This investigation demonstrates the feasibility of the radial and azimuthal axially symmetric LC structure using double-side photoalignment in a dye-doped liquid crystal (DDLC) cell. A linear and linearly polarized beam is applied to a rotated DDLC cell to produce an axially symmetric LC alignment. Notably, double-sided photoalignment is performed at a temperature that is maintained just above the clear point. Conformation of the axially symmetric LC devices can be controlled by varying the polarization direction of the pumping light, and the simulation results correlate well with OR closely correspond to the experimental results.
©2008 Optical Society of America
Liquid crystals (LCs) have highly anisotropic optical and dielectric characteristics, which are sensitive to an applied voltage. Therefore, they have recently been extensively utilized in light modulators , optical switches , filters , lenses  and displays .
LC molecules are conventionally aligned by rubbing of the alignment layers, typically unidirectionally. However, LC devices based on non-unidirectionally aligned layers are required for numerous applications, such as cells with axially symmetric liquid crystal (LC) structures, which can be used to select wavelengths for a Fabry-Perot filter . Many methods of designing particular LC-alignment devices have also been realized. These include an approach utilizes an LC spatial light modulator to cause axial polarization  and the use of concentrical circular rubbing . Wu et al. also presented a polarization converter based on a sheared polymer network LC and an LC gel [9, 10]. However, these approaches involve a complex fabrication procedure or lack flexibility. The authors recently reported an axially symmetric polarization converter based on single-side photo-alignment technique .
This investigation demonstrates the feasibility of axially symmetric radial and azimuthal LC devices based on double-sided photo-alignment. The axially symmetric structure of the formed cell is highly uniform, and only a single-step exposure process is required to produce the structure. The structure is easily modified by changing the polarization direction of the pump beam. The transmittance of the axially symmetric LC cell is simulated using the Jones matrix formulism. The simulation results closely correspond to the experimental results.
2. Device fabrication
The LC and azo dye used in this experiment were E7 (Merck) and Methyl Red (MR; Aldrich), respectively. The MR:E7 mixing ratio was 1:99 wt%. Two indium-tin-oxide (ITO)-coated glass slides, separated by 12um ball spacers, were used to fabricate an empty cell. No surface treatment was applied to the two cleaned glass slides. The homogeneously mixed MR/E7 compound was then injected into an empty cell in the isotropic state to produce a dye-doped LC sample.
As described above , the MR dyes undergo trans-cis isomerization after they are pumped by a green-blue light, and then molecular reorientation occurs continuously. Finally, the excited MR dyes are diffused and adsorbed on the un-treated ITO surface that faces the incident pump beam, with their long axes perpendicular to the polarization of the pump beam. The adsorbed dyes then align LC molecules perpendicular to the polarization and the propagation of the light wave. This method is called the single-side photo-alignment technique. However, if a DDLC cell is heated to a temperature just above the clear point of LCs, then MR dyes are adsorbed onto two substrates of the cell. This process is referred to as double-sided photo-alignment .
Photo-alignment was achieved using a linearly polarized DPSS (Diode-Pump Solid State) laser (λ=532 nm), whose wavelength was close to the peak of the MR absorption spectrum . Figure 1 presents the experimental setup. The pump laser beam, propagating along the z-axis, with an intensity of 0.361 W/cm2, was expanded into a collimated beam with a diameter of ~21 mm. It then passed through a linear mask with a line-width of ~200 um, and was focused by a cylindrical lens onto the cell. The sample was attached to a rotating motor, and thermally controlled at a temperature of ~65°C (which is above the clear temperature of E7 of ~61°C) during the pumping to ensure double-sided photo-alignment. The angle, θ, made between the polarization of the pump beam and the x-axis (Fig. 1) can be controlled using the rotator with a rotating speed ~140 rpm. The period of illumination was ~60 minutes. As mentioned above, the LC molecules on the double-sided substrate surfaces are photo-aligned perpendicular to the polarization. Therefore, a cell with a double-sided DDLC axially symmetric structure was produced. Notably, reliable double-sided photo-alignment can be produced by rotating the sample at a speed of ~60 to 800 rpm under illumination for 60 minutes.
3. Results and discussion
Initially, the pumping laser irradiates the sample while it is being rotated about the z-axis with a polarization angle of θ=90° (with polarization along the y-axis). As reported above , the excited dyes undergo trans-cis isomerization, molecular reorientation, diffusion and, finally, adsorption onto the ITO surfaces with their long axes perpendicular to the polarization of the pump beam. The adsorbed dyes then cause the LC molecules to reorient perpendicular to the polarization and propagation of the light wave. The dyes can be adsorbed onto both of the substrates of the cell if the cell is optically excited at a temperature that is just above the clear temperature of LC . Since the sample is rotated, the double-sided photo-alignment gives rise to the formation of a double-side axially-symmetric radial LC cell, presented in Fig. 2(a). The diameter of the pattern is ~20 mm.
Figures 2(b) and 2(c) present the images of an axially symmetric radial LC sample under the crossed polarizers and the polarized optical microscope, respectively. After the axially symmetric double-sided photo-alignment process, the LC directors align towards the center of the pattern. The double-cross pattern arises from the light that passes through the cell by the cross-polarizer. To confirm the axially symmetric properties of the axially symmetric radial LC structure, the sample was rotated through 360° while the crossed polarizer/analyzer was held stationary. The results demonstrate that the black cross pattern remains unchanged. The image is independent of the sample rotation. This observation confirms that the LC directors are indeed axially symmetric.
To understand the details of the structure of the axially-symmetric radial LC film, the T-V (transmission versus applied voltage) curve of the cell at various positions was plotted. In making the measurement, the cell was placed between crossed polarizers and the probe beam (He-Ne laser, λ=634 nm) was normally incident on the cell. Figures 3(a)–3(d) present the T-V curves at the four points, A, B, C and D, marked in Fig. 3(e), respectively. Figure 3 clearly demonstrates that the measured T-V curves at these four positions are almost identical, implying that the orientation of the LC directors at each position on the axially-symmetric radial LC film have identical phase retardation and surface alignment. Therefore, the radial cell has a uniform symmetric structure.
A similar approach was used to fabricate an axially-symmetric azimuthal LC film (Fig. 4(a)), but without the polarization angle θ (Fig. 1). In this part of the experiment, the polarization angle θ was set to 0° (with polarization along the x-axis). Figures 4(b) and 4(c) show images of the axially symmetric azimuthal LC sample under crossed polarizers and a polarized optical microscope, respectively. The results can be understood based on the same argument that was made to explain the results in Fig. 2. Notably, T-V measurements of the axially symmetric azimuthal LC sample were also made. The results are given in Fig. 5, which is very similar to Fig. 3.
Figure 6 shows the pattern of simulated transmittance of double-sided azimuthally aligned LC cell. The simulation is performed using the Jones matrix formalism with the probe beam being normally incident onto the sample, which is sandwiched between crossed polarizers. In the simulation, the LC directors in the bulk are assumed to be oriented parallel arrangement from the top to the bottom substrates of the cell, and the probe is propagating along z-axis.
where is the Jones vector of the incident beam, and equals to in the present setup. R is the coordinate rotation matrix and P is the Jones matrix for the liquid crystal film. θ c is defined as the angle made between the x-axis and the director of liquid crystal, and it is a function of position (x, y). For axially symmetric azimuthally aligned LC structure, θ c equals to tan -1(y/x)+π/2. For crossed polarizers, the transmittance T=|A ′ y|2 gives rise to the pattern, as depicted in Fig. 6. The simulated results agree well with the experimental results (Fig. 4(c)). Similarly, the simulated results for the double-sided radially aligned cell also match well with the experimental results.
Two double-sided axially symmetric LC cells were successfully demonstrated. The axially symmetric structure of these cells is highly uniform, and easy to fabricate. Furthermore, the temporal stability of these devices is good. A five-month old sample exhibited no significant aging effect. Axially symmetric structure devices have potential application for spatial polarization converters.
The authors would like to thank the National Science Council (NSC) of the Republic of China (Taiwan) for financially supporting this research under Grants No. NSC 96-2112-M-110-015- MY3 and NSC 95-2112-M-006-022-MY3.
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