Patent Publication Number: US-2023152622-A1

Title: Spatially variable liquid crystal diffraction gratings

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a divisional application of U.S. patent application Ser. No. 15/815,449, filed Nov. 16, 2017, entitled “SPATIALLY VARIABLE LIQUID CRYSTAL DIFFRACTION GRATINGS,” which claims the benefit of priority to U.S. Provisional Patent Application No. 62/424,310, filed Nov. 18, 2016, entitled “SPATIALLY VARIABLE LIQUID CRYSTAL DIFFRACTION GRATINGS.” The content of each of these applications is hereby incorporated by reference herein in its entirety. 
    
    
     BACKGROUND 
     Field 
     The present disclosure relates to display systems and, more particularly, to augmented reality display systems. 
     Description of the Related Art 
     Modern computing and display technologies have facilitated the development of systems for so called “virtual reality” or “augmented reality” experiences, wherein digitally reproduced images or portions thereof are presented to a user in a manner wherein they seem to be, or may be perceived as, real. A virtual reality, or “VR”, scenario typically involves presentation of digital or virtual image information without transparency to other actual real-world visual input; an augmented reality, or “AR”, scenario typically involves presentation of digital or virtual image information as an augmentation to visualization of the actual world around the user. A mixed reality, or “MR”, scenario is a type of AR scenario and typically involves virtual objects that are integrated into, and responsive to, the natural world. For example, in an MR scenario, AR image content may be blocked by or otherwise be perceived as interacting with objects in the real world. 
     Referring to  FIG.  1   , an augmented reality scene  1  is depicted wherein a user of an AR technology sees a real-world park-like setting  1100  featuring people, trees, buildings in the background, and a concrete platform  1120 . In addition to these items, the user of the AR technology also perceives that he “sees” “virtual content” such as a robot statue  1110  standing upon the real-world platform  1120 , and a cartoon-like avatar character  1130  flying by which seems to be a personification of a bumble bee, even though these elements  1130 ,  1110  do not exist in the real world. Because the human visual perception system is complex, it is challenging to produce an AR technology that facilitates a comfortable, natural-feeling, rich presentation of virtual image elements amongst other virtual or real-world imagery elements. 
     Systems and methods disclosed herein address various challenges related to AR and VR technology. 
     SUMMARY 
     Accordingly, numerous devices, systems, structures and methods are disclosed herein. For instance, an example diffraction grating is disclosed that includes a plurality of different diffracting zones having a periodically repeating lateral dimension corresponding to a grating period adapted for light diffraction. The diffraction grating additionally includes a plurality of different liquid crystal layers corresponding to the different diffracting zones. The different liquid crystal layers have liquid crystal molecules that are aligned differently, such that the different diffracting zones have different optical properties associated with light diffraction. 
     An example method of fabricating a diffraction grating is disclosed that includes providing a substrate and providing a plurality of different diffracting zones on the substrate having a periodically repeating lateral dimension corresponding to a grating period adapted for light diffraction. The method further includes forming a plurality of different liquid crystal layers comprising liquid crystal molecules over the substrate, the different liquid crystal layers corresponding to the different diffracting zones, wherein forming the different liquid crystal layers comprises aligning the liquid crystal molecules differently, thereby providing different optical properties associated with light diffraction to the different diffracting zones. 
     Another example diffraction grating is disclosed that includes a plurality of contiguous liquid crystal layers extending in a lateral direction and arranged to have a periodically repeating lateral dimension, a thickness and indices of refraction such that the liquid crystal layers are configured to diffract light. Liquid crystal molecules of the liquid crystal layers are arranged differently in different liquid crystal layers along the lateral direction such that the contiguous liquid crystal layers are configured to diffract light with a gradient in diffraction efficiency. 
     An example head-mounted display device that is configured to project light to an eye of a user to display augmented reality image content is also disclosed. The head-mounted display device includes a frame configured to be supported on a head of the user. The head-mounted display device additionally includes a display disposed on the frame, at least a portion of said display comprising one or more waveguides, said one or more waveguides being transparent and disposed at a location in front of the user&#39;s eye when the user wears said head-mounted display device such that said transparent portion transmits light from a portion of an environment in front of the user to the user&#39;s eye to provide a view of said portion of the environment in front of the user, said display further comprising one or more light sources and at least one diffraction grating configured to couple light from the light sources into said one or more waveguides or to couple light out of said one or more waveguides. The diffraction grating includes a plurality of different diffracting zones having a periodically repeating lateral dimension corresponding to a grating period adapted for light diffraction. The diffraction grating additionally includes a plurality of different liquid crystal layers corresponding to the different diffracting zones, wherein the different liquid crystal layers have liquid crystal molecules that are aligned differently, such that the different diffracting zones have different optical properties associated with light diffraction. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    illustrates a user&#39;s view of augmented reality (AR) through an AR device. 
         FIG.  2    illustrates an example of wearable display system. 
         FIG.  3    illustrates a conventional display system for simulating three-dimensional imagery for a user. 
         FIG.  4    illustrates aspects of an approach for simulating three-dimensional imagery using multiple depth planes. 
         FIGS.  5 A- 5 C  illustrate relationships between radius of curvature and focal radius. 
         FIG.  6    illustrates an example of a waveguide stack for outputting image information to a user. 
         FIG.  7    illustrates an example of exit beams outputted by a waveguide. 
         FIG.  8    illustrates an example of a stacked waveguide assembly in which each depth plane includes images formed using multiple different component colors. 
         FIG.  9 A  illustrates a cross-sectional side view of an example of a set of stacked waveguides that each includes an incoupling optical element. 
         FIG.  9 B  illustrates a perspective view of an example of the plurality of stacked waveguides of  FIG.  9 A . 
         FIG.  9 C  illustrates a top-down plan view of an example of the plurality of stacked waveguides of  FIGS.  9 A and  9 B . 
         FIGS.  10 A- 10 C  illustrate cross-sectional side views of diffraction gratings having zones in which liquid crystal molecules have different pre-tilt angles, according to embodiments. 
         FIGS.  11 A- 11 B  are cross-sectional side views of an intermediate structure and a diffraction grating illustrating a method of fabricating the diffraction gratings illustrated in  FIGS.  10 A- 10 C , according to embodiments. 
         FIGS.  12 A- 12 C  are cross-sectional side views of intermediate structures and a diffraction grating illustrating a method of fabricating the diffraction gratings illustrated in  FIGS.  10 A- 10 C , according to embodiments. 
         FIGS.  13 A- 13 B  illustrate cross-sectional side views of diffraction gratings having zones in which liquid crystal molecules have different pre-tilt angles, according to embodiments. 
         FIGS.  14 A- 14 B  are cross-sectional side views of an intermediate structure and a diffraction grating illustrating a method of fabricating the diffraction gratings illustrated in  FIGS.  13 A- 13 B , according to embodiments. 
         FIGS.  15 A- 15 C  illustrate top down plan views of diffraction gratings having zones in which liquid crystal molecules have different azimuthal angles, according to embodiments. 
         FIG.  16 A  illustrates a top down plan view of a diffraction grating having zones in which liquid crystal molecules have different azimuthal angles, according to embodiments. 
         FIG.  16 B  is a schematic graph illustrating variations in azimuthal angles in a lateral direction across different zones of the diffraction grating illustrated in  FIG.  16 A . 
         FIGS.  17 A- 17 D  illustrate cross-sectional side views of intermediate structures and a diffraction gratings illustrating a method of fabricating the diffraction gratings illustrated in  FIGS.  15 A- 15 C , according to embodiments. 
         FIG.  17 E  illustrates a top down plan view of the diffraction grating illustrated in  FIG.  17 D , according to embodiments. 
         FIGS.  18 A- 18 C  illustrate cross-sectional side views of intermediate structures and a diffraction gratings illustrating a method of fabricating the diffraction gratings illustrated in  FIGS.  16 A , according to embodiments. 
         FIG.  18 D  illustrates a top down plan view of the diffraction grating illustrated in  FIG.  18 C , according to embodiments. 
         FIGS.  19 A- 19 B  illustrate top down and cross-sectional side views of a diffraction grating having zones in which liquid crystal molecules have different chirality, according to embodiments. 
         FIG.  20    is a cross-sectional side view of a diffraction grating having zones in which liquid crystal molecules have different chirality, according to embodiments. 
         FIGS.  21    is a cross-sectional side view of a diffraction grating having zones in which liquid crystal layers are formed of different liquid crystal materials, according to embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     AR systems may display virtual content to a user, or viewer, while still allowing the user to see the world around them. Preferably, this content is displayed on a head-mounted display, e.g., as part of eyewear, that projects image information to the user&#39;s eyes. In addition, the display may also transmit light from the surrounding environment to the user&#39;s eyes, to allow a view of that surrounding environment. As used herein, it will be appreciated that a “head-mounted” display is a display that may be mounted on the head of a viewer. 
     Reference will now be made to the drawings, in which like reference numerals refer to like parts throughout. 
       FIG.  2    illustrates an example of wearable display system  80 . The display system  80  includes a display  62 , and various mechanical and electronic modules and systems to support the functioning of that display  62 . The display  62  may be coupled to a frame  64 , which is wearable by a display system user or viewer  60  and which is configured to position the display  62  in front of the eyes of the user  60 . The display  62  may be considered eyewear in some embodiments. In some embodiments, a speaker  66  is coupled to the frame  64  and positioned adjacent the ear canal of the user  60  (in some embodiments, another speaker, not shown, is positioned adjacent the other ear canal of the user to provide for stereo/shapeable sound control). In some embodiments, the display system may also include one or more microphones  67  or other devices to detect sound. In some embodiments, the microphone is configured to allow the user to provide inputs or commands to the system  80  (e.g., the selection of voice menu commands, natural language questions, etc.), and/or may allow audio communication with other persons (e.g., with other users of similar display systems The microphone may further be configured as a peripheral sensor to continuously collect audio data (e.g., to passively collect from the user and/or environment). Such audio data may include user sounds such as heavy breathing, or environmental sounds, such as a loud bang indicative of a nearby event. The display system may also include a peripheral sensor  30 a, which may be separate from the frame  64  and attached to the body of the user  60  (e.g., on the head, torso, an extremity, etc. of the user  60 ). The peripheral sensor  30   a  may be configured to acquire data characterizing the physiological state of the user  60  in some embodiments, as described further herein. For example, the sensor  30   a  may be an electrode. 
     With continued reference to  FIG.  2   , the display  62  is operatively coupled by communications link  68 , such as by a wired lead or wireless connectivity, to a local data processing module  70  which may be mounted in a variety of configurations, such as fixedly attached to the frame  64 , fixedly attached to a helmet or hat worn by the user, embedded in headphones, or otherwise removably attached to the user  60  (e.g., in a backpack-style configuration, in a belt-coupling style configuration). Similarly, the sensor  30   a  may be operatively coupled by communications link  30 b, e.g., a wired lead or wireless connectivity, to the local processor and data module  70 . The local processing and data module  70  may comprise a hardware processor, as well as digital memory, such as non-volatile memory (e.g., flash memory or hard disk drives), both of which may be utilized to assist in the processing, caching, and storage of data. The data include data a) captured from sensors (which may be, e.g., operatively coupled to the frame  64  or otherwise attached to the user  60 ), such as image capture devices (such as cameras), microphones, inertial measurement units, accelerometers, compasses, GPS units, radio devices, gyros, and/or other sensors disclosed herein; and/or b) acquired and/or processed using remote processing module  72  and/or remote data repository  74  (including data relating to virtual content), possibly for passage to the display  62  after such processing or retrieval. The local processing and data module  70  may be operatively coupled by communication links  76 ,  78 , such as via a wired or wireless communication links, to the remote processing module  72  and remote data repository  74  such that these remote modules  72 ,  74  are operatively coupled to each other and available as resources to the local processing and data module  70 . In some embodiments, the local processing and data module  70  may include one or more of the image capture devices, microphones, inertial measurement units, accelerometers, compasses, GPS units, radio devices, and/or gyros. In some other embodiments, one or more of these sensors may be attached to the frame  64 , or may be standalone structures that communicate with the local processing and data module  70  by wired or wireless communication pathways. 
     With continued reference to  FIG.  2   , in some embodiments, the remote processing module  72  may comprise one or more processors configured to analyze and process data and/or image information. In some embodiments, the remote data repository  74  may comprise a digital data storage facility, which may be available through the internet or other networking configuration in a “cloud” resource configuration. In some embodiments, the remote data repository  74  may include one or more remote servers, which provide information, e.g., information for generating augmented reality content, to the local processing and data module  70  and/or the remote processing module  72 . In some embodiments, all data is stored and all computations are performed in the local processing and data module, allowing fully autonomous use from a remote module. 
     The perception of an image as being “three-dimensional” or “3-D” may be achieved by providing slightly different presentations of the image to each eye of the viewer.  FIG.  3    illustrates a conventional display system for simulating three-dimensional imagery for a user. Two distinct images  5 ,  7 —one for each eye  4 ,  6 —are outputted to the user. The images  5 ,  7  are spaced from the eyes  4 ,  6  by a distance  10  along an optical or z-axis parallel to the line of sight of the viewer. The images  5 ,  7  are flat and the eyes  4 ,  6  may focus on the images by assuming a single accommodated state. Such systems rely on the human visual system to combine the images  5 ,  7  to provide a perception of depth and/or scale for the combined image. 
     It will be appreciated, however, that the human visual system is more complicated and providing a realistic perception of depth is more challenging. For example, many viewers of conventional “3-D” display systems find such systems to be uncomfortable or may not perceive a sense of depth at all. Without being limited by theory, it is believed that viewers of an object may perceive the object as being “three-dimensional” due to a combination of vergence and accommodation. Vergence movements (i.e., rotation of the eyes so that the pupils move toward or away from each other to converge the lines of sight of the eyes to fixate upon an object) of the two eyes relative to each other are closely associated with focusing (or “accommodation”) of the lenses and pupils of the eyes. Under normal conditions, changing the focus of the lenses of the eyes, or accommodating the eyes, to change focus from one object to another object at a different distance will automatically cause a matching change in vergence to the same distance, under a relationship known as the “accommodation-vergence reflex,” as well as pupil dilation or constriction. Likewise, a change in vergence will trigger a matching change in accommodation of lens shape and pupil size, under normal conditions. As noted herein, many stereoscopic or “3-D” display systems display a scene using slightly different presentations (and, so, slightly different images) to each eye such that a three-dimensional perspective is perceived by the human visual system. Such systems are uncomfortable for many viewers, however, since they, among other things, simply provide a different presentation of a scene, but with the eyes viewing all the image information at a single accommodated state, and work against the “accommodation-vergence reflex.” Display systems that provide a better match between accommodation and vergence may form more realistic and comfortable simulations of three-dimensional imagery contributing to increased duration of wear and in turn compliance to diagnostic and therapy protocols. 
       FIG.  4    illustrates aspects of an approach for simulating three-dimensional imagery using multiple depth planes. With reference to  FIG.  4   , objects at various distances from eyes  4 ,  6  on the z-axis are accommodated by the eyes  4 ,  6  so that those objects are in focus. The eyes ( 4  and  6 ) assume particular accommodated states to bring into focus objects at different distances along the z-axis. Consequently, a particular accommodated state may be said to be associated with a particular one of depth planes  14 , with has an associated focal distance, such that objects or parts of objects in a particular depth plane are in focus when the eye is in the accommodated state for that depth plane. In some embodiments, three-dimensional imagery may be simulated by providing different presentations of an image for each of the eyes  4 ,  6 , and also by providing different presentations of the image corresponding to each of the depth planes. While shown as being separate for clarity of illustration, it will be appreciated that the fields of view of the eyes  4 ,  6  may overlap, for example, as distance along the z-axis increases. In addition, while shown as flat for ease of illustration, it will be appreciated that the contours of a depth plane may be curved in physical space, such that all features in a depth plane are in focus with the eye in a particular accommodated state. 
     The distance between an object and the eye  4  or  6  may also change the amount of divergence of light from that object, as viewed by that eye.  FIGS.  5 A- 5 C  illustrates relationships between distance and the divergence of light rays. The distance between the object and the eye  4  is represented by, in order of decreasing distance, R 1 , R 2 , and R 3 . As shown in  FIGS.  5 A- 5 C , the light rays become more divergent as distance to the object decreases. As distance increases, the light rays become more collimated. Stated another way, it may be said that the light field produced by a point (the object or a part of the object) has a spherical wavefront curvature, which is a function of how far away the point is from the eye of the user. The curvature increases with decreasing distance between the object and the eye  4 . Consequently, at different depth planes, the degree of divergence of light rays is also different, with the degree of divergence increasing with decreasing distance between depth planes and the viewer&#39;s eye  4 . While only a single eye  4  is illustrated for clarity of illustration in  FIGS.  5 A- 5 C  and other figures herein, it will be appreciated that the discussions regarding eye  4  may be applied to both eyes  4  and  6  of a viewer. 
     Without being limited by theory, it is believed that the human eye typically can interpret a finite number of depth planes to provide depth perception. Consequently, a highly believable simulation of perceived depth may be achieved by providing, to the eye, different presentations of an image corresponding to each of these limited number of depth planes. The different presentations may be separately focused by the viewer&#39;s eyes, thereby helping to provide the user with depth cues based on the accommodation of the eye required to bring into focus different image features for the scene located on different depth plane and/or based on observing different image features on different depth planes being out of focus. 
       FIG.  6    illustrates an example of a waveguide stack for outputting image information to a user. A display system  1000  includes a stack of waveguides, or stacked waveguide assembly,  1178  that may be utilized to provide three-dimensional perception to the eye/brain using a plurality of waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190 . In some embodiments, the display system  1000  is the system  80  of  FIG.  2   , with  FIG.  6    schematically showing some parts of that system  80  in greater detail. For example, the waveguide assembly  1178  may be part of the display  62  of  FIG.  2   . It will be appreciated that the display system  1000  may be considered a light field display in some embodiments. 
     With continued reference to  FIG.  6   , the waveguide assembly  1178  may also include a plurality of features  1198 ,  1196 ,  1194 ,  1192  between the waveguides. In some embodiments, the features  1198 ,  1196 ,  1194 ,  1192  may be one or more lenses. The waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190  and/or the plurality of lenses  1198 ,  1196 ,  1194 ,  1192  may be configured to send image information to the eye with various levels of wavefront curvature or light ray divergence. Each waveguide level may be associated with a particular depth plane and may be configured to output image information corresponding to that depth plane. Image injection devices  1200 ,  1202 ,  1204 ,  1206 ,  1208  may function as a source of light for the waveguides and may be utilized to inject image information into the waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190 , each of which may be configured, as described herein, to distribute incoming light across each respective waveguide, for output toward the eye  4 . Light exits an output surface  1300 ,  1302 ,  1304 ,  1306 ,  1308  of the image injection devices  1200 ,  1202 ,  1204 ,  1206 ,  1208  and is injected into a corresponding input surface  1382 ,  1384 ,  1386 ,  1388 ,  1390  of the waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190 . In some embodiments, the each of the input surfaces  1382 ,  1384 ,  1386 ,  1388 ,  1390  may be an edge of a corresponding waveguide, or may be part of a major surface of the corresponding waveguide (that is, one of the waveguide surfaces directly facing the world  1144  or the viewer&#39;s eye  4 ). In some embodiments, a single beam of light (e.g. a collimated beam) may be injected into each waveguide to output an entire field of cloned collimated beams that are directed toward the eye  4  at particular angles (and amounts of divergence) corresponding to the depth plane associated with a particular waveguide. In some embodiments, a single one of the image injection devices  1200 ,  1202 ,  1204 ,  1206 ,  1208  may be associated with and inject light into a plurality (e.g., three) of the waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190 . 
     In some embodiments, the image injection devices  1200 ,  1202 ,  1204 ,  1206 ,  1208  are discrete displays that each produce image information for injection into a corresponding waveguide  1182 ,  1184 ,  1186 ,  1188 ,  1190 , respectively. In some other embodiments, the image injection devices  1200 ,  1202 ,  1204 ,  1206 ,  1208  are the output ends of a single multiplexed display which may, e.g., pipe image information via one or more optical conduits (such as fiber optic cables) to each of the image injection devices  1200 ,  1202 ,  1204 ,  1206 ,  1208 . It will be appreciated that the image information provided by the image injection devices  1200 ,  1202 ,  1204 ,  1206 ,  1208  may include light of different wavelengths, or colors (e.g., different component colors, as discussed herein). 
     In some embodiments, the light injected into the waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190  is provided by a light projector system  2000 , which comprises a light module  2040 , which may include a light emitter, such as a light emitting diode (LED). The light from the light module  2040  may be directed to and modified by a light modulator  2030 , e.g., a spatial light modulator, via a beam splitter  2050 . The light modulator  2030  may be configured to change the perceived intensity of the light injected into the waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190 . Examples of spatial light modulators include liquid crystal displays (LCD) including a liquid crystal on silicon (LCOS) displays. 
     In some embodiments, the display system  1000  may be a scanning fiber display comprising one or more scanning fibers configured to project light in various patterns (e.g., raster scan, spiral scan, Lissajous patterns, etc.) into one or more waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190  and ultimately to the eye  4  of the viewer. In some embodiments, the illustrated image injection devices  1200 ,  1202 ,  1204 ,  1206 ,  1208  may schematically represent a single scanning fiber or a bundles of scanning fibers configured to inject light into one or a plurality of the waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190 . In some other embodiments, the illustrated image injection devices  1200 ,  1202 ,  1204 ,  1206 ,  1208  may schematically represent a plurality of scanning fibers or a plurality of bundles of scanning, fibers each of which are configured to inject light into an associated one of the waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190 . It will be appreciated that the one or more optical fibers may be configured to transmit light from the light module  2040  to the one or more waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190 . It will be appreciated that one or more intervening optical structures may be provided between the scanning fiber, or fibers, and the one or more waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190  to, e.g., redirect light exiting the scanning fiber into the one or more waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190 . 
     A controller  1210  controls the operation of one or more of the stacked waveguide assembly  1178 , including operation of the image injection devices  1200 ,  1202 ,  1204 ,  1206 ,  1208 , the light source  2040 , and the light modulator  2030 . In some embodiments, the controller  1210  is part of the local data processing module  70 . The controller  1210  includes programming (e.g., instructions in a non-transitory medium) that regulates the timing and provision of image information to the waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190  according to, e.g., any of the various schemes disclosed herein. In some embodiments, the controller may be a single integral device, or a distributed system connected by wired or wireless communication channels. The controller  1210  may be part of the processing modules  70  or  72  ( FIG.  1   ) in some embodiments. 
     With continued reference to  FIG.  6   , the waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190  may be configured to propagate light within each respective waveguide by total internal reflection (TIR). The waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190  may each be planar or have another shape (e.g., curved), with major top and bottom surfaces and edges extending between those major top and bottom surfaces. In the illustrated configuration, the waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190  may each include outcoupling optical elements  1282 ,  1284 ,  1286 ,  1288 ,  1290  that are configured to extract light out of a waveguide by redirecting the light, propagating within each respective waveguide, out of the waveguide to output image information to the eye  4 . Extracted light may also be referred to as outcoupled light and the outcoupling optical elements light may also be referred to light extracting optical elements. An extracted beam of light is outputted by the waveguide at locations at which the light propagating in the waveguide strikes a light extracting optical element. The outcoupling optical elements  1282 ,  1284 ,  1286 ,  1288 ,  1290  may, for example, be gratings, including diffractive optical features, as discussed further herein. While illustrated disposed at the bottom major surfaces of the waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190  for ease of description and drawing clarity, in some embodiments, the outcoupling optical elements  1282 ,  1284 ,  1286 ,  1288 ,  1290  may be disposed at the top and/or bottom major surfaces, and/or may be disposed directly in the volume of the waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190 , as discussed further herein. In some embodiments, the outcoupling optical elements  1282 ,  1284 ,  1286 ,  1288 ,  1290  may be formed in a layer of material that is attached to a transparent substrate to form the waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190 . In some other embodiments, the waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190  may be a monolithic piece of material and the outcoupling optical elements  1282 ,  1284 ,  1286 ,  1288 ,  1290  may be formed on a surface and/or in the interior of that piece of material. 
     With continued reference to  FIG.  6   , as discussed herein, each waveguide  1182 ,  1184 ,  1186 ,  1188 ,  1190  is configured to output light to form an image corresponding to a particular depth plane. For example, the waveguide  1182  nearest the eye may be configured to deliver collimated light, as injected into such waveguide  1182 , to the eye  4 . The collimated light may be representative of the optical infinity focal plane. The next waveguide up  1184  may be configured to send out collimated light which passes through the first lens  1192  (e.g., a negative lens) before it can reach the eye  4 ; such first lens  1192  may be configured to create a slight convex wavefront curvature so that the eye/brain interprets light coming from that next waveguide up  1184  as coming from a first focal plane closer inward toward the eye  4  from optical infinity. Similarly, the third up waveguide  1186  passes its output light through both the first  1192  and second  1194  lenses before reaching the eye  4 ; the combined optical power of the first  1192  and second  1194  lenses may be configured to create another incremental amount of wavefront curvature so that the eye/brain interprets light coming from the third waveguide  1186  as coming from a second focal plane that is even closer inward toward the person from optical infinity than was light from the next waveguide up  1184 . 
     The other waveguide layers  1188 ,  1190  and lenses  1196 ,  1198  are similarly configured, with the highest waveguide  1190  in the stack sending its output through all of the lenses between it and the eye for an aggregate focal power representative of the closest focal plane to the person. To compensate for the stack of lenses  1198 ,  1196 ,  1194 ,  1192  when viewing/interpreting light coming from the world  1144  on the other side of the stacked waveguide assembly  1178 , a compensating lens layer  1180  may be disposed at the top of the stack to compensate for the aggregate power of the lens stack  1198 ,  1196 ,  1194 ,  1192  below. Such a configuration provides as many perceived focal planes as there are available waveguide/lens pairings. Both the outcoupling optical elements of the waveguides and the focusing aspects of the lenses may be static (i.e., not dynamic or electro-active). In some alternative embodiments, either or both may be dynamic using electro-active features. 
     In some embodiments, two or more of the waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190  may have the same associated depth plane. For example, multiple waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190  may be configured to output images set to the same depth plane, or multiple subsets of the waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190  may be configured to output images set to the same plurality of depth planes, with one set for each depth plane. This can provide advantages for forming a tiled image to provide an expanded field of view at those depth planes. 
     With continued reference to  FIG.  6   , the outcoupling optical elements  1282 ,  1284 ,  1286 ,  1288 ,  1290  may be configured to both redirect light out of their respective waveguides and to output this light with the appropriate amount of divergence or collimation for a particular depth plane associated with the waveguide. As a result, waveguides having different associated depth planes may have different configurations of outcoupling optical elements  1282 ,  1284 ,  1286 ,  1288 ,  1290 , which output light with a different amount of divergence depending on the associated depth plane. In some embodiments, the light extracting optical elements  1282 ,  1284 ,  1286 ,  1288 ,  1290  may be volumetric or surface features, which may be configured to output light at specific angles. For example, the light extracting optical elements  1282 ,  1284 ,  1286 ,  1288 ,  1290  may be volume holograms, surface holograms, and/or diffraction gratings. In some embodiments, the features  1198 ,  1196 ,  1194 ,  1192  may not be lenses; rather, they may simply be spacers (e.g., cladding layers and/or structures for forming air gaps). 
     In some embodiments, the outcoupling optical elements  1282 ,  1284 ,  1286 ,  1288 ,  1290  are diffractive features that form a diffraction pattern, or “diffractive optical element” (also referred to herein as a “DOE”). Preferably, the DOE&#39;s have a sufficiently low diffraction efficiency so that only a portion of the light of the beam is deflected away toward the eye  4  with each intersection of the DOE, while the rest continues to move through a waveguide via total internal reflection. The light carrying the image information is thus divided into a number of related exit beams that exit the waveguide at a multiplicity of locations and the result is a fairly uniform pattern of exit emission toward the eye  4  for this particular collimated beam bouncing around within a waveguide. 
     In some embodiments, one or more DOEs may be switchable between “on” states in which they actively diffract, and “off” states in which they do not significantly diffract. For instance, a switchable DOE may comprise a layer of polymer dispersed liquid crystal, in which microdroplets comprise a diffraction pattern in a host medium, and the refractive index of the microdroplets may be switched to substantially match the refractive index of the host material (in which case the pattern does not appreciably diffract incident light) or the microdroplet may be switched to an index that does not match that of the host medium (in which case the pattern actively diffracts incident light). 
     In some embodiments, a camera assembly  500  (e.g., a digital camera, including visible light and infrared light cameras) may be provided to capture images of the eye  4  and/or tissue around the eye  4  to, e.g., detect user inputs and/or to monitor the physiological state of the user. As used herein, a camera may be any image capture device. In some embodiments, the camera assembly  500  may include an image capture device and a light source to project light (e.g., infrared light) to the eye, which may then be reflected by the eye and detected by the image capture device. In some embodiments, the camera assembly  500  may be attached to the frame  64  ( FIG.  2   ) and may be in electrical communication with the processing modules  70  and/or  72 , which may process image information from the camera assembly  500  to make various determinations regarding, e.g., the physiological state of the user, as discussed herein. It will be appreciated that information regarding the physiological state of user may be used to determine the behavioral or emotional state of the user. Examples of such information include movements of the user and/or facial expressions of the user. The behavioral or emotional state of the user may then be triangulated with collected environmental and/or virtual content data so as to determine relationships between the behavioral or emotional state, physiological state, and environmental or virtual content data. In some embodiments, one camera assembly  500  may be utilized for each eye, to separately monitor each eye. 
     With reference now to  FIG.  7   , an example of exit beams outputted by a waveguide is shown. One waveguide is illustrated, but it will be appreciated that other waveguides in the waveguide assembly  1178  ( FIG.  6   ) may function similarly, where the waveguide assembly  1178  includes multiple waveguides. Light  400  is injected into the waveguide  1182  at the input surface  1382  of the waveguide  1182  and propagates within the waveguide  1182  by TIR. At points where the light  400  impinges on the DOE  1282 , a portion of the light exits the waveguide as exit beams  402 . The exit beams  402  are illustrated as substantially parallel but, as discussed herein, they may also be redirected to propagate to the eye  4  at an angle (e.g., forming divergent exit beams), depending on the depth plane associated with the waveguide  1182 . It will be appreciated that substantially parallel exit beams may be indicative of a waveguide with outcoupling optical elements that outcouple light to form images that appear to be set on a depth plane at a large distance (e.g., optical infinity) from the eye  4 . Other waveguides or other sets of outcoupling optical elements may output an exit beam pattern that is more divergent, which would require the eye  4  to accommodate to a closer distance to bring it into focus on the retina and would be interpreted by the brain as light from a distance closer to the eye  4  than optical infinity. 
     In some embodiments, a full color image may be formed at each depth plane by overlaying images in each of the component colors, e.g., three or more component colors.  FIG.  8    illustrates an example of a stacked waveguide assembly in which each depth plane includes images formed using multiple different component colors. The illustrated embodiment shows depth planes  14   a - 14   f,  although more or fewer depths are also contemplated. Each depth plane may have three component color images associated with it: a first image of a first color, G; a second image of a second color, R; and a third image of a third color, B. Different depth planes are indicated in the figure by different numbers for diopters (dpt) following the letters G, R, and B. Just as examples, the numbers following each of these letters indicate diopters (1/m), or inverse distance of the depth plane from a viewer, and each box in the figures represents an individual component color image. In some embodiments, to account for differences in the eye&#39;s focusing of light of different wavelengths, the exact placement of the depth planes for different component colors may vary. For example, different component color images for a given depth plane may be placed on depth planes corresponding to different distances from the user. Such an arrangement may increase visual acuity and user comfort and/or may decrease chromatic aberrations. 
     In some embodiments, light of each component color may be outputted by a single dedicated waveguide and, consequently, each depth plane may have multiple waveguides associated with it. In such embodiments, each box in the figures including the letters G, R, or B may be understood to represent an individual waveguide, and three waveguides may be provided per depth plane where three component color images are provided per depth plane. While the waveguides associated with each depth plane are shown adjacent to one another in this drawing for ease of description, it will be appreciated that, in a physical device, the waveguides may all be arranged in a stack with one waveguide per level. In some other embodiments, multiple component colors may be outputted by the same waveguide, such that, e.g., only a single waveguide may be provided per depth plane. 
     With continued reference to  FIG.  8   , in some embodiments, G is the color green, R is the color red, and B is the color blue. In some other embodiments, other colors associated with other wavelengths of light, including magenta and cyan, may be used in addition to or may replace one or more of red, green, or blue. In some embodiments, features  198 ,  196 ,  194 , and  192  may be active or passive optical filters configured to block or selectively light from the ambient environment to the viewer&#39;s eyes. 
     It will be appreciated that references to a given color of light throughout this disclosure will be understood to encompass light of one or more wavelengths within a range of wavelengths of light that are perceived by a viewer as being of that given color. For example, red light may include light of one or more wavelengths in the range of about 620-780 nm, green light may include light of one or more wavelengths in the range of about 492-577 nm, and blue light may include light of one or more wavelengths in the range of about 435-493 nm. 
     In some embodiments, the light source  2040  ( FIG.  6   ) may be configured to emit light of one or more wavelengths outside the visual perception range of the viewer, for example, infrared and/or ultraviolet wavelengths. In addition, the incoupling, outcoupling, and other light redirecting structures of the waveguides of the display  1000  may be configured to direct and emit this light out of the display towards the user&#39;s eye  4 , e.g., for imaging and/or user stimulation applications. 
     With reference now to  FIG.  9 A , in some embodiments, light impinging on a waveguide may need to be redirected to incouple that light into the waveguide. An incoupling optical element may be used to redirect and incouple the light into its corresponding waveguide.  FIG.  9 A  illustrates a cross-sectional side view of an example of a plurality or set  1200  of stacked waveguides that each includes an incoupling optical element. The waveguides may each be configured to output light of one or more different wavelengths, or one or more different ranges of wavelengths. It will be appreciated that the stack  1200  may correspond to the stack  1178  ( FIG.  6   ) and the illustrated waveguides of the stack  1200  may correspond to part of the plurality of waveguides  1182 ,  1184 ,  1186 ,  1188 ,  1190 , except that light from one or more of the image injection devices  1200 ,  1202 ,  1204 ,  1206 ,  1208  is injected into the waveguides from a position that requires light to be redirected for incoupling. 
     The illustrated set  1200  of stacked waveguides includes waveguides  1210 ,  1220 , and  1230 . Each waveguide includes an associated incoupling optical element (which may also be referred to as a light input area on the waveguide), with, e.g., incoupling optical element  1212  disposed on a major surface (e.g., an upper major surface) of waveguide  1210 , incoupling optical element  1224  disposed on a major surface (e.g., an upper major surface) of waveguide  1220 , and incoupling optical element  1232  disposed on a major surface (e.g., an upper major surface) of waveguide  1230 . In some embodiments, one or more of the incoupling optical elements  1212 ,  1222 ,  1232  may be disposed on the bottom major surface of the respective waveguide  1210 ,  1220 ,  1230  (particularly where the one or more incoupling optical elements are reflective, deflecting optical elements). As illustrated, the incoupling optical elements  1212 ,  1222 ,  1232  may be disposed on the upper major surface of their respective waveguide  1210 ,  1220 ,  1230  (or the top of the next lower waveguide), particularly where those incoupling optical elements are transmissive, deflecting optical elements. In some embodiments, the incoupling optical elements  1212 ,  1222 ,  1232  may be disposed in the body of the respective waveguide  1210 ,  1220 ,  1230 . In some embodiments, as discussed herein, the incoupling optical elements  1212 ,  1222 ,  1232  are wavelength selective, such that they selectively redirect one or more wavelengths of light, while transmitting other wavelengths of light. While illustrated on one side or corner of their respective waveguide  1210 ,  1220 ,  1230 , it will be appreciated that the incoupling optical elements  1212 ,  1222 ,  1232  may be disposed in other areas of their respective waveguide  1210 ,  1220 ,  1230  in some embodiments. 
     As illustrated, the incoupling optical elements  1212 ,  1222 ,  1232  may be laterally offset from one another. In some embodiments, each incoupling optical element may be offset such that it receives light without that light passing through another incoupling optical element. For example, each incoupling optical element  1212 ,  1222 ,  1232  may be configured to receive light from a different image injection device  1200 ,  1202 ,  1204 ,  1206 , and  1208  as shown in  FIG.  6   , and may be separated (e.g., laterally spaced apart) from other incoupling optical elements  1212 ,  1222 ,  1232  such that it substantially does not receive light from the other ones of the incoupling optical elements  1212 ,  1222 ,  1232 . 
     Each waveguide also includes associated light distributing elements, with, e.g., light distributing elements  1214  disposed on a major surface (e.g., a top major surface) of waveguide  1210 , light distributing elements  1224  disposed on a major surface (e.g., a top major surface) of waveguide  1220 , and light distributing elements  1234  disposed on a major surface (e.g., a top major surface) of waveguide  1230 . In some other embodiments, the light distributing elements  1214 ,  1224 ,  1234 , may be disposed on a bottom major surface of associated waveguides  1210 ,  1220 ,  1230 , respectively. In some other embodiments, the light distributing elements  1214 ,  1224 ,  1234 , may be disposed on both top and bottom major surface of associated waveguides  1210 ,  1220 ,  1230 , respectively; or the light distributing elements  1214 ,  1224 ,  1234 , may be disposed on different ones of the top and bottom major surfaces in different associated waveguides  1210 ,  1220 ,  1230 , respectively. 
     The waveguides  1210 ,  1220 ,  1230  may be spaced apart and separated by, e.g., gas, liquid, and/or solid layers of material. For example, as illustrated, layer  1218   a  may separate waveguides  1210  and  1220 ; and layer  1218   b  may separate waveguides  1220  and  1230 . In some embodiments, the layers  1218   a  and  1218   b  are formed of low refractive index materials (that is, materials having a lower refractive index than the material forming the immediately adjacent one of waveguides  1210 ,  1220 ,  1230 ). Preferably, the refractive index of the material forming the layers  1218   a,    1218   b  is 0.05 or more, or 0.10 or more less than the refractive index of the material forming the waveguides  1210 ,  1220 ,  1230 . Advantageously, the lower refractive index layers  1218   a,    1218   b  may function as cladding layers that facilitate total internal reflection (TIR) of light through the waveguides  1210 ,  1220 ,  1230  (e.g., TIR between the top and bottom major surfaces of each waveguide). In some embodiments, the layers  1218   a,    1218   b  are formed of air. While not illustrated, it will be appreciated that the top and bottom of the illustrated set  1200  of waveguides may include immediately neighboring cladding layers. 
     Preferably, for ease of manufacturing and other considerations, the material forming the waveguides  1210 ,  1220 ,  1230  are similar or the same, and the material forming the layers  1218   a,    1218   b  are similar or the same. In some embodiments, the material forming the waveguides  1210 ,  1220 ,  1230  may be different between one or more waveguides, and/or the material forming the layers  1218   a,    1218   b  may be different, while still holding to the various refractive index relationships noted above. 
     With continued reference to  FIG.  9 A , light rays  1240 ,  1242 ,  1244  are incident on the set  1200  of waveguides. It will be appreciated that the light rays  1240 ,  1242 ,  1244  may be injected into the waveguides  1210 ,  1220 ,  1230  by one or more image injection devices  1200 ,  1202 ,  1204 ,  1206 ,  1208  ( FIG.  6   ). 
     In some embodiments, the light rays  1240 ,  1242 ,  1244  have different properties, e.g., different wavelengths or different ranges of wavelengths, which may correspond to different colors. The incoupling optical elements  1212 ,  122 ,  1232  each deflect the incident light such that the light propagates through a respective one of the waveguides  1210 ,  1220 ,  1230  by TIR. 
     For example, incoupling optical element  1212  may be configured to deflect ray  1240 , which has a first wavelength or range of wavelengths. Similarly, the transmitted ray  1242  impinges on and is deflected by the incoupling optical element  1222 , which is configured to deflect light of a second wavelength or range of wavelengths. Likewise, the ray  1244  is deflected by the incoupling optical element  1232 , which is configured to selectively deflect light of third wavelength or range of wavelengths. 
     With continued reference to  FIG.  9 A , the deflected light rays  1240 ,  1242 ,  1244  are deflected so that they propagate through a corresponding waveguide  1210 ,  1220 ,  1230 ; that is, the incoupling optical elements  1212 ,  1222 ,  1232  of each waveguide deflects light into that corresponding waveguide  1210 ,  1220 ,  1230  to incouple light into that corresponding waveguide. The light rays  1240 ,  1242 ,  1244  are deflected at angles that cause the light to propagate through the respective waveguide  1210 ,  1220 ,  1230  by TIR. The light rays  1240 ,  1242 ,  1244  propagate through the respective waveguide  1210 ,  1220 ,  1230  by TIR until impinging on the waveguide&#39;s corresponding light distributing elements  1214 ,  1224 ,  1234 . 
     With reference now to  FIG.  9 B , a perspective view of an example of the plurality of stacked waveguides of  FIG.  9 A  is illustrated. As noted above, the incoupled light rays  1240 ,  1242 ,  1244 , are deflected by the incoupling optical elements  1212 ,  1222 ,  1232 , respectively, and then propagate by TIR within the waveguides  1210 ,  1220 ,  1230 , respectively. The light rays  1240 ,  1242 ,  1244  then impinge on the light distributing elements  1214 ,  1224 ,  1234 , respectively. The light distributing elements  1214 ,  1224 ,  1234  deflect the light rays  1240 ,  1242 ,  1244  so that they propagate towards the outcoupling optical elements  1250 ,  1252 ,  1254 , respectively. 
     In some embodiments, the light distributing elements  1214 ,  1224 ,  1234  are orthogonal pupil expanders (OPE&#39;s). In some embodiments, the OPE&#39;s both deflect or distribute light to the outcoupling optical elements  1250 ,  1252 ,  1254  and also increase the beam or spot size of this light as it propagates to the outcoupling optical elements. In some embodiments, e.g., where the beam size is already of a desired size, the light distributing elements  1214 ,  1224 ,  1234  may be omitted and the incoupling optical elements  1212 ,  1222 ,  1232  may be configured to deflect light directly to the outcoupling optical elements  1250 ,  1252 ,  1254 . For example, with reference to  FIG.  9 A , the light distributing elements  1214 ,  1224 ,  1234  may be replaced with outcoupling optical elements  1250 ,  1252 ,  1254 , respectively. In some embodiments, the outcoupling optical elements  1250 ,  1252 ,  1254  are exit pupils (EP&#39;s) or exit pupil expanders (EPE&#39;s) that direct light in a viewer&#39;s eye  4  ( FIG.  7   ). 
     Accordingly, with reference to  FIGS.  9 A and  9 B , in some embodiments, the set  1200  of waveguides includes waveguides  1210 ,  1220 ,  1230 ; incoupling optical elements  1212 ,  1222 ,  1232 ; light distributing elements (e.g., OPE&#39;s)  1214 ,  1224 ,  1234 ; and outcoupling optical elements (e.g., EP&#39;s)  1250 ,  1252 ,  1254  for each component color. The waveguides  1210 ,  1220 ,  1230  may be stacked with an air gap/cladding layer between each one. The incoupling optical elements  1212 ,  1222 ,  1232  redirect or deflect incident light (with different incoupling optical elements receiving light of different wavelengths) into its waveguide. The light then propagates at an angle which will result in TIR within the respective waveguide  1210 ,  1220 ,  1230 . In the example shown, light ray  1240  (e.g., blue light) is deflected by the first incoupling optical element  1212 , and then continues to bounce down the waveguide, interacting with the light distributing element (e.g., OPE&#39;s)  1214  and then the outcoupling optical element (e.g., EPs)  1250 , in a manner described earlier. The light rays  1242  and  1244  (e.g., green and red light, respectively) will pass through the waveguide  1210 , with light ray  1242  impinging on and being deflected by incoupling optical element  1222 . The light ray  1242  then bounces down the waveguide  1220  via TIR, proceeding on to its light distributing element (e.g., OPEs)  1224  and then the outcoupling optical element (e.g., EP&#39;s)  1252 . Finally, light ray  1244  (e.g., red light) passes through the waveguide  1220  to impinge on the light incoupling optical elements  1232  of the waveguide  1230 . The light incoupling optical elements  1232  deflect the light ray  1244  such that the light ray propagates to light distributing element (e.g., OPEs)  1234  by TIR, and then to the outcoupling optical element (e.g., EPs)  1254  by TIR. The outcoupling optical element  1254  then finally outcouples the light ray  1244  to the viewer, who also receives the outcoupled light from the other waveguides  1210 ,  1220 . 
       FIG.  9 C  illustrates a top-down plan view of an example of the plurality of stacked waveguides of  FIGS.  9 A and  9 B . As illustrated, the waveguides  1210 ,  1220 ,  1230 , along with each waveguide&#39;s associated light distributing element  1214 ,  1224 ,  1234  and associated outcoupling optical element  1250 ,  1252 ,  1254 , may be vertically aligned. However, as discussed herein, the incoupling optical elements  1212 ,  1222 ,  1232  are not vertically aligned; rather, the incoupling optical elements are preferably non-overlapping (e.g., laterally spaced apart as seen in the top-down view). As discussed further herein, this nonoverlapping spatial arrangement facilitates the injection of light from different resources into different waveguides on a one-to-one basis, thereby allowing a specific light source to be uniquely coupled to a specific waveguide. In some embodiments, arrangements including nonoverlapping spatially-separated incoupling optical elements may be referred to as a shifted pupil system, and the in coupling optical elements within these arrangements may correspond to sub pupils. 
     Spatially Variable Liquid Crystal Diffraction Gratings 
     As described above in reference to  FIGS.  6  and  7   , display systems according to various embodiments described herein may include outcoupling optical elements (e.g., optical elements  1282 ,  1284 ,  1286 ,  1288 ,  1290  in  FIG.  6   ), which may include diffraction gratings. As described above in reference to  FIG.  7   , light  400  that is injected into the waveguide  1182  at the input surface  1382  of the waveguide  1182  propagates within the waveguide  1182  by total internal reflection (TIR). Referring back to  FIG.  7   , at points where the light  400  impinges on the outcoupling optical element  1282 , a portion of the light exits the waveguide as exit beams  402 . In some implementations, it may be desirable to have the optical element  1282  be configured as a diffraction grating having spatially varying optical properties, including diffraction properties. Such configuration may be desirable, for example, when the intensity of the light substantially attenuates as it propagates within the waveguide  1182 . Under such circumstances, it may be desirable have certain diffraction characteristics of the grating  1282 , e.g., diffraction efficiency (a ratio of diffracted beam intensity to the incident beam intensity) or refractive index, vary along the light propagation direction, such that uniformity of the intensity of the exiting beams  402  are improved. Such configurations may also be desirable, for example, to intentionally skew the light intensity across the grating  1282  to adapt to spatial and/or angular variation of sensing efficiencies associated with the human eye to maximize the user experience. Thus, there is a need for outcoupling optical elements, e.g., diffraction gratings, having spatially varying optical characteristics. 
     For some applications, graded diffraction properties can be achieved by structurally varying periodic structures of the grating, e.g., by using semiconductor processing technology. For example, semiconductor etching technology can be used to holographically pattern gratings into rigid substrate materials such as fused silica. By spatially varying the etch profiles, for instance, correspondingly spatially varying duty cycle or grating depth can be produced. However, such approaches often involve relatively complex and expensive processes, e.g., multiple etch processes. Thus, diffraction gratings with spatially varying optical properties, which can be fabricated with relatively simple processing technologies, could be beneficial. To this end, according to various embodiments disclosed herein, liquid crystal materials are used to spatially vary diffraction characteristics across the area of a diffraction gratings, e.g., by spatially varying alignment characteristics or other material properties of the liquid crystal molecules. In various embodiments, photo-polymerizable liquid crystal materials, or reactive mesogens, are used to spatially vary the diffraction characteristics of diffraction gratings. For example, by coating different areas of a grating with a liquid crystal material and spatially varying its properties, e.g., alignment properties, spatially varying diffraction properties can be generated. 
     In the following, various embodiments of liquid crystal (LC) gratings having varying optical properties, e.g., gradient optical properties, such as varying diffraction properties including diffraction efficiency. Generally, diffraction gratings have a periodic structure, which splits and diffracts light into several beams travelling in different directions. The directions of these beams depend, among other things, on the period of the periodic structure and the wavelength of the light. To achieve certain optical properties that spatially vary across the area of the grating, e.g., spatially varying diffraction efficiencies, for certain applications such as outcoupling optical element  282  having uniform intensity of the exiting light beams  402 , material properties of liquid crystals can be spatially varied. 
     Generally, liquid crystals possess physical properties that may be intermediate between conventional fluids and solids. While liquid crystals are fluid-like in some aspects, unlike most fluids, the arrangement of molecules within them exhibits some structural order. Different types of liquid crystals include thermotropic, lyotropic, and polymeric liquid crystals. Thermotropic liquid crystals disclosed herein can be implemented in various physical states, e.g., phases, including a nematic state/phase, a smectic state/phase, a chiral nematic state/phase or a chiral smectic state/phase. 
     As described herein, liquid crystals in a nematic state or phase can have calamitic (rod-shaped) or discotic (disc-shaped) organic molecules that have relatively little positional order, while having a long-range directional order with their long axes being roughly parallel. Thus, the organic molecules may be free to flow with their center of mass positions being randomly distributed as in a liquid, while still maintaining their long-range directional order. In some implementations, liquid crystals in a nematic phase can be uniaxial; i.e., the liquid crystals have one axis that is longer and preferred, with the other two being roughly equivalent. In other implementations, liquid crystals can be biaxial; i.e., in addition to orienting their long axis, the liquid crystals may also orient along a secondary axis. 
     As described herein, liquid crystals in a smectic state or phase can have the organic molecules that form relatively well-defined layers that can slide over one another. In some implementations, liquid crystals in a smectic phase can be positionally ordered along one direction. In some implementations, the long axes of the molecules can be oriented along a direction substantially normal to the plane of the liquid crystal layer, while in other implementations, the long axes of the molecules may be tilted with respect to the direction normal to the plane of the layer. 
     As described herein, nematic liquid crystals are composed of rod-like molecules with the long axes of neighboring molecules approximately aligned to one another. To describe this anisotropic structure, a dimensionless unit vector n called the director, may be used to describe the direction of preferred orientation of the liquid crystal molecules. 
     As describe herein, liquid crystals in a nematic state or a smectic state can also exhibit chirality. In a chiral phase, the liquid crystals can exhibit a twisting of the molecules perpendicular to the director, with the molecular axis parallel to the director. The finite twist angle between adjacent molecules is due to their asymmetric packing, which results in longer-range chiral order. 
     As described herein, liquid crystals in a chiral smectic state or phase can be configured such that the molecules have positional ordering in a layered structure, with the molecules tilted by a finite angle with respect to the layer normal. In addition, chirality can induce successive azimuthal twists from one layer to the next, producing a spiral twisting of the molecular axis along the layer normal. 
     As described herein, liquid crystals displaying chirality can be described as having a chiral pitch, p, which can refer to the distance over which the liquid crystal molecules undergo a full 360° twist. The pitch, p, can change when the temperature is altered or when other molecules are added to the liquid crystal host (an achiral liquid host material can form a chiral phase if doped with a chiral material), allowing the pitch of a given material to be tuned accordingly. In some liquid crystal systems, the pitch is of the same order as the wavelength of visible light. As described herein, liquid crystals displaying chirality can also be described as having a twist angle, which can refer, for example, to the relative azimuthal angular rotation between an uppermost liquid crystal molecule and a lowermost liquid crystal molecule across a thickness of the liquid crystal material. 
     According to various embodiments described herein, liquid crystals having various states or phases as described above can be configured to offer various desirable material properties for diffraction gratings, including, e.g., birefringence, optical anisotropy, and manufacturability using thin-film processes. For example, by changing surface conditions of liquid crystal layers and/or mixing different liquid crystal materials, grating structures that exhibit spatially varying diffraction properties, e.g., gradient diffraction efficiencies, can be fabricated. 
     As described herein, “polymerizable liquid crystals” may refer to liquid crystal materials that can be polymerized, e.g., in-situ photopolymerized, and may also be described herein as reactive mesogens (RM). 
     It will be appreciated that the liquid crystal molecules may be polymerizable in some embodiments and, once polymerized, may form a large network with other liquid crystal molecules. For example, the liquid crystal molecules may be linked by chemical bonds or linking chemical species to other liquid crystal molecules. Once joined together, the liquid crystal molecules may form liquid crystal domains having substantially the same orientations and locations as before being linked together. For ease of description, the term “liquid crystal molecule” is used herein to refer to both the liquid crystal molecules before polymerization and to the liquid crystal domains formed by these molecules after polymerization. 
     According to particular embodiments described herein, photo-polymerizable liquid crystal materials can be configured to form a diffraction grating, whose material properties, including birefringence, chirality, and ease for multiple-coating, can be utilized to create gratings with graded diffraction efficiencies, as changes in these material properties (e.g., birefringence, chirality, and thickness) result in variations in diffraction efficiencies accordingly. 
     It will be appreciated that, as described herein, a “transmissive” or “transparent” structure, e.g., a transparent substrate, may allow at least some, e.g., at least 20, 30 or 50%, of an incident light, to pass therethrough. Accordingly, a transparent substrate may be a glass, sapphire or a polymeric substrate in some embodiments. In contrast, a “reflective” structure, e.g., a reflective substrate, may reflect at least some, e.g., at least 20, 30, 50, 70, 90% or more of the incident light, to reflect therefrom. 
     Optical properties of a grating are determined by the physical structures of the grating (e.g., the periodicity, the depth, and the duty cycle), as well as material properties of the grating (e.g., refractive index, absorption, and birefringence). When liquid crystals are used, optical properties of the grating can be controlled by controlling, e.g., molecular orientation or distribution of the liquid crystal materials. For example, by varying molecular orientation or distribution of the liquid crystal material across the grating area, the grating may exhibit graded diffraction efficiencies. Such approaches are described in the following, in reference to the figures. 
     In various embodiments, a diffraction grating comprises a substrate and a plurality of different diffracting zones having a periodically repeating lateral dimension corresponding to a grating period adapted for light diffraction. The diffraction grating further comprises a plurality of different liquid crystal layers corresponding the different diffracting zones, wherein the different liquid crystal layers have liquid crystal molecules that are aligned differently, such that the different diffracting zones have different optical properties associated with light diffraction. 
     Photo-Aligned Spatially Variable Liquid Crystal Diffraction Gratings 
     Referring to  FIGS.  10 A- 10 C , cross-sectional side views (viewed along the x-z plane) of diffraction gratings  100 A- 100 C according to some embodiments are illustrated. Each of the diffraction gratings  100 A- 100 C comprises a substrate  104  and a plurality of diffracting zones, i.e., diffracting zones  108 A- 1 ,  108 A- 2 , . . . and  108 A- n  as illustrated in  FIG.  10 A , diffracting zones  108 B- 1 ,  108 B- 2 , . . . and  108 B- n  as illustrated in  FIG.  10 B , and diffracting zones  108 C- 1 ,  108 C- 2 , . . . and  108 C- n  as illustrated in  FIG.  10 C . 
     The diffracting zones of each of the diffraction gratings  100 A- 100 C have a periodically repeating lateral dimension or a grating period A and include corresponding liquid crystal layers formed of liquid crystal molecules  112 . In the illustrated embodiment and throughout this disclosure, the liquid crystal molecules  112  can be in a nematic state or a smectic state, or a mixture thereof, among other possible states of liquid crystal molecules. In the illustrated embodiment and throughout, various embodiments can have the grating period A that is between about 100 nm and about 10,000 nm, between about 200 nm and about 2000 nm or between about 300 nm and about 1000 nm, such that the plurality of diffracting zones are configured to diffract visible light. 
     The diffracting zones  108 A- 1 ,  108 A- 2 , . . .  108 A- n  of the diffraction grating  100 A have corresponding liquid crystal layers  116 A- 1 ,  116 A- 2 , . . .  116 A- n,  respectively; diffracting zones  108 B- 1 ,  108 B- 2 , . . .  108 B- n  of the diffraction grating  100 B have corresponding liquid crystal layers  116 B- 1 ,  116 B- 2 , . . .  116 B- n,  respectively; and diffracting zones  108 C- 1 ,  108 C- 2 , . . .  108 C- n  of the diffraction grating  100 C have corresponding liquid crystal layers  116 C- 1 ,  116 C- 2  and  116 C- n,  respectively. 
     It will be understood herein and throughout the specification that “n” can be a suitable integer for representing the number of different zones. For example, diffracting zones  108 B- 1 ,  108 B- 2 , . . .  108 B- n  indicates that there can be n number of diffracting zones, where n is an integer. The number (n) of diffracting zones that is omitted from the Figures can be, for example, between 1 and about 500, between about 1 and about 200 or between about 1 and about 100. In some implementations, optical properties of a diffraction grating can vary continuously across the surface. In one implementation, for example, there can be one grating period A per diffracting zone for at least some of the diffracting zones. When each diffracting zone has one grating period Λ, the number (n) of diffracting zones can represent the number of grating periods Λ. 
     It will be understood herein and throughout the specification that, “. . . ,” when indicated in a Figure, can represent the presence of additional diffracting zones between the illustrated zones, which can be contiguously connected and similar or the same as any other adjacently illustrated zone. In addition, “. . . ” can also represent an arrangement of diffracting zones that periodically repeat any suitable number of times. 
     Each of the liquid crystal layers  116 A- 1 ,  116 A- 2  and  116 A- n  of the diffraction grating  100 A in turn has differently arranged first and second diffracting regions  116 A- 1 L and  116 A- 1 R,  116 A- 2 L and  116 A- 2 R, . . . and  116 A- n L and  116 A- n R, respectively. Similarly, each of the liquid crystal layers  116 B- 1 ,  116 B- 2  and  116 B- n  of the diffraction grating  100 B in turn has differently arranged first and second diffracting regions  116 B - 1 L and  116 B- 1 R,  116 B- 2 L and  116 B- 2 R, . . . and  116 B- n L and  116 B- n R, respectively. Similarly, each of the liquid crystal layers  116 C- 1 ,  116 C- 2  and  116 C- n  of the diffraction grating  100 C in turn has differently arranged first and second diffracting regions  116 C- 1 L and  116 C- 1 R,  116 C- 2 L and  116 C- 2 R, . . . and  116 C- n L and  116 C- n R, respectively. The regions are sometimes referred to as domains of liquid crystal molecules 
     Still referring to  FIGS.  10 A- 10 C , each of the different diffracting zones further comprises an alignment layer  120  interposed between the substrate  104  and the corresponding liquid crystal layer, wherein the alignment layer is configured to induce the alignment of the liquid crystal molecules in different regions of each zone. Interposed between the substrate  104  and the first/second diffracting regions  116 A- 1 L/ 116 A- 1 R,  116 A- 2 L/ 116 A- 2 R, . . . and  116 A- n L/ 116 A- n R of the diffraction grating  100 A of  FIG.  10 A  are first and second alignment layers  120 A- 1 L/ 120 A- 1 R,  120 A- 2 L/ 120 A- 2 R, . . . and  120 A- n L/ 120 A- n R, respectively. Similarly interposed between the substrate  104  and the first/second diffracting regions  116 B- 1 L/ 116 B- 1 R,  116 B- 2 R/ 116 B- 2 R, . . . and  116 B- n L/ 116 B- n R of the diffraction grating  100 C of  FIG.  10 B  are first/second alignment layers  120 B- 1 L/ 120 B- 1 R,  120 B- 2 L/ 120 B- 2 R, . . . and  120 B- n L/ 120 B- n R, respectively. Similarly, interposed between the substrate  104  and differently arranged first/second diffracting regions  116 C- 1 L/ 116 C- 1 R,  116 C- 2 L/ 116 C- 2 R, . . . and  116 C- n L/ 116 C- n R of the diffraction grating  100 C of  FIG.  10 C  are first/second alignment layers  120 C- 1 L/ 120 C- 1 R,  120 C- 2 L/ 120 C- 2 R, . . . and  120 C- n L/ 120 C- n R, respectively. 
     Herein and throughout the disclosure, an alignment direction of elongated liquid crystal molecules can refer to the direction of elongation of the liquid crystal molecules, or the direction of the director vector  n . 
     Herein and throughout the disclosure, a tilt angle or a pre-tilt angle Φ can refer to an angle measured in a plane perpendicular to a major surface (in an x-y plane) of the liquid crystal layers or of the substrate, e.g., the x-z plane, and measured between an alignment direction and the major surface or a direction parallel to the major surface, e.g., the x-direction. 
     Herein and throughout the disclosure, an azimuthal angle or a rotation angle y is used to describe an angle of rotation about an axis normal to a major surface (in an x-y plane), which is measured in a plane parallel to a major surface of the liquid crystal layers or of the substrate, e.g., the x-y plane, and measured between an alignment direction and a direction parallel to the major surface, e.g., the y-direction. 
     Herein and throughout the disclosure, when an alignment angle such as a pre-tilt angle φ or a rotation angle y are referred to as being substantially the same between different regions, it will be understood that an average alignment angles can, for example, be within about 1%, about 5% or about 10% of each other although the average alignment can be larger in some cases. 
     Herein and throughout the specification, a duty cycle can, for example, refers to a ratio between a first lateral dimension of a first region having liquid crystal molecules aligned in a first alignment direction, and the grating period of the zone having the first region. Where applicable, the first region corresponds to the region in which the alignment of the liquid crystals does not vary between different zones. 
     Still referring to  FIGS.  10 A- 10 C , each zone of the diffraction gratings  100 A,  100 B and  100 C include first and second regions that alternate in the x-direction. Each of the first regions  116 A- 1 L,  116 A- 2 L, . . . and  116 A- n L of the diffraction grating  100 A, each of the first regions  116 B- 1 L,  116 B- 2 L, . . . and  116 B- n L of the diffraction grating  100 B and each of the first regions  116 C- 1 L,  116 C- 2 L, . . . and  116 A- n L of the diffraction grating  100 C have liquid crystal molecules  112  that are aligned substantially along the same first alignment direction and have a first pre-tilt angle Φ that is substantially the same. Each of the second regions  116 A- 1 R,  116 A- 2 R, . . . and  116 A- n R of the diffraction grating  100 A, each of the second regions  116 B- 1 R,  116 B- 2 R, . . . and  116 B- n L of the diffraction grating  100 B and each of the second regions  116 C- 1 R,  116 C- 2 R, . . . and  116 C- n R of the diffraction grating  100 C have liquid crystal molecules  112  that are aligned substantially along a second alignment direction different from the first alignment direction and have second pre-tilt angles Φ that are different, e.g., greater, than the first pre-tilt angle Φ of the respective first regions. 
     In each of the diffraction gratings  100 A- 100 C of  FIGS.  10 A- 10 C , respectively, at least some of the diffracting zones have liquid crystal layers formed of liquid crystal molecules that are spatially arranged differently, e.g., have different pre-tilt angles from each other ( FIGS.  10 A and  10 C ), or have laterally varying duty cycles ( FIGS.  10 B and  10 C ), such that the diffracting zones have different optical properties, e.g., different refractive indices and different diffraction efficiencies, according to embodiments. 
     In particular, referring to diffraction grating  100 A of  FIG.  10 A , in addition to having alignment directions and pre-tilt angles Φ that are different from the first pre-tilt angle Φ of the first regions  116 A- 1 L,  116 A- 2 L, . . . and  116 A- n L, the liquid crystal molecules of different second regions  116 A- 1 R,  116 A- 2 R, . . . and  116 A- n R are aligned along second alignment directions that are different from each other. For example, in the illustrated embodiment, the zones  108 A- 1 ,  108 A- 2  and  108 A- n  are arranged such that the first regions and second regions alternate in the x-direction, where each of the first regions  116 A- 1 L,  116 A- 2 L, . . . and  116 A- n L has substantially the same pre-tilt angle Φ, while the second regions  116 A- 1 R,  116 A- 2 R, . . . and  116 A- n R have pre-tilt angles Φ that are different from each other. By way of example, the first regions  116 A- 1 L,  116 A- 2 L, . . . and  116 A- n L have a pre-tilt angle Φ that is between about ±15 degrees or between about ±10 degrees or between about ±5, e.g., 0 degrees. The second regions  116 A- 1 R,  116 A- 2 R, . . . and  116 A- n R can have pre-tilt angles Φ that are different from each other and are each between about 60 degrees and about 90 degrees or between about 65 degrees and about 85 degrees, for instance about 75 degree; between about 35 degrees and about 65 degrees or between about 40 degrees and about 60 degrees, for instance about 50 degrees; between about 10 degrees and about 40 degrees or between about 15 degrees and about 35 degrees, for instance about 25 degrees. 
     Still referring to  FIG.  10 A , in some embodiments, as illustrated, the second regions  116 A- 1 R,  116 A- 2 R, . . . and  116 A- n R can have tilt angles Φ that vary, e.g., increase or decrease in one direction in a lateral direction, such that a gradient in diffraction properties is created. In other embodiments, the second regions  116 A- 1 R,  116 A- 2 R, . . . and  116 A- n R can have tilt angles Φ that do not vary in one direction in the lateral direction. 
     Still referring to  FIG.  10 A , the duty cycle, defined above, can be between about 10% and about 30%, between about 30% and about 50%, between about 40% and 60% (e.g., about 50%), between about 50% and about 70% or between about 70% and about 90%. 
     Referring now to  FIG.  10 B , the diffraction grating  100 B share some common features as the diffraction grating  100 A of  FIG.  10 A . However, unlike the diffracting grating  100 B of  FIG.  10 A , while the liquid crystal molecules of different second regions  116 B- 1 R,  116 B- 2 R, . . . and  116 B- n R have pre-tilt angles Φ that are different from the first pre-tilt angle Φ of the first regions  116 B- 1 L,  116 B- 2 L, . . . and  116 B- n L, they are not aligned differently from each other. For example, in the illustrated embodiment, the zones  108 B- 1 ,  108 B- 2  and  108 B- n  are arranged such that the first regions and second regions alternate in the x-direction, where each of the first regions  116 B- 1 L,  116 B- 2 L, . . . and  116 B- n L has substantially the same first pre-tilt angle Φ, and each of the second regions  116 B- 1 R,  116 B- 2 R, . . . and  116 B- n R has substantially the same second pre-tilt angles Φ. The first and second pre-tilt angles of the first and second regions can have any of the values discussed above with respect to the diffraction grating  100 A of  FIG.  10 A . 
     Still referring to  FIG.  10 B , unlike the grating  100 A of  FIG.  10 A , the zones  116 B- 1 ,  116 B- 2  and  116 B- 3  have substantially the same pre-tilt angle, e.g., between about 0 to 90 degrees, while having a duty cycle between about 40% and about 60%, for instance about 50%; between about 30% and about 50%, for instance about 40% and a duty cycle between about 20% and about 40%, for instance about 30%, respectively, such that the diffraction grating  100 B has spatially varying optical properties. 
     Still referring to  FIG.  10 B , in some embodiments, as illustrated, the zones can have duty cycles that vary, e.g., increase or decrease in one direction in a lateral direction, such that a gradient in optical properties is created. In other embodiments, the duty cycles do not vary in one direction in the lateral direction. 
     Referring now to  FIG.  10 C , the illustrated diffraction grating  100 C combines features similar to those described above with respect to the diffraction gratings  100 A and  100 B of  FIGS.  10 A and  10 B . In particular, the liquid crystal molecules of different second regions  116 C- 1 R,  116 C- 2 R, . . . and  116 C- n R can have pre-tilt angles Φ that are different from the first pre-tilt angle Φ of the first regions  116 C- 1 L,  116 C- 2 L, . . . and  116 C- n L, and aligned differently from each other. In addition, the duty cycle varies between adjacent zones across a lateral direction, e.g., x-direction. The first and second pre-tilt angles of the first and second regions can have any of the values discussed above with respect to the diffraction grating  100 A of  FIG.  10 A . In addition, the duty cycle variation between adjacent zones across a lateral direction, e.g., x-direction, can also have values discussed above with respect to the diffraction grating  100 B of  FIG.  10 B . 
     In the diffraction gratings  100 A- 100 C illustrated in  FIGS.  10 A- 10 C  and throughout the disclosure, it will be appreciated that, in addition to the grating period and duty cycle discussed above, the diffraction properties can be further defined by, among other things, the thickness and the refractive index of the liquid crystal layer  116 . According to various embodiments disclosed herein, the thickness of the liquid crystal layers disclosed herein can have a thickness between about 1 μm and about 100 μm, between about 0.5 μm and about 20 μm or between about 0.1 μm and about 10 μm. An average refractive index of the liquid crystal layers disclosed herein can be between about 1.8 and about 2.0, between about 1.6 and about 1.8 or between about between about 1.4 and about 1.2. The resulting average diffraction efficiency of various diffraction gratings disclosed herein can be between about 1% and about 80%, between about 1% and about 50% or between about between about 5% and about 30%. 
     As a result of implementing various embodiments disclosed herein and throughout the disclosure, different zones can have indices of refraction that vary between about −30% and about +30%, between about −20% and about +20% or between about −10% and about +10% across the surface area of the diffraction grating, with respect to the average refractive index. As a further result, different zones can have diffraction efficiencies that vary between about 1% and about 80%, between about 1% and about 50% or between about 1% and about 30% across the surface area of the diffraction grating, with respect to the average diffraction efficiency. 
       FIGS.  11 A and  11 B  illustrate a method for fabricating diffraction gratings having liquid crystal molecules with non-uniform pre-tilt angles across the surface such as, e.g., diffraction gratings  100 A- 100 C of  FIGS.  10 A- 10 C  described above, using photo-alignment techniques, according to embodiments. 
     Referring to an intermediate structure  100   a  of  FIG.  11 A , a substrate  104  is provided, on which a photo-alignment layer  120  is formed. The substrate  104  can be an optically transparent substrate that is transparent in the visible spectrum, such as, e.g., silica-based glass, quartz, sapphire, indium tin oxide (ITO) or polymeric substrates, to name a few examples. 
     As described herein, a photo-alignment layer can refer to a layer on which, when a liquid crystal molecules are deposited, the liquid crystal molecules become oriented, for example, due to anchoring energy exerted on the liquid crystal molecule by the photo-alignment layer. Examples of photo-alignment layers include polyimide, linear-polarization photopolymerizable polymer (LPP), azo-containing polymers, courmarine-containing polymers and cinnamate-containing polymers, to name a few. 
     The photo-alignment layer  120  can be formed by dissolving precursors, e.g., monomers, in a suitable solvent and coating, spin-coating, the surface of the substrate  104  with the solution. The solvent can thereafter be removed from the coated solution. 
     After coating and drying the photo-alignment layer  120 , a photomask  130  can be used to expose different regions of the underlying photo-alignment layer  120  to different doses of light and/or different polarizations of light. For example, the regions of the photo-alignment layer  120  that are to be exposed differently can correspond to first (e.g., left) and second (e.g., right) regions of each of zones  108 A- 1  and  108 A- 2  described above with respect to the diffraction grating  100 A of  FIG.  10 A . 
     In some embodiments, the photo-alignment layer  120  can be configured such that the resulting liquid crystal molecules are oriented substantially parallel to the polarization direction of the exposure light (e.g., the azimuthal angle y and the linear polarization angle of the exposure light are substantially the same). In other embodiments, the photo-alignment layer  120  can be configured such that the liquid crystal molecules are oriented substantially orthogonal to the polarization direction of the exposure light (e.g., the azimuthal angle y and the linear polarization angle of the exposure light are substantially offset by about +/−90 degrees). 
     In one example, the photomask  130  can be a gray-scale mask having a plurality of mask regions  130   a - 130   d  that are at least partially transparent and possibly have one or more opaque regions. Different ones of the plurality of mask regions  130   a - 130   d  may be configured to transmit different amounts of the incident light  140 , such that transmitted light  140   a - 140   d  transmitted through different ones of the plurality of mask regions  130   a - 130   d  has varying intensities that are proportional to the relative transparency of the different mask regions  130   a - 130   d  to the incident light  140 . However, embodiments are not so limited and other mask types can be used. For example, the photomask  130  can be a binary mask having the plurality of mask regions  130   a - 130   d  each being fully or nearly fully transparent or fully or nearly fully opaque, such that transmitted light  140   a - 140   d  transmitted through the plurality of mask regions  130   a - 130   d  has binary intensities. 
     The photomask  130  can be formed of a suitable material which at least partially absorbs UV light. In some embodiments, the varying intensities of transmitted light across different mask regions  130   a - 130   d  can be achieved by using different materials (e.g., having different absorption coefficients) in the different regions, materials doped possibly different amounts in different regions or by using different thicknesses in the different regions. Other types of masks can be used. In some embodiments, the photomask  130  can contact the underlying photo-alignment layer  120 , while in other embodiments, the photomask  130  does not contact the underlying photo-alignment layer  120 . 
     The incident light can be UV light, e.g., from a high pressure Hg-lamp, e.g., for their spectral lines at  436  nm (“g-line”),  405  nm (“h-line”) and  365  nm (“i-line”). However, embodiments are not so limited, and the incident light can be any suitable light to which the photo-alignment layer  120  is responsive, including visible light. When polarized, the incident UV-light can be polarized using a suitable polarizer. Accordingly, in various cases, the mask is transmissive to UV-light. Other ways of patterning besides utilizing a photo-mask can be employed. 
     In some embodiments, the incident light  140  can be generated for a duration by using a single uniform incident light source. However, embodiments are not so limited, and in other embodiments, the incident light  140  can vary in intensity across different mask regions  130   a - 130   d.  Furthermore, in yet other embodiments, the incident light  140  can be selectively generated for different durations across different mask regions  130   a - 130   d.    
     Furthermore, in the illustrated embodiment, the incident light  140  can be polarized, e.g., linearly polarized, as schematically depicted by polarization vectors  134   a - 134   d.  However, the incident light  140  according to other embodiments can be circularly or elliptically polarized. In some embodiments, the polarization vectors  134   a - 134   d  can represent different polarization angles, while in some other embodiments, the incident light  140  can have a single polarization angle. 
     Without being bound to any theory, the combination of the photo-alignment material and the different doses and polarization(s) of the transmitted light  140   a - 140   d  causes various regions of the resulting photo-alignment layer  120  to exert different amounts of anchoring energy on the overlying liquid crystal molecules, thereby causing the different orientations of the liquid crystal molecules, as described herein. Other methods that may or may not employ masks may be used as well. 
     Referring to  FIG.  11 B , after exposing the photo alignment layer  120  to varying doses of transmitted light  140   a - 140   d  using various techniques described above, a liquid crystal layer  116  can be formed on the photo alignment layer  120 . 
     The liquid crystal layer  116  can be formed by dissolving liquid crystal precursors, e.g., monomers, in a suitable solvent and coating, e.g., spin-coating, the surface of the alignment layer  120  with the solution having the liquid crystal precursors dissolved therein. The solvent can thereafter be removed from the coated solution 
     In various embodiments, the reactive mesogen materials used for forming the liquid crystal layer  116  include liquid crystalline mono- or di-acrylate, for example. 
     Because of the different doses and or polarization angle of light received by different regions of the photo alignment layer  120  as described above, the liquid crystal layer, e.g., as-deposited, forms the liquid crystal layers  116 A- 1  and  116 A- 2  in zones  108 A- 1  and  108 A- 2 , respectively. The liquid crystal layers  116 A- 1  and  116 A- 2 , in turn, have first and second diffracting regions  116 A- 1 L and  116 A- 1 R, and  116 A- 2 L and  116 A- 2 R, respectively. As described above with respect to  FIG.  10 A , the first regions and second regions alternate in the x-direction, where each of the first regions  116 A- 1 L and  116 A- 2 L has substantially the same first pre-tilt angle Φ, while the second regions  116 A- 1 R and  116 A- 2 R have pre-tilt angles Φ that are different from each other and from the first pre-tilt angle of the first regions. Without being bound to any theory, in some types of photo-alignment materials, exposure of the underlying photo-alignment layer  120  to light is believed to increase the anchoring energy that causes the in-plane alignment of the liquid crystal molecules. As a result, in these photo—alignment materials, increasing the exposure leads to a corresponding reduction in the pre-tile angle Φ of the liquid crystal layers formed thereon, according to embodiments. However, in other types of photo-alignment materials, exposure of the underlying photo-alignment layer  120  to light is believed to decrease the anchoring energy that causes the in-plane alignment of the liquid crystal molecules. As a result, in these photo—alignment materials, increasing the exposure leads to a corresponding increase in the pre-tilt angle Φ of the liquid crystal layers formed thereon, according to embodiments. 
     Thus, according to embodiments, the degree of tilt, as measured by the pre-tilt angle Φ, is inversely proportional to the dose of transmitted light received by the underlying photo-alignment layer  120 . For example, in the illustrated embodiment, the photo-alignment layers  120 A- 1 L and  120 A- 2 L receive the highest amount of incident light, followed by the alignment layer  120 A- 1 R, followed by the alignment layer  120 - 2 R. As a result, the resulting pre-tilt angles are highest for the second region  116 A- 2 R of the zone  108 A- 2 , followed by the second region  116 A- 1 R of the zone  108 A- 1 , followed by the first regions  116 A- 1 L and  116 A- 2 L of the zones  108 A- 1  and  108 A- 2 , respectively. 
       FIGS.  12 A- 12 C  illustrate another method for fabricating diffraction gratings having non-uniform pre-tilt angles, e.g., diffraction gratings  100 A- 100 C of  FIGS.  10 A- 10 C  described above, using photo-alignment techniques, according to embodiments. In particular, in the illustrated embodiment, the method uses multiple exposures of the alignment layers prior to formation of the liquid crystals. 
     In the illustrated method of  FIGS.  12 A- 12 C , similar to the method illustrated with respect to  FIGS.  11 A- 11 B , a substrate  104  is provided on which a photo-alignment layer  120  is formed. However, unlike the method illustrated with respect to  FIGS.  11 A- 11 B , prior to using a photomask  130  to expose different regions of the underlying photo-alignment layer  120  to different doses of light and/or different polarizations of light, the photo-alignment layer  120  is exposed to a primary (e.g., blanket) pattern of light using a first incident light  140 A. The primary pattern of light may be produced using, e.g., blanket exposing using, e.g., a blanket semitransparent gray scale mask (not shown). In the illustrated embodiment, a mask may be omitted for the blanket exposure to the primary pattern of light. 
     The first incident light  140 A can be polarized, e.g., linearly polarized at a first polarization angle, as schematically depicted by polarization vectors  134   a - 134   d.  The first incident light  140 A that is linearly polarized can create a uniform alignment of the liquid crystal molecules. Subsequent to exposing to the primary (e.g., blanket) pattern of light, the alignment layer  120  may be further exposed to a secondary pattern of light using a second incident light  140 B and a photomask  130 , which is configured to expose different regions of the underlying photo-alignment layer  120  to different doses of light and/or different polarizations of light, in a manner substantially similar to the method described above with respect to  FIGS.  11 A- 11 B . For example, different regions of the photo-alignment layer  120  corresponding to first (e.g., left) and second (e.g., right) regions of each of zones  108 A- 1  and  108 A- 2  as described above with respect to the diffraction grating  100 A can be exposed to different doses and/or different polarization of light. Unlike the first incident light  140 A, the second incident light  140 B can be unpolarized or circularly polarized. The second incident light  140 B that is unpolarized or circularly polarized can redistribute alignment directions of the liquid crystal molecules. The resulting diffraction grating  100 A is similar to that described above with respect to  FIG.  11 B , where first regions and second regions alternate in the x-direction, and where each of the first regions  116 A- 1 L and  116 A- 2 L has substantially the same first pre-tilt angle Φ, while the second regions  116 A- 1 R and  116 A- 2 R have pre-tilt angles Φ that are different from each other and from the first pre-tilt angle of the first regions. 
     The second incident light  140 B can be polarized, e.g., linearly polarized at a second polarization angle different from, e.g., orthogonal to, the second polarization angle of the first incident light  140 A, as schematically depicted by polarization vectors  134   e - 134   h.  In some other embodiments, the first and second polarization angles are the same. In yet some other embodiments, the first and second polarization angles are different while not orthogonal. Furthermore, the second incident light  140 B according to other embodiments can be circularly or elliptically polarized, having similar or different polarization orientation relative to the first incident light  140 A. 
     In the embodiments described above in reference to  FIGS.  11 A- 11 B  and  FIGS.  12 A- 12 C , methods of controlling pre-tilt angles of liquid crystals using photo-alignment technique have been described. However, it will be appreciated that other embodiments are possible, including a process referred to as micro-rubbing, in which the alignment layers are rubbed with a metallic object, e.g., a metallic sphere under a load. For example, a metallic sphere is in direct contact with the alignment layer may be moved across the alignment layer to creating micrometer-sized rubbed lines, which induce the pre-tilting of the subsequently deposited liquid crystals. In yet other embodiments, alignment materials pre-configured to induce different pre-tilt angles can be deposited, instead of post-treating them to induce the pre-tilting of the liquid crystal molecules. 
     Referring now to  FIGS.  13 A and  13 B , cross-sectional (x-z plane) views of diffraction gratings  103 A and  103 B according to some other embodiments are illustrated. The diffraction gratings  103 A and  103 B can be polarization gratings (PGs), which are configured to locally modify the polarization state of transmitted light, which can be achieved by spatially varying birefringence and/or dichroism. While not shown for clarity, each of the diffraction gratings  103 A and  103 B comprises a substrate and an alignment layer formed thereon, and a plurality of differently arranged diffracting zones  154 A- 1  and  154 A- 2  in  FIG.  13 A  and diffracting zones  154 B- 1  and  154 B- 2  in  FIG.  13 B . The diffracting zones  154 A- 1  and  154 A- 2  of the diffraction grating  103 A have corresponding liquid crystal layers  144 A- 1  and  144 A- 2 , respectively and diffracting zones  154 A- 1  and  154 A- 2  of the diffraction grating  103 B have corresponding liquid crystal layers  154 B- 1  and  154 B- 2 , respectively. 
     Each of the liquid crystal layers  144 A- 1  and  144 A- 2  of the diffraction grating  103 A in turn has a plurality of differently arranged diffracting regions  144 A- 1   a  through  144 A- 1   g  and  144 A- 2   a  through  144 A- 2   g,  respectively. Similarly, each of the liquid crystal layers  144 B- 1  and  144 B- 2  of the diffraction grating  103 B in turn has a plurality of differently arranged diffracting regions  144 B- 1   a  through  144 B- 1   g  and  144 B- 2   a  through  144 A- 2   g,  respectively. 
     Referring to the diffraction grating  103 A of  FIG.  13 A , each of the plurality of regions  144 A- 1   a  to  144 A- 1   g  of the zone  154 A- 1  and each of the plurality of regions  144 A- 2   a  to  144 A- 2   g  of the zone  154 A- 2  has liquid crystal molecules  112  that are aligned substantially along the same alignment direction within the same region. The liquid crystal molecules  112  of all regions of the zone  154 A- 1  have a first pre-tilt angle Φ that is substantially the same. In contrast, the liquid crystal molecules  112  of different regions of the zone  154 A- 2  have different pre-tilt angles Φ. While in the illustrated embodiment, the pre-tilt angle Φ of a central region ( 144 A- 2 d) of the zone  154 A- 2  has a pre-tilt angle Φ that is the smallest with increasing pre-tilt angles Φ for increasingly outer regions of the zone  154 A- 2 , embodiments are not so limited. In addition, while the central region ( 144 A- 2   d ) in the illustrated embodiment has a pre-tilt angle Φ that is similar to the first pre-tilt angle Φ of the zone  154 A- 1 , embodiments are not so limited. The pre-tilt angles of different regions of the diffraction grating  103 A can have any of the magnitudes described supra with respect to  FIGS.  10 A- 10 C . 
     Still referring to  FIG.  13 A , in the illustrated embodiment, the liquid crystal molecules  112  of different regions of the zone  154 A- 1  have different azimuthal angles φ. However, embodiments are not so limited and in other embodiments, the liquid crystal molecules  112  of different regions of the zone  154 A- 1  can have the same azimuthal angles φ. The azimuthal angles of different regions of the diffraction grating  103 A can have any of the magnitudes described infra with respect to  FIGS.  15 A- 15 C . 
     Referring to the diffraction grating  103 B of  FIG.  13 B , similar to the diffraction grating  103 A of  FIG.  13 A , each of the plurality of regions  144 B- 1   a  to  144 B- 1   g  of the zone  154 B- 1  has liquid crystal molecules  112  that are aligned substantially along the same alignment direction within the same region. Similar to the zone  154 A- 2  of the diffraction grating  103 A of  FIG.  13 A , the liquid crystal molecules  112  of different regions of the zone  154 B- 1  have substantially different pre-tilt angles Φ and substantially different azimuthal angles φ. In contrast, each of the plurality of regions  144 B- 2   a  to  144 B- 2   g  of the zone  154 B- 2  has liquid crystal molecules  112  that are aligned substantially differently within the same region. That is, the individual liquid crystal molecules  112  of each region of the zone  154 B- 2  have substantially different pre-tilt angles Φ and substantially different azimuthal angles φ. For example, the liquid crystal molecules  112  of each region of the zone  154 B- 2  can have chirality, as described more in detail with respect to  FIGS.  19 A and  19 B , infra. 
     Still referring to  FIGS.  13 A and  13 B , while specific combinations of zones and regions within different zones have been presented as examples, it will be appreciated that the zone and regions within the zones can be mixed and matched. For example, a combination of the zone  154 A- 1  of  FIG.  13 A  and the zone  154 B- 2  of  FIG.  13 B  in a diffraction grating is possible. 
       FIGS.  14 A- 14 B  illustrate another method for fabricating diffraction gratings having non-uniform pre-tilt angles, e.g., diffraction gratings  103 A and  103 B of  FIGS.  13 A and  13 B , respectively, using photo-alignment techniques, according to embodiments. In particular, in the illustrated embodiment, the method comprises polarization interference holographic exposure using a gray-scale mask, according to embodiments. 
     Polarization interference holographic exposure is a technique to create an interference pattern using multiple beams of coherent light. While most conventional holography uses an intensity modulation, polarization holography involves a modulation of the polarization state to create an interference pattern. 
     Referring to  FIG.  14 A , in the illustrated method, processes leading up to exposing the photo-alignment layer  120  to UV light is similar to the method described above with respect to  FIGS.  11 A- 11 B . In particular, the photo-alignment layer  120  is formed on a substrate  104  and a gray scale mask  130  is disposed partially over the photo-alignment layer  120 . Thereafter, a plurality of coherent light beams  142   a,    142   b  having different polarizations are directed to the plurality of differently arranged diffracting zones  154 A- 1  and  154 A- 2 . In the illustrated embodiment, the light beams  142   a  and  142   b  include orthogonal circular polarized light beams. However, the light beams  142   a  and  142   b  can include non-orthogonal circular polarized light beams, for example. In the illustrated embodiment, the zone  154 A- 1  is exposed while the zone  154 A- 2  is masked with the gray scale mask  130 . The plurality of light beams  142   a  and  142   b  are positioned and polarized such that the resulting interference effect results in the liquid crystal layers  144 A- 1  and  144 A- 2  of the diffraction grating  103 A having a plurality of differently arranged diffracting regions  144 A- 1   a  through  144 A- 1   g  and  144 A- 2   a  through  144 A- 2   g,  respectively, as described above with respect to  FIG.  13 A . Similarly, using similar concepts, referring back to  FIG.  13 B , the liquid crystal layers  144 B- 1  and  144 B- 2  of the diffraction grating  103 B having a plurality of differently arranged diffracting regions  144 B-la through  144 B- 1 g and  144 B- 2   a  through  144 B- 2 g, respectively, can be fabricated. 
     Referring to  FIGS.  15 A- 15 C , top-down views (viewed along the x-y plane) of diffraction gratings  150 A- 150 C according to various embodiments are illustrated. Because  FIGS.  15 A- 15 C  are top down views, only the liquid crystal layers (as opposed to the alignment layer or substrate) are illustrated, while underlying features are not shown. However, it will be understood that the liquid crystal layer of each of the diffraction gratings  150 A- 150 C is formed over a substrate and comprises a plurality of diffracting zones, i.e., diffracting zones  148 A- 1 ,  148 A- 2 , . . . and  148 A- n  in  FIG.  15 A , diffracting zones  148 B- 1 ,  148 B- 2 , . . . and  148 B- n  in  FIG.  15 B , and diffracting zones  148 C- 1 ,  148 C- 2 , . . . and  148 C- n  in  FIG.  15 C . 
     The diffracting zones of each of the diffraction gratings  150 A- 150 C have a periodically repeating lateral dimension or a grating period A and include corresponding liquid crystal layers formed of liquid crystal molecules  112 . The lateral dimension or the grating A can be similar to those described above with respect to  FIGS.  10 A- 10 C . 
     Analogous to  FIGS.  10 A- 10 C , the diffracting zones  148 A- 1 ,  148 A- 2 , . . .  148 A- n  of the diffraction grating  150 A have corresponding liquid crystal layers  156 A- 1 ,  156 A- 2 , . . .  156 A- n,  respectively; diffracting zones  148 B- 1 ,  148 B- 2 , . . .  148 B- n  of the diffraction grating  150 B have corresponding liquid crystal layers  156 B- 1 ,  156 B- 2 , . . .  156 B- n,  respectively; and diffracting zones  148 C- 1 ,  148 C- 2 , . . .  148 C- n  of the diffraction grating  150 C have corresponding liquid crystal layers  156 C- 1 ,  156 C- 2  and  156 C- n,  respectively. The number of each type of diffracting zones can be similar to those described above with respect to  FIGS.  10 A- 10 C . In addition, the diffracting zones as arranged can periodically repeat any suitable number of times. 
     Each of the liquid crystal layers  156 A- 1 ,  156 A- 2  and  156 A- n  of the diffraction grating  150 A in turn has differently arranged first and second diffracting regions  156 A- 1 L and  156 A- 1 R,  156 A- 2 L and  156 A- 2 R, . . . and  156 A- n L and  156 A- n R, respectively. Similarly, each of the liquid crystal layers  156 B- 1 ,  156 B- 2  and  156 B - n  of the diffraction grating  150 B in turn has differently arranged first and second diffracting regions  156 B - 1 L and  156 B- 1 R,  156 B- 2 L and  156 B- 2 R, . . . and  156 B- n L and  156 B- n R, respectively. Similarly, each of the liquid crystal layers  156 C- 1 ,  156 C- 2  and  156 C- n  of the diffraction grating  150 C in turn has differently arranged first and second diffracting regions  156 C- 1 L and  156 C- 1 R,  156 C- 2 L and  156 C- 2 R, . . . and  156 C- n L and  156 C- n R, respectively. 
     Analogous to the diffraction gratings  100 A- 100 C described above with respect to  FIGS.  10 A- 10 C , each of the different diffracting zones further comprises an alignment layer (not shown) interposed between the substrate and the corresponding liquid crystal layer. That is, while not shown for clarity, interposed between the substrate  104  and differently arranged first/second diffracting regions  156 A- 1 L/ 156 A- 1 R,  156 A- 2 L/ 156 A- 2 R, . . . and  156 A- n L/ 156 A- n R of the diffraction grating  150 A of  FIG.  15 A  are first and second alignment layers  160 A- 1 L/ 160 A- 1 R,  160 A- 2 L/ 160 A- 2 R, . . . and  160 A- n L/ 160 A- n R, respectively. Similarly interposed between the substrate  104  and differently arranged first/second diffracting regions  156 B - 1 L/ 156 B- 1 R,  156 B- 2 L/ 156 B - 2 R, . . . and  156 B - n L/ 156 B- n R of the diffraction grating  150 C of  FIG.  15 B  are first/second alignment layers  160 B- 1 L/ 160 B- 1 R,  160 B - 2 L/ 160 B - 2 R, . . . and  160 B - n L/ 160 B- n R, respectively. Similarly, interposed between the substrate  104  and differently arranged first/second diffracting regions  156 C- 1 L/ 156 C- 1 R,  156 C- 2 L/ 156 C- 2 R, . . . and  156 C- n L/ 156 C- n R of the diffraction grating  150 C of  FIG.  15 C  are first/second alignment layers  160 C- 1 L/ 160 C- 1 R,  160 C- 2 L/ 160 C- 2 R, . . . and  160 C- n L and  160 C- n R, respectively. 
     Still referring to  FIGS.  15 A- 15 C , each zone of the diffraction gratings  150 A,  150 B and  150 C include first and second regions that alternate in the x-direction. Each of the first regions  156 A- 1 L,  156 A- 2 L, . . . and  156 A- n L of the diffraction grating  150 A, each of the first regions  156 B- 1 L,  156 B- 2 L, . . . and  156 B- n L of the diffraction grating  150 B and each of the first regions  156 C- 1 L,  156 C- 2 L, . . . and  156 C- n L of the diffraction grating  150 C have liquid crystal molecules  112  that are aligned substantially along the same first alignment direction and have an azimuthal angle y that is substantially the same. In contrast, each of the second regions  156 A- 1 R,  156 A- 2 R, . . . and  156 A- n R of the diffraction grating  150 A, each of the second regions  156 B- 1 R,  156 B- 2 R, . . . and  156 B- n L of the diffraction grating  150 B and each of the second regions  156 C- 1 R,  156 C- 2 R, . . . and  156 A- n R of the diffraction grating  150 C have liquid crystal molecules  112  that are aligned substantially along a second alignment direction different from the first alignment direction and have a second azimuthal angle y that is different, e.g., smaller, than the first azimuthal angle y of the respective first regions. 
     In each of the diffraction gratings  150 A- 150 C of  FIGS.  15 A- 15 C , respectively, at least some of the diffracting zones have liquid crystal layers formed of liquid crystal molecules that are spatially arranged differently, e.g., have azimuthal angles that are different from each other ( FIGS.  15 A and  15 C ), or have different duty cycles that are different from each other ( FIGS.  15 B and  15 C ), such that the diffracting zones have different optical properties, e.g., different refractive indices and/or different diffraction efficiencies, according to embodiments. 
     In particular, referring to diffraction grating  150 A of  FIG.  15 A , in addition to having alignment directions and azimuthal angles y that are different from the first azimuthal angle y of the first regions  156 A- 1 L,  156 A- 2 L, . . . and  156 A- n L, the liquid crystal molecules of the second regions  156 A- 1 R,  156 A- 2 R, . . . and  156 A- n R are aligned along second alignment directions that are different from each other. For example, in the illustrated embodiment, the zones  148 A- 1 ,  148 A- 2  and  148 A- n  are arranged such that the first regions and second regions alternate in the x-direction, where each of the first regions  156 A- 1 L,  156 A- 2 L, . . . and  156 A- n L has substantially the same azimuthal angle gyp, while the second regions  156 A- 1 R,  156 A- 2 R, . . . and  156 A- n R have azimuthal angles y that are different from each other. By way of example, the first regions  156 A- 1 L,  156 A- 2 L, . . . and  156 A- n L have a an azimuthal angles y that is between about 0 and about 15 degrees or between about 0 and 10 degrees, for instance 0 degrees. The second regions  156 A- 1 R,  156 A- 2 R, . . . and  156 A- n R can have azimuthal angles y that are different from each other, where each can be between about 75 degrees and about 90 degrees, for instance about 90 degrees; between about 60 degrees and about 90 degrees or between about 65 degrees and about 85 degrees, for instance about 75 degree; between about 30 degrees and about 60 degrees or between about 35 degrees and about 55 degrees, for instance about 45 degrees; between about 10 degrees and about 40 degrees or between about 15 degrees and about 35 degrees, for instance about 25 degrees. 
     Still referring to  FIG.  15 A , in some embodiments, as illustrated, the second regions  156 A- 1 R,  156 A- 2 R, . . . and  156 A- n R can have azimuthal angles y that vary, e.g., increase or decrease in one direction in a lateral direction, such that a gradient in diffraction properties is created. In other embodiments, the second regions  156 A- 1 R,  156 A- 2 R, . . . and  156 A- n R can have azimuthal angles y that do not vary in one direction in the lateral direction. 
     Still referring to  FIG.  15 A , the duty cycle can be between about 10% and about 30%, between about 30% and about 50%, between about 50% and about 70% or between about 70% and about 90%, which in the illustrated embodiment is substantially constant in the x-direction. 
     Referring now to  FIG.  15 B , as discussed above, the diffraction grating  150 B share some common features as the diffraction grating  150 A of  FIG.  15 A . However, unlike the diffracting grating  150 B of  FIG.  15 A , while the liquid crystal molecules of different second regions  156 B- 1 R,  156 B - 2 R, . . . and  156 B - n R have azimuthal angles φ that are different from the first azimuthal angle y of the first regions  156 B- 1 L,  156 B- 2 L, . . . and  156 B- n L, they are not aligned differently from each other. For example, in the illustrated embodiment, the zones  148 B- 1 ,  148 B- 2  and  148 B- n  are arranged such that the first regions and second regions alternate in the x-direction, where each of the first regions  156 B- 1 L,  156 B- 2 L, . . . and  156 B- n L has substantially the same first azimuthal angle φ, and each of the second regions  156 B- 1 R,  156 B- 2 R, . . . and  156 B- n R has substantially the same second azimuthal angle φ. The first and second azimuthal angles of the first and second regions can have any of the values discussed above with respect to the diffraction grating  150 A of  FIG.  15 A . 
     However, unlike the grating  150 A of  FIG.  15 A , the zones  148 B- 1 ,  148 B- 2  and  148 B- 3  have substantially the same azimuthal angle, e.g., between about 0 to 50 degrees, while having substantially different duty cycles, e.g., between about 40% and about 60%, for instance about 50%; between about 30% and about 50%, for instance about 40% and a duty cycle between about 20% and about 40%, for instance about 30%, respectively, such that the diffraction grating  150 B has spatially varying optical properties. 
     Still referring to  FIG.  15 B , in some embodiments, as illustrated, the zones can have duty cycles that vary, e.g., increase or decrease in one direction in a lateral direction, such that a gradient in optical properties is created. In other embodiments, the duty cycles do not vary in one direction in the lateral direction. 
     Referring now to  FIG.  15 C , the illustrated diffraction grating  150 C combines features similar to those described above with respect to the diffraction gratings  150 A and  150 B of  FIGS.  15 A and  15 B . In particular, the liquid crystal molecules of different second regions  156 C- 1 R,  156 C- 2 R, . . . and  156 C- n R can have azimuthal angles y that are different from the first azimuthal angles y of the first regions  116 C- 1 L,  116 C- 2 L, . . . and  116 C- n L, and different from each other. In addition, the duty cycle varies between adjacent zones across a lateral direction, e.g., x-direction. The first and second azimuthal angles of the first and second regions can have any of the values discussed above with respect to the diffraction grating  150 A of  FIG.  15 A . In addition, the duty cycle variation between adjacent zones across a lateral direction, e.g., x-direction, can also have values discussed above with respect to the diffraction grating  150 B of  FIG.  15 B . 
     Referring now to  FIGS.  16 A , a top-down view (x-y plane) of a diffraction grating  160  according to some other embodiments are illustrated, in which azimuthal angles of liquid crystal molecules rotate across a lateral length of a zone. The diffraction grating having such arrangement is sometimes referred a polarization grating. While not shown for clarity, the diffraction grating  160  comprises a substrate and an alignment layer formed thereon, and a plurality of differently arranged diffracting zones  164 - 1  and  164 - 2 . The diffracting zones  164 - 1  and  164 - 2  have corresponding liquid crystal layers  168 - 1  and  168 - 2 , respectively. Each of the liquid crystal layers liquid crystal layers  168 - 1  and  168 - 2  of the diffraction grating  160  in turn has a plurality of differently arranged diffracting regions  168 - 1   a  to  168 - 1   i  and  168 - 2   a  to  168 - 2   i,  respectively. Each of the plurality of regions  168 - 1   a  to  168 - 1   i  of the zone  164 - 1  and each of the plurality of regions  168 - 2   a  to  168 - 2   i  of the zone  164 - 2  has liquid crystal molecules  112  that are aligned substantially along the same alignment direction within the same region. Thus, it will be understood that, each of the zones include a stack of liquid crystal molecules stacked in the z-direction. 
     The liquid crystal molecules  112  of each of the diffracting regions  168 - 1   a  to  168 - 1   i  of the zone  164 - 1  and regions  168 - 2   a  to  168 - 2   i  of the zone  164 - 2  have substantially the same azimuthal angle y within the same region. However, the liquid crystal molecules  112  of different diffracting regions have substantially different azimuthal angles. In addition, the liquid crystal molecules  112  of different diffracting regions can have substantially the same or different pre-tilt angle Φ, similar to as described above with respect to  FIGS.  13 A and  13 B . 
     In the illustrate embodiment, the liquid crystal molecules  112  of each of the diffracting regions  168 -la to  168 -li of the zone  164 - 1  and the corresponding regions  168 - 2   a  to  168 - 2   i  of the zone  164 - 2  have substantially the same azimuthal angle y within the same region. However, distances between adjacent regions are substantially different between the zone  164 - 1  and the zone  164 - 2 , such that spatially varying diffraction properties are generated, as illustrated in reference to  FIG.  16 B . Referring to  FIG.  16 B , a graph  162  schematically showing the azimuthal angle y as a function of a lateral position x for the diffraction grating  160  in  FIG.  16 A  is illustrated. The x-axis represents a lateral distance in the x-direction and the y-axis represents the azimuthal angle φ. The curves  162 - 1  and  162 - 1  represent the azimuthal angle φ as a function of the lateral position x for the zone  164 - 1  and the zone  164 - 2 , respectively. 
     Referring back to  FIG.  16 A , the liquid crystal molecules  112  of the diffracting region  164 - 1  are arranged such that the rate of change in azimuthal angle φ per a unit of lateral length, i.e., Δφ/Δx in the x-direction, is relatively constant, as illustrated by the curve  162 - 1  of  FIG.  16 B . In contrast, the liquid crystal molecules  112  of the diffracting region  164 - 2  are arranged such that the Δφ/Δx in the x-direction varies substantially across x, as illustrated by the curve  162 - 2  of  FIG.  16 B . As a result, the curve  162 - 2  is characterized by a central region of the zone  164 - 2  in which the Δφ/Δx varies relatively slowly and end regions of the zone  164 - 2  in which the Ay/Ax varies relatively rapidly. As a result, the diffraction properties (including efficiencies and refractive indices) differ from those of the grating with a uniform variation of its azimuthal angle of liquid crystals. 
       FIGS.  17 A- 17 E  illustrate a method for fabricating diffraction gratings having non-uniform azimuthal angles, e.g., diffraction gratings  150 A- 150 C of  FIGS.  15 A- 15 C  described above, using photo-alignment techniques, according to embodiments. In particular, in the illustrated embodiment, the method uses multiple exposures of the alignment layers prior to deposition of the liquid crystals. In the illustrated method of  FIGS.  17 A- 17 E , similar to the method illustrated with respect to  FIGS.  11 A- 11 B , a substrate  104  is provided on which a photo-alignment layer  120  is formed. 
     Referring to an intermediate structure  150 A illustrated in  FIG.  17 A , after forming the photo-alignment layer  120  on the substrate  104 , a first photomask  174 A is used to expose different regions of the underlying photo-alignment layer  120  to different doses of light and/or different polarizations of light. For example, different regions of the photo-alignment layer  120  corresponds to first (e.g., left) and second (e.g., right) regions of each of the zones  148 A- 1  and  148 A- 2  as described above with respect to the diffraction grating  150 A in  FIG.  15 A . 
     In some embodiments, the first photomask  174 A can be a gray-scale mask having a plurality of mask regions  174 A- 1 -to  174 A- 4  that are at least partially transparent and possibly have one or more opaque regions. Different one of the plurality of mask regions  174 A- 1 -to  174 A- 4  may be configured to transmit different doses of a first incident light  172 A, such that transmitted light  172 A transmitted through different ones of the plurality of mask regions have varying intensities that are proportional to the relative transparency of the different mask regions. In other embodiments, the photomask  174 A can be a binary mask having the plurality of mask regions  174 A- 1 -to  174 A- 4  each being fully or nearly fully transparent or fully or nearly fully opaque, such that transmitted light  172 A has binary intensities. In the illustrated example, the first incident light  172 A can be polarized, e.g., linearly polarized at a first angle, e.g., 0 degrees, as schematically depicted by polarization vectors  178 A, and substantially transmits through the mask regions  174 A- 1  and  174 A- 3  corresponding to first (e.g., left) regions of each of the zones  148 A- 1  and  148 A- 2  of the diffraction grating  150 A as illustrated in  FIG.  15 A , while substantially being blocked in other regions. 
     Referring to an intermediate structure  150 B illustrated in  FIG.  17 B , after exposing different regions of the photo-alignment layer  120  to the first incident light  172 A, a second photomask  174 B is used to expose different regions of the underlying photo-alignment layer  120  to different doses of light and/or different polarizations of light using a second incident light  172 B. 
     In some embodiments, the second photomask  174 B can be a gray-scale mask different from the first photomask  174 A and having a plurality of mask regions  174 B- 1 -to  174 B- 4  that are at least partially transparent and possibly have one or more opaque regions. Different ones of the plurality of mask regions  174 B- 1 -to  174 B- 4  may be configured to transmit different doses of the second incident light  172 B. In other embodiments, the photomask  174 B can be a binary mask having the plurality of mask regions  174 B- 1 -to  174 B- 4  each being fully or nearly fully transparent or fully or nearly fully opaque, such that transmitted light  172 B has binary intensities. The second incident light  172 B can be polarized, e.g., linearly polarized at a second angle different, e.g., orthogonal, from the first polarization angle of the first incident light  178 A. For example, the second incident light  172 B can be orthogonally linearly polarized relative to the first incident light  172 A, e.g., at 90 degrees, as schematically depicted by polarization vectors  178 B and substantially transmits through the mask region  174 B- 2  corresponding to a second (e.g., right) region of the zone  148 A- 1  of the diffraction grating  150 A illustrated in  FIG.  15 A , while substantially being blocked in other regions. 
     Referring to an intermediate structure in  FIG.  17 C , after exposing different regions of the photo-alignment layer  120  to the second incident light  172 B, a third photomask  174 C is used to expose different regions of the underlying photo-alignment layer  120  to different doses of light and/or different polarizations of light using a third incident light  172 C. 
     In some embodiments, the third photomask  174 C can be a gray-scale mask different from the first and second photomasks  174 A,  174 B and having a plurality of mask regions  174 C- 1 -to  174 C- 4  that are at least partially transparent and possibly have one or more opaque regions. Different ones of the plurality of mask regions  174 C- 1 -to  174 C- 4  may be configured to transmit different doses of the third incident light  172 C. In other embodiments, the photomask  174 C can be a binary mask having the plurality of mask regions  174 C- 1 -to  174 C- 4  each being fully or nearly fully transparent or fully or nearly fully opaque, such that transmitted light  172 C has binary intensities. The third incident light  178 C can be polarized, e.g., linearly polarized at a third angle different from the first and second polarization angles of the first and second incident lights  178 A and  178 B. In the illustrated embodiment, the third incident light  172 C is linearly polarized at 45 degrees, as schematically depicted by polarization vectors  178 C and substantially transmits through the mask region  174 A- 4  corresponding to a second (e.g., right) region of the zone  148 A- 2  of the diffraction grating  150 A illustrated in  FIG.  15 A , while substantially being blocked in other regions. 
     Referring to  FIGS.  17 D  (cross-sectional view) and  17 E (top-down view), after exposing different regions of the photo alignment layer  120  through the multi-exposure process described above with respect to  FIGS.  17 A- 17 C , a liquid crystal layer can be deposited on the photo alignment layer  120 . As a result of the different doses and/or polarizations of light received by different regions of the photo alignment layer  120 , differently configured liquid crystal layers  156 A- 1  and  156 A- 2  are formed in respective zones  148 A- 1  and  148 A- 2 , respectively. The liquid crystal layers  156 A- 1  and  156 A- 2  have first and second diffracting regions  156 A- 1 L and  156 A- 1 R and  156 A- 2 L and  156 A- 2 R, respectively. As described above with respect to  FIG.  15 A , the first regions and second regions alternate in the x-direction, where each of the first regions  156 A- 1 L and  156 A- 2 L has substantially the same first azimuthal angle φ, while the second regions  156 A- 1 R and  156 A- 2 R have azimuthal angles y that are different from each other and from the first azimuthal angle of the first regions. Without being bound to any theory, in some cases, exposure of the underlying photo-alignment layer  120  to light having different polarization angles leads to different azimuthal angles of the liquid crystal molecules. 
     Still referring to  FIGS.  17 D and  17 E , the azimuthal angle y of the liquid crystal molecules can be determined by the linear polarization angle of the exposure light and the type of photo-alignment layer  120 . In the illustrated embodiment, the photo-alignment layer  120  is configured such that the degree of rotation of the liquid crystal molecules, as measured by an absolute value the azimuthal angle y up to +/−90 degrees, is determined by the linear polarization orientation angle of transmitted light received by the underlying alignment layer up to +/−90 degrees. In some embodiments, such as the illustrated embodiment, the photo-alignment layer  120  can be configured such that the liquid crystal molecules are oriented substantially parallel to the polarization direction of the exposure light (e.g., the azimuthal angle y and the linear polarization angle of the exposure light are substantially the same). Embodiments are not so limited, however, and in other embodiments, the photo-alignment layer  120  can be configured such that the liquid crystal molecules are oriented substantially orthogonal to the polarization direction of the exposure light (e.g., the azimuthal angle y and the linear polarization angle of the exposure light are substantially offset by about +/−90 degrees). For example, in the illustrated embodiment, the photo-alignment layers  160 A- 1 L and  160 A- 2 L receive light with the same linear polarization orientation and the photo alignment layer  160 A- 1 R receives light with the larger difference in linear polarization orientation angle with respect to the linear polarization orientation of the photo-alignment layers  160 A- 1 L and  160 A- 2 L, followed by the photo alignment layer  160 A- 2 R. As a result, the resulting azimuthal angles are the same for the first regions  156 A- 1 L and  156 A- 2 L and the difference in the resulting azimuthal angles with respect to the first regions  156 A- 1 L and  156 A- 2 L is larger for the second region  156 A- 1 R than that for the second region  156 A- 2 R. 
     In various embodiments described herein, photomasks can comprise linear polarizers such as wire-grid polarizers having a regular array of parallel metallic wires placed in a plane perpendicular to the direction of propagation of the incident light. In some embodiments described herein, the photomasks may be configured to provide illumination having uniform polarization angle across the photo-alignment layer. When comprising wire-grid polarizers, these embodiments may be realized by configuring the array of metallic wires to be uniform across the photomasks, e.g., uniform in the thickness and/or the density of the metallic wires. In other embodiments, the photomasks may be configured to provide illumination having non uniform or having multiple polarization angles across different regions of the photo-alignment layer. When comprising wire-grid polarizers, these embodiments may be realized by configuring the array of metallic wires to be nonuniform and varying across the photomasks, e.g., nonuniform and varying in the thickness and/or the density of the metallic wires. Thus, varying the thickness and density of metallic wires, both the polarization angle and the transmittance of the light can be controlled, according to various embodiments. 
       FIGS.  18 A- 18 D  illustrate another method for fabricating a diffraction grating  160  according to some other embodiments, in which azimuthal angles of liquid crystal molecules rotate across a lateral length of a zone, e.g., polarization grating. In particular, in the illustrated embodiment, the method uses polarization interference holographic exposure using a gray-scale mask, according to embodiments. 
     Referring to  FIG.  18 A  showing an intermediate structure  160 A, in the illustrated method, processes leading up to forming the photo-alignment layer  120  to UV light is similar to the method described above with respect to  FIGS.  17 A- 17 E . Thereafter, a plurality of coherent light beams  182 A,  182 B having different polarizations are directed to the plurality of differently arranged diffracting zones  164 A- 1  and  164 A- 2 . In the illustrated embodiment, the light beams  182 A and  182 B include orthogonal circular polarized light beams. However, the light beams  182 A and  182 B can include elliptical polarized light beams, for example. In the illustrated embodiment, both zones  164 - 1  and  164 - 2  are unmasked. 
     Thereafter, referring to  FIG.  18 B  showing an intermediate structure  160 B, a photomask  184  is used to expose different zones of the underlying photo-alignment layer  120  to different doses of light and/or different polarizations of light using a linearly polarized incident light  188  having any polarization angle discussed above with respect to 
       FIGS.  17 A- 17 E . For example, different zones of the photo-alignment layer  120  may correspond to the zones  164 - 1  and  164 - 2  as described above with respect to the diffraction grating  160  in  FIG.  16 B . As a result of the secondary exposure to linearly polarized light  188 , a fraction of the photo-alignment layer  120  can be realigned. Without being bound to any theory, when the photo-alignment layer  120  is exposed twice with different linear polarization orientations, the orientations of the liquid crystal molecules can be determined by the relative linear polarization orientations and the exposure doses of two exposures. 
     Referring now to  FIGS.  18 C and  18 D , a cross-sectional view (x-z plane) and a top-down view (x-y plane) of the diffraction grating  160  corresponding to that in  FIG.  16 B  is illustrated. At least in part as a result of the first and second exposures as described above with respect to  FIG.  18 A and  18 B , liquid crystal layers  168 - 1  and  168 - 2  having a plurality of differently arranged diffracting regions  168 - 1   a  to  168 - 1   i  and  168 - 2   a  to  168 - 2   i  are generated, respectively. Each of the plurality of regions  168 - 1   a  to  168 - 1   i  of the zone  164 - 1  and each of the plurality of regions  168 - 2   a  to  168 - 2   i  of the zone  164 - 2  has liquid crystal molecules  112  that are aligned substantially along the same alignment direction within the same region. Thus, it will be understood that, each of the zones include a stack of liquid crystal molecules stacked in the z-direction. 
     Spatially Variable Liquid Crystal Diffraction Gratings Based on Spatially Varying Liquid Crystal Materials 
     In various embodiments discussed supra, the liquid crystal molecules are fabricated using photo-alignment techniques. However, other embodiments are possible, which can be fabricated with or without photo-alignment. 
     Referring to  FIGS.  19 A and  19 B , top-down (viewed along the x-y plane) and side (viewed along the x-z plane) views of a diffraction grating  190 , which can be fabricated with or without photo-alignment, according to some embodiments are illustrated. The diffraction grating  190  comprises a plurality of diffracting zones, i.e., diffracting zones  198 - 1 ,  198 - 2 , . . . and  198 - n  that have a periodically repeating lateral dimension or a grating period A and include corresponding liquid crystal layers formed of liquid crystal molecules  112 . The lateral dimension or the grating period A can be similar to those described above with respect to  FIGS.  10 A- 10 C . 
     The diffracting zones  198 - 1 ,  198 - 2 , . . .  198 - n  of the diffraction grating  190  have corresponding liquid crystal layers  186 - 1 ,  186 - 2 , . . .  186 -n, respectively. The number of each type of diffracting zones can be similar to those described above with respect to  FIGS.  10 A- 10 C . In addition, the diffracting zones as arranged can periodically repeat any suitable number of times. Each of the liquid crystal layers  186 - 1 ,  186 - 2  and  186 - n  of the diffraction grating  190  in turn has differently arranged first and second diffracting regions  186 - 1 L and  186 - 1 R,  186 - 2 L and  186 - 2 R, . . . and  186 - n L and  186 - n R, respectively. 
     The different liquid crystal layers  186 - 1 ,  186 - 2  and  186 - n  have liquid crystal molecules  112  that are arranged to have different degrees of chirality. As described above, chirality can be described by a chiral pitch, p, which can refer to the distance over which the liquid crystal molecules undergo a full  360 ° twist. The chirality can also be characterized by a twist deformation angle, which is an angle of twist the liquid crystal molecules undergo within a thickness of the liquid crystal layer. For example, in the illustrated embodiment, the first liquid crystal layer  186 - 1  has the first and second diffracting regions  186 - 1 L and  186 - 1 R that have liquid crystal molecules  112  having different azimuthal angles with little or no chirality (very large or infinite chiral pitch p). The second and third liquid crystal layers  186 - 2  and  186 - n  have respective first/second diffracting regions  186 - 2 L/ 186 - 2 R and  186 - n L/ 186 - n R, respectively, that have liquid crystal molecules  112  having substantial and substantially different degrees of chirality. Similarly, in various embodiments, the azimuthal angles of or the difference in azimuthal angles between the uppermost liquid crystal molecules in the first and second diffracting regions  186 - 2 L/ 186 - 2 R and  186 - n L/ 186 - n R of the second and nth liquid crystal layers  186 - 2  and  186 -n, respectively, can be any value described above with respect to the diffraction gratings  150 A- 150 C in  FIGS.  15 A- 15 C . 
     In some embodiments, each pair of first/second diffracting regions within a zone, e.g., the pair of regions  186 - 2 L/ 186 - 2 R of the zone  198 - 2  (see  FIG.  19 A ) and the pair of regions  186 - n L/ 186 - n R of the zone  198 - n  have uppermost liquid crystal molecules that have different azimuthal angles y but have the same chiral pitch p. In some other embodiments, the pairs of regions within zones have uppermost liquid crystal molecules that have the same azimuthal angles y but have different chiral pitches p. In various embodiments, a chiral twist (e.g., twist angle or twist deformation angle) of the liquid crystal molecules in a given region of the pair of regions  186 - 2 L/ 186 - 2 R of the zone  198 - 2  and the pair of regions  186 - n L/ 186 - n R of the zone  198 - n  can be, e.g., about +/−45°, about +/−90°, about +/−135°, or about +/−180°. The corresponding chiral period p can be 8D, 4D, or 3D, where 2D is the thickness of the liquid crystal layers. 
     For example, in the illustrated embodiment, the uppermost liquid crystal molecules of the first and second regions  186 - 2 L and  186 - 2 R have first and second azimuthal angles y of, e.g., 135° and 45°, respectively, while having a first chiral pitch, e.g., of about 8D, where D is the thickness of the liquid crystal layers. As a result, in each of the first and second regions  186 - 2 L and  186 - 2 R, the uppermost liquid crystal molecule and the lowermost liquid crystal molecule are twisted relative to each other by about −45 degrees. In addition, in the illustrated embodiment, the uppermost liquid crystal molecules of the first and second regions  186 - n L,  186 - n R have third and fourth azimuthal angles φ of, e.g., 90° and 0°, respectively, while having a second chiral pitch of about 4D, where D is the thickness of the liquid crystal layers. As a result, in each of the first and second regions  186 - n L and  186 - n R, the uppermost liquid crystal molecule and the lowermost liquid crystal molecule are twisted relative to each other by about −90 degrees. However, the azimuthal angles φ of uppermost liquid crystal molecules of the first/second diffracting regions  186 - 2 L/ 186 - 2 R and  186 - n L/ 186 - n R can have any value such as described above with respect to  FIG.  15 A- 15 C . 
     Still referring to  FIGS.  19 A and  19 B , in some embodiments, the liquid crystal molecules  112  in each region have the same pre-tilt angle Φ, which can be zero or higher. 
     Still referring to  FIGS.  19 A and  19 B , the duty cycle of different liquid crystal layers  186 - 1 ,  186 - 2  and  186 - n,  can be different, and each can be between about 10% and about 30%, between about 30% and about 50%, between about 50% and about 70% or between about 70% and about 90%. 
     Referring now to  FIG.  20   , cross-sectional side (x-z plane) view of a diffraction grating  200  according to some other embodiments are illustrated. While not shown for clarity, the diffraction grating  200  comprises a substrate and a plurality of differently arranged diffracting zones  208 - 1  and  208 - 2  having corresponding liquid crystal layers  196 - 1  and  196 - 2 , respectively. Each of the liquid crystal layers liquid crystal layers  196 - 1  and  196 - 2  of the diffraction grating  200  in turn has a plurality of differently arranged diffracting regions  196 -la through  196 - 1 g and  196 - 2   a  through  196 - 2 g, respectively. 
     Similar to liquid crystal molecules  112  of the liquid crystal layer  186 - 1  of  FIGS.  19 A / 19 B, the liquid crystal molecules  112  of the diffracting regions  196 -la through  196 - 1 g of the liquid crystal layer  196 - 1  illustrated in  FIG.  20    has different azimuthal angles but little or no chirality (very large or infinite chiral pitch p) from layer to layer. The azimuthal angles and other arrangements of adjacent diffracting regions  196 - 1   a  through  196 - 1   g  are similar to those described with respect to the first and second diffracting regions  186 - 1 L and  186 - 1 R with respect to  FIGS.  19 A / 19 B. 
     Similar to liquid crystal molecules  112  of the liquid crystal layers  186 - 2  and  186 - n  of  FIGS.  19 A / 19 B, the liquid crystal molecules  112  of the diffracting regions  196 - 2   a  through  196 - 2   g  of the liquid crystal layer  196 - 2  illustrated in  FIG.  20    have substantial and substantially different degrees of chirality along the length of the zone (along the x direction), and have uppermost liquid molecules that have different azimuthal angles. The azimuthal angles, the chirality and other arrangements of adjacent diffracting regions  196 - 2   a  through  196 - 2   g  are similar to those described with respect to the first and second diffracting regions  186 - 2 L/ 186 - 2 R and  186 - n L/ 186 - n R of the second and nth liquid crystal layers  186 - 2  and  186 - n.    
     It will be appreciated that, when a twist is induced to liquid crystal molecules as illustrated above with respect to  FIGS.  19 A / 19 B and  20 , the resulting diffraction grating exhibits spatially varying diffraction properties, including refractive index and diffraction efficiencies. Some liquid crystal molecules can be made chiral by substituting one or more of the carbon atoms asymmetrically by four different ligands. Other liquid crystal molecules can be made chiral by adding mesogenic or non-mesogenic chiral dopants at varying concentration to one of liquid crystal phases described above. According to embodiments, by adding small concentrations, including, for example, but not limited to below 5%-10% by weight, chirality related effects can be increased with the concentration of the dopant. Some examples of chiral liquid crystal molecules include cholesteryl-benzoate, a ferroelectric liquid crystal N(p-n-Decyloxybenzylidene) p-amino 2-methylbutyl cinnamate (DOBAMBC), and achiral MBBA (4-butyl-N-[4-methoxy-benzylidene]-aniline), which is a room temperature nematic, doped with chiral R 1011 . Other chiral liquid crystal molecules may be used. 
     Referring to  FIG.  21   , a side view (viewed along the x-z plane) of a diffraction grating  210 , which can be fabricated with or without photo-alignment, according to some embodiments are illustrated. The diffraction grating  210  comprises a plurality of diffracting zones, i.e., diffracting zones  218 - 1 ,  218 - 2 , . . . and  218 - n  that have a periodically repeating lateral dimension or a grating period A in a similar manner to those described above with respect to  FIGS.  10 A- 10 C . The diffracting zones  218 - 1 ,  218 - 2 , . . . and  218 - n  of the diffraction grating  210  have corresponding liquid crystal layers  206 - 1 ,  206 - 2 , . . . and  206 - n,  respectively. The number of each type of diffracting zones can be similar to those described above with respect to  FIGS.  10 A- 10 C . In addition, the diffracting zones as arranged can periodically repeat any suitable number of times. 
     In the diffraction grating  210 , different liquid crystal layers  206 - 1 ,  206 - 2  and  206 - n  comprise different liquid crystal materials. In particular, first and second diffracting regions  206 - 1 L and  206 - 1 R,  206 - 2 L and  206 - 2 R, . . . and  206 - n L and  206 - n R have liquid crystal molecules  212 - 1 L and  212 - 1 R,  212 - 2 L and  212 - 2 R, . . . and  212 - n L and  212 - n R, respectively which can be the same or different liquid crystal molecules. For example, in some implementations, regions within a first zone can have a first liquid crystal material, regions within a second zone can have a first liquid crystal material and regions within a third zone can have a third liquid crystal material. In other implementations, any given zone can have a first region having a first liquid crystal material and a second region having a second liquid crystal material. Accordingly, the optical properties can be changed along the length of the diffraction grating by changing the composition of the material, for example, using the same host material with different level of the same dopant (or with different dopants with same or different levels), and not necessary changing the orientation of the liquid crystal molecules. 
     In some embodiments, different zones have different liquid crystal molecules while other aspects of the liquid crystal orientation, e.g., the tilt angle, the azimuthal angle, and chirality as described above are similar or the same between different zones. In some other embodiments, different zones have different liquid crystal molecules while having other aspects of the liquid crystal orientation, e.g., the tilt angle, the azimuthal angle, and chirality that are also different, as discussed supra in the context of various embodiments. 
     By depositing different liquid crystal materials during deposition or by modifying the liquid crystal material after deposition, local birefringence can be controlled to be different across different zones. In various embodiments, birefringence of individual zones can be between about 0.05 and about 0.15, for instance about 0.10, between about 0.15 and about 0.25, for instance about 0.2, and between about 0.25 and about 0.35, for instance about 0.3. 
     Additional Examples 
     In a 1 st  example, a diffraction grating includes a plurality of different diffracting zones having a periodically repeating lateral dimension corresponding to a grating period adapted for light diffraction. The diffraction grating additionally includes a plurality of different liquid crystal layers corresponding to the different diffracting zones. The different liquid crystal layers have liquid crystal molecules that are aligned differently, such that the different diffracting zones have different optical properties associated with light diffraction. 
     In a 2 nd  example, in the diffraction grating of the 1 st  example, the optical properties include one or more of refractive index, absorption coefficient, diffraction efficiency and birefringence. 
     In a 3 rd  example, in the diffraction grating of any of the 1 st  to 2 nd  examples, each of the different liquid crystal layers has a plurality of differently arranged regions, wherein the differently arranged regions have liquid crystal molecules that are aligned differently with respect to each other. 
     In a 4 th  example, in the diffraction grating of any of the 1 st  to 3 rd  examples, each of the different diffracting zones further comprises an alignment layer interposed between a substrate and the corresponding liquid crystal layer, wherein different alignment layers between the different diffracting zones and the substrate are formed of the same material composition, said different alignment layers causing the liquid crystal molecules to be aligned differently in the different diffracting zones. 
     In a 5 th  example, in the diffraction grating of any of the 1 st  to 4 th  examples, the liquid crystal molecules comprise calamitic liquid crystal molecules that are elongated and aligned along an elongation direction. 
     In a 6 th  example, in the diffraction grating of any of the 1 st  to 5 th  examples, the different liquid crystal layers include a first region and a second region, wherein liquid crystal molecules of the first region are aligned along a first alignment direction which forms a first alignment angle with respect to a reference direction, and wherein liquid crystal molecules of the second region are aligned along a second alignment direction which forms a second alignment angle with respect to the reference direction, the second alignment angle different from the first alignment angle. 
     In a 7 th  example, in the diffraction grating of the 6 th  example, liquid crystal molecules of a first region of a first liquid crystal layer and liquid crystal molecules of a corresponding first region of a second liquid crystal layer have substantially the same alignment angle. 
     In an 8 th  example, in the diffracting grating of the 7 th  example, liquid crystal molecules of a second region of the first liquid crystal layer and liquid crystal molecules of a corresponding second region of the second liquid crystal layer have different alignment angles. 
     In a 9 th  example, in the diffraction grating of the 6 th  example, liquid crystal molecules of a first region of a first liquid crystal layer and the liquid crystal molecules of a corresponding first region of a second liquid crystal layer have substantially different alignment angles, and wherein liquid crystal molecules of a second region of the first liquid crystal layer and liquid crystal molecules of a corresponding second region of the second liquid crystal layer have different alignment angles. 
     In a 10 th  example, in the diffraction grating of the  6   th  example, a ratio of lateral widths between first regions and second regions is substantially the same between different zones. 
     In an  11   th  example, in the diffraction grating of the 6 th  example, liquid crystal molecules of a second region of a first liquid crystal layer and liquid crystal molecules of a second region of a second liquid crystal layer have substantially same alignment angles, and wherein a ratio of lateral widths between the first regions and the second regions is substantially different between different zones. 
     In a 12 th  example, in the diffraction grating of the 6 th  example, liquid crystal molecules of a second region of a first liquid crystal layer and liquid crystal molecules of a second region of a second liquid crystal layer have different alignment angles, and wherein a ratio of lateral widths between the first regions and the second regions is substantially different between different zones. 
     In a 13 th  example, in the diffracting grating of the 6 th  example, the first and second alignment angles are pre-tilt angles that are measured in a plane perpendicular to a major surface of a substrate and between respective alignment directions and the major surface. 
     In a 14 th  example, in the diffraction grating of the 6 th  example, the first and second alignment angles are azimuthal angles that are measured in a plane parallel to a major surface of the substrate and between respective alignment directions and a reference direction parallel to the major surface. 
     In a 15 th  example, in the diffraction grating of the 3 rd  example, the different liquid crystal layers include a first region and a second region, wherein liquid crystal molecules of the first region are aligned along a plurality of first alignment directions which forms a plurality of first alignment angles with respect to a reference direction, and wherein liquid crystal molecules of the second region are aligned along a plurality of second alignment directions which forms a plurality of second alignment angles with respect to the reference direction. 
     In a 16 th  example, in the diffraction grating of any of the 1 st  to 15 th  examples, the diffraction grating is a transmissive diffraction grating having a transparent substrate. 
     In a 17 th  example, in the diffraction grating of any of the 1 st  to 16 th  examples, different diffracting zones comprise different material compositions such that the different diffracting zones have different optical properties associated with light diffraction. 
     In an 18 th  example, a method of fabricating a diffraction grating includes providing a substrate. The method additionally includes providing a plurality of different diffracting zones having a periodically repeating lateral dimension corresponding to a grating period adapted for light diffraction. The method further includes forming a plurality of different liquid crystal layers comprising liquid crystal molecules over the substrate, the different liquid crystal layers corresponding to the different diffracting zones, wherein forming the different liquid crystal layers comprises aligning the liquid crystal molecules differently, thereby providing different optical properties associated with light diffraction to the different diffracting zones. 
     In a 19 th  example, in the method of the 18 th  example, the method further includes forming a photo-alignment layer on the substrate prior to forming the liquid crystal layers and illuminating the photo-alignment layer thereby causing the liquid crystal molecules formed on the alignment layer to be aligned differently in the different diffracting zone. 
     In a 20 th  example, in the method of the 19 th  example, forming the photo-alignment layer includes depositing a material selected from the group consisting of polyimide, linear-polarization photopolymerizable polymer, azo-containing polymers, courmarine-containing polymers, cinnamate-containing polymers and combinations thereof. 
     In a 21 st  example, in the method of any of the 19 th  and 20 th  examples, the method further includes, after forming the photo-alignment layer and prior to forming the liquid crystal layers, exposing the different diffracting zones to different doses of light using a gray scale mask. 
     In a 22 nd  example, in the method of any of 19 th  to 21 st  examples, forming the different liquid crystal layers includes forming a plurality of differently arranged regions in the different liquid crystal layers, wherein the differently arranged regions have liquid crystal molecules that are aligned differently with respect to each other. 
     In a 23 rd  example, in the method of the 22 nd  example, forming the different liquid crystal layers comprises forming a first region and a second region, wherein forming the first region comprises aligning liquid crystal molecules of the first region along a first alignment direction which forms a first alignment angle with respect to a reference direction, and wherein forming the second region comprises aligning liquid crystal molecules of the second region along a second alignment direction which forms a second alignment angle with respect to the reference direction, wherein the second alignment angle different from the first alignment angle. 
     In a 24 th  example, in the method of the 23 rd  example, aligning the liquid molecules of the first and second regions includes forming the respective first and second alignment angles that are inversely proportional to the different doses of light. 
     In a 25 th  example, in the methods of any of the 18 th  to 24 th  examples, forming the plurality of different liquid crystal layers comprises inducing chirality in at least some of the liquid crystal molecules by adding a chiral dopant to the liquid crystal layers. 
     In a 26 th  example, in the method of the 18 th  example, forming the different liquid crystal layers includes forming a first region and a second region in the liquid crystal layers, wherein liquid crystal molecules of the first region are aligned along a plurality of first alignment directions which forms a plurality of first alignment angles with respect to a reference direction, and wherein liquid crystal molecules of the second region are aligned along a plurality of second alignment directions which forms a plurality of second alignment angles with respect to the reference direction. 
     In a 27 th  example, a diffraction grating includes a plurality of contiguous liquid crystal layers extending in a lateral direction and arranged to have a periodically repeating lateral dimension, a thickness and indices of refraction such that the liquid crystal layers are configured to diffract light. Liquid crystal molecules of the liquid crystal layers are arranged differently in different liquid crystal layers along the lateral direction such that the contiguous liquid crystal layers are configured to diffract light with a gradient in diffraction efficiency. 
     In a 28 th  example, in the diffraction grating of the 27 th  example, the liquid crystal layers have a first region and a second region, and wherein the contiguous liquid crystal layers are arranged such that a plurality of first regions and a plurality of second regions alternate in the lateral direction. 
     In a 29 th  example, in the diffraction grating of the 28 th  example, the liquid crystal molecules in the first regions have substantially the same alignment orientation, whereas the liquid crystal molecules in the second regions are have substantially different alignment directions. 
     In a 30 th  example, a head-mounted display device is configured to project light to an eye of a user to display augmented reality image content. The head-mounted display device includes a frame configured to be supported on a head of the user. The head-mounted display device additionally includes a display disposed on the frame, at least a portion of said display comprising one or more waveguides, said one or more waveguides being transparent and disposed at a location in front of the user&#39;s eye when the user wears said head-mounted display device such that said transparent portion transmits light from a portion of an environment in front of the user to the user&#39;s eye to provide a view of said portion of the environment in front of the user, said display further comprising one or more light sources and at least one diffraction grating configured to couple light from the light sources into said one or more waveguides or to couple light out of said one or more waveguides. The diffraction grating includes a plurality of different diffracting zones having a periodically repeating lateral dimension corresponding to a grating period adapted for light diffraction. The diffraction grating additionally includes a plurality of different liquid crystal layers corresponding to the different diffracting zones, wherein the different liquid crystal layers have liquid crystal molecules that are aligned differently, such that the different diffracting zones have different optical properties associated with light diffraction. 
     In a 31 st  example, in the device of the 30 th  example, the one or more light sources include a fiber scanning projector. 
     In a 32 nd  example, in the device of any of the 30 th  to 31 st  examples, the display is configured to project light into the user&#39;s eye so as to present image content to the user on a plurality of depth planes. 
     In a 33 rd  example, in the diffraction grating of any of the 30 th  to 32 nd  examples, the optical properties include one or more of refractive index, absorption coefficient, diffraction efficiency and birefringence. 
     In the embodiments described above, augmented reality display systems and, more particularly, spatially varying diffraction gratings are described in connection with particular embodiments. It will be understood, however, that the principles and advantages of the embodiments can be used for any other systems, apparatus, or methods with a need for the spatially varying diffraction grating. In the foregoing, it will be appreciated that any feature of any one of the embodiments can be combined and/or substituted with any other feature of any other one of the embodiments. 
     Unless the context clearly requires otherwise, throughout the description and the claims, the words “comprise,” “comprising,” “include,” “including” and the like are to be construed in an inclusive sense, as opposed to an exclusive or exhaustive sense; that is to say, in the sense of “including, but not limited to.” The word “coupled”, as generally used herein, refers to two or more elements that may be either directly connected, or connected by way of one or more intermediate elements. Likewise, the word “connected”, as generally used herein, refers to two or more elements that may be either directly connected, or connected by way of one or more intermediate elements. Additionally, the words “herein,” “above,” “below,” “infra,” “supra,” and words of similar import, when used in this application, shall refer to this application as a whole and not to any particular portions of this application. Where the context permits, words in the above Detailed Description using the singular or plural number may also include the plural or singular number, respectively. The word “or” in reference to a list of two or more items, that word covers all of the following interpretations of the word: any of the items in the list, all of the items in the list, and any combination of the items in the list. 
     Moreover, conditional language used herein, such as, among others, “can,” “could,” “might,” “may,” “e.g.,” “for example,” “such as” and the like, unless specifically stated otherwise, or otherwise understood within the context as used, is generally intended to convey that certain embodiments include, while other embodiments do not include, certain features, elements and/or states. Thus, such conditional language is not generally intended to imply that features, elements and/or states are in any way required for one or more embodiments or whether these features, elements and/or states are included or are to be performed in any particular embodiment. 
     While certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the disclosure. Indeed, the novel apparatus, methods, and systems described herein may be embodied in a variety of other forms; furthermore, various omissions, substitutions and changes in the form of the methods and systems described herein may be made without departing from the spirit of the disclosure. For example, while blocks are presented in a given arrangement, alternative embodiments may perform similar functionalities with different components and/or circuit topologies, and some blocks may be deleted, moved, added, subdivided, combined, and/or modified. Each of these blocks may be implemented in a variety of different ways. Any suitable combination of the elements and acts of the various embodiments described above can be combined to provide further embodiments. The various features and processes described above may be implemented independently of one another, or may be combined in various ways. All suitable combinations and subcombinations of features of this disclosure are intended to fall within the scope of this disclosure.