beams are *s*polarized, the intensity was modulated one-dimensionally and the polarization state was remained in the medium. In contrast, the polarization state was two-dimensionally modulated when both the beams are *q*<sup>+</sup> - or *r*-polarized. This is because *s*-polarized light propagates with no change of polarization state since the electric field vector is parallel to

=− = ° 1.5 (i.e., ( )

, exp

exp

we obtain the polarization distribution in interference light with the use of the Stokes

 θ

*zz* =+ − *n nn* sin . (15)

**E** , (16)

. (17)

12 F + ≡= /2 0 ), **E**<sup>1</sup> = ( ) 0, 1 (i.e.,

sin sin 10 μm . As seen

φ

0 (i.e., the

 θ

ε

*x z*

1 2 3

*S*

By setting

0 θ = 0 , 0 φ = π

parameters as (Kliger, 1990)

 2 , 532 nm λ

 = , 1 2 θ

pattern also depended on φ<sup>0</sup> . This fact suggests that the periodic structure, recorded by the 3D vector holography, is affected by the initial alignment of the medium.

Fig. 2. Spatial distribution of the Stokes parameters in interference light calculated by varying the refractive indexes

Three-Dimensional Vector Holograms in Photoreactive Anisotropic Media 185

*S*2

*S*3

−1 1

−1 1

*S*1

−1 1

Fig. 4. Spatial distribution of the Stokes parameters in interference light calculated by

beams, optical anisotorpy of the medium, and alignment of the optical axis.

**3. Photoreactive anisotropic medium with uniaxial anisotropy** 

In conclusion, we confirmed theoretically that 3D vector holography realizes fabrication of various multidimensional anisotropic structures owing to polarization states of recording

In order to confirm the principle described in section 2, a grating was recorded in a model medium by 3D vector holography and its diffraction properties were observed. We prepared an azo-dye doped liquid crystalline material as the photoreactive anisotropic medium by mixing nematic mixture E7, a side-chain liquid crystalline polymer (SLCP), and azo-dye 4-[N-(2-hydroxyethyl)-N-ethyl]amino-4'-nitroazobenzene, more commonly known as disperse red 1 (DR1), with a weight ratio of E7 : SLCP : DR1 = 59 : 40 : 1. Here, E7 and DR1 were obtained from BDH-Merck and Ardrich, respectively. SLCP was synthesized using a poly(methyl methacrylate) backbone comprising 4-cyanophenyl benzoate side groups. The number and weight averages of SLCP used in this study were 11,700 and 32,800, respectively. The chemical structures of the three components were illustrated in Fig. 5. They were stirred at around 100°C until a homogeneous solution was obtained. The

*S*0

0 1

0 Λ*<sup>x</sup>*

*z d*

φ0

0

π/8

π/4

3π/8

varying the direction of the optical axis

*x*

Fig. 3. Spatial distribution of the Stokes parameters in interference light calculated by varying polarization states of two recording beams

*S*1

*S*2

*S*3

−1 1

−1 1

−1 1

Fig. 3. Spatial distribution of the Stokes parameters in interference light calculated by

varying polarization states of two recording beams

*S*0

0 1

0 Λ*<sup>x</sup>*

*z d*

**E**1*,* **E**<sup>2</sup>

*s*, *s*

*q*+, *q*<sup>+</sup>

*r*, *r*

*s*, *p*

*q*+, *q*<sup>−</sup>

*r*, *l*

*x*

Fig. 4. Spatial distribution of the Stokes parameters in interference light calculated by varying the direction of the optical axis

In conclusion, we confirmed theoretically that 3D vector holography realizes fabrication of various multidimensional anisotropic structures owing to polarization states of recording beams, optical anisotorpy of the medium, and alignment of the optical axis.
