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Patent: Liquid crystal mixtures for pitch variable optical elements

Drawings: Click to check drawins

Publication Number: 20210116776

Publication Date: 20210422

Applicant: Facebook

Abstract

A liquid crystal (LC) mixture for a pitch variable optical element is provided. The LC mixture includes a host LC and one or more LC dimers dissolved as a guest in the host LC. The host LC and the one or more LC dimers have respective dielectric anisotropies of opposite signs in nematic phase. A net dielectric anisotropy of the LC mixture is substantially neutral.

Claims

  1. A liquid crystal (LC) mixture for a pitch variable optical element, comprising a composition of: a host LC; and one or more LC dimers dissolved as a guest in the host LC, the host LC and the one or more LC dimers having respective dielectric anisotropies of opposite signs in nematic phase, wherein a net dielectric anisotropy of the LC mixture is substantially neutral.

  2. The LC mixture of claim 1, wherein the LC mixture has the nematic phase in a temperature range that includes a room temperature.

  3. The LC mixture of claim 1, wherein the host LC and the one or more LC dimers have the nematic phase in a temperature range that includes a room temperature.

  4. The LC mixture of claim 1, wherein the host LC has negative dielectric anisotropy in the nematic phase, and the one or more LC dimers have positive dielectric anisotropy in the nematic phase.

  5. The LC mixture of claim 1, wherein an LC dimer of the one or more LC dimers has a bent-shaped molecular structure where long axes of mesogenic groups are inclined at a non-zero angle with respect to each other.

  6. The LC mixture of claim 1, wherein an LC dimer of the one or more LC dimers has a pear-shaped molecular structure.

  7. The LC mixture of claim 1, wherein an LC dimer of the one or more LC dimers includes a cyanobiphenyl-based LC dimer.

  8. The LC mixture of claim 7, wherein the cyanobiphenyl-based LC dimer includes a member of 1,.omega.-bis(4-cyanobiphenyl-4’-yl) alkane (CBnCB) homologous series.

  9. The LC mixture of claim 8, wherein the cyanobiphenyl-based LC dimer includes an odd-member of the CBnCB homologous series.

  10. The LC mixture of claim 9, wherein the cyanobiphenyl-based LC dimer includes at least one of CB5CB or CB7CB.

  11. The LC mixture of claim 1, wherein a weight percentage of the one or more LC dimers in the LC mixture is in a range of about 15% to about 40%.

  12. The LC mixture of claim 1, wherein the host LC includes HNG7267 having the dielectric anisotropy of about -1.9 and optical anisotropy of about 0.15.

  13. An optical element, comprising: a first electrode and a second electrode configured to provide a driving voltage to the optical device; and a liquid crystal (LC) mixture coupled to the first electrode and the second electrode, a pitch of flexoelectric domains induced in the LC mixture being continuously variable with the driving voltage, wherein the LC mixture includes: a host LC, and one or more LC dimers dissolved as a guest in the host LC, the host LC and the one or more LC dimers having respective dielectric anisotropies of opposite signs in nematic phase, and a net dielectric anisotropy of the LC mixture being substantially neutral.

  14. The optical element of claim 13, wherein the driving voltage is a direct current (DC) voltage or an ultra-low frequency alternating current (AC) voltage.

  15. The optical element of claim 13, wherein the first electrode and the second electrode are planar electrodes arranged opposite to each other.

  16. The optical element of claim 15, further comprising a first alignment layer and a second alignment layer disposed at the first electrode and the second electrode, respectively, the first alignment layer and the second alignment layer providing opposite alignment directions to LCs in the LC mixture.

  17. The optical element of claim 13, wherein the first electrode and the second electrode are arranged opposite to each other, and at least one of the first electrode and the second electrode includes a plurality of sub-electrodes.

  18. The optical element of claim 17, wherein the driving voltage varies spatially across the sub-electrodes of the at least one of the first electrode and the second electrode.

  19. The optical element of claim 17, wherein the driving voltage is spatially uniform across the remaining one of the first electrode and the second electrode.

Description

BACKGROUND

[0001] The present disclosure generally relates to a liquid crystal (LC) mixture and, in particular, to a nematic LC mixture that exhibits a substantially neutral net dielectric anisotropy at a room temperature and is intended for pitch variable optical elements, and a pitch variable optical element containing the same.

[0002] As one of the well-known types of functional materials, LCs are widely applied in diffractive optical elements, such as diffraction gratings, diffractive lenses. LCs have become increasingly important for future information processing due to their advantages of low cost, low power consumption and simple preparation. In general, traditional electrically switchable diffractive optical elements using LCs have two categories: one is based on a nonuniform electric field distribution in LCs induced by patterned electrodes on one or both substrates, and the other is based on a periodic refractive index profile induced by multiple alignment regions or holographic recordings in a polymer-network liquid crystal composite. However, the manufacture and control of existing diffractive optical elements using LCs are complicated and expensive and, more important, the pitch of the diffraction structures in the existing diffractive optical elements using LCs is fixed and cannot be electrically continuously adjusted. Thus, the diffraction angle is fixed or cannot be electrically continuously adjusted.

BRIEF SUMMARY OF THE DISCLOSURE

[0003] One aspect of the present disclosure provides an LC mixture for a pitch variable optical element. The LC mixture includes a host LC and one or more LC dimers dissolved as a guest in the host LC. The host LC and the one or more LC dimers have respective dielectric anisotropies of opposite signs in nematic phase. A net dielectric anisotropy of the LC mixture is substantially neutral at a room temperature.

[0004] Another aspect of the present disclosure provides an optical element containing an LC mixture in accordance with the present discourse. The optical element includes a first electrode and a second electrode configured to provide a driving voltage to the optical element; and a disclosed LC mixture coupled to the first electrode and the second electrode. A pitch of flexoelectric domains (FDs) induced in the LC mixture is continuously variable with the driving voltage.

[0005] Other aspects of the present disclosure can be understood by those skilled in the art in light of the description, the claims, and the drawings of the present disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

[0006] The following drawings are provided for illustrative purposes according to various disclosed embodiments and are not intended to limit the scope of the present disclosure.

[0007] FIG. 1A is a schematic diagram illustrating spontaneous polarization of pear-shaped liquid crystal (LC) molecules under splay deformation;

[0008] FIG. 1B is a schematic diagram illustrating spontaneous polarization of bend-shaped LC molecules under bend deformation;

[0009] FIG. 2A is a schematic diagram illustrating a cross-section of an LC cell containing an LC mixture, according to an embodiment of the present disclosure;

[0010] FIG. 2B is a schematic diagram illustrating flexoelectric domains (FDs) induced in the LC cell in FIG. 2A under a relatively low driving voltage, according to an embodiment of the present disclosure;

[0011] FIG. 2C is a schematic diagram illustrating FDs induced in the LC cell in FIG. 2A under a relatively high driving voltage, according to an embodiment of the present disclosure;

[0012] FIG. 3A is a group of photomicrographs illustrating an LC cell filled with an LC mixture under different driving voltages, according to an embodiment of the present disclosure;

[0013] FIG. 3B is a schematic diagram illustrating a relationship between a pitch of FDs induced in the LC cell in FIG. 3A and an amplitude of the driving voltage, according to an embodiment of the present disclosure;

[0014] FIG. 4 is a group of images illustrating laser diffraction spots produced by the LC cell in FIG. 3A under different driving voltages, according to an embodiment of the present disclosure;

[0015] FIG. 5A is a schematic diagram illustrating a cross-section of an LC cell containing an LC mixture, according to another embodiment of the disclosure;

[0016] FIG. 5B is a schematic diagram illustrating a top view of the LC cell in FIG. 5A, according to an embodiment of the present disclosure;

[0017] FIG. 6A is a schematic diagram illustrating a schematic diagram of an optical assembly including a pitch variable optical element, according to an embodiment of the present disclosure;

[0018] FIG. 6B is a schematic diagram illustrating a schematic diagram of a controller in FIG. 6A, according to an embodiment of the present disclosure;

[0019] FIG. 7 is a schematic diagram illustrating a schematic diagram of an optical assembly including a pitch variable optical element, according to another embodiment of the disclosure;

[0020] FIG. 8 is a schematic diagram illustrating a schematic diagram of a near-eye display (NED), according to an embodiment of the present disclosure;

[0021] FIG. 9A is an isometric diagram illustrating a wire diagram of a NED, according to another embodiment of the disclosure; and

[0022] FIG. 9B is a cross-sectional view of the NED in FIG. 9A, according to an embodiment of the present disclosure.

DETAILED DESCRIPTION

[0023] Reference will now be made in detail to exemplary embodiments of the disclosure, which are illustrated in the accompanying drawings. Hereinafter, embodiments consistent with the disclosure will be described with reference to drawings. In the drawings, the shape and size may be exaggerated, distorted, or simplified for clarity. Wherever possible, the same reference numbers will be used throughout the drawings to refer to the same or like parts, and a detailed description thereof may be omitted.

[0024] Further, in the present disclosure, the disclosed embodiments and the features of the disclosed embodiments may be combined under conditions without conflicts. It is apparent that the described embodiments are some but not all of the embodiments of the present disclosure. Based on the disclosed embodiments, persons of ordinary skill in the art may derive other embodiments consistent with the present disclosure, all of which are within the scope of the present disclosure.

[0025] LC molecules usually have permanent dipoles, but they do not exhibit spontaneous polarization because of equal probability for the dipoles to point to two opposite directions respectively. LCs are anisotropic dielectric media and their orientations can be changed by an externally applied field, such as an external electric field. The interaction energy between an externally applied electric field and the LCs is given by the following equation:

f.sub.dielectric=1/2.DELTA..epsilon.({right arrow over (E)}{right arrow over (n)}).sup.2, (1)

where .DELTA..epsilon. is the dielectric anisotropy of the LCs, {right arrow over (n)} is the LC director pointing in the direction of the average molecular orientation, and {right arrow over (E)} is the externally applied electric field intensity. According to the Eq. (1), the interaction energy f.sub.dielectric is insensitive to the polarity of the electric field. However, for the LC molecules that do not have a perfect rod-shaped structure but have either a bend-shaped or a pear-shaped structure, when the LC orientations are not uniform in space, their dipoles may point to the same direction and thus, a spontaneous polarization (also referred to as a flexoelectric polarization) may be produced and given by the following equation:

{right arrow over (P)}.sub.flexoelectric=e.sub.s{right arrow over (n)}(.gradient.{right arrow over (n)})+e.sub.b{right arrow over (n)}.times..gradient..times.{right arrow over (n)}, (2)

where e.sub.s and e.sub.b are splay and bend flexoelectric coefficients, respectively. FIG. 1A illustrates that pear-shaped LC molecules 100 with longitudinal dipoles may exhibit spontaneous polarization under splay deformation. FIG. 1B illustrates that bend-shaped LC molecules 150 with longitudinal dipoles may exhibit spontaneous polarization under bend deformation. The interaction energy of the spontaneous polarization and the externally applied electric field is described by the following equation:

f.sub.flexoelectric=-P.sub.flexoelectric{right arrow over (E)}=-[e.sub.s{right arrow over (n)}(.gradient.{right arrow over (n)})+e.sub.b{right arrow over (n)}.times..gradient..times.{right arrow over (n)}]{right arrow over (E)}. (3)

[0026] According to the above Eq. (3), the interaction energy fflexoelectnc is sensitive to the polarity of the externally applied electric field, i.e., the polarity of the applied voltage.

[0027] The orientations of the LCs under the externally applied electric field are usually determined by both the dielectric effect and the flexoelectric effect, i.e., determined by both f.sub.flexoelectric and f.sub.dielectric. However, when the dielectric effect is much stronger than the flexoelectric effect, the dielectric effect becomes the dominant effect to determine the orientations of the LCs. On contrary, when the flexoelectric effect is much stronger than the dielectric effect, the flexoelectric effect becomes the dominant effect to determine the orientations of the LCs. Theoretical study demonstrates that the flexoelectric effect itself becomes suppressed by increasing the dielectric anisotropy (.DELTA..epsilon.) of the LCs and, in contrary, becomes enhanced by decreasing the dielectric anisotropy (.DELTA..epsilon.) of the LCs.

[0028] The present disclosure provides a LC mixture that exhibits an enhanced flexoelectric effect under an externally applied electric field. The LC mixture may have a nematic phase at a room temperature. As used herein, “room temperature” means a temperature ranging from 15.degree. C. to 40.degree. C. both inclusive. A composition of the LC mixture may include a nematic host LC and one or more LC dimers dissolved as a guest in the host LC, where the host LC and the one or more LC dimers may have respective dielectric anisotropies of opposite signs in nematic phase. A weight percentage of the LC dimer in the LC mixture is designed in such a way that a net dielectric anisotropy of the LC mixture may significantly approach neutral, i.e., the net dielectric anisotropy .DELTA..epsilon. may significantly approach zero. The disclosed LC mixture may be used for an electro-optical element operated at a room temperature. The electro-optical element may be a pitch variable optical element where a pitch of flexoelectric domains (FDs) induced in the LC mixture in accordance with the present disclosure is electrically continuously variable.

[0029] The host LC may be the majority of the LC mixture, i.e., a weight percentage of the host LC in the LC mixture may be larger than 50%. The host LC may have a substantially low dielectric anisotropy (.DELTA..epsilon.) in the nematic phase. In some embodiments, the host LC may be a positive LC material, i.e., the dielectric anisotropy (.DELTA..epsilon.) of the host LC is positive. In some embodiments, the host LC may be a negative LC material, i.e., the dielectric anisotropy (.DELTA..epsilon.) of the host LC is negative. In some embodiments, the host LC may be in the nematic phase at a room temperature, i.e., a temperature range of the nematic phase of the host LC may include the room temperature. Compounds and mixtures that are suitable as the host LC are to a large extent known and many of them are also commercially available.

[0030] LC dimers is a new type of LCs that possesses some unique properties, such as exhibiting a new type nematic phase called twist-bend nematic phase, having abnormal small bend elastic constant and possessing large flexoelectricity. The LC mixture in accordance with the present disclosure may include one or more LC dimers dissolved as a guest in the host LC. The one or more LC dimers may have a substantially low dielectric anisotropy (.DELTA..epsilon.) in the nematic phase, and the dielectric anisotropy (.DELTA..epsilon.) of the one or more LC dimers may have an opposite sign as that of the LC host in the nematic phase. For example, when the host LC is a positive LC material, the one or more LC dimers may be negative LC materials; and when the host LC is a negative LC material, the one or more LC dimers may be positive LC materials. In addition, the one or more LC dimers may have molecular structures that could promote the formation of the twist-bend nematic phase and large flexoelectricity at a room temperature, for example, a pear-shaped molecular structure exhibiting a large splay flexoelectric coefficient, a bent-shaped molecular structure exhibiting a large bend flexoelectric coefficient, a semi-flexible bent core molecular structure. Further, the one or more LC dimers may have a good solubility in the LC host. The weight percentage of the one or more LC dimers in the LC mixture may be determined by various factors, such as the solubility of the LC dimers in the LC mixture, the desired net dielectric anisotropy and desired flexoelectric coefficients of the LC mixture, etc. The net dielectric anisotropy and flexoelectric coefficients of the LC mixture may be adjustable by varying the weight percentages of the LC dimers in the LC mixture, however, the solubility of the LC dimers in the nematic host LC is desired to be considered.

[0031] Compounds and mixtures that are suitable as the one or more LC dimers that are dissolved as a guest in the host LC are to a large extent known and many of them are also commercially available. In some embodiments, the one or more LC dimers may include cyanobiphenyl-based LC dimer. In some embodiments, the cyanobiphenyl-based LC dimer may include a member of 1,.omega.-bis(4-cyanobiphenyl-4’-yl) alkane homologous series having the following chemical structure:

STR00001

where two mesogenic units (i.e., cyanobiphenyl groups) are connected using a flexible linkage consisting of an alkyl chain. 1,.omega.-bis(4-cyanobiphenyl-4’-yl) alkane homologous series is referred to using an acronym CBnCB, where CB denotes cyanobiphenyl and n denotes a number of methylene units in the flexible linkage. An odd-numbered member of CBnCB may have a molecular structure, where the two cyanobiphenyl groups at the two ends are connected via the alkyl chain with an odd number of carbons and are inclined at some angle with respect to each other. That is, an odd-numbered member of CBnCB may have a bent molecular shape, and such a conformation facilitates a large bend flexoelectric coefficient. An even-numbered member of CBnCB may have a molecular structure where the long axes of the two cyanobiphenyl groups at the two ends are parallel to each other. That is, an even-numbered member of CBnCB may have a linear molecular shape, and the bend flexoelectric coefficient of the even-numbered members of CBnCB may be suppressed as compared to the that of the odd-numbered members of CBnCB.

[0032] CB7CB, CB9CB and CB11CB are examples of odd-membered LC dimers. CB7CB has the following molecular structure:

STR00002

where the two cyanobiphenyl groups at the two ends are connected via the alkyl chain with seven carbons and are inclined at some angle with respect to each other. CB9CB has the following molecular structure:

STR00003

[0033] which is similar to that of CB9CB except the alkyl chain consists of nine carbons. A large bend flexoelectric coefficient e.sub.b of about -31 pC/m was reported for the LC dimer CB7CB, and a similar bend flexoelectric coefficient is expected for the LC dimer CB9CB. CB7CB and CB9CB also have a similar positive dielectric anisotropy (.DELTA..epsilon.) of about 2.

[0034] The LC mixture in accordance with the present disclosure may be prepared in a manner known per se, for example, heating a mixture of the host LC and the one or more LC dimer to a temperature approximately above the clearing point, then cooling the mixture to the room temperature. For discussion purposes, an LC mixture in accordance with the present disclosure (referred to as LC mixture A) was prepared by mixing HNG7267 (.DELTA..epsilon.=-1.9, .DELTA.n=0.15, from Jiangsu Hecheng Display Technology Co., Ltd (HCCH)) as the host LC with CB7CB and CB9CB as the LC dimers, where weight percentages of the host LC and LC dimers in the LC mixture A are about 70% and 30%, respectively. Both CB7CB and CB9CB were doped into the host LC to enhance the solubility of the LC dimers in the nematic host LC. The LC mixture A was measured to have a negative dielectric anisotropy (.DELTA..epsilon.) of about -0.2 at a room temperature, which is substantially neutral. The bend flexoelectric coefficient of the LC mixture A is about -10 pC/m.

[0035] The LC mixture in accordance with the present disclosure may exhibit unique optical properties at a room temperature, such as light diffraction, electrically tunable pitch of diffraction structures, electrically tunable diffraction angle and electrically tunable diffraction efficiency after filled into a suitable LC cell and applied with a suitable external driving voltage. The production of an LC cell containing an LC mixture in accordance with the present disclosure may be carried out in a manner known per se, for example, by evacuating the LC cell and introducing the LC mixture into the evacuated LC cell.

[0036] FIG. 2A illustrates a cross-section of an LC cell 200 containing an LC mixture according to an embodiment of the present disclosure. As shown in FIG. 2A, the LC cell 200 may include two opposite substrates 210 and an LC mixture layer 220 sandwiched between the two substrates 210. The LC mixture layer 220 may be a thin film of an LC mixture in accordance with an embodiment of the present disclosure. The substrates 210 may provide support and protection to the LC mixture layer 220. The substrates 210 may be substantially transparent in the visible band (about 380 nm to about 700 nm). In some embodiments, the substrates 210 may also be transparent in some or all of the infrared (IR) band (about 700 nm to about 1 mm). The substrate 210 may include a suitable material that is substantially transparent to the light of above-listed wavelengths range, e.g., glass, plastic, sapphire, etc. A conductive electrode 230 such as an indium tin oxide (ITO) electrode may be disposed on opposing surfaces of the substrates 210 to apply a driving voltage by a power source 280 to the LC cell 200. The driving voltage may be a direct current (DC) voltage or an ultra-low frequency alternating current (AC) voltage (e.g., 0.01 Hz AC voltage). All such alternative usages of the power source are within the scope to the present disclosure. The conductive electrode 230 may be, for example, a continuous planar electrode, a patterned planar electrode, or a protrusion electrode. An alignment layer 240 may be disposed on opposing surfaces of the conductive electrodes 230, and the LC mixture layer 220 may be sandwiched between the two alignment layers 240. The alignment layers 240 may provide an original alignment to LC molecules 250 in the LC mixture layer 220. The various materials of the alignment layers 240, and the alignment direction and strength, may cause the LC molecules 250 at the boundaries to have different original alignments. In some embodiments, the conductive electrodes 230 each may be covered with an insulated layer of, for example, SiO.sub.2, to prevent the injection of charge carriers through the conductive electrode 230. In one embodiment, as shown in FIG. 2A, the conductive electrode 230 may be a continuous planar electrode, and the two alignment layers 240 may be configured with homogeneous anti-parallel alignment directions, respectively, for example, in +y-direction and -y-direction, respectively, through which the LC molecules 250 may be oriented in an anti-parallel direction at a voltage-off state (V=0).

[0037] FIG. 2B and FIG. 2C illustrate orientations of the LC molecules 250 at a voltage-on state under different driving voltages provided by the power source 280. The driving voltage V of the power source 280 is applied on the two conductive electrodes 230, and an electric field along the z-direction is generated. As shown in FIG. 2B, a plurality of flexodomains (FDs) 260 may begin to be induced in the LC mixture layer 220 as the driving voltage V exceeds a threshold value. For illustrative purposes, FIG. 2B shows three FDs 260, and a single FD 260 is denoted by a dashed box. The FDs 260 are a kind of electric field induced deformation that appears solely due to the flexoelectric effect. The emergence of the FDs in the LC mixture layer 220 may be related to various factors, such as the amplitude and frequency of the driving voltage, the operating temperature, etc. The structures of the FDs 260 may be similar to an optical grating. As shown in FIG. 2B, the FDs 260 induced in the LC mixture layer 220 may be arranged in a spatially periodic pattern with a uniform pitch (or period) A, and a single FD 260 may extend parallel to the original alignment direction (e.g., y-direction in FIG. 2B). That is, a length direction of the single FD 260 may be parallel to the original alignment direction (e.g., y-direction in FIG. 2B). The azimuth angles (.phi.) of the LC molecules 250 may be changed in a linearly repetitive pattern from a center to an edge of the LC mixture layer 220, with the uniform pitch (or period) A. The pitch A may be the size along the width direction (e.g., x-direction) of a single FD 260, or the pitch A may be the distance along the x-direction between repeated portions of the pattern. The pitch A may determine, in part, the optical properties of the optical grating consisting of the FDs 260. For example, the pitch A may determine the diffraction angles of an incident light beam. Generally, the smaller the pitch A, the larger the diffraction angle for a designed wavelength.

[0038] It is to be noted that, the LC cell 200 may be polarization selective. The LC cell 200 may selectively diffract a light beam having a first polarization but transmit a light beam having a second polarization with negligible diffraction. For example, as shown in FIG. 2B, a light beam 265 linearly polarized in the alignment direction (e.g., x-direction in FIG. 2B) may experience a periodic refractive index modulation as propagating through the LC cell 200 and, thus, may be diffracted by the LC cell 200. For illustrative purposes, FIG. 2B shows a +1’ order diffraction of the light beam 260, where a diffraction angle .theta. is an angle between a diffracted light beam 270 and the normal of the light incident surface. A light beam linearly polarized in direction (e.g., y-direction in FIG. 2B) perpendicular to the alignment direction may experience a uniform refractive index as propagating through the LC cell 200 and, thus, may be transmitted through with negligible diffraction. In some embodiments, a linearly polarizer may be optically coupled to the LC cell 200, such that the light beam incident onto the LC cell 200 may have a desired polarization that matches the requirements of the LC cell 200.

[0039] The structures of the FDs 260 induced in the LC mixture layer 220 may be controlled by various factors, such as the amplitude and frequency of the driving voltage provided by the power source 280, the operating temperature, etc. As shown in FIG. 2C, as the amplitude of the driving voltage increases (the driving voltage is V.sub.high in FIG. 2C as compared to the driving voltage V.sub.low in FIG. 2B), the pitch A of the FDs 260 induced in the LC mixture layer 220 may decrease. Accordingly, the diffraction angle may increase. For illustrative purposes, FIG. 2C shows a +1.sup.st order diffraction of the light beam 260, where the diffraction angle .theta. is an angle between a diffracted light beam 275 and the normal of the light incident surface. The diffraction angle .theta. in FIG. 2C obviously increases as compared to that in FIG. 2B. As the amplitude of the driving voltage continuously increases, the pitch A of the FDs 260 induced in the LC mixture layer 220 may continuously decrease. That is, the pitch A of the optical grating consisting of the FDs 260 may be continuously adjustable by an externally applied voltage. Accordingly, the diffraction angle of a light beam incident onto the optical grating consisting of the FDs 260 may be continuously adjustable by an externally applied voltage. The continuously adjustable pitch may have a great potential for important and extended applications of optical gratings.

[0040] The pitch A of the FDs 260 induced in the LC mixture layer 220 may be on a micrometer (.mu.m) scale and may be observed under a polarizing microscope (POM). FIG. 3A illustrates photomicrographs of an LC cell filled with the LC mixture A under different driving voltages. The LC cell may have a cell structure shown in FIG. 2A. The cell gap is about 3.7 .mu.m, and the operating temperature is room temperature. The photomicrographs are taken under POM with the LC cell arranged between two crossed polarizers. As shown in FIG. 3A, the morphology of the FDs induced in the LC mixture A is changing as the driving voltage applied to the LC cell varies. FDs are not observed in the LC mixture A as the driving voltage gradually increases from 0V to 6V. As the driving voltage increases to 8V, the FDs are observed to be induced in the LC mixture A, where the FDs manifest themselves as a spatially periodic array of bright and dark stripes parallel to the initial LC director alignment direction under the POM. The pitch A of the FDs is about 5 .mu.m. As the amplitude of the driving voltage further increases, the pitch A of the FDs in the LC mixture A obviously decrease, for example, decreases to about 2.7 .mu.m, 1.7 .mu.m, 1.5 .mu.m and 1.1 .mu.m as the driving voltage increases to 12V, 16V, 20V and 24V, respectively. FIG. 3B illustrates a relationship between the pitch A of the FDs induced in the LC mixture A and the amplitude of the driving voltage. As shown by a curve 310 in FIG. 3B, the pitch A of the FDs induced in the LC mixture A has a substantially linear relationship with the reciprocal of the amplitude of the driving voltage. A linear fitting is also conducted between the pitch A and the reciprocal of various amplitude of the driving voltage, as shown by a curve 320 in FIG. 3B, which substantially matches the curve 310.

[0041] As discussed above, the structures of FDs induced in the LC mixture are similar to optical grating and, thus, the FDs may generate laser diffraction spots when an incident laser beam satisfies a certain diffraction condition, e.g., Bragg condition. FIG. 4 illustrates images of laser diffraction spots produced by the LC cell in FIG. 3A under different driving voltages. A paper is used as a screen for the diffraction spots to be displayed on, and a camera placed at a fixed position is used to capture various images of the screen showing the diffraction spots. Referring to FIG. 3A and FIG. 4, as the driving voltage increase to 8V, diffraction spots are present as the optical grating consists of the FDs appears, and the diffraction spots generated by the 0th, .+-.1.sup.st order, .+-.2.sup.nd order and .+-.3.sup.rd order diffraction are observed and captured by the camera. As the driving voltage increases from 8V to 20V, the pitch A gradually decreases and, thus, the diffraction angles gradually increases. Provided the distance between the screen and the LC cell is constant, the distance between the 0th diffraction spot and a non-zero order diffraction spot may gradually increase as the diffraction angle of the non-zero order diffraction gradually increases. For example, when the driving voltage is 12V, the diffraction spots of the .+-.3.sup.rd order diffraction are out of the camera’s view, and only the diffraction spots of the 0th, .+-.1’ order, and .+-.2.sup.nd order diffraction are observed. When the driving voltage is 16V, the diffraction spots of the 2.sup.nd order and .+-.3.sup.rd order diffraction are out of the camera’s view ultimately with a decrease in the pitch A, and only the diffraction spots of the 0.sup.th and .+-.1’ order diffraction are observed.

[0042] Referring to FIGS. 2A-2B, FIGS. 3A-3B and FIG. 4, the LC cell 200 filled with an LC mixture in accordance with the present discourse (e.g., the LC mixture A) may function as an optical grating formed by spatially periodic arranged FDs, where the pitch of the optical grating (or the pitch of the spatially periodic arranged FDs) may be electrically continuously tunable and, accordingly, the diffraction angle of an incident light beam may be may be electrically continuously tunable. Such an optical element with continuously variable pitch may have significant potential applications for manipulating light beams, such as diffraction optics, laser displays, beam shaping or steering, switchable holograms, and adaptive microdevices.

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