Patent Publication Number: US-8537310-B2

Title: Polarization-independent liquid crystal display devices including multiple polarization grating arrangements and related devices

Description:
STATEMENT OF GOVERNMENT SUPPORT 
     This invention was made with Government support by the National Science Foundation (NSF) under contract 0621906. The U.S. Government has certain rights to this invention. 
    
    
     CLAIM OF PRIORITY 
     This application is a 35 U.S.C. §371 national phase application of PCT International Application No. PCT/US2008/011611, filed Oct. 9, 2008, the entire contents of which is incorporated by reference herein in its entirety. The above-referenced PCT International Application was published in the English language as International Publication No. WO 2010/042089 on Apr. 15, 2010. 
     FIELD OF THE INVENTION 
     The present invention relates to liquid crystal displays, and more particularly, to liquid crystal polarization gratings and related methods of fabrication. 
     BACKGROUND OF THE INVENTION 
     Liquid crystals may include liquids in which an ordered arrangement of molecules exists. Typically, liquid crystal (LC) molecules may be anisotropic, having either an elongated (rod-like) or flat (disk-like) shape. As a consequence of the ordering of the anisotropic molecules, a bulk LC often exhibits anisotropy in its physical properties, such as anisotropy in its mechanical, electrical, magnetic, and/or optical properties. 
     As a result of the rod-like or disk-like nature, the distribution of the orientation of LC molecules may play an important role in optical applications, such as in liquid crystal displays (LCDs). In these applications, LC alignment may be dictated by an alignment surface. The alignment surface may be treated so that the LC aligns relative to the surface in a predictable and controllable way. In many cases, the alignment surface may ensure a single domain through the LC device. In the absence of a treated alignment surface, the LC may have many domains and/or many discontinuities in orientation. In optical applications, these domains and discontinuities may cause scattering of light, leading to degradation in the performance of the display. 
     Many liquid crystal devices (including liquid crystal displays) may require input light that is polarized in order to correctly function. However, since most light sources produce unpolarized light (e.g., fluorescent lamps, light emitting diodes, Ultra High Performance lamps, incandescent lamps), liquid crystal devices may use one or more linear polarizers to convert the unpolarized light from a light source into light of a desired polarization state. Conventional linear polarizers may permit light of the desired polarization state to pass therethrough; however such linear polarizers may also absorb light of other polarization states. As such, at least 50% of the available light from the light source may be lost, for example, as heat. Liquid crystal devices may therefore have significant optical power losses (for example, greater than 50%), and as such, may require light sources more powerful than necessary. This may be undesirable, for example, for reasons relating to power consumption, heat, and/or costs. 
     SUMMARY OF THE INVENTION 
     According to some embodiments of the present invention, a liquid crystal device includes a first polarization grating, a liquid crystal layer, and a second polarization grating. The first polarization grating is configured to polarize and diffract incident light into first and second beams having different polarizations and having different directions of propagation than that of the incident light. The liquid crystal layer is configured to receive the first and second beams from the first polarization grating, and is configured to be switched between a first state that does not substantially affect respective polarizations of the first and second beams traveling therethrough and a second state that alters the respective polarizations of the first and second beams traveling therethrough. The second polarization grating is configured to receive the first and second beams from the liquid crystal layer, and is configured to analyze and diffract the first and second beams to alter the directions of propagation thereof in response to the state of the liquid crystal layer. 
     In some embodiments, the second polarization grating may be configured to alter the directions of propagation of the first and second beams to transmit light that propagates in a direction substantially parallel to that of the incident light when the liquid crystal layer is in the second state, and to transmit light that does not propagate in the direction substantially parallel to that of the incident light when the liquid crystal layer is in the first state. In such embodiments, the first polarization grating may have a first periodic birefringence pattern, and the second polarization grating may have a second periodic birefringence pattern that is inverted relative to the first periodic birefringence pattern. For example, the first polarization grating may be a polymerized liquid crystal layer including a first periodic nematic director pattern, and the second polarization grating may be a polymerized liquid crystal layer including a second periodic nematic director pattern having a same periodicity but globally rotated about 180 degrees relative to the first nematic director pattern. 
     In other embodiments, the second polarization grating may be configured to alter the directions of propagation of the first and second beams to transmit light that propagates in a direction substantially parallel to that of the incident light when the liquid crystal layer is in the first state, and to transmit light that does not propagate in the direction substantially parallel to that of the incident light when the liquid crystal layer is in the second state. In such embodiments, the first and second polarization gratings may have respective first and second periodic birefringence patterns having a same periodicity and a same orientation. For example, the first and second polarization gratings may be polymerized liquid crystal layers including similarly-oriented local nematic director patterns. 
     In some embodiments, the liquid crystal device may include an angle filtering stage configured to receive the output light transmitted from the second polarization grating. The angle filtering stage may be configured to block the output light that propagates at angles greater than a desired angle and direct the output light that propagates at angles less than the desired angle towards a screen. For example, the angle filtering stage may be configured to permit the output light that propagates in the direction substantially parallel to the incident light but block the output light that does not propagate in the direction substantially parallel to the incident light. In some embodiments, the angle filtering stage may include at least one lens and an aperture stop. In other embodiments, the angle filtering stage may be a privacy film. 
     In other embodiments, the incident light may be unpolarized light, and the first polarization grating may be configured to diffract the incident light such that the first and second beams respectively comprise greater than about 25% of an intensity of the incident light over a visible wavelength range. In addition, the second polarization grating may be configured to diffract the first and second beams to transmit light comprising greater than about 50% of the intensity of the incident light over the visible wavelength range. In some embodiments, the second polarization grating may be configured to transmit the output light with a transmittance of greater than about 90% over a wavelength range of about 400 nm to about 700 nm. 
     In some embodiments, the liquid crystal device may include a third polarization grating, an intermediate layer, and a fourth polarization grating that define an offset compensator. 
     The third polarization grating may be configured to receive and diffract the first and second beams from the second polarization to alter the respective directions of propagation thereof. The intermediate layer may be configured to transmit the first and second beams from the third polarization grating therethrough without substantially altering the respective directions of propagation thereof. The fourth polarization grating may be configured to receive and diffract the first and second beams from the intermediate layer, to alter the respective directions of propagation thereof to provide offset-compensated output light that propagates in a direction substantially parallel to that of the first and second beams output from the second polarization grating. The intermediate layer may have a thickness configured to separate the third and fourth polarization gratings by a distance substantially similar to a distance between the second polarization and the liquid crystal layer such that the offset-compensated output light has a reduced spatial offset relative to that of the first and second beams output from the second polarization grating. 
     According to other embodiments of the present invention, a liquid crystal device includes a polarization grating, a liquid crystal layer, and a reflective substrate. The polarization grating is configured to polarize and diffract input light into first and second beams having different polarizations and having different directions of propagation than that of the input light. The liquid crystal layer is configured to receive the first and second beams from the first polarization grating. The liquid crystal layer is configured to be switched between a first state that does not substantially alter respective polarizations of the first and second beams traveling therethrough and a second state that alters the respective polarizations of the first and second beams traveling therethrough. The reflective substrate is configured to receive the first and second beams from the liquid crystal layer and reflect the first and second beams back through the liquid crystal layer and the polarization grating. The polarization grating is configured to analyze and diffract the reflected first and second beams from the reflective substrate to alter the respective directions of propagations thereof in response to the state of the liquid crystal layer to provide output light therefrom. 
     In some embodiments, the polarization grating may be a second polarization grating, and the device may include a first polarization grating configured to polarize and diffract incident light into the first and second beams having different polarizations and having different directions of propagation than that of the incident light. The device may also include a lens configured to receive the first and second beams from the first polarization grating and provide the first and second beams to the second polarization grating as the input light thereto. 
     In other embodiments, the device may include a reflective aperture stop configured to receive the first and second beams from the lens and reflect the first and second beams onto the second polarization grating to provide the input light thereto. The reflective aperture stop may be configured to transmit the output light from the second polarization grating therethrough towards a screen. 
     According to further embodiments of the present invention, a device includes a first polarization grating configured to receive incident light and transmit light therefrom, and a second polarization grating configured to receive the light from the first polarization grating and transmit output light therefrom comprising first and second component beams having different polarizations. At least one of the first and second polarization gratings is a switchable polarization grating configured to be switched between a first state that does not substantially alter respective polarizations and directions of propagation of the light traveling therethrough, and a second state that alters the respective polarizations and directions of the light traveling therethrough. 
     In some embodiments, the first polarization grating may be the switchable polarization grating. In the first state, the first polarization grating may be configured to transmit the incident light therethrough without substantially altering the respective polarizations and directions of propagation thereof. In the second state, the first polarization grating may be configured to polarize and diffract the incident light into first and second beams having different polarizations and different directions of propagation than that of the incident light. The second polarization grating may be a fixed grating configured to analyze and diffract the first and second beams from the first polarization grating to alter the respective directions of propagation thereof when the first polarization grating is in the second state, and may be configured to polarize and diffract the incident light into the first and second beams having the different polarizations and different directions of propagation when the first polarization grating is in the first state. 
     In other embodiments, the first polarization grating may be a fixed grating configured to polarize and diffract the incident light into first and second beams having different polarizations and different directions of propagation than that of the incident light, and the second polarization grating may be the switchable polarization grating. In the first state, the second polarization grating may be configured to transmit the first and second beams from the first polarization grating therethrough without substantially altering the respective polarizations and directions of propagation thereof. In the second state, the second polarization grating may be configured to analyze and diffract the first and second beams from the first polarization grating to alter the respective polarizations and directions of propagation thereof. 
     In some embodiments, the first and second polarization gratings may have respective birefringence patterns having orientations that are inverted relative to one another. In other embodiments, the first and second polarization gratings may have respective birefringence patterns having substantially similar orientations. 
     Other elements and/or devices according to some embodiments will become apparent to one with skill in the art upon review of the following drawings and detailed description. It is intended that all such additional devices be included within this description, be within the scope of the invention, and be protected by the accompanying claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS. 1A and 1B  are block diagrams illustrating multi-polarization grating arrangements according to some embodiments of the present invention. 
         FIGS. 1C and 1D  are alternate views illustrating the local nematic director orientations of the polarization gratings of  FIGS. 1A and 1B . 
         FIGS. 2A and 2B  are block diagrams illustrating direct-view liquid crystal display devices including multi-polarization grating arrangements according to some embodiments of the present invention. 
         FIG. 3A  is a block diagram illustrating projection-type liquid crystal display devices including multi-polarization grating arrangements according to some embodiments of the present invention. 
         FIG. 3B  is a block diagram illustrating projection-type liquid crystal display devices including multi-polarization grating arrangements and a reflective substrate in a non-telecentric configuration according to some embodiments of the present invention. 
         FIG. 3C  is a block diagram illustrating projection-type liquid crystal display devices including multi-polarization grating arrangements and a reflective substrate in a telecentric configuration according to some embodiments of the present invention. 
         FIGS. 4A and 4B  are block diagrams illustrating projection-type liquid crystal display devices including multi-polarization grating arrangements according to further embodiments of the present invention. 
         FIG. 5  is a block diagram illustrating projection-type liquid crystal display devices including multi-polarization grating arrangements and an offset compensator according to still further embodiments of the present invention. 
         FIG. 6  is a diagram illustrates an example simulation space for polarization grating arrangements according to some embodiments of the present invention. 
         FIGS. 7A-7G  are graphs illustrating simulation results for polarization grating arrangements according to the simulation space of  FIG. 6 . 
         FIGS. 8A-8F  are graphs illustrating experimental results for polarization grating arrangements according to some embodiments of the present invention. 
         FIG. 9A  is a diagram illustrating an achromatic polarization grating according to some embodiments of the present invention. 
         FIG. 9B  is a photograph illustrating the light output from the achromatic polarization grating of  FIG. 9A . 
         FIG. 10A  is a diagram illustrating parallel and antiparallel polarization grating configurations according to some embodiments of the present invention. 
         FIG. 10B  is a graph illustrating measured transmittance spectra for both polarization grating configurations of  FIG. 10A . 
         FIG. 10C  is a graph illustrating the measured extinction ratio for the an anti-parallel polarization grating arrangement of  FIG. 10A . 
         FIGS. 11A and 11B  are graphs illustrating transmittance and contrast ratios, respectively, for liquid crystal display devices according to some embodiments of the present invention. 
         FIGS. 12A-12C  illustrate a prototype projector in accordance with some embodiments of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION 
     The present invention is described more fully hereinafter with reference to the accompanying drawings, in which embodiments of the invention are shown. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. In the drawings, the size and relative sizes of layers and regions may be exaggerated for clarity. Like numbers refer to like elements throughout. 
     It will be understood that, although the terms first, second, third etc. may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. These terms are only used to distinguish one element, component, region, layer or section from another region, layer or section. Thus, a first element, component, region, layer or section discussed below could be termed a second element, component, region, layer or section without departing from the teachings of the present invention. 
     Spatially relative terms, such as “beneath”, “below”, “lower”, “under”, “above”, “upper” and the like, may be used herein for ease of description to describe one element or feature&#39;s relationship to another element(s) or feature(s) as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as “below” or “beneath” or “under” other elements or features would then be oriented “above” the other elements or features. Thus, the exemplary terms “below” and “under” can encompass both an orientation of above and below. The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly. In addition, it will also be understood that when a layer is referred to as being “between” two layers, it can be the only layer between the two layers, or one or more intervening layers may also be present. 
     The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items. 
     It will be understood that when an element or layer is referred to as being “on”, “connected to”, “coupled to”, or “adjacent to” another element or layer, it can be directly on, connected, coupled, or adjacent to the other element or layer, or intervening elements or layers may be present. In contrast, when an element is referred to as being “directly on,” “directly connected to”, “directly coupled to”, or “immediately adjacent to” another element or layer, there are no intervening elements or layers present. Likewise, when light is received or provided “from” one element, it can be received or provided directly from that element or from an intervening element. On the other hand, when light is received or provided “directly from” one element, there are no intervening elements present. 
     Embodiments of the invention are described herein with reference to cross-section illustrations that are schematic illustrations of idealized embodiments (and intermediate structures) of the invention. As such, variations from the shapes of the illustrations as a result, for example, of manufacturing techniques and/or tolerances, are to be expected. Thus, embodiments of the invention should not be construed as limited to the particular shapes of regions illustrated herein but are to include deviations in shapes that result, for example, from manufacturing. Accordingly, the regions illustrated in the figures are schematic in nature and their shapes are not intended to illustrate the actual shape of a region of a device and are not intended to limit the scope of the invention. 
     Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and/or the present specification and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein. 
     It will be understood by those having skill in the art that, as used herein, a “transmissive” or “transparent” substrate may allow at least some of the incident light to pass therethrough. Accordingly, the transparent substrate may be a glass substrate in some embodiments. In contrast, a “reflective” substrate as described herein may reflect at least some of the incident light. Also, “polymerizable liquid crystals” may refer to relatively low-molecular weight liquid crystal materials that can be polymerized, and may also be described herein as “reactive mesogens”. In contrast, “non-reactive liquid crystals” may refer to relatively low-molecular weight liquid crystal materials that may not be polymerized. 
     Embodiments of the present invention are described herein with reference to liquid crystal (LC) materials and polarization gratings composed thereof. As used herein, the liquid crystals can have a nematic phase, a chiral nematic phase, a smectic phase, a ferroelectric phase, and/or another phase. In addition, a number of photopolymerizable polymers may be used as alignment layers to create the polarization gratings described herein. In addition to being photopolymerizable, these materials may be inert with respect to the LC, should provide stable alignment over a range of operating temperatures of the LC device (e.g., from about −50° C. to about 100° C.), and should be compatible with manufacturing methods described herein. Some examples of photopolymerizable polymers include polyimides (e.g., AL 1254 commercially available from JSR Micro, Inc (Sunnyvale, Calif.)), Nissan RN-1199 available from Brewer Science, Inc. (Rolla, Mo.), and cinnamates (e.g., polyvinyl 4-methoxy-cinnamate as described by M. Schadt et al., in “Surface-Induced Parallel Alignment of Liquid Crystals by Linearly Polymerized Photopolymers,” Jpn. J. Appl. Phys., Vol. 31 (1992), pp. 2155-2164). Another example of a photopolymerizable polymer is Staralign™, commercially available from Vantico Inc. (Los Angeles, Calif.). Further examples include chalcone-epoxy materials, such as those disclosed by Dong Hoon Choi and co-workers in “Photo-alignment of Low-molecular Mass Nematic Liquid Crystals on Photochemically Bifunctional Chalcone-epoxy Film by Irradiation of a Linearly Polarized UV,” Bull. Korean Chem. Soc., Vol. 23, No. 4 587 (2002), and coumarin side chain polyimides, such as those disclosed by M. Ree and co-workers in “Alignment behavior of liquid-crystals on thin films of photosensitive polymers—Effects of photoreactive group and UV-exposure,” Synth. Met., Vol. 117(1-3), pp. 273-5 (2001) (with these materials, the LC aligns nearly perpendicularly to the direction of polarization). Additional examples of methods of liquid crystal alignment are also discussed in and U.S. Pat. No. 7,196,758 to Crawford et al. Furthermore, some structures described herein may involve precise fabrication through a balance of spin-coating processes and liquid crystal materials. Additional structures and/or methods for use with some embodiments of the present invention are discussed in PCT Publication No. WO 2006/092758 to Escuti, et al., the disclosure of which is incorporated by reference herein in its entirety. 
     Polarization gratings according to some embodiments of the present invention may be transparent, thin-film, beam-splitters that periodically alter the local polarization state and propagation direction of light traveling therethrough. In contrast, conventional linear polarizers may operate by converting incident light into a single polarization state, permitting light of that polarization state to travel therethrough, but absorbing light of other polarization states. 
     Polarization gratings according to some embodiments of the present invention may have a spatially-variant uniaxial birefringence (i.e., n(x)=[cos(πx/Λ), sin(πx/Λ), 0]), and may provide non-zero-order diffraction efficiencies of up to 100%. As used herein, “zero-order” light propagates in a direction substantially parallel to that of the incident light, i.e., at a substantially similar angle of incidence, and is also referred to herein as “on-axis” light. For example, in several of the embodiments described in detail below, the incident light is normal to the first polarization grating; thus, “zero-order” or “on-axis” light would also propagate substantially normal to the first polarization grating in these embodiments. In contrast, “non-zero-order light”, such as “first-order” light and/or “second-order light”, propagates in directions that are not parallel to the incident light. In particular, the second-order light propagates at greater angles than the first-order light relative to the angle of incidence. As such, first- and second-order light are collectively referred to herein as “off-axis” light. 
     Some embodiments of the present invention arise from realization that a sequential arrangement of two parallel polarization gratings may be used to diffract incident light into two zero-order beams without significant losses, while a sequential arrangement of two antiparallel polarization gratings may be used to diffract incident light into two non-zero-order beams without significant losses. As used herein, a “parallel” polarization grating arrangement includes first and second polarization gratings with the same birefringence n(x), i.e., the respective birefringence patterns of the first and second polarization gratings have substantially similar orientations. In contrast, an “antiparallel” polarization grating arrangement includes first and second polarization gratings having opposite birefringence, i.e., n(x) and n(−x). In other words, the second polarization grating has a birefringence pattern that is inverted or rotated by about 180 degrees relative to that of the first polarization grating. 
     Accordingly, some embodiments of the present invention provide polarization grating arrangements including two or more polarization gratings positioned relative to a liquid crystal (LC) layer. This arrangement may be used to provide liquid crystal display (LCD) devices that work directly with unpolarized light and/or light of any polarization, without substantial polarization-related losses. More particularly, the first and second polarization gratings may be positioned at the input and the output of the liquid crystal layer, respectively. In such an arrangement, the second polarization grating is generally referred to herein as an “analyzer”, and thus, “analyzes” (i.e., polarizes) the polarized light received from the first polarization grating and/or liquid crystal layer. The liquid crystal layer is configured to be switched between a first state that does not substantially affect the polarization of light traveling therethrough, and a second state that “reverses” the polarization of the light traveling therethrough (i.e., converts the light to its opposite or orthogonal polarization). For example, the liquid crystal layer may be a switchable birefringent liquid crystal layer that can be electrically switched between zero and half-wave retardation responsive to a voltage applied thereto, with relatively high accuracy and relatively wide bandwidth. The liquid crystal layer may be monolithic, or may define a pixel array including a plurality of pixels. 
     Because polarization gratings according to some embodiments of the present invention may be used to diffract incident light into two beams without significant losses, the first polarization grating may be used to diffract the incident light into two non-zero-order beams (with up to 50% efficiency into each beam) for input to the LC layer, and the second polarization grating may be used to diffract the two beams output from the LC layer back to the original angle of incidence to provide zero-order output light to a viewing screen in response to the state of the LC layer. When combined with angle filtering and imaging means as described herein, some embodiments of the present invention may provide LCD devices with improved brightness (for example, twice the brightness of conventional LCD devices) and high contrast (up to 5000:1) as compared to conventional LCD devices. Embodiments of the present invention may be used in both projection-type LCD devices (front or rear, reflective or transmissive), and/or in direct-view type LCD devices. 
     As used herein, the “transmittance” of a grating arrangement may refer the intensity of the output light divided by the intensity of the input light, and thus, includes the effects of the grating layer plus all other layers or substrates. In contrast, as used herein, “diffraction efficiency” may refer to the output intensity of a particular diffraction order divided by the total light intensity transmitted, which may be used as a normalization to remove the effects of the substrates and/or other layers. 
       FIGS. 1A and 1B  illustrate multi-polarization grating arrangements according to some embodiments of the present invention. In particular,  FIG. 1A  illustrates a dual polarization grating arrangement in a first state where no voltage is applied to its liquid crystal layer, while  FIG. 1B  illustrates the dual polarization grating arrangement in a second state where a voltage is applied to its liquid crystal layer. Referring now to  FIGS. 1A and 1B , the dual polarization grating arrangement includes a first polarization grating  101 , a liquid crystal layer  103 , and a second polarization grating  102  provided between transmissive substrates, shown as glass substrates  110  and  115 . The substrates  110  and/or  115  may also include one or more electrodes (not shown) on surfaces thereof, for instance, as provided by a transparent indium tin oxide (ITO) coating. The polarization gratings  101  and  102  include respective alignment layers  107  and  108  thereon, and the liquid crystal layer  103  is aligned in the cell gap between the polarization gratings  101  and  102  according to the periodic alignment condition provided by the alignment layers  107  and  108 . The liquid crystal layer  103  includes liquid crystal molecules that are configured to be switched between first and second orientations responsive to a voltage applied thereto. 
     The polarization gratings  101  and  102  are configured to polarize and diffract incident light into at least two beams having different polarization states and/or different directions of propagation without substantial absorption of any one polarization state. Polarization gratings that may be used in some embodiments of the present invention are described, for example, in PCT Application No. PCT/US2008/004897 to Escuti, et al. entitled “Multi-Layer Achromatic Liquid Crystal Polarization Gratings and Related Fabrication Methods”, filed Apr. 16, 2008, and/or PCT Application No. PCT/US2008/004888 to Escuti, et al. entitled “Low-Twist Chiral Liquid Crystal Polarization Gratings and Related Fabrication Methods”, filed Apr. 16, 2008, the disclosures of which are hereby incorporated by reference herein as if set forth in their entireties. 
     The polarization gratings  101  and/or  102  may provide diffraction properties such as at least three diffracted orders (0, ±1), orthogonal circular polarizations of the non-zero-orders, and/or highly polarization-sensitive non-zero-orders (which may be linearly proportional to the Stokes parameter). For example, the polarization gratings  101  and/or  102  may be polymerized liquid crystal films including anisotropic periodic molecular structures with birefringence patterns configured to diffract the incident light with a diffraction efficiency of greater than about 50%, and in some embodiments, greater than about 90%. In particular, with incident circular polarization, the polarization gratings  101  and/or  102  may provide up to about 100% efficiency into the non-zero orders. With linear incident polarization or unpolarized input light, the polarization gratings  101  and/or  102  may provide up to about 50% efficiency into each of the first orders. In some embodiments, the polarization gratings  101  and/or  102  may include multiple polarization grating layers having respective periodic local anisotropy patterns that are offset relative to one another to define a phase shift therebetween and/or rotated (or “twisted”) by a twist angle over respective thicknesses thereof. Also, one or more of the polarization grating layers may be a nematic liquid crystal layer, so as to provide a switchable liquid crystal polarization grating. 
     In some embodiments, the polarization gratings  101  and  102  may be identical in type, thickness, periodicity, and/or molecular orientation. For example, the polarization gratings  101  and  102  may include periodic molecular structures such that their local birefringence patterns have the same orientation, i.e., a “parallel” arrangement. In other embodiments, the periodic molecular structures of the polarization gratings  101  and  102  may have their respective local birefringence patterns oriented oppositely (i.e., rotated by about 180 degrees) in an “antiparallel” arrangement. 
     As shown in  FIGS. 1A and 1B , the polarization gratings  101  and  102  are polymerized liquid crystal layers having an antiparallel arrangement.  FIGS. 1C and 1D  provide alternate views illustrating the nematic director orientation of the polarization gratings  101  and  102  in greater detail. In particular,  FIG. 1C  illustrates the nematic director orientation  101 ′ of the polarization grating  101 , while  FIG. 1D  illustrates the opposite nematic director orientation  102 ′ of the polarization grating  102 . However, in other embodiments, the molecular structures of the polarization gratings  101  and  102  may be parallel and may have the same periodicity, but may be offset such that their local anisotropy patterns are shifted relative to one another by an angular shift or phase shift of between about 0° (degrees) to about 180° (degrees). 
     In  FIGS. 1A and 1B , the liquid crystal layer  103  is a vertically aligned nematic (VAN) type layer in which the LC molecules have a homeotropic alignment. As such, when no voltage is applied to the liquid crystal layer  103 , the LC molecules are oriented normal to the adjacent surfaces of the polarization gratings  101  and  102 , as shown in  FIG. 1A . When oriented in such a manner, also referred to herein as the “OFF” state, the liquid crystal layer  103  is configured to allow light to pass therethrough without substantially affecting its polarization state (i.e., with substantially zero retardation). In contrast, as shown in  FIG. 1B , the LC molecules are oriented substantially parallel to the surfaces of the polarization gratings  101  and  102  when a switching voltage is applied to the liquid crystal layer  103 . When oriented as shown in  FIG. 1B , also referred to herein as the “ON” state, the liquid crystal layer  103  is configured to alter the polarization state of light passing therethrough. In some embodiments, the liquid crystal layer  103  may have a thickness configured to provide half-wave retardation of light that passes therethrough. However, liquid crystal layers with other thicknesses and/or phase shifts may also be used. 
     Example operation of dual polarization grating arrangements in accordance with some embodiments of the present invention will now be described with reference to the OFF state of  FIG. 1A  and the ON state of  FIG. 1B . Referring now to  FIG. 1A , the first polarization grating  101  is configured to polarize input or incident light  190  into first and second component beams  195  and  196  having different polarizations. The incident light  190  may be unpolarized in some embodiments, but may be polarized in other embodiments. In some embodiments, the polarization of the first beam  195  may be orthogonal to the polarization of the second beam  196 . For example, the first beam  195  may be left-handed circularly polarized, while the second beam  196  may be right-handed circularly polarized. The first polarization grating  101  is also configured to diffract the incident light  190  such that the first and second beams  195  and  196  have different directions of propagation than that of the incident light  190 . In other words, the beams  195  and  196  propagate at different diffractive angles relative to the angle of incidence of the incident light  190 . For example, the incident light  190  may be diffracted with up to about 50% efficiency into each of the first-order beams  195  and  196  at diffractive angles having a range of about ±5° to about ±30°, and in some embodiments, about ±20° degrees. 
     As shown in  FIG. 1A , in the OFF state, no voltage is applied to the liquid crystal layer  103 . As such, the orientation  103   a  of the molecules of the liquid crystal layer  103  is configured such that the first and second beams  195  and  196  are transmitted therethrough without substantially affecting the respective polarizations of the first and second beams  195  and  196 . The second polarization grating  102  is likewise configured to analyze and diffract the first and second beams  195  and  196  received from the liquid crystal layer  103 . As the second polarization grating  102  is antiparallel to the first polarization grating  101 , the second polarization grating  102  changes the polarizations of the left- and right-beams  195  and  196  to right- and left-handed beams, respectively, and alters the respective directions of propagation of the beams  195  and  196  to transmit output light  199   a  that is further diffracted away from the direction of propagation of the incident light  190  (i.e., away from the angle of incidence) when the LC layer  103  is in the OFF state. More generally, the second polarization grating  102  is configured to diffract the beams  195  and  196  into different directions or angles based on their respective polarizations after being output from the liquid crystal layer  103 . This “first-order” output light  199   a  may have a substantially similar intensity as that of the input light  190 , but may be blocked and/or otherwise prevented from being transmitted to a viewing screen to provide improved contrast, as discussed in detail below. 
     Referring now to  FIG. 1B , the first polarization grating  101  is similarly configured to polarize and diffract the incident light  190  into first and second component beams  195  and  196  having different polarizations and different directions of propagation relative to the incident light  190 . For example, as noted above, the first beam  195  may be left-handed circularly polarized, while the second beam  196  may be right-handed circularly polarized. However, as a switching voltage is applied to the liquid crystal layer  103 , the orientation  103   b  of the molecules of the liquid crystal layer  103  is configured to alter the respective polarizations of the first and second beams  195  and  196  as they pass therethrough. In the above example, the liquid crystal layer  103  in the ON state may retard the polarizations of the left- and right-handed circularly polarized beams  195  and  196  by a half wavelength (i.e., by 180°) to provide right- and left-handed circularly polarized beams  195 ′ and  196 ′. The second polarization grating  102  is configured to analyze and diffract the beams  195 ′ and  196 ′ received from the liquid crystal layer  103 . However, as the beams  195 ′ and  196 ′ have the opposite circular polarization than those output from the liquid crystal layer  103  in  FIG. 1A , the second polarization grating, which is antiparallel to the first polarization grating  101 ,  102  is configured to alter the respective directions of propagation of the beams  195 ′ and  196 ′ to transmit output light  199   b  that is diffracted towards the direction of propagation of the incident light  190 . In particular, as shown in  FIG. 1B , the second polarization grating  102  re-directs the beams  195 ′ and  196 ′ in parallel, such that the output light  199   b  propagates in a direction substantially parallel to that of the incident light  190  (i.e., toward from the angle of incidence) when the liquid crystal layer  103  is in the ON state. The polarization grating  102  may diffract the incident circularly polarized beams  195 ′ and  196 ′ with up to 100% efficiency. Thus, the “zero-order” output light  199   b  may have an intensity substantially similar to that of the incident light  190  in some embodiments, and may thereby be transmitted to a viewing screen without significant polarization-related losses to provide improved brightness, as discussed in detail below. 
     Although described above with reference to a vertically aligned nematic (VAN) liquid crystal layer  103 , it is to be understood that other types of liquid crystal materials may be used to provide the liquid crystal layer  103 . For example, in some embodiments, a uniform planar liquid crystal layer, in which LC molecules are homogeneously aligned parallel to the surfaces of the polarization gratings  101  and  102  when no voltage is applied, may be used as the liquid crystal layer  103 . Other liquid crystal materials may also be used. Such materials are well-known in the art and need not be discussed further herein. Also, although illustrated in  FIGS. 1A-1B  with reference to an arrangement where the polarization gratings  101  and  102  and the liquid crystal layer  103  are provided between the transmissive substrates  110  and  115 , it is to be understood that the transmissive substrates  110  and  115  and the liquid crystal layer  103  may be provided between the polarization gratings  101  and  102  in some embodiments, for example, as illustrated below in  FIGS. 2A-4C . 
       FIGS. 2A and 2B  illustrate multi-polarization grating arrangements according to some embodiments of the present invention as implemented in a direct view liquid crystal display (LCD) device. In particular,  FIG. 2A  illustrates a LCD device  200   a  that includes polarization gratings  201   a  and  202   a  implemented in an antiparallel arrangement (i.e., where the nematic director patterns thereof are of opposite handedness), while FIG.  2 B illustrates a LCD device  200   b  that includes polarization gratings  201   b  and  202   b  implemented in a parallel arrangement (i.e., where the nematic director patterns thereof are of the same handedness). The LCD devices  200   a  and  200   b  respectively include a light source  205 , transmissive substrates  210  and  215  including alignment layers  207  and  208  thereon, and a liquid crystal layer  203  between the transmissive substrates  210  and  215  and aligned according to the periodic alignment conditions provided by the alignment layers  207  and  208 .  FIGS. 2A and 2B  illustrate the liquid crystal layer  203  as including two pixels by way of example; however, the liquid crystal layer  203  may include fewer or more pixels in some embodiments of the present invention. The LCD devices  200   a  and  200   b  further include an angle-filtering stage  227  including micro-lenses  225  and  226  and a pinhole aperture  220 , and a viewing screen  230 . The light source  205  may include a fluorescent lamp, a light emitting diode (LED)-based lamp, a backlight, and/or other light source configured to emit unpolarized light  290 . However, it is to be understood that, in some embodiments, the light source  205  may be configured to emit polarized light. The angle-filtering stage  227  is configured to permit output light propagating in a direction substantially parallel to the incident light  290  to be imaged on the viewing screen  230 , but block output light that is not propagating direction parallel to the incident light  290 . 
     Example operations of the LCD devices  200   a  and  200   b  will now be described. Referring now to the antiparallel polarization grating arrangement of  FIG. 2A , the unpolarized incident light  290  from the light source  205  enters the first polarization grating  201   a , and is polarized and diffracted into two orthogonal, circularly polarized beams  295   a  (left-handed circularly polarized) and  296   a  (right-handed circularly polarized) having different, non-zero-order propagation directions. Depending on the diffraction efficiency of the polarization grating  201   a , the beams  295   a  and  296   a  may include all wavelengths of visible light (e.g., from about 400 nm to about 700 nm), nearly 50% in each order. Both beams  295   a  and  296   a  pass through the LC layer  203 , illustrated as including a first pixel  204  in the OFF state, and a second pixel  206  in the ON state. The beams  295   a  and  296   a  passing through the OFF pixel  204  do not experience a change in their respective polarizations, and are then analyzed and diffracted by the second polarization grating  202   a  into output light  299   a  at greater angles relative to the angle of incidence of the unpolarized input light  290 . This off-axis output light  299   a  is then blocked by the angle-filtering stage  227  to prevent the light  299   a  from reaching the viewing screen  230 . As such, a “dark” pixel  232  (representing as little as 0% of the input light  290 ) is presented to a viewer. 
     In contrast, the beams  295   a  and  296   a  passing through the ON pixel  206  experience half-wave retardation, and are both converted into the opposite circular polarizations  295   a ′ (right-handed circularly polarized) and  296   a ′ (left-handed circularly polarized), respectively. The beams  295   a ′ and  296   a ′ are then analyzed and diffracted by the second polarization grating  202   a  into output light  299   b  at an angle substantially similar to the original angle of incidence of the input light  290 . This on-axis light  299   b  is provided to the viewing screen  230  via the angle-filtering stage  227 . As such, a “bright” pixel  234  (representing up to 100% of the intensity/brightness of the input light  290 ) is presented to the viewer. 
     Referring now to the parallel polarization grating arrangement of  FIG. 2B , the unpolarized input light  290  from the light source  205  is similarly polarized and diffracted into two orthogonal, circularly polarized beams  295   b  (left-handed circularly polarized) and  296   b  (right-handed circularly polarized) by the first polarization grating  201   b . The beams  295   b  and  296   b  passing through the OFF pixel  204  of the liquid crystal layer  203  do not experience a change in their respective polarizations, while the beams  295   b  and  296   b  passing through the ON pixel  206  experience half-wave retardation to provide beams of the opposite circular polarizations  295   b ′ (right-handed circularly polarized) and  296   b ′ (left-handed circularly polarized), respectively. As such, due to their altered polarizations, the beams  295   b ′ and  296   b ′ are analyzed and diffracted by the second polarization grating  202   b  to transmit off-axis output light  299   a , which is blocked by the angle-filtering stage  227 . In contrast, the beams  295   b  and  296   b  are analyzed and diffracted by the second polarization grating  202   b  to transmit on-axis output light  299   b , which is provided to the viewing screen  230  via the angle-filtering stage  227 . Thus, in the embodiment of  FIG. 2B , the OFF pixel  204  provides the bright pixel  234 , while the ON pixel  206  provides the dark pixel  232 . 
     Accordingly, some embodiments of the present invention as described above with reference to  FIGS. 2A and 2B  may provide direct view LCD devices that may have twice the brightness of conventional LCD devices. In some embodiments, the polarization gratings  201  and  202  may be achromatic polarization gratings used to achieve relatively high contrast for a broad wavelength range including red, green, and blue light. In addition, a diffuser (not shown) may be included in some embodiments of the present invention to expand the viewing angle. Also, a privacy film (such as those manufactured by 3M™ Company) that blocks off-axis light but passes on-axis light may be used as the angle filtering stage  227  in some embodiments. 
       FIGS. 3A-3C  illustrate multi-polarization grating arrangements according to some embodiments of the present invention as implemented in a projection system including a liquid crystal microdisplay. In particular,  FIG. 3A  illustrates a transmissive-mode projection-type LCD device  300   a , while  FIGS. 3B and 3C  illustrate reflection-mode projection-type LCD devices  300   b  and  300   c . The LCD devices  300   a - 300   c  respectively include first and second polarization gratings  301  and  302 , substrates  305   a / 305   b / 305   c  and  315  including alignment layers  307  and  308  thereon, and a liquid crystal layer  303  between the substrates  305   a / 305   b / 305   c  and  315  and aligned according to the periodic alignment conditions provided by the alignment layers  307  and  308 . The polarization gratings  301  and  302  have an antiparallel arrangement where the birefringence pattern of polarization grating  301  is inverted (i.e., rotated by about 180°) relative to that of polarization grating  302 . The liquid crystal layer  303  defines a pixel array illustrated by way of example as including two pixels; however, the liquid crystal layer  303  may include fewer or more pixels in some embodiments of the present invention. The LCD devices  300   a - 300   c  further include an angle filtering stage  327  including projection lenses  325  and  326  and an aperture stop  320 , and a viewing screen  330 . The angle filtering stage  327  is configured to permit output light propagating in a direction substantially parallel to the input/incident light  390  (i.e., zero-order light) to be imaged on the viewing screen  330 , but block output light that is not propagating direction parallel to the incident light  390  (i.e., first- and/or second-order light). 
     Example operations of the LCD devices  300   a - 300   c  will now be described. Referring now to  FIG. 3A , the unpolarized incident light  390  enters the first polarization grating  301 , and is polarized and diffracted into two orthogonal, circularly polarized beams  395   a  (left-handed circularly polarized) and  396   a  (right-handed circularly polarized) having different, non-zero-order propagation directions. Due to the diffraction efficiency of the polarization grating  301 , the beams  395   a  and  396   a  may include all wavelengths of visible light, nearly 50% in each order. Both beams  395   a  and  396   a  pass through a transmissive substrate  305   a  and the LC layer  303 , illustrated as including a first pixel  304  in the OFF state, and a second pixel  306  in the ON state. The beams  395   a  and  396   a  passing through the OFF pixel  304  do not experience a change in their respective polarizations, and are transmitted through a transmissive substrate  315  and then analyzed and diffracted by the second polarization grating  302  into output light  399   a  at greater angles relative to the angle of incidence of the unpolarized input light  390 . This off-axis output light  399   a  is then blocked by the angle filtering stage  327 , thereby preventing the light  399   a  from reaching the viewing screen  330 . As such, a “dark” pixel  332  representing as little as 0% of the input light  390  is seen by a viewer. 
     In contrast, still referring to  FIG. 3A , the beams  395   a  and  396   a  passing through the ON pixel  306  experience half-wave retardation, and are both converted into the opposite circular polarizations  395   a ′ (right-handed circularly polarized) and  396   a ′ (left-handed circularly polarized), respectively. The beams  395   a ′ and  396   a ′ are then diffracted by the second polarization grating  302  into output light  399   b  at an angle substantially similar to the original angle of incidence of the input light  390 . This on-axis (i.e., zero-order) light  399   b  is permitted by the angle filtering stage  327  and projected and imaged on the viewing screen  330 . As such, a “bright” pixel  334  representing up to 100% of the intensity/brightness of the input light  390  is presented to the viewer. Accordingly, nearly all of the light  399   b  from the ON pixel  306  is provided to the screen  330 , while almost none of the light  399   a  from the OFF pixel  304  is provided to the screen  330 . As such, when the LC layer  303  defines a pixel array including a plurality of pixels, the projector-type LCD device  300   a  of  FIG. 3A  may be used to project a viable image on the screen  330 . 
       FIG. 3B  illustrates a non-telecentric projection-type LCD device  300   b  that includes a reflective substrate  305   b  in place of the transmissive substrate  305   a  of  FIG. 3A . Referring now to  FIG. 3B , the unpolarized incident light  390  is similarly polarized and diffracted into two orthogonal, circularly polarized beams  395   b  (left-handed circularly polarized) and  396   b  (right-handed circularly polarized) by the polarization grating  302 . The incident light  390  may be out-of-plane as compared to the diffraction direction in some embodiments. Both beams  395   b  and  396   b  pass through the transmissive substrate  315  and the LC layer  303 . The beams  395   b  and  396   b  passing through the OFF pixel  304  of the liquid crystal layer  303  do not experience a change in their respective polarizations, but are reflected by the reflective substrate  305   b  into opposite polarizations back through the LC layer  303  and towards the polarization grating  302 , which analyzes and diffracts the beams  395   b  and  396   b  to provide the on-axis output light  399   b . The on-axis output light  399   b  is permitted by the angle filtering stage  327  and projected and imaged on the viewing screen  330  to present the bright pixel  334  to the viewer. 
     Still referring to  FIG. 3B , the beams  395   b  and  396   b  passing through the ON pixel  306  experience half-wave retardation to provide beams of the opposite circular polarizations, which are reflected by the reflective substrate  305   b  back through the LC layer  303  and towards the polarization grating  302 . More particularly, the LC layer of  FIG. 3B  may have a thickness of about half of that of the LC layer of  FIG. 3A , and as such, may provide quarter-wave retardation of the beams  395   b  and  396   b  both before and after reflection by the reflective substrate  305   b . The polarization grating  302  analyzes and diffracts the beams  395   b  and  396   b  to provide the off-axis output light  399   a , which is blocked by the angle filtering stage  327 , preventing the light  399   a  from reaching the viewing screen  330  and presenting the dark pixel  332  to the viewer. 
       FIG. 3C  illustrates a telecentric projection-type LCD device  300   c  that includes a reflective substrate  305   c  in place of the transmissive substrate  305   a  of  FIG. 3A . Referring now to  FIG. 3C , the unpolarized incident light  390  is similarly polarized and diffracted into two orthogonal, circularly polarized beams  395   c  (left-handed circularly polarized) and  396   c  (right-handed circularly polarized) by the first polarization grating  301 . The beams  395   c  and  396   c  are then directed by a lens  329   a  toward a reflective aperture stop  345 , which reflects the beams into opposite polarizations and through a lens  329   b  towards the second polarization grating  302 . The second polarization grating  302  analyzes and diffracts the beams  395   c  and  396   c  reflected by the reflective aperture stop  345 , and both beams  395   c  and  396   c  pass through the transmissive substrate  315  and the LC layer  303 . The beams  395   c  and  396   c  passing through the OFF pixel  304  of the liquid crystal layer  303  do not experience a change in their respective polarizations, but are reflected by the reflective substrate  305   c  into opposite polarizations back through the LC layer  303  and towards the second polarization grating  302 , which again analyzes and diffracts the beams  395   c  and  396   c  to provide the off-axis output light  399   a . The off-axis output light  399   a  is blocked by the reflective aperture stop  345 , preventing the light  399   a  from reaching the viewing screen  330  and presenting the dark pixel  332  to the viewer. 
     Still referring to  FIG. 3C , the beams  395   c  and  396   c  passing through the ON pixel  306  experience half-wave retardation to provide beams of the opposite circular polarizations, which are reflected by the reflective substrate  305   b  back through the LC layer  303  and towards the second polarization grating  302 . More particularly, the LC layer  303  provides quarter-wave retardation of the beams  395   c  and  396   c  both before and after reflection by the reflective substrate  305   c . The second polarization grating  302  again analyzes and diffracts the beams  395   c  and  396   c  to provide the on-axis output light  399   b , which is permitted by the reflective aperture stop  345  and projected and imaged on the viewing screen  330  by the projection lenses  325 / 326  to present the bright pixel  334  to the viewer. 
     Accordingly, some embodiments of the present invention as described above with reference to  FIGS. 3A-3C  may provide projection-based LCD devices that may have twice the brightness of conventional LCD devices. Also, the polarization gratings  301  and/or  302  may be achromatic to achieve relatively high contrast for a broad wavelength range including red, green, and blue light. Although illustrated as including the transmissive substrates  305   a  and  315  between the polarization gratings  301  and  302  in  FIG. 3A , it is to be understood that the polarization gratings  301  and  302  may be provided between the substrates  305   a  and  315  in some embodiments, as similarly illustrated in  FIGS. 1A and 1B . Furthermore, although illustrated with reference to unpolarized input light  390 , it is to be understood that polarized input light may be used in the projection systems of  FIGS. 3A-3C  in some embodiments. Also, well-known retardation compensation techniques may be used in conjunction with the arrangements illustrated in  FIGS. 3A-3C . 
       FIGS. 4A and 4B  illustrate multi-polarization grating arrangements implemented in projection systems  400   a  and  400   b , respectively, according to further embodiments of the present invention. In particular, the LCD devices  400   a  and  400   b  each include first and second polarization gratings  401  and  402 , substrates  410  and  415  including alignment layers  407  and  408  thereon, and a liquid crystal layer  403  between the substrates  410  and  415  and aligned according to the periodic alignment conditions provided by the alignment layers  407  and  408 . The polarization gratings  401  and  402  have a parallel arrangement where the birefringence pattern of polarization grating  401  has the same orientation as that of polarization grating  402 . The liquid crystal layer  403  defines a pixel array illustrated by way of example as including two pixels; however, the liquid crystal layer  403  may include fewer or more pixels in some embodiments of the present invention. The LCD devices  400   a - 400   b  further include an angle filtering stage  427  including projection lenses  425  and  426  and an aperture stop  420 , and a viewing screen  430 . The angle filtering stage  427  is configured to permit output light propagating in a direction substantially parallel to the incident light  490  (i.e., zero-order light) to be imaged on the viewing screen  430 , but block output light that is not propagating direction parallel to the incident light  490  (i.e., first- and/or second-order light). 
     In many projection display designs, the input light from a light source is provided on-axis, and the image from the microdisplay may be collected by the projection lens in either the bright-field (i.e., zero-order, on-axis light) or the dark field (first-order, off-axis light). Accordingly, such designs may arrange the projection optics in a telecentric configuration such that light propagates normal to the field of view, and may collect the zero-order (i.e., on-axis) light with a relatively small aperture. In contrast, some embodiments of the present invention as illustrated in  FIGS. 4A and 4B  provide improved contrast (and thus image quality) by using a projection lens or micro lens array  405  to collect the first-order (i.e., off-axis) diffracted light. When the incident light  490  is arranged to enter the LC layer  403  off-axis (i.e., at first- and/or second-order angles), the properties of the bright pixel and dark pixel configurations may be inverted. In other words, better contrast may be observed in the on-axis light. 
       FIG. 4A  illustrates a LCD device  400   a  that further includes the lens  405  as an imaging source for providing off-axis light to the liquid crystal layer  403  and the second polarization grating  402 . In particular, unpolarized light  490  enters the first polarization grating  401 , and is polarized and diffracted into two orthogonal, circularly polarized beams  495   a  (left-handed circularly polarized) and  496   a  (right-handed circularly polarized) having different, non-zero-order propagation directions. Due to the diffraction efficiency of the polarization grating  401 , the beams  495   a  and  496   a  may each include red, green, and blue light, nearly 50% in each order. The lens  405  images the beams  495   a  and  496   a  to provide symmetric off-axis input light into the liquid crystal layer  403  and the second polarization grating  402 . Both beams  495   a  and  496   a  pass through a transmissive substrate  410  the LC layer  403 , illustrated as including a first pixel  404  in the OFF state, and a second pixel  406  in the ON state. The beams  495   a  and  496   a  passing through the OFF pixel  404  do not experience a change in their respective polarizations, and are transmitted through a transmissive substrate  415  and then analyzed and diffracted by the second polarization grating  402  into output light  499   a  at greater angles relative to the angle of incidence of the incident unpolarized light  490 . This off-axis output light  499   a  is blocked by the angle filtering stage  427 , thereby preventing the light  499   a  from reaching the viewing screen  430 . As such, a “dark” pixel  432  representing as little as 0% of the input light  490  is seen by a viewer. 
     In contrast, the beams  495   a  and  496   a  passing through the ON pixel  406  experience half-wave retardation, and are both converted into the opposite circular polarizations  495   a ′ (right-handed circularly polarized) and  496   a ′ (left-handed circularly polarized), respectively. The beams  495   a ′ and  496   a ′ are then analyzed and diffracted by the second polarization grating  402  into output light  499   b  at an angle substantially similar to the original angle of incidence of the input light  490 . This on-axis (i.e., zero-order) light  499   b  is permitted by the angle filtering stage  427  and projected and imaged on the viewing screen  430 . As such, a “bright” pixel  434  representing up to 100% of the intensity/brightness of the input light  490  is presented to the viewer. 
       FIG. 4B  illustrates a similar LCD device  400   b  that arranges the lens  405  after the liquid crystal layer  403  to provide the off-axis light to the second polarization grating  402 . As such, as similarly described above with reference to  FIG. 4A , the unpolarized input light  490  is polarized and diffracted into two orthogonal, circularly polarized beams  495   b  (left-handed circularly polarized) and  496   b  (right-handed circularly polarized) by the first polarization grating  401  having different directions of propagation relative to that of the incident light  490 . The beams  495   b  and  496   b  pass through the transmissive substrate  410  and the liquid crystal layer  403 . The beams  495   b  and  496   b  passing through the OFF pixel  404  of the liquid crystal layer  403  do not experience a change in their respective polarizations, while the beams  495   b  and  496   b  passing through the ON pixel  406  experience half-wave retardation to provide beams of the opposite circular polarizations  495   b ′ (right-handed circularly polarized) and  496   b ′ (left-handed circularly polarized), respectively. The lens  405  images the beams  495   b - 496   b  and/or  495   b ′- 496   b ′ to provide symmetric off-axis input light into the second polarization grating  402 . The beams  495   b  and  496   b  are analyzed and diffracted by the second polarization grating  402  to provide the off-axis output light  499   a , which is blocked by the angle filtering stage  427 . The beams  495   b ′ and  496   b ′ are analyzed and diffracted by the second polarization grating  402  to provide the on-axis output light  499   b , which is provided to the viewing screen  430  via the angle filtering stage  427 , as similarly described with reference to  FIG. 4A . 
     Accordingly, some embodiments of the present invention as described above with reference to  FIGS. 4A and 4B  may provide projection-based LCD devices that may have improved contrast over conventional LCD devices. Although illustrated with reference to unpolarized input light  490 , it is to be understood that polarized input light may be used in the projection systems of  FIGS. 4A and 4B  in some embodiments. Also, in some embodiments, switchable liquid crystal polarization gratings, such as those described in PCT Application No. PCT/US2008/004888 to Escuti, et al., may be used in place of the LC layer  403 , the substrates  410  and  415 , and the polarization grating  402 . Thus, such embodiments provide a sequential arrangement of the polarization gratings  401  and  402 , where at least one of the polarization gratings  401  and  402  is configured to be switched between a first state that does not substantially alter respective polarizations and/or propagation directions of the light traveling therethrough, and a second state that alters the respective polarizations and propagation directions of the light traveling therethrough. The other of the polarization gratings  401  and  402  may be a fixed or non-switchable grating configured to polarize and diffract input light, as discussed above. In other words, some embodiments of the present invention may include a sequential arrangement of two polarization gratings, one or more of which may be switchable, and one or more of which could be pixelated. 
       FIG. 5  illustrates a multi-polarization grating arrangement implemented in projection system  500  according to still further embodiments of the present invention. In particular, the LCD device  500  includes first and second polarization gratings  501  and  502 , substrates  510  and  515  including alignment layers  507  and  508  thereon, and a liquid crystal layer  503  between the substrates  510  and  515  and aligned according to the periodic alignment conditions provided by the alignment layers  507  and  508 . The polarization gratings  501  and  502  have a parallel arrangement. The liquid crystal layer  503  defines a pixel array illustrated by way of example as including two pixels; however, the liquid crystal layer  503  may include fewer or more pixels in some embodiments of the present invention. The LCD device  500  further includes an angle filtering stage  527  including projection lenses  525  and  526  and an aperture stop  520 , and a viewing screen  530 . The angle filtering stage  527  is configured to permit output light propagating in a direction substantially parallel to the incident light  590  (i.e., zero-order light) to be imaged on the viewing screen  530 , but block output light that is not propagating direction parallel to the incident light  590  (i.e., first- and/or second-order light). 
     Still referring to  FIG. 5 , the LCD device  500  further includes an offset compensator  550  after the first and second polarization gratings  501  and  502 . The offset compensator  550  includes third and fourth polarization gratings  551  and  552 , and an intermediate layer  553  therebetween. The intermediate layer  553  has a thickness t substantially similar to the distance d between the liquid crystal layer  503  and the second polarization grating  502  and may be a transmissive substrate in some embodiments. The polarization gratings  551  and  552  have a parallel arrangement such that the local nematic director orientation of polarization grating  551  is of the same handedness as that of polarization grating  552 . The offset compensator  550  is configured to substantially reduce and/or remove the spatial offset of the output light transmitted by the polarization grating  502  without substantially altering the directions of propagation thereof, and provide this light to the angle filtering stage  527  for imaging on the viewing screen  530 . In other words, an offset compensator  550  having an intermediate layer  553  with a thickness t may improve parallax issues resulting from the spatial offset of the light from the polarization grating  502 . 
     More particularly, as shown in  FIG. 5 , the unpolarized input light  590  is polarized and diffracted into two orthogonal, circularly polarized beams  595  (left-handed circularly polarized) and  596  (right-handed circularly polarized) by the first polarization grating  501 . The beams  595  and  596  passing through the OFF pixel  504  of the liquid crystal layer  503  do not experience a change in their respective polarizations, while the beams  595  and  596  passing through the ON pixel  506  experience half-wave retardation to provide beams of the opposite circular polarizations  595 ′ (right-handed circularly polarized) and  596 ′ (left-handed circularly polarized), respectively. The beams  595 ′ and  596 ′ are analyzed and diffracted by the second polarization grating  502  to transmit off-axis output light  599   a , while the beams  595  and  596  are analyzed and diffracted by the second polarization grating  502  to transmit on-axis output light  599   b.    
     The third polarization grating  551  receives light transmitted from the second polarization grating  502  and diffracts the on- and off-axis beams  599   b  and  599   a  to off- and on-axis  599   b ′ and  599   a ′, respectively. The intermediate layer  553  transmits both beams  599   b ′ and  599   a ′ to the fourth polarization grating  552  through the thickness t without substantially altering their directions of propagation. The fourth polarization grating  552  diffracts the on- and off-axis beams  599   b ′ and  599   a ′ back to the off- and on-axis beams  599   b ″ and  599   a ″, respectively, to provide offset-compensated output light with the same polarization and direction as the beams  599   b  and  599   a  transmitted from the second polarization grating  502 , but with a reduced spatial offset. In particular, the thickness of the intermediate layer produces a spatial offset to compensate for the offset that results from the distance d between the liquid crystal layer  503  and the second polarization grating  502 , which causes the parallax problem. As such, off-axis output light  599   a ″ is blocked by the angle filtering stage  527  to present the dark pixel  532  to the viewer, while on-axis output light  599   b ″ is permitted by the angle filtering stage  527  and projected and imaged on the viewing screen  530  to present the bright pixel  534  to the viewer. 
     In some embodiments, the intermediate layer  553  may be a substrate that is similar to the transparent substrate  515  between the liquid crystal layer  503  and the second polarization grating  502  (i.e., having the same thickness and/or the same refractive index). The optical path length of the first and second beams within the intermediate layer  553  may be matched to that of the first and second beams within the transparent substrate  515 . This optical path length may depend on the diffraction angle, the thickness t, and/or the optical (refractive) index of the material of the intermediate layer  553 . In some embodiments, the intermediate layer  553  may be an isotropic and transparent medium, such as glass. 
       FIG. 6  illustrates an example simulation space for polarization grating arrangements according to some embodiments of the present invention used to provide the simulation data of  FIGS. 7A-7G . Referring now to  FIG. 6 , a uniform planar liquid crystal layer  603  including homogeneously aligned LC molecules is provided between alignment layers  607  and  608  on achromatic polarization gratings  601  and  602 , and the polarization gratings  601  and  602  are provided between transmissive substrates  610  and  615 . The LC layer  603  is configured to be switched between an “OFF” state, which provides no retardation of the input light, and an “ON” state, which provides half-wave retardation of the input light, in response to a voltage applied thereto. Characteristics of the LC layer  603  include a thickness d (as measured along a direction between opposing surfaces of the polarization gratings  601  and  602 ) of about 1.7 μm, an ordinary index of refraction n o  of about 1.42, and a linear birefringence Δn of about 0.159. 
     The polarization grating  601  includes two polarization grating layers  601   a  and  601   b . The polarization grating layers  601   a  and  601   b  include chiral molecules (i.e., asymmetric molecules having different left-handed and right-handed forms) of opposite handedness. As such, the orientation of the molecules of the polarization grating layer  601   a  is rotated or “twisted” by a twist angle Φ of −70° over a thicknesses thereof to provide a continuous phase shift in its local anisotropy pattern. The orientation of the molecules of the polarization grating layer  601   b  is oppositely twisted by a twist angle Φ of +70° over a thicknesses thereof As such, the polarization grating  601  includes two polarization grating layers  601   a  and  601   b  of opposite twist sense. The polarization grating  602  similarly includes two polarization grating layers  602   a  and  602   b  having opposite twist angles Φ of −70° and +70°, respectively. Other characteristics of each of the polarization gratings  601  and  602  include an optical pitch of about 1-4 μm, an ordinary index of refraction n o  of about 1.42, a linear birefringence Δn of about 0.159, and an antiparallel arrangement. 
     Gradient-index anti-reflection (AR) coatings  606  are applied to the polarization gratings  601  and  602  at the interfaces with the transmissive substrates  610  and  615 , respectively. Periodic boundaries  611  and matched layer boundaries  612  using the Uniaxial Perfectly Matched Layer (UPML) technique may be employed to terminate the simulation space and/or to reduce simulation time. The input/incident light  609  is a Gaussian pulse having a center wavelength λ 0  of about 550 nm provided at a line  613  before the polarization grating  601 , and the output diffraction efficiencies may be calculated from the electric field at a line  614  immediately after the polarization grating  602 . The polarization gratings  601  and  602  have a grid spacing of λ 0 /40=13.75 nm, also referred to as a grid density N of 40. 
       FIGS. 7A-7G  illustrate simulation results showing diffraction properties for polarization grating arrangements according to some embodiments of the present invention in response to varying the tilt angle θ tilt  of the molecules of the LC layer  603  over a range of about 0° to about 90° by changing the applied voltage to the LC layer  603 . More particularly,  FIGS. 7A-7F  illustrate the zero, first, and second order diffraction efficiencies as a function of normalized retardation (Δnd/λ) for different tilt angles (θ tilt ) 90°, 60°, 45°, 30°, 15°, and 0°, respectively, relative to the opposing faces of the polarization gratings  601  and  602 . The sum of the zero-order diffraction efficiencies are respectively represented by waveforms  700   a - 700   f  in  FIGS. 7A-7F , and indicate light output from the polarization grating arrangement that propagates at an angle substantially parallel to that of the input light  690 . Likewise, in  FIGS. 7A-7F , the sum of the first-order diffraction efficiencies (indicating light output from the polarization grating arrangement that propagates at different angles than that of the input light  690 ) are represented by waveforms  701   a - 701   f , and the sum of the second-order diffraction efficiencies (indicating light output from the polarization grating arrangement that propagates at even greater angles relative to that of the input light  690 ) are represented by waveforms  702   a - 702   f.    
     As shown in  FIG. 7A , a relatively high diffraction efficiency is provided for light diffracted into the second-order when the LC layer  603  is in the “OFF” state (i.e., where θ tilt =90°) over a wavelength range of about 400 nm to 700 nm, which includes blue, green, and red light. Accordingly, this second-order output light can be blocked and/or otherwise prevented from being transmitted to a viewing screen, as discussed above. In contrast, as shown in  FIG. 7F , a relatively high diffraction efficiency is provided for the zero-order light when the LC layer  603  is in the “ON” state (i.e., where θ tilt =0°) over a similar wavelength range. This zero-order output light may thereby be provided to a viewing screen with little to no polarization-related losses.  FIG. 7G  illustrates the zero-order diffraction efficiency of polarization grating arrangements according to some embodiments of the present invention by superimposing the zero-order efficiency  700   a  for θ tilt =90° of  FIG. 7A  with the zero-order efficiency  700   f  for θ tilt =0° of  FIG. 7F . Thus, embodiments of the present invention may provide both increased brightness (as indicated by  700   f ) and high contrast (as indicated by  700   a ) over a relatively wide range of the spectrum. 
       FIGS. 8A-8F  provide experimental results illustrating transmission spectra for polarization grating arrangements according to some embodiments of the present invention. In particular,  FIGS. 8A-8F  illustrate transmittance vs. wavelength characteristics as measured by a spectraphotometer for a polarization grating arrangement including a homogeneous liquid crystal layer  803  with a half-wave retardation thickness between two reactive mesogen achromatic polarization gratings  801  and  802 . The liquid crystal layer has an ordinary index of refraction n o  of about 1.49, a linear birefringence Δn of about 0.11, and a thickness of about 2.8 μm. The polarization gratings have an ordinary index of refraction n o  of about 1.45, and a linear birefringence Δn of about 0.159. As shown in  FIGS. 8A and 8B , the waveforms  800   a  and  800   b  illustrate the individual zero-order transmittances of the polarization gratings  801  and  802 , respectively, prior to assembly with an LC layer  803 . As such, the polarization gratings  801  and  802  diffract incident light into non-zero-order light with an efficiency of nearly 100%.  FIG. 8F  illustrates the zero-order transmittance for an arrangement including the combination of the polarization gratings  801  and  802  in sequence. The first polarization grating  801  is used to polarize and diffract the incident light away from the angle of incidence, and the second polarization grating  802  is used to analyze and diffract the light back to the angle of incidence to provide a transmittance of about 80% or more of the incident light, as shown by the waveform  800   f . The waveform  800   c  in  FIG. 8C  illustrates the zero order transmittance of a polarization grating arrangement in accordance with some embodiments of the present invention including a liquid crystal layer  803  having a tilt angle of 0° and an azimuth angle of 45° between parallel polarization gratings  801  and  802 .  FIGS. 8D and 8E  likewise illustrate zero-order transmittance characteristics for an antiparallel arrangement of the polarization gratings  801  and  802  where the liquid crystal layer  803  has a tilt angle of 90° and 0°, as shown by waveforms  800   d  and  800   e , respectively. 
     Accordingly, some embodiments of the present invention provide multi-polarization grating arrangements where diffraction is performed by the polarization gratings, but modulation is performed by the liquid crystal layer. More particularly, the polarization gratings are used as diffractive optical elements to control the direction and/or polarization state of transmitted light over a broad spectral range. Such arrangements may be used to provide projection and/or direct-view LCD devices with significant improvements in brightness and contrast, while using conventional liquid crystal materials as the switching element. Further embodiments of the present invention are described in detail below. 
     Some embodiments of the present invention may allow for doubling the light efficiency of liquid crystal (LC) microdisplays by replacing the polarizers in conventional LCD devices with transparent polymer, thin-film, polarizing beam-splitters, known as polarization gratings (PGs). In particular, achromatic, the reactive mesogen (polymerizable LC) films shown in  FIGS. 9A and 10A  may be employed as both polarizer and analyzer. The result is that both orthogonal polarizations (i.e., substantially all of the unpolarized light) can be directed through the microdisplay simultaneously, so that the display may have ˜100% (brightness) efficiency (as opposed to &lt;50% efficiency when using polarizers). Such “polymer-PG displays” may require little-or-no modifications to commercial, off-the-shelf LC microdisplays.  FIGS. 10B ,  10 C,  11 A, and  11 B provide experimental results illustrating the operation principles of such polymer-PG displays, and experimentally show an overall ˜90% efficiency and contrast ratios &gt;200:1 for unpolarized LED light with up to ±7° aperture. Additionally,  FIGS. 12A and 12B  illustrate a prototype of a polymer-PG projection system using a modified commercial microdisplay. 
     Increased light efficiency and reduced power consumption presents a challenge for today&#39;s LCD market. Since the invention of twisted-nematic liquid crystals in 1971, LCDs have been the primary source of flat-panel displays. However, the efficiencies of LCDs may be limited due to losses (&gt;50%) from polarizers. This is because most LCDs operate by controlling the direction of light polarization via the birefringence and twist of the LC layer, while the most efficient light sources (i.e. CCFLs and LEDs) produce on unpolarized light. There are a number of different approaches for polarizer-free displays, including LC gels, PDLCs, H-PDLCs, and binary LC gratings. All of them, however, may suffer to some degree or another from low contrast ratios, very narrow acceptance angles, and/or limited peak efficiencies. Recently, electrically switchable LCPGs have been used as highly efficient, polarization-independent light modulators. Furthermore, microdisplay prototypes for projection systems using LCPGs have been demonstrated, most recently using an LCOS backplane. 
     Polarization gratings have unique diffractive properties due to their spatially variant uniaxial birefringence. Some embodiments of the present invention employ polarization gratings having a periodic LC profile that experimentally has &gt;99% diffraction efficiency over the entire visible wavelength range, formed in highly cross-linked acrylate polymer films, and which has the same polarization dependent properties of conventional PGs.  FIG. 9A  illustrates the behavior of an achromatic polarization grating (PG)  901  according to some embodiments of the present invention with white, unpolarized, input light. As shown in the photograph of  FIG. 9B , the ±1 diffraction orders  902  and  903  are each circularly polarized, orthogonal, and can have (in total) up to 100% of the incident light propagating in them. 
     Embodiments of the present invention provide a highly efficient, polarization-independent microdisplay (“polymer-PG LC display”) with achromatic PGs acting as polarizing and analyzing elements instead of polarizers.  FIGS. 1A and 1B  illustrate the basic geometry and operation principles of polymer-PG LC displays according to some embodiments of the present invention. Since conventional polarizers are not used, the light efficiency of the display can potentially be improved by a factor of two. It should be noted that contrast may be obtained using aperture stops and lenses to filter the diffraction orders. However, modification of the microdisplay may not be needed. 
     As in conventional LCDs, LC switching leads to light modulation. The first PG outputs circular polarizations in the first orders, the handedness of which is affected by LC switching and the relative orientation between the first and second PGs, as shown in  FIGS. 1A and 1B . The second PG either diffracts the light into higher angles or directs it toward the normal direction based on the polarization handedness of light from the first PG. Although illustrated in  FIGS. 1A and 1B  as having an anti-parallel alignment of PGs, it is to be understood that embodiments of the present invention may include parallel alignment of PGs and/or other varied designs. 
       FIG. 10A  illustrates parallel  1001  and antiparallel  1002  PG configurations according to embodiments of the present invention, which are described below to highlight the upper limits for brightness and contrast ratios. For experimental demonstration, a pair of achromatic PG samples (grating period=4 μm, acceptance angle±7° for green light) with high efficiencies (&gt;98%) for red, green, and blue LED lights. Fabrication methods and optical properties of these gratings have been previously described. The parallel  1001  and anti-parallel  1002  orientations are nearly equivalent to the bright-state and dark-state of the display, respectively.  FIG. 10B  illustrates the true (measured) transmittance spectra of both configurations, for unpolarized input light. Waveform  1003  shows that parallel PGs may manifest about 90% transmittance, while waveform  1004  shows that anti-parallel PGs may leak less than about 0.5% for visible light (400-700 nm). Waveform  1005  illustrates the transmittance spectra for parallel polarizers. Waveform  1006  of  FIG. 10C  shows that the measured extinction ratio of an anti-parallel PG arrangement  1002  according to some embodiments of the present invention (analogous to crossed-polarizers) is ≧200, and has a peak of ˜500 in the red). It should be noted that anti-reflection coated glasses were used to reduce Fresnel losses. 
     Electro-optical switching was also demonstrated with a single monolithic pixel with a conventional LC cells (with vertical-alignment (VA) mode). As shown in  FIGS. 1A and 1B ) two achromatic polymer PGs were aligned in anti-parallel orientations to a LC cell, which controls the polarization of light passing through it. More particularly, when a relatively high voltage (˜5V) is applied, the VA-mode LC cell will present a half-wave retardation due to its predominantly planar alignment, and will therefore reverse the polarizations of the two beams (simultaneously) passing through it (from the first PG). This light will then be directed toward the normal direction by the second PG, as shown in FIG.  1 B, and subsequently projected to the screen/viewer. However, when no voltage is applied to the VA-mode LC cell, it presents very little retardation, and light entering the LC layer from the first PG will retain its original polarization (simultaneously) and be diffracted to even higher angles by the second PG, as shown in  FIG. 1A . 
     The transmittance and contrast ratios for three LED colors (unpolarized!) in a polymer-PG LC display according to some embodiments of the present invention are presented in the graphs of  FIGS. 11A and 11B , respectively. In particular, bright-state transmittance is shown for red  1101  (625 nm), green  1102  (530 nm), and blue  1103  (470 nm) unpolarized LEDs in  FIG. 11A , while contrast ratios (bright/dark) for the three LEDs  1101 ,  1102 , and  1103  is shown in  FIG. 11B . The dashes  1105  in  FIG. 11A  illustrate the estimated transmittance of a crossed-polarizer LC pixel in the same configuration. As shown in  FIG. 11A , the true transmittance to unpolarized light for the polymer-PG LC modulator according to some embodiments of the present invention is ≧80%, more than double that of a conventional polarizer-based display, while still maintaining modest contrast ratios (200:1 to 500:1), as shown in  FIG. 11B . 
     To confirm the imaging properties of the Polymer-PG Display, a prototype projector was built using a commercial LC microdisplay panel (Iljin Display, 0.41″ VGA, planar-alignment mode) with achromatic PG films in accordance with some embodiments of the present invention, as shown in  FIGS. 12A-12C . A Golden-eye LED light source was used, which supports color-sequential display operation, and the polarizers were removed from the commercial microdisplay. The PG films according to some embodiments of the present invention were aligned in anti-parallel configuration and the grating direction. The overall geometry of the system  1200  is shown in  FIG. 12A , and a photograph of the system  1200  is shown in  FIG. 12B . The elements of the system  1200  may correspond to similar elements illustrated in the system  300   a  of  FIG. 3A . Parallax was observed in projected images with a small spatial offset, which may be attribute to the distance (glass thickness) between the imaging plane and the second PG. This parallax problem can be avoided by inserting the second PG inside the LC cell in some embodiments. An alternative solution is to arrange two additional parallel PGs (similar or identical to the PGs already chosen) with the same gap thickness as the glass after the second PG, which may perfectly compensate for the spatial offset, as discussed above with reference to the embodiment of  FIG. 5 . 
     The Polymer-PG display projects bright pixels that may be up to twice as bright as the polarizer-based display.  FIG. 12C  provides a comparison of projected images from the original display  1204  and a polymer-PG display according to some embodiments of the present invention  1205 , which shows equivalently sharp edges and excellent image focus. It should be noted that color degradations and low image contrasts seen in the polymer-PG display image  1205  of  FIG. 12C  may be due to the absence of any retardation compensation (removed from the original display along with the polarizers) in these initial tests, which will be integrated in production displays. 
     Thus, polymer-PG displays according to some embodiments of the present invention may improve the light efficiency of LC microdisplays by using diffractive transparent polymer thin films. Brightness of (unmodified) commercial LC microdisplays can be roughly doubled, and standard étendue-limited light sources may be used. Embodiments of the present invention may be targeted for use in portable projectors, due to the high efficiency of the system. 
     The foregoing is illustrative of the present invention and is not to be construed as limiting thereof. Although a few exemplary embodiments of this invention have been described, those skilled in the art will readily appreciate that many modifications are possible in the exemplary embodiments without materially departing from the novel teachings and advantages of this invention. For example, it is to be understood that the polarization gratings described above with reference to  FIGS. 1-12  can be fabricated using non-switchable and/or switchable LC materials. Moreover, the substrates described herein may include one or more electrodes on surfaces thereof, for instance, provided by a transparent indium-tin-oxide (ITO) coating on the substrates. Accordingly, all such modifications are intended to be included within the scope of this invention. Therefore, it is to be understood that the foregoing is illustrative of the present invention and is not to be construed as limited to the specific embodiments disclosed, and that modifications to the disclosed embodiments, as well as other embodiments, are intended to be included within the scope of the invention.