Polarization converting textures of nematic liquid

Polarization converting textures of nematic liquid crystal in glass cavities Xiahui Wang, Miao Xu, and Hongwen Ren Citation: Journal of Applied Physics 115, 023111 (2014); doi: 10.1063/1.4862185 View online: http://dx.doi.org/10.1063/1.4862185 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/115/2?ver=pdfcov Published by the AIP Publishing

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JOURNAL OF APPLIED PHYSICS 115, 023111 (2014)

Polarization converting textures of nematic liquid crystal in glass cavities Xiahui Wang, Miao Xu, and Hongwen Rena) BK Plus Haptic Polymer Composite Research Team, Department of Polymer Nano-Science and Technology, Chonbuk National University, Jeonju, Jeonbuk 561-756, South Korea

(Received 26 October 2013; accepted 22 December 2013; published online 14 January 2014) When a nematic liquid crystal (LC) is filled in a glass cavity, the LC molecules present azimuthal orientations in the cavity. If the surface of the cavity is coated with a homeotropic polyimide, then the LC molecules exhibit radial orientations. By treating the LC on one side of the cavity with homogeneous alignment, the former orientations change to a twisted-azimuthal texture, while the latter orientations change to a twisted-radial texture. Both textures are verified experimentally, and they can convert a linearly polarization light to an azimuthal and/or radial polarization light, depending on the polarization direction of the incident light. In contrast to previous approaches, various LC textures can be easily formed in a cavity, and the fabrication procedure is simple. Since the LC texture is confined in a cavity, an array pattern of the texture can be obtained, if the employed substrate has multiple cavities. A LC with twisted-azimuthal and/or twisted-radial textures in a cavity array has potential applications in phase modulation, C 2014 AIP Publishing LLC. polarization compensating, sharp focus, and material processing. V [http://dx.doi.org/10.1063/1.4862185] I. INTRODUCTION

Nematic liquid crystals (NLCs) are fascinating optical materials that exhibit the properties of a liquid, yet have the long range ordering of a solid. NLCs with such unique properties make them attractive for applications in displays,1 phase modulators,2 tunable-focus lenses,3–6 and other photonic devices.7–9 Usually, the employed liquid crystal (LC) in these devices is treated with unidirectional or twisted alignment. Due to the alignment of rod-like molecules, the LC can present considerable optical activity, i.e., it can rotate the polarization of a light beam passing through it. A 90 twisted nematic LC cell, which can rotate the plane of a linear polarization light by 90 , is a good example.1 Owing to the optical activity, LC has become a strong contender as a polarization converter. When a LC is treated with unidirectional or non-unidirectional texture, it is capable of converting a linearly polarized light to circular, linear, axial, azimuthal or radial polarized light. Among them, the radial and azimuthal polarization lights are very attractive due to their optical symmetry. One important application of the two polarization lights is in material processing. Unlike a linear polarization beam, whose polarization direction is unchanged as it is focused, the polarization direction of a radial polarized laser beam at the focus point is along the direction of propagation. Owing to this result, the focused spot size of the radial polarized beam can be reduced by more than 30%, in contrast to a liner polarized beam, and hence considerably increase the power density. It has been reported that a radial polarization beam can increase the machining efficiency by 40%–100%, with maximum precision.10,11 In addition to material processing, a radial or azimuthal polarization light can also find applications in biological tissue analysis or polarizing material,12 particle a)

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trapping,13,14 tight focusing,15–17 and polarization camera imaging.18 To realize an azimuthal and/or radial polarization light, LC must be treated with special orientations. Various LC converters have been demonstrated, which can convert a linear polarization light to a radial and/or azimuthal polarization light.19–27 Most of them have been made by using the method of circular rubbing19,24,25 or photoinduced alignment.22,26 Because only a single converter can be created in one LC cell, it is unable to process multiple beams at the same time. Moreover, the two methods involve a complex fabrication procedure. In our previous work, we used cylindrical polymer cavities, to prepare an array of polarization converters.27 In each cavity, LC presents azimuthal orientations, without circular rubbing treatment. When one side of the LC in the cavity is treated with a homogeneous alignment, a twisted-azimuthal texture can be obtained. Such a texture functions as a polarization converter. Although a converter array can be integrated into one cell, and the individual converter could be of miniature size, the cavity-patterned polymer film is not easy to be held, because of its flexibility. Therefore, the fabrication process becomes complicated, and the LC could not present highly symmetrical orientations in the cavities. In this paper, we report a polarization converter by replacing the previous polymer film with a cavity-patterned glass substrate. Owing to the high rigidity of glass, LC can present a high symmetrical texture in a cavity. When LC directly contacts the surface of the cavity, an azimuthal texture is obtained. If the surface of the cavity is coated with a homeotropic polyimide layer, then a radial texture is formed. Both textures are self-assembled without rubbing treatment. By treating LC on one side of the cavity with homogenous alignment, the former (symmetrical) can change to a twistedazimuthal texture, while the latter (radial) can form a twisted-radial texture. Both textures function as a polarization converter. In contrast to the previous polarization

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FIG. 1. Method of forming two different LC textures (a) azimuthal and (b) radial.

converter, the fabrication process of our device is simplified. LC can also present highly symmetric orientations in a glass cavity. Moreover, various textures can be obtained, and it is feasible to prepare an array of pattern with high density. II. SYMMETRICAL TEXTURES

When a LC is confined between solid surfaces, it can exhibit an equilibrium director texture that is highly dependent on the chemical and physical properties of the surfaces. Typically, a solid substrate can align the LC director to orient either parallel or perpendicular to its surface, after physical or chemical treatment. It has been discovered that a glass surface can induce LC with approximately planar orientations, while a homeotropic polyimide can induce LC with homeotropic alignment. Based on the alignment of a nematic LC on solid surface, various LC textures can be obtained in a glass cavity. Figure 1 shows the method of achieving azimuthal and radial textures. When LC molecules directly contact a glass substrate, they are supposed to orient along the substrate surface, as shown in the left side of Fig. 1(a). If the flat surface is bent to form a cylindrical shape (cavity), then the LC can present circular orientations on the surface, as shown in the middle of Fig. 1(a). According to elastic deformations of the continuum theory, when the cavity is filled with more LC, the LC presents an azimuthal texture, except for a defect point in the center, as shown in the right side of Fig. 1(a). In the real case, if the glass substrate is untreated, the LC will present randomly planar orientations along the surface. However, the LC molecules can present concentrically circular orientations in a cavity. This is because the LC with such orientations has minimum potential energy. If the substrate

J. Appl. Phys. 115, 023111 (2014)

is coated with a homeotropic polyimide (PI) layer, then the LC molecules can be induced with homeotropic alignment, as shown in the left side of Fig. 1(b). Similarly, the LC molecules still keeps the homeotropic alignment if the substrate is bent to form a cylindrical shape, as shown in the middle of Fig. 1(b). If the cavity is filled with more LC, then LC can present a radial texture, except for the defect point in the center, as shown in the right side of Fig. 1(b). From Fig. 1, both azimuthal and radial textures are selfaligned in the cavities without rubbing treatment. Due to highly symmetrical, both textures function as a polarization converter. If one side of LC in the cavity is treated with homogeneous alignment, the azimuthal texture can change to twisted-azimuthal texture, while the radial texture can change to twisted-radial texture. III. DEVICE FABRICATION

To prove the two textures, as shown in the right side of Fig. 1, a clean substrate is drilled with two through cavities using a laser beam (DPSS laser, k ¼ 532 nm, Jiangyin Deli laser Solution CO, China). The thickness of the substrate is 0.5 mm, and the diameter of each cavity is 0.35 mm, as shown in Fig. 2(a). The two cavities can be considered as the hollow cylinder of Fig. 1. A homeotropic PI (SE-1211, Nissan Chemical) in solvent is coated on the surface of cavity-2. After pre-baking at 80  C for 15 min, and hardbaking at 220  C for 1 h, a thin PI layer is formed on the surface of the cavity. Then, the substrate is combined with another glass substrate (the bottom) to form a cell (cell-1), as shown in Fig. 2(b). The thickness of the cell is controlled using 15 lm-thick mylar film. The cavities are filled with nematic LC SLC-9023 (no ¼ 1.522, Dn ¼ 0.251, Chengzhi Yonghua Display Material, China). The bottom substrate is used to hold the LC. To avoid the oriented LC on the bottom substrate degrading the formed texture in the cavities, the surface of the bottom substrate is coated with the same homeotropic PI layer. To convert the azimuthal orientations to a twistedazimuthal texture, and the radial orientations to a twistedradial texture accordingly, another cell (cell-2) that has the same structure as that of cell-1 is prepared, as shown in Fig. 2(c). In contrast to cell-1, the bottom substrate of cell-2 is overcoated with a homogeneous polyimide (PI) layer, and buffed in one direction, so that the LC can present a homogeneous alignment on the bottom substrate surface. The surface of cavity-3 is bare, and the surface of cavity-4 is coated with the same PI as that of cavity-2. LC molecules near the bottom substrate present homogeneous alignment in the PI

FIG. 2. Structures of two different LC cells: (a) the top substrate, (b) the cross-sectional structure of cell-1, and (c) the cross-sectional structure of cell-2.

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rubbing direction. Then, a small amount of the same LC is filled in the cavities. Owing to the elastic deformations of the continuum theory, the LC in each cavity will generate a new texture. IV. RESULTS AND DISCUSSION

To study the textures of LC formed in cavity-1 and cavity-2, we use a polarizing optical microscope (POM) to observe cell-1 between crossed polarizers. A white light is used to illuminate the cell from the bottom substrate side. The output light is monitored through eyepiece, and a twodimensional light intensity pattern is recorded using a CCD camera. Figure 3(a) shows the intensity pattern through cavity-1. The intensity presents a crosshair pattern. When the cavity-1 is rotated circularly along its axis on the stage, the observed pattern remains unchanged. Such a result implies that the orientation of LC in the cavity is highly symmetrical. Figure 3(b) shows the intensity pattern observed through cavity-2. The observed pattern is quite similar to the pattern of Fig. 3(a), except that the intensity is intentionally adjusted to be different. When cavity-2 is rotated along its axis, the pattern does not change either. From Fig. 1, both azimuthal and radial textures present a similar crosshair pattern, when they are observed between crossed polarizers. Therefore, LC presents either an azimuthal, or a radial texture, in the two cavities. According to the textures formed in Fig. 1, LC should present azimuthal (radial) texture in cavity-1 (cavity-2). Although the LC in cavity-1 and cavity-2 touches the bottom substrate, and is directly exposed to air, the formed textures will not degrade. It has been proven that LC presents homeotropic orientations, when they are exposed to air.28 To analyze the effect of homeotropic orientation on the formed LC texture, a xyz coordinate is established in the cavity, as shown in Fig. 4(a). For the azimuthal texture, LC molecules exhibit hybrid, planar, and hybrid orientations from top to bottom. Fig. 4(b) shows the orientations of the LC along AB, but in the plane perpendicular to the yoz-plane. Since the cavity is thick, the hybrid, planar, and hybrid orientations are due to the impacts of air/cavity, cavity, and cavity/PI layer, respectively. Because LC molecules have no twist effect along the AB axis, the hybrid can be treated as an equivalent planar. By doing so, the effective thickness of the LC layer should be reduced. Figure 4(c) shows the equivalent orientations of Fig. 4(b). One can see that the homeotropic LC will not degrade the formed textures. Therefore, the azimuthal

FIG. 3. Crosshair pattern observed between crossed polarizers: (a) cavity-1 and (b) cavity-2.

FIG. 4. Analysis of LC orientations in a cavity: (a) xyz coordinate in a cavity, (b) LC orientations, and (c) equivalent orientation of (b).

texture [Fig. 3(a)] is induced by the surface of cavity-1, rather than by the PI layer or air. Similarly, if the LC in Fig. 4(a) exhibits a radial texture, LC molecules still present hybrid, planar, and hybrid orientations from top to bottom. The orientations are the same as shown in Fig. 4(b) but in the plane of yoz. Because such orientations [Fig. 4(b)] have an equivalent planar orientation [Fig. 4(c)], the radial texture will not be degraded by the homeotropic LC, either. Therefore, the surface of the cavity plays a key role for both textures. According to our previous report,27 azimuthal (radial) orientations can be changed to a twisted-azimuthal (twistedradial) texture, if the LC on the bottom side of cavity-1 (cavity-2) is treated with a planar alignment. To experimentally prove the LC orientations in cavity-1 and cavity-2, we evaluated the second cell [cell-2, Fig. 2(c)] between two polarizers. Figure 5(a) shows the light transmission of cavity-3 between two polarizers. A fan-shaped intensity pattern is observed, when the polarization axis of the polarizer (P) is set to be parallel to the PI rubbing direction. When the axis of the analyzer (A) is orthogonal to the axis of the polarizer (A?P, left), the bright fan shaped pattern is along the horizontal position. It should be noted that the formed pattern is surrounded by a dark zone. The dark zone is mainly due to the deflection of the cavity surface to the incident light. When the analyzer is rotated in the counterclockwise direction, the axis of the fan-shaped pattern rotates synchronously. When A/P ¼ 45 and 0 , the pattern rotates 45 (middle) and 90 (right), respectively. By continuously rotating the analyzer, the shape of the intensity pattern remains unchanged. The symmetrical fan-shaped pattern implies that the linear polarization light has been converted to either radial, or azimuthal, polarization light. Figure 5(b) shows the intensity pattern observed through cavity-4 between two polarizers. The polarization axis of the polarizer is along the rubbing direction. When A?P, a fanshaped intensity pattern is observed too (left). By rotating the analyzer in the counterclockwise direction, the pattern rotates synchronously. When A/P ¼ 45 and 0 , the intensity pattern rotates 45 (middle) and 90 (right), respectively.

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J. Appl. Phys. 115, 023111 (2014)

FIG. 5. Fan-shaped intensity patterns observed between two polarizers, through (a) cavity-3 and (b) cavity-4.

Similar to the results of Fig. 5(a), the shape of the intensity pattern does not change, when the analyzer is continuously rotated. From the symmetrical pattern, cavity-4 has also converted the linear polarization light into either azimuthal or radial polarization light. In contrast to the fan-shaped intensity patterns observed through cavity-3 and cavity-4, their axes are always perpendicular, when their A/P is set with the same angle. Such a result indicates that the newly formed textures in cavity-3 and cavity-4 are different. According to previous polarizations converters,22,27 when LC molecules on the left substrate present homogeneous alignment, and on the right substrate exhibit azimuthal orientations, a twisted-azimuthal texture is formed. When a linear polarization beam passes through such a texture, as shown in Fig. 6(a), an azimuthal polarization light is converted. When such a light passes through the analyzer, the output intensity presents a fan-shaped pattern. If the axis of the analyzer is set in the vertical direction, then the axis of the intensity pattern is in the horizontal position. In contrast to the pattern formed in Fig. 5(a), the LC in cavity-3 indeed presents a twisted-azimuthal texture. We then conclude that LC presents azimuthal orientations in cavity-1. If LC molecules on the right substrate present radial alignment, then a twisted-radial texture is obtained. Such a texture can convert

a linear polarization light to a radial polarization light, as depicted in Fig. 6(b). When the radial polarization light passes through the analyzer, a fan-shaped pattern with its axis placed in the vertical position is observed. Comparing to the intensity pattern of Fig. 5(b), the texture of LC in cavity4 is twisted-radial. Moreover, we conclude that the LC in cavity-2 presents radial orientations. Because the formed azimuthal and radial polarization lights are owing to the twisted effect, according to the Mauguin condition, the plane of a linear polarization light can only be rotated if the below limit is satisfied29 u  2pdDn=k;

(1)

where / is the twisted angle, d is the thickness of the twisted LC layer, Dn is the LC birefringence, and k is the wavelength of light. For a 90 twisted LC, Eq. (1) reduces to k  4dDn:

(2)

For our LC cell with d  15 lm and Dn ¼ 0.251, the calculated dDn is much larger than k/4 (k  0.55 lm). Because the twisted LC layer satisfies this condition, the twisted LC can rotate the plane of a linear polarization light.

FIG. 6. Light intensity pattern, after passing through the analyzer: (a) azimuthal polarization light and (b) radial polarization light.

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TABLE I. Conversion of a linear polarization to other types of polarization. Texture Linear polarizer light (input)

Azimuthal

Radial

Twisted-azimuthal

Twisted-radial

Axial polarizer light (output)

Axial polarizer light (output)

Radial polarizer light (output) Azimuthal polarization light (output)

Radial polarizer light (output) Azimuthal polarization light (output)

From LC textures formed in cavities from 1 to 4, various polarization converters can be obtained. Table I lists the function of each texture as a polarization converter. Both twisted-azimuthal and twisted-radial textures can convert a linear polarization light into either a radial polarization light or an azimuthal polarization light, depending on the polarization direction of the incident light. From Fig. 2, the filled LC in each cavity is directly exposed to air. The textures can remain stable only when the cells are placed in a horizontal position. To fix the formed LC textures, a polymer network can be used to stabilize the LC orientations.20 Owing to the low surface tension of LC, the top surface of the LC in each cavity is fairly flat. The lens character of the LC in each cavity is not distinct. As a result, each LC texture can be considered as a pure polarization converter. There is no doubt that a cavity array with a high density can be drilled in a glass substrate, because of its good rigidity. Therefore, it is feasible to fabricate a polarization converter array, which would be difficult to achieve using previous methods. Similar to the LC converter formed in a polymer cavity, the aperture of our converter is suitable for being prepared in miniature size, typically from tens of micrometers to several millimeters. This is because the effect of the cavity surface on the LC orientation should be in the work distance. Owing to the glass surface, LC molecules can be aligned well in its cavity. As a result, the formed LC texture can present good characteristics as a polarization converter. Unlike a single converter, a polarization converter array has the advantage of processing multiple beams at the same time. In contrast to previous LC texture formed in a polymer cavity, various textures can easy form in a glass cavity. Our device has the advantages of easy fabrication and good optical performance. Based on this approach, the formed LC texture has potential applications in polarization compensating, sharp focus, and material processing. V. CONCLUSION

We have reported the method of forming various LC textures in a glass cavity. If the cavity is bare, then symmetrical-azimuthal orientations can be obtained. The azimuthal orientations can change to a twisted-azimuthal texture if one side of the LC in the cavity is treated with homogeneous alignment. By coating the surface of the cavity with a homeotropic PI layer, LC with radial orientations can be induced. If the LC on one side of the cavity is treated with homogeneous alignment, a twisted-radial texture is obtained. The four textures are very useful as polarization converters. In particular, the twisted-azimuthal and twisted-radial

textures can convert a linear polarization light to an azimuthal, or a radial polarization light. Due to the high optical symmetry, the two polarized lights have potential applications in phase modulation, tight focusing, imaging, and material processing. In contrast to previous approaches, a converter based on this approach has the advantages of easy fabrication, good optical performance, and miniature aperture size. Moreover, it is feasible to integrate an array of converters with high density into one cell. ACKNOWLEDGMENTS

The authors are grateful for the financial support of the National Research Foundation (NRF) of Korea under grant 2013000352 and supported in part by the Basic Research Program of NRF of Korea under grant 2013063265. 1

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