This work demonstrates axially symmetric polarization converters based on photo-alignment in dye-doped liquid crystal (DDLC) films. A linear-shape and linearly polarized beam is applied onto a rotated homogeneous DDLC cell to achieve three axially symmetric polarizations - radial, azimuthal and vortical. Additionally, the spiral degree of the axially symmetric vortical polarization can be controlled by varying the polarization of the pumping light and the simulation results agree well with the experiment.
©2008 Optical Society of America
Axially symmetric polarized beams have attracted much interest in recent years. They can be adopted in diffractive optics and imaging systems [1, 2]. An important property of these beams is their unique cylindrical symmetry polarization, which enables the amplification of axially polarized beams to high power and good beam quality . Radially and azimuthally polarized beams can be generated inside a laser cavity [4–6]. The adopted approaches, however, are based on complex resonator configurations, or require special fabricating techniques. Alternatively, radially or azimuthally polarized beams can be obtained directly from a Gaussian beam, outside the laser cavity, with specially designed mode converters. Such a conversion can be performed using various interferometric arrangements by interferometric superposition of linearly polarized beams [7, 8] or the use of a spatially varying retarder .
Liquid crystals (LCs) are commonly employed as polarization-converting materials because its director, which is an unit vector along the common axis of LC molecular orientation, can be modulated by an external field. Numerous methods have been realized. The first approach utilizes an LC spatial light modulator to cause axial polarization . The second method is to control LC directors by concentrically circular rubbing . Recently, Wu, et al., presented a polarization converter using a sheared polymer network LC and LC gel [12, 13]. Some common concerns about the aforementioned approaches are their complex fabrication processes, and flexibility.
Photo-alignment is a novel technique for fabricating LC devices. One of the photoalignment methods is based on the photoinduced adsorption effect of the azo dye doped in the LC host. When an azo dye-doped LC (DDLC) cell is irradiated by the proper light, the azo dye (such as methyl red) molecules in the LC host undergo trans–cis isomerization, causing reorientation, diffusion and finally, adsorption onto the substrate surface [14–17]. The adsorbed dyes then align the LC molecules. Several researchers have recently exploited this photo-alignment effect to fabricate various optical devices, such as gratings, Fresnel lenses and reflective displays [18–21].
This work demonstrates three types of axially symmetric polarization converters fabricated by photoalignment in a dye-doped liquid crystal film. A linear-shape and linearly polarized beam is applied onto a rotated homogeneous DDLC cell to achieve radial, azimuthal and vortical LC alignments on the front substrate. The LCs in the bulk follow the alignment directions of the cell, and produce axially symmetric conformations. The main benefit of the presented approach is that the spiral degree of the axially symmetric vortical polarization can be controlled by varying the polarization of the pumping light.
2. Device fabrication
The LC and azo dye used in the present 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 plastic spacers were used to fabricate an empty cell. On the ITO film, one of the two glass slides was coated with an alignment film, polyvinyl alchohol (PVA), and rubbed, while the other was not treated. The homogeneously mixed compound was then injected into an empty cell to form a dye-doped LC sample. The LC molecules aligned with each other close to the rubbed surface and extended through the bulk of the sample to another surface without alignment of the film. The homogeneity of the cell was confirmed using a conoscope.
The LC molecules on the un-treated surface are photo-aligned in a desired direction. Photo-alignment was achieved using a linearly polarized DPSS (Diode-Pump Solid State) laser (λ = 532 nm), whose wavelength was close to the wavelength of the Azo dye’s absorption peak . Figure 1 presents the 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 from the un-treated surface. The sample was attached to a rotating motor. The polarization of the light source with respect to the x-axis (Fig. 1), defined as θ, can be controlled using the rotator with a rotating speed ~140 rpm. The illumination duration was ~60 minutes. Notably, the property of the adsorbed dye layer is determined by a few factors, such as the concentration of the dyes doped in LCs, the intensity of the pumped beam, the illumination duration . In the present experiment, reliable photoalignment by the adsorbed dye layer could be achieved with the sample rotating at a speed in the range ~60 to 800 rpm under the illumination duration of 1 hour.
3. Results and discussions
Initially, the pumping laser irradiates the sample that is being rotated about the z-axis with a polarization angle at θ =0°. As reported previously , the excited dyes undergo trans–cis isomerization, molecular reorientation, diffusion and finally adsorption on the un-treated ITO surface with their long axes perpendicular to the polarization of the pump beam. The adsorbed dyes then cause LC molecules to reorient perpendicular to the polarization and propagation of the light wave. Since the sample is rotated, the polarization of the pumping beam on the sample is rotated azimuthally. Therefore, a radial alignment film is expected to be formed on the un-treated surface. Finally, a hybrid LC sample homogeneously aligned on one substrate and radially aligned on the other is formed; it is called a homogeneous-radial sample (Fig. 2(a)).
Since the homogeneous-radial LC sample satisfies Mauguin’s condition, Δnd ≫λ in this case (where Δn, d and λ are the birefringence of LC, the cell gap and the wavelength of the probe beam, respectively) for all the visible light, the polarization of the probe light rotates following the LC molecules in the sample. Therefore, when a linearly polarized white light with its polarization parallel to the rubbing direction probes the formed homogeneous-radial LC sample, the emerging beam is radially polarized as presented in Fig. 2(a). Figure 2(b) shows the image of the homogeneous-radial LC film under a crossed-polarized optical microscope (POM). The result is reasonable, and expected with the radially polarized emerging light. In the POM setup, the polarizer axis is parallel to the front LC director. Hence, the region from which the emerging beam is polarized perpendicular (parallel) to the analyzer axis is dark (bright), and a brightness gradient exists between these two directions. If the incident linearly polarized light with its polarization is set perpendicular to the front LC director (Fig. 2(c)), then the linearly polarized beam is converted to an azimuthally polarized beam. The image of the homogeneous-radial LC film under a crossed POM becomes that in Fig. 2(d), as expected.
Since no chiral agent is added to the nematic liquid crystal in this experiment, the twist angles in the sample are always smaller than π/2 because the elastic energy is minimized. Therefore, a reversed twist effect produces a disclination line, as observed in Fig. 2 across the diameter of the cell at a boundary between the right-handed and the left-handed 90 degree twist.
An approach similar to that used to fabricate the homogeneous-radial sample, described above, except for the polarization angle θ (Fig. 1), can be employed to fabricate a homogeneous-azimuthal LC film (Fig. 3(a)). In this part of the experiment, the polarization angle of θ is set to 90°. As presented in Fig. 3(a), when a linearly polarized beam with polarization parallel to the rubbing direction probes the formed homogeneous-azimuthal LC sample, the emerging beam is azimuthally polarized. If the polarization of the probe beam is set perpendicular to the front LC director (Fig. 3(c)), then the linearly polarized beam is converted to a radially polarized beam (Fig. 3(c)). Images of the homogeneous-azimuthal LC film under a polarized optical microscope, shown in Figs. 3(c) and 3(d), can be understood based on the same argument as used to understand the similar results in Fig. 2. Similarly, a reversed twist effect producing a disclination line, as observed in Fig. 3 across the diameter of the cell at a boundary is observed.
Vortically polarized light is typically produced using discretely oriented space-variant sub-wavelength gratings . However, the fabrication process is rather complex. A vortex polarized light converter can be fabricated using the same rotating photo-alignment technique described above. If the polarization angle is set to θ = 22.5° (Fig. 1), then as presented in Fig. 4(a), a homogeneous-vortex LC film is formed. An image of the homogeneous-vortex LC film under a crossed polarized optical microscope reveals that the dark region with a fan shape is centered with a line which has an angle θ = 22.5° from the x direction. Similar results are obtained by setting the polarization angles of the line-shape light source at θ = 45° and 67.5°, the spiral angles, and the images under a crossed polarized optical microscope then become those in Figs. 4(b) and 4(c), respectively. Simulation results using the Jones matrix formulism with the probe beam being normally incident onto the sample are also presented in Fig. 4. In our simulation, the LCs in the bulk linearly are assumed to twist from one side of the cell to another following the continuous elasticity theory. It is clear to see that the simulated results agree quite well with the experimental ones.
To verify that the LC cell indeed functions as an axially symmetric polarization rotator, we measured the polarization state of a probe beam (un-focused He-Ne laser; λ = 634 nm) emerging from each of the axially symmetric LC polarization convertors (Figures 2(a), 3(a), 4(a), 4(b), and 4(c)). Experimentally, the probe beam was incident normally onto the sample placed between two polarizers from the homogeneously rubbed side. The polarizer axis was parallel to the rubbing direction, and the analyzer was rotated. It is noted that the diameters of the devices and the probe beam are ~21 mm, and ~1.4 mm, respectively. Thus, it allows us to probe the device at a local region in a device. The probed region is defined by an azimuthal angle,Φ, that is made by the line connecting the centers of the device and the probe-beam spot with the rubbing direction in the clockwise direction (Fig. 5(f)). The polarization states at four angles of Φ (0°, 30°, 60°, and 90°, i. e. the triangular green dots marked in Fig. 5) were measured. We then rotated the analyzer for each measurement to determine the polarization state of the emerging beam from the device. The maximum (minimum) intensity measured from the analyzer is defined as Imax (Imin). The measured results show that Imin is negligible in comparison with Imax for each device. Thus, the polarization of the emerging probe beam is approximately linear. Since the polarization direction changes locally from point to point in a cell, the measured polarization direction is then represented using the Poincare sphere described by stokes parameters (S1, S2, S3) . Figures 5(a)–(e) give the measured results of the polarization states of the probe beams emerging from the devices of Figures 2(a), 3(a), 4(a), 4(b), and 4(c), respectively. The red (green triangular) dots represent the measured (theoretical) polarization states of the samples on the Poincare sphere. It is known that each point on the periphery of the circle in Fig. 5, i.e. (S1, S2, 0), represents a linear polarization state with the polarization direction being continuously rotating along the circle. Following the reference , (1, 0, 0) and (-1, 0, 0) describe linearly polarized light along x-axis, and y-axis, respectively.
It is noted in Fig. 5 that the measured results deviate slightly from the theoretical ones. The cause is believed to result from the fact that the spot size of the probe beam is not small enough to probe a locally enough region. In addition, the probe beam may be incident onto the device at an angle deviated slightly from the designed angle.
Figure 6 presents the dynamic image of homogeneous-radial LC film observed under the operation shown in Fig. 2(a). The bright (dark) region of the sample is rotating with the analyzer. Notably, the bright and dark axes are always parallel and perpendicular to the analyzer axis, respectively. The direction perpendicular to the analyzer axis is always dark. Clearly, such a device can be used to determine a polarization axis.
Various axially symmetric polarization converters are demonstrated using photo-alignment based on dye-doped liquid crystal (DDLC) films. The devices can convert the polarization of a light beam from linear to axially symmetric radial, azimuthally and vortex polarizations. Moreover, the spiral angle of the axially symmetric vortex of LC alignment can be controlled by changing the polarization of the pumping light. The main advantages of these devices are the simplicity in fabrication, the large size and the potential for use in real applications. In addition, the temporal stability of these devices is good. No significant aging effect is found for a three-month old sample.
The authors would like to thank the National Science Council of the Republic of China (Taiwan), (Contract No. NSC 95-2112-M-006-022-MY3 and NSC 96-2112-M-110-015-MY3) and National Cheng Kung University (NCKU) (under the NCKU Landmark Project Contract No. B0055) for financially supporting this research.
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