Patent Publication Number: US-2023161217-A1

Title: Light guide display system for providing increased pixel density

Description:
TECHNICAL FIELD 
     The present disclosure relates generally to optical devices and, more specifically, to a light guide display system for providing an increased pixel density. 
     BACKGROUND 
     An artificial reality system, such as a head-mounted display (“HMD”) or heads-up display (“HUD”) system, generally includes a near-eye display (“NED”) system in the form of a headset or a pair of glasses, and configured to present content to a user via an electronic or optic display within, for example, about 10-20 mm in front of the eyes of a user. The NED system may display virtual objects or combine images of real objects with virtual objects, as in virtual reality (“VR”), augmented reality (“AR”), or mixed reality (“MR”) applications. For example, in an AR system, a user may view both images of virtual objects (e.g., computer-generated images (“CGIs”)) and the surrounding environment by, for example, seeing through transparent display glasses or lenses (also referred to as an optical see-through AR system). 
     One example of an optical see-through AR system may include a pupil-expansion light guide display system, in which an image light representing a CGI may be coupled into a light guide (e.g., a transparent substrate), propagate within the light guide, and be coupled out of the light guide at different locations to expand an effective pupil. Diffractive optical elements may be coupled with the light guide to couple the image light into or out of the light guide via diffraction, such as surface relief gratings, holographic gratings, metasurface gratings, etc. 
     SUMMARY OF THE DISCLOSURE 
     Consistent with a disclosed embodiment of the present disclosure, a device is provided. The device includes a light guide. The device also includes an in-coupling element coupled with the light guide and configured to couple an input image light into the light guide. The device also includes an out-coupling element coupled with the light guide and configured to couple the input image light out of the light guide as an output image light. The device also includes a controller configured to control at least one of the in-coupling element or the out-coupling element during a first time period and a second time period. The out-coupling element is configured to output a first output image light having a first field of view (“FOV”) during the first time period, and a second output image light having a second FOV during the second time period. The first FOV substantially overlaps with the second FOV, and an axis of symmetry of the first FOV is rotated relative to an axis of symmetry of the second FOV. 
     Consistent with a disclosed embodiment of the present disclosure, a method is provided. The method includes controlling, by a controller during a first time period, at least one of an in-coupling element or an out-coupling element to couple an input image light into a light guide, and couple the input image light out of the light guide as a first output image light having a first FOV. The method also includes controlling, by the controller during a second time period, at least one of the in-coupling element or the out-coupling element to couple the input image light into the light guide, and couple the input image light out of the light guide as a second output image light having a second FOV. The second FOV substantially overlaps with the first FOV. An axis of symmetry of the first FOV is rotated from an axis of symmetry of the second FOV. 
     Other aspects of the present disclosure can be understood by those skilled in the art in light of the description, the claims, and the drawings of the present disclosure. The foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The following drawings are provided for illustrative purposes according to various disclosed embodiments and are not intended to limit the scope of the present disclosure. In the drawings: 
         FIGS.  1 A and  1 B  schematically illustrate diagrams of a conventional light guide display system implemented in a near-eye display (“NED”); 
         FIG.  2 A  schematically illustrates a diagram of a light guide display assembly configured to provide an increased pixel density, according to an embodiment of the present disclosure; 
         FIG.  2 B  schematically illustrates a diagram of a light guide display assembly configured to provide an increased pixel density, according to an embodiment of the present disclosure; 
         FIGS.  2 C- 2 E  schematically illustrate diagrams of a light guide display assembly configured to provide an increased pixel density, according to an embodiment of the present disclosure; 
         FIG.  3 A  schematically illustrates a diagram of a light guide display assembly configured to provide an increased pixel density, according to an embodiment of the present disclosure; 
         FIG.  3 B  schematically illustrates a diagram of a light guide display assembly configured to provide an increased pixel density, according to an embodiment of the present disclosure; 
         FIGS.  4 A and  4 B  schematically illustrate diagrams of a light guide display assembly configured to provide an increased pixel density, according to an embodiment of the present disclosure; 
         FIGS.  5 A- 5 C  schematically illustrate diagrams of a light guide display assembly configured to provide an increased pixel density, according to an embodiment of the present disclosure; 
         FIG.  6    is a flowchart illustrating a method for providing an increased output pixel density, according to an embodiment of the present disclosure; 
         FIG.  7 A  schematically illustrates a diagram of a near-eye display (“NED”), according to an embodiment of the present disclosure; 
         FIG.  7 B  schematically illustrates a cross-sectional view of half of the NED shown in  FIG.  7 A , according to an embodiment of the present disclosure; 
         FIGS.  8 A and  8 B  illustrate schematic diagrams of a grating in a diffraction state and a non-diffraction state, respectively, according to an embodiment of the present disclosure; 
         FIGS.  9 A and  9 D  illustrate schematic diagrams of a grating in a diffraction state, according to an embodiment of the present disclosure; 
         FIGS.  9 B and  9 E  illustrate schematic diagrams of the grating shown in  FIG.  9 A  in a non-diffraction state, according to an embodiment of the present disclosure; 
         FIGS.  9 C and  9 F  illustrate schematic diagrams of the grating shown in  FIG.  9 A  in a non-diffraction state, according to an embodiment of the present disclosure; 
         FIG.  9 G  illustrates a schematic diagram of the grating shown in  FIG.  9 A  implemented in a light guide display assembly, according to an embodiment of the present disclosure; 
         FIGS.  10 A and  10 B  illustrate schematic diagrams of a grating in a diffraction state and a non-diffraction state, respectively, according to an embodiment of the present disclosure; 
         FIGS.  10 C and  10 D  illustrate schematic diagrams of a grating in a diffraction state and a non-diffraction state, respectively, according to an embodiment of the present disclosure; 
         FIG.  11 A  schematically illustrates a three-dimensional (“3D”) view of a liquid crystal polarization hologram (“LCPH”) element, according to an embodiment of the present disclosure; 
         FIGS.  11 B- 11 D  schematically illustrate various views of a portion of the LCPH element shown in  FIG.  11 A , showing in-plane orientations of optically anisotropic molecules in the LCPH element, according to various embodiments of the present disclosure; and 
         FIGS.  11 E- 11 H  schematically illustrate various views of a portion of the LCPH element shown in  FIG.  11 A , showing out-of-plane orientations of optically anisotropic molecules in the LCPH element, according to various embodiments of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments consistent with the present disclosure will be described with reference to the accompanying drawings, which are merely examples for illustrative purposes and are not intended to limit the scope of the present disclosure. Wherever possible, the same reference numbers are used throughout the drawings to refer to the same or similar parts, and a detailed description thereof may be omitted. 
     Further, in the present disclosure, the disclosed embodiments and the features of the disclosed embodiments may be combined. The described embodiments are some but not all of the embodiments of the present disclosure. Based on the disclosed embodiments, persons of ordinary skill in the art may derive other embodiments consistent with the present disclosure. For example, modifications, adaptations, substitutions, additions, or other variations may be made based on the disclosed embodiments. Such variations of the disclosed embodiments are still within the scope of the present disclosure. Accordingly, the present disclosure is not limited to the disclosed embodiments. Instead, the scope of the present disclosure is defined by the appended claims. 
     As used herein, the terms “couple,” “coupled,” “coupling,” or the like may encompass an optical coupling, a mechanical coupling, an electrical coupling, an electromagnetic coupling, or any combination thereof. An “optical coupling” between two optical elements refers to a configuration in which the two optical elements are arranged in an optical series, and a light output from one optical element may be directly or indirectly received by the other optical element. An optical series refers to optical positioning of a plurality of optical elements in a light path, such that a light output from one optical element may be transmitted, reflected, diffracted, converted, modified, or otherwise processed or manipulated by one or more of other optical elements. In some embodiments, the sequence in which the plurality of optical elements are arranged may or may not affect an overall output of the plurality of optical elements. A coupling may be a direct coupling or an indirect coupling (e.g., coupling through an intermediate element). 
     The phrase “at least one of A or B” may encompass all combinations of A and B, such as A only, B only, or A and B. Likewise, the phrase “at least one of A, B, or C” may encompass all combinations of A, B, and C, such as A only, B only, C only, A and B, A and C, B and C, or A and B and C. The phrase “A and/or B” may be interpreted in a manner similar to that of the phrase “at least one of A or B.” For example, the phrase “A and/or B” may encompass all combinations of A and B, such as A only, B only, or A and B. Likewise, the phrase “A, B, and/or C” has a meaning similar to that of the phrase “at least one of A, B, or C.” For example, the phrase “A, B, and/or C” may encompass all combinations of A, B, and C, such as A only, B only, C only, A and B, A and C, B and C, or A and B and C. 
     When a first element is described as “attached,” “provided,” “formed,” “affixed,” “mounted,” “secured,” “connected,” “bonded,” “recorded,” or “disposed,” to, on, at, or at least partially in a second element, the first element may be “attached,” “provided,” “formed,” “affixed,” “mounted,” “secured,” “connected,” “bonded,” “recorded,” or “disposed,” to, on, at, or at least partially in the second element using any suitable mechanical or non-mechanical manner, such as depositing, coating, etching, bonding, gluing, screwing, press-fitting, snap-fitting, clamping, etc. In addition, the first element may be in direct contact with the second element, or there may be an intermediate element between the first element and the second element. The first element may be disposed at any suitable side of the second element, such as left, right, front, back, top, or bottom. 
     When the first element is shown or described as being disposed or arranged “on” the second element, term “on” is merely used to indicate an example relative orientation between the first element and the second element. The description may be based on a reference coordinate system shown in a figure, or may be based on a current view or example configuration shown in a figure. For example, when a view shown in a figure is described, the first element may be described as being disposed “on” the second element. It is understood that the term “on” may not necessarily imply that the first element is over the second element in the vertical, gravitational direction. For example, when the assembly of the first element and the second element is turned 180 degrees, the first element may be “under” the second element (or the second element may be “on” the first element). Thus, it is understood that when a figure shows that the first element is “on” the second element, the configuration is merely an illustrative example. The first element may be disposed or arranged at any suitable orientation relative to the second element (e.g., over or above the second element, below or under the second element, left to the second element, right to the second element, behind the second element, in front of the second element, etc.). 
     When the first element is described as being disposed “on” the second element, the first element may be directly or indirectly disposed on the second element. The first element being directly disposed on the second element indicates that no additional element is disposed between the first element and the second element. The first element being indirectly disposed on the second element indicates that one or more additional elements are disposed between the first element and the second element. 
     The term “processor” used herein may encompass any suitable processor, such as a central processing unit (“CPU”), a graphics processing unit (“GPU”), an application-specific integrated circuit (“ASIC”), a programmable logic device (“PLD”), or any combination thereof. Other processors not listed above may also be used. A processor may be implemented as software, hardware, firmware, or any combination thereof. 
     The term “controller” may encompass any suitable electrical circuit, software, or processor configured to generate a control signal for controlling a device, a circuit, an optical element, etc. A “controller” may be implemented as software, hardware, firmware, or any combination thereof. For example, a controller may include a processor, or may be included as a part of a processor. 
     The term “non-transitory computer-readable medium” may encompass any suitable medium for storing, transferring, communicating, broadcasting, or transmitting data, signal, or information. For example, the non-transitory computer-readable medium may include a memory, a hard disk, a magnetic disk, an optical disk, a tape, etc. The memory may include a read-only memory (“ROM”), a random-access memory (“RAM”), a flash memory, etc. 
     The term “film,” “layer,” “coating,” or “plate” may include rigid or flexible, self-supporting or free-standing film, layer, coating, or plate, which may be disposed on a supporting substrate or between substrates. The terms “film,” “layer,” “coating,” and “plate” may be interchangeable. The term “film plane” refers to a plane in the film, layer, coating, or plate that is perpendicular to the thickness direction. The film plane may be a plane in the volume of the film, layer, coating, or plate, or may be a surface plane of the film, layer, coating, or plate. The term “in-plane” as in, e.g., “in-plane orientation,” “in-plane direction,” “in-plane pitch,” etc., means that the orientation, direction, or pitch is within the film plane. The term “out-of-plane” as in, e.g., “out-of-plane direction,” “out-of-plane orientation,” or “out-of-plane pitch” etc., means that the orientation, direction, or pitch is not within a film plane (i.e., is non-parallel with a film plane). For example, the direction, orientation, or pitch may be along a line that is perpendicular to a film plane, or that forms an acute or obtuse angle with respect to the film plane. For example, an “in-plane” direction or orientation may refer to a direction or orientation within a surface plane, an “out-of-plane” direction or orientation may refer to a thickness direction or orientation non-parallel with (e.g., perpendicular to) the surface plane. 
     The wavelength ranges, spectra, or bands mentioned in the present disclosure are for illustrative purposes. The disclosed optical device, system, element, assembly, and method may be applied to a visible wavelength band, as well as other wavelength bands, such as an ultraviolet (“UV”) wavelength band, an infrared (“IR”) wavelength band, or a combination thereof. The term “substantially” or “primarily” used to modify an optical response action, such as “transmit,” “reflect,” “diffract,” “block” or the like that describes processing of a light means that a major portion, including all, of a light is transmitted, reflected, diffracted, or blocked, etc. The major portion may be a predetermined percentage (greater than 50%) of the entire light, such as 100%, 98%, 90%, 85%, 80%, etc., which may be determined based on specific application needs. 
       FIGS.  1 A and  1 B  illustrate x-z sectional views of a conventional light guide display system or assembly  100 . As shown in  FIG.  1 A , the system  100  may include a light source assembly  105 , a light guide  110 , and a controller  115 . The system  100  may also include an in-coupling grating  135  and an out-coupling grating  145  coupled to the light guide  110 . The light source assembly  105  may include a display panel  120  and a collimating lens  125 . The display panel  120  may include a plurality of pixels  121  arranged in an pixel array, in which neighboring pixels  121  may be separated by, e.g., a black matrix  122 . The black matrix  122  may be a matrix of light absorbing or blocking materials. For illustrative purposes,  FIG.  1 A  shows that the display panel  120  includes three pixels  121 . The respective pixel  121  may output a bundle of divergent rays  129   a ,  129   b , or  129   c , and the collimating lens  125  may convert the bundle of divergent rays  129   a ,  129   b , or  129   c  into a bundle of parallel rays  130   a ,  130   b , or  130   c . The respective bundles of parallel rays  130   a ,  130   b , and  130   c  may have different incidence angles relative to the light guide  110 . That is, the collimating lens  125  may transform or convert a linear distribution of the pixels  121  in the display panel  120  into an angular distribution of the pixels  121  at the input side of the light guide  110 . 
     The light guide  110  coupled with the in-coupling grating  135  and the out-coupling grating  145  may replicate the respective bundle of parallel rays  130   a ,  130   b , and  130   c  at the output side, to expand an effective pupil of the system  100 . For example, the in-coupling grating  135  may couple the bundle of parallel rays  130   a ,  130   b , or  130   c  as a bundle of parallel rays  131   a ,  131   b , or  131   c , which may propagate inside the light guide  110  via total internal reflection (“TIR”). The out-coupling grating  145  may couple the bundle of parallel rays  131   a ,  131   b , or  131   c  output of the light guide  110  as a plurality of bundles of parallel rays  132   a ,  132   b , or  132   c , which may propagate toward a plurality of exit pupils  157  positioned in an eye-box region  159  of the system  100 . 
     For a simplified illustration,  FIG.  1 B  shows the light propagation, from the display panel  120  to the exit pupil  257 , of a single ray  129   a ,  129   b , or  129   c  in each bundle output from the display panel  120 . Referring to  FIGS.  1 A and  1 B , the bundle of the rays  129   a ,  129   b , and  129   c  may be collectively referred to as an image light  129  output from the display panel  120 . The bundle of rays  130   a ,  130   b , and  130   c  may be collectively referred to as an input image light  130  of the light guide  110 . The bundle of rays  131   a ,  131   b , and  131   c  propagating inside the light guide  110  via TIR may be collectively referred to as an in-coupled image light  131 . The bundles of rays  132   a ,  132   b , and  132   c  propagating from the out-coupling grating  145  toward the same exit pupil  157  may be collectively referred to as an output image light  132  of the light guide  110 . 
     As shown in  FIG.  1 B , the display panel  120  may generate the image light  129  representing a virtual image  150  having a predetermined image size associated with a linear size of the display panel  120 . The collimating lens  125  may condition the image light  129  and output the input image light  130  having an input FOV  133  (e.g., a) toward the light guide  110 . The in-coupling grating  135  may couple the image light  130  into the light guide  110  as the in-coupled image light  131 . The out-coupling grating  145  may couple the in-coupled image light  131  incident onto different portions of the out-coupling grating  145  out of the light guide  110  as a plurality of output image lights  132 , each of which may have an output FOV  134  that may be substantially the same as the input FOV  133  (e.g., as represented by an angle α). Each output image light  132  may represent or form an image  155  that may be substantially the same as (or may have the same image content as) the virtual image  150  output from the display panel  120 . 
     The plurality of image lights  132  may propagate toward a plurality of exit pupils  157  positioned in the eye-box region  159  of the system  100 . The output image lights  132  may one-to-one correspond to the exit pupils  157 . The size of a single exit pupil  157  may be larger than and comparable with the size of the eye pupil  158 . The exit pupils  157  may be sufficiently spaced apart, such that when one of the exit pupils  157  substantially coincides with the position of the eye pupil  158 , the remaining one or more exit pupils  157  may be located beyond the position of the eye pupil  158  (e.g., falling outside of the eye  160 ). Thus, the eye  160  positioned at one of the exit pupils  157  may receive a single image light  132 . 
     The pixel density at an output side of a light guide display system (referred to as an output pixel density for discussion purposes) is defined as the number of pixels per degree the light guide display system presents to the eye  160 . The output pixel density of the light guide display system may be calculated by dividing the number of pixels in a horizontal display line by the horizontal output FOV. For example, when the display panel  120  and the output FOV  134  shown in  FIG.  1 B  are designed for a single eye  160 , the output pixel density (at the horizontal pupil expansion direction) of the system  100  may be equal to 3/α (unit: pixel per degree (“PPD”)). When the output FOV  134  of the system  100  is fixed, the output pixel density (PPD) of the system  100  may be limited by the pixel density (e.g., pixel per inch) of the display panel  120 . When the panel size of the display panel  120  is fixed, the pixel density (e.g., pixel per inch) of the display panel  120  may be limited by the pixel size or the pixel pitch. 
     In addition, a pixel density at the input side of the system  100  (referred to as an input pixel density for discussion purposes) may be calculated by dividing the number of pixels in a horizontal display line by the horizontal input FOV. For example, when the display panel  120  and the input FOV  133  shown in  FIG.  1 B  are designed for a single eye  160 , the input pixel density of the system  100  may be equal to 3/α (unit: PPD). Thus, in the conventional light guide display system  100 , the output pixel density may be substantially equal to the input pixel density. 
     Nowadays, many of the artificial reality applications require a high output pixel density and a large output FOV, e.g., the retinal resolution is about 60 pixels/degree. There is a tradeoff between the output pixel density and the output FOV. A larger output FOV may result in a lower output pixel density, and a smaller output FOV may result in a higher output pixel density. When the output FOV  134  of the system  100  is fixed, increasing the pixel density of the display panel  120  (pixel per inch) and reducing the pixel size (or pixel pitch) of the display panel  120  may increase the output pixel density of the system  100 . However, the form factor, the power consumption, and the cost of the conventional light guide display system  100  may also increase. In addition, there is a limitation on the smallest pixel size in the display panel  120 . 
     The present disclosure provides a light guide display system configured to provide an increased output pixel density.  FIG.  2 A  illustrates a schematic diagram of a light guide display system or assembly  200  for providing an increased pixel density (pixel per degree), according to an embodiment of the present disclosure. As shown in  FIG.  2 A , the light guide display system  200  may include a light source assembly  205 , a light guide  210 , and a controller  215 . The light guide  210  may be coupled with an in-coupling element  235  and an out-coupling element  245 . The light source assembly  205  may include a display element  220  and a collimating lens  225 . The display element  220  may include a display panel that includes a plurality of pixels  221  arranged in an pixel array, in which neighboring pixels  221  may be separated by, e.g., a black matrix  222 . For illustrative purposes,  FIG.  2 A  shows that the display element  220  includes three pixels  221 . 
     The light source assembly  205  may output an input image light  230  having an input FOV  233  (e.g., a) toward the light guide  210 . The light guide  210  coupled with the in-coupling element  235  and the out-coupling element  245  may direct the input image light  230  to an eye-box region  259  of the light guide display system  200  as a plurality of output image lights  232 . Each of the output image lights  232  may have an output FOV  234  (e.g., a) that may be substantially the same as the input FOV  233  (e.g., a). For example, the output image light  232 - 1  may have a first FOV  234 - 1 , and the output image light  232 - 2  may have a second FOV  234 - 2 . The FOVs  234 - 1  and  234 - 2  may have the same size, substantially overlap each other with a slight shift or rotation. The size of the FOV  234 - 1  and FOV  234 - 2  are referred to as the size of the FOV  234 . Each output FOV  234  ( 234 - 1  and  234 - 2 ) may include an axis of symmetry  236  ( 236 - 1  and  236 - 2 ) that equally divides the output FOV  234  ( 234 - 1  and  234 - 2 ) in a first half (e.g., α/2) and a second half (e.g., α/2). 
     The plurality of output image lights  232  may propagate toward a plurality of exit pupils  257  positioned in an eye-box region  259  of the light guide display system  200 . The exit pupil  257  may be a location where an eye pupil  258  of an eye  260  of a user is positioned in the eye-box region  259  to receive a virtual image output from the display element  220 . In some embodiments, the exit pupils  257  may be arranged in a one-dimensional (“1D”) or a two-dimensional (“2D”) array within the eye-box region  259 . The size of a single exit pupil  257  may be larger than and comparable with the size of the eye pupil  258 . The exit pupils  257  may be sufficiently spaced apart, such that when one of the exit pupils  257  substantially coincides with the position of the eye pupil  258 , the remaining one or more exit pupils  257  may be located beyond the position of the eye pupil  258  (e.g., falling outside of the eye  260 ). In some embodiments, all of the exit pupils  257  may be simultaneously available at the eye-box region  259 . In some embodiments, one or more of the exit pupils  257  (less than all of the exit pupils  257 ) may be simultaneously available at the eye-box region  259 , e.g., depending on the position of the eye pupil  258 . 
     In the embodiment shown in  FIG.  2 A , the plurality of output image lights  232  may not correspond to the plurality of exit pupils  257  on a one-to-one basis. Instead, at least two of the plurality of output image lights  232  (e.g.,  232 - 1  and  232 - 2 ) may propagate toward the same exit pupil  257 . The in-coupling element  235  and/or the out-coupling element  245  may be configured, such that for the output image light  232 - 1  and the output image light  232 - 2  propagating toward the same exit pupil  257 , an axis of symmetry  236 - 1  of the output FOV  234 - 1  of the output image light  232 - 1  may be unparallel with an axis of symmetry  236 - 2  of the output FOV  234 - 2  of the output image light  232 - 2 . Instead, the axis of symmetry  236 - 1  of the output FOV  234 - 1  may be rotated with respective to the axis of symmetry  236 - 2  of the output FOV  234 - 2  in a clockwise or counterclockwise direction. An angle representing the relative rotation between the axis of symmetry  236 - 1  and the axis of symmetry  236 - 2  may be smaller than the angular resolution of the eye  260  at the exit pupil  257 . Thus, the angular separation between the axis of symmetry  236 - 1  and the axis of symmetry  236 - 2  may not be observable by the eye  260 . 
     In some embodiments, an angle representing the relative rotation between the axis of symmetry  236 - 1  and the axis of symmetry  236 - 2  (or between the FOV  234 - 1  and FOV  234 - 2  of the same FOV size) may be smaller than a first predetermined percentage of the output FOV  234 . For example, the first predetermined percentage of the output FOV  234  may be 1%, 2%, 3%, 4%, 5%, 6%, 7%, 8%, 9%, 10%, 11%, 12%, 13%, 14%, 15%, 16%, 17%, 18%, 19%, or 20%, etc. In some embodiments, the relative rotation between the axis of symmetry  236 - 1  and the axis of symmetry  236 - 2  may be 0.5°, 1°, 2°, 3°, 4°, 5°, 6°, 7°, 8°, 9°, 10°, etc. In some embodiments, the relative rotation may be less than or equal to 3°, less than or equal to 5°, or less than or equal to 10°, etc. In some embodiments, the relative rotation may be within a range of 1°-10°, 1°-5°, 3°-5°, 0.5°-3°, 5°-10°, or any other range between 0.5° and 10°. In addition, the output FOV  234 - 1  of the output image light  232 - 1  and the output FOV  234 - 2  of the output image light  232 - 2  may have a substantially wide or large overlapping area (or overlapping FOV portion). The overlapping FOV portion may be greater than a predetermined overlapping percentage of the output FOV  234 , and less than the full output FOV  234 . For example, the predetermined overlapping percentage between the output FOVs  234 - 1  and  234 - 2  may be 80%, 85%, 90%, or 95%, etc., of the FOV  234 . For example, in some embodiments, the FOVs  234 - 1  and  234 - 2  may overlap with one another with an overlapping portion that is 80%-95% of the FOV  234 , 80%-90% of the FOV  234 , 80%-85% of the FOV  234 , 85%-90% of the FOV  234 , 85%-95% of the FOV  234 , 90%-95% of the FOV  234 , etc. 
     Compared to the conventional light guided display system  100  shown in  FIGS.  1 A and  1 B , the light guided display system  200  may provide an increased (e.g., doubled) number of image lights  232  with slightly shifted (e.g., tilted) output FOVs  234  propagating through the same exit pupil  257 . Thus, the output pixel density of the light guide display system  200  may be increased (e.g., doubled) as compared to the output pixel density of the conventional light guide display system  100  shown in  FIGS.  1 A and  1 B . The output pixel density of the light guide display system  200  may be increased (e.g., doubled) as compared to the input pixel density at the input side of the light guide  210 . 
     The display element  220  may include a display panel, such as a liquid crystal display (“LCD”) panel, a liquid-crystal-on-silicon (“LCoS”) display panel, an organic light-emitting diode (“OLED”) display panel, a micro light-emitting diode (“micro-LED”) display panel, a laser scanning display panel, a digital light processing (“DLP”) display panel, or a combination thereof. In some embodiments, the display element  220  may include a self-emissive panel, such as an OLED display panel or a micro-LED display panel. In some embodiments, the display element  220  may include a display panel that is illuminated by an external source, such as an LCD panel, an LCoS display panel, or a DLP display panel. Examples of an external source may include a laser diode, a vertical cavity surface emitting laser, a light emitting diode, or a combination thereof. The display element  220  may output an image light  229  toward the collimating lens  225 . The image light  229  may represent a virtual image having a predetermined image size. 
     The collimating lens  225  may be configured to condition the image light  229  from the display element  220  and output the input image light  230  having the input FOV  233  toward the light guide  210 . The collimating lens  225  may transform a linear distribution of pixels in the virtual image having the predetermined image size into an angular distribution of pixels in the image light  230  having the input FOV  233 . The input FOV  233  may correspond to an angular region bounded by the leftmost ray and the rightmost ray of the image light  230 . In some embodiments, the light source assembly  205  may include one or more addition optical components configured to condition the image light  229  output from the display element  220 . 
     In some embodiments, the in-coupling element  235  may be disposed at a first portion (e.g., an input portion) of the light guide  210 . The in-coupling element  235  may couple the image light  230  into a total internal reflection (“TIR”) path inside the light guide  210  as one or more in-coupled image lights  231  (or TIR propagating image lights  231 ). The one or more in-coupled image lights  231  may have different TIR propagating angles inside the light guide  210 . When a light propagates within the light guide through TIR, the angle formed by the TIR path of a light/ray and the normal of the inner surface of the light guide (or the incidence angle of the light/ray incident onto the inner surface of the light guide) may be referred to as a TIR guided angle or a TIR propagation angle. For discussion purposes,  FIG.  2 A  shows the in-coupling element  235  couples the image light  230  into the light guide  210  as a single in-coupled image light  231 . The in-coupled image light  231  may propagate inside the light guide  210  through TIR to the out-coupling element  245 . For example, the out-coupling element  245  may be disposed at a second portion (e.g., an output portion) of the light guide  210 . The first portion and the second portion may be located at different locations of the light guide  210 . The out-coupling element  245  may be configured to couple the TIR propagating image light  231  out of the light guide  210  as the plurality of output image lights  232  toward the eye-box region  259 . In some embodiments, the out-coupling element  245  may consecutively couple the TIR propagating image light  231 , which is incident onto the different positions of the out-coupling element  245 , out of the light guide  210  at different positions of the out-coupling element  245 . Thus, the out-coupling element  245  may replicate the image light  230  at the output side of the light guide  210 , to expand an effective pupil of the light guide display system  200 . In some embodiments, the light guide  210  may also receive a light  255  from a real-world environment, and may combine the light  255  with the output image light  232 , and deliver the combined light to the eye  260 . 
     In some embodiments, each of the in-coupling element  235  and the out-coupling element  245  may be formed or disposed at (e.g., affixed to) a first surface  210 - 1  or a second surface  210 - 2  of the light guide  210 . In some embodiments, each of the in-coupling element  235  and the out-coupling element  245  may be integrally formed as a part of the light guide  210 , or may be a separate element coupled to the light guide  210 . In some embodiments, the in-coupling element  235  and/or the out-coupling element  245  may include one or more diffraction gratings, one or more cascaded reflectors, one or more prismatic surface elements, and/or an array of holographic reflectors, or any combination thereof. 
     The light guide  210  may include one or more materials configured to facilitate the TIR of the TIR propagating image light  231 . The light guide  210  may include, for example, a plastic, a glass, and/or polymers. The light guide  210  may have a relatively small form factor. In some embodiments, the light guide display system  200  may include additional elements configured to redirect, fold, and/or expand the TIR propagating image light  231 . For example, as shown in  FIG.  2 A , one or more redirecting/folding elements  240  may be coupled to the light guide  210  to direct the TIR propagating image light  231  propagating inside the light guide  210  in a predetermined direction. In some embodiments, the redirecting element  240  and the out-coupling element  245  may be disposed at a same surface or at different surfaces of the light guide  210 . In some embodiments, the redirecting element  240  may be separately formed and disposed at (e.g., affixed to) the first surface  210 - 1  or the second surface  210 - 2 , or may be integrally formed as a part of the light guide  210 . In some embodiments, the redirecting element  240  may be configured to expand the TIR propagating image light  231  in a first direction (e.g., a y-axis direction in  FIG.  2 A ). The redirecting element  240  may redirect the expanded TIR propagating image light  231  to the out-coupling element  245 . The out-coupling element  245  may couple the TIR propagating image light  231  out of the light guide  210 , and expand the TIR propagating image light  231  in a second direction (e.g., an x-axis direction in  FIG.  2 A ). Thus, a two-dimensional (“2D”) expansion of the image light  230  may be provided at the output side of the light guide  210 . In some embodiments, multiple functions, e.g., out-coupling, redirecting, folding, and/or expanding the image light  230  may be combined into a single element, e.g. the out-coupling element  245 , and hence, the redirecting element  240  may be omitted. For example, the out-coupling element  245  itself may provide a 2D expansion of the image light  230  at the output side of the light guide  210 . 
     Although the light guide  210 , the in-coupling element  235 , and the out-coupling element  245  are shown as having flat surfaces for illustrative purposes, any of the light guides, in-coupling elements, out-coupling elements, and redirecting elements disclosed herein may include one or more curved surfaces or may have curved shapes. The controller  215  may be communicatively coupled with the light source assembly  205 , and may control the operations of the light source assembly  205  to generate an input image light. The controller  215  may also control the operation state (e.g., a diffraction state or a non-diffraction state) of the in-coupling element  235 , the out-coupling element  245 , and/or the redirecting element  240 . The controller  215  may include a processor or processing unit  201 . The controller  215  may include a storage device  202 . The storage device  202  may be a non-transitory computer-readable medium, such as a memory, a hard disk, etc., for storing data, information, and/or computer-executable program instructions or codes. 
     In some embodiments, the light guided display system  200  may include a plurality of light guides  210  disposed in a stacked configuration (not shown in  FIG.  2 A ). At least one (e.g., each) of the plurality of light guides  210  coupled with one or more diffractive elements (e.g., in-coupling element, out-coupling element, and/or redirecting or folding element) may provide an increased pixel density at the output side. In some embodiments, the plurality of light guides  210  in the stacked configuration may be configured to output a polychromatic image light (e.g., a full-color image light including components of multiple colors). 
     In some embodiments, the light guided display system  200  may include one or more light source assemblies  205  coupled to the one or more light guides  210 . In some embodiments, at least one (e.g., each) of the light source assemblies  205  may be configured to emit a monochromatic image light of a specific wavelength band corresponding to a primary color (e.g., red, green, or blue) and an input FOV. In some embodiments, the light guided display system  200  may include three light guides  210  to deliver a component color image (e.g., a primary color image), e.g., red, green, and blue lights, respectively, in any suitable order, or simultaneously. At least one (e.g., each) of the three light guides  210  may be coupled with or include one or more diffractive elements (e.g., in-coupling element, out-coupling element, and/or redirecting element). In some embodiments, the light guide display system  200  may include two light guides configured to deliver component color images (e.g., primary color images) by in-coupling and subsequently out-coupling, e.g., a combination of red and green lights, and a combination of green and blue lights, respectively, in any suitable order or simultaneously. 
     For discussion purposes, in the following descriptions, the light guide display system  200  is presumed to include the in-coupling element  235  and the out-coupling element  245  without the redirecting element  240 . In some embodiments, at least one of the in-coupling element  235  or the out-coupling element  245  may be a diffractive element that includes one or more diffraction gratings. For discussion purposes, a diffraction grating included in the in-coupling element  235  may be referred to as an in-coupling grating  235 , and a diffraction grating included in the out-coupling element  245  may be referred to as an out-coupling grating  245 . 
     In some embodiments, at least one of the in-coupling grating  235  or the out-coupling grating  245  may be an active grating. In some embodiments, the active grating may be controlled or switched, e.g., by the controller  215 , between operating in a diffraction state to diffract an incident light, and operating in a non-diffraction state to transmit the incident light with substantially zero or negligible diffraction. In some embodiments, the active grating that operates in the diffraction state may provide a fixed diffraction angle for an incident light with a fixed incidence angle. In some embodiments, the active grating that operates in the diffraction state may provide a tunable diffraction angle for the incident light with a fixed incidence angle. For example, the active grating may operate in different diffraction states when driven by different driving voltages, thereby diffracting the incident light with the fixed incidence angle at different diffraction angles. In some embodiments, when the driving voltage applied to the active grating is changed, the grating period of the active grating may be changed, such that the active grating may diffract the incident light with the fixed incidence angle to different diffraction angles. In some embodiments, when the driving voltage applied to the active grating is changed, a modulation of the refractive index of the active grating may be changed, such that the active grating may diffract the incident light with the fixed incidence angle to different diffraction angles. 
     The active grating may be polarization sensitive (or polarization selective) or polarization insensitive (or polarization non-selective). The active grating may be a reflective grating or a transmissive grating. The active grating may be fabricated based on any suitable materials. In some embodiments, the active grating fabricated based on active liquid crystals (“LCs”) may include active LC molecules, orientations of which may be changeable by the external field (e.g., external electric field). Examples of active gratings may include, but not be limited to, holographic polymer-dispersed liquid crystal (“H-PDLC”) gratings, surface relief gratings provided (e.g., filled) with active LCs, Pancharatnam-Berry phase (“PBP”) gratings based on active LCs, polarization volume holograms (“PVHs”) based on active LCs, etc. 
     In the following, exemplary light guide display systems for providing an increased output pixel density will be described. For illustrative purposes, various light guide display systems for one-dimensional (“1D”) pupil expansion and output pixel density increase (e.g., in an x-axis direction) are used as examples to explain the principle of increasing the output pixel density, such as those shown in  FIGS.  2 A- 5 C . In some embodiments, two-dimensional (“2D”) pupil expansion and output pixel density increase (e.g., in both x-axis direction and y-axis direction) may be achieved by introducing an additional diffractive optical element (e.g., a folding or redirecting element) that folds the in-coupled image light by 90° toward the out-coupling element. In some embodiments, the out-coupling elements shown in the  FIGS.  2 A- 5 C  may include the folding function, and the redirecting element may be omitted. Thus, although 1D pupil expansion and output pixel density increase (e.g., in an x-axis direction) are used to explain the principle of the embodiments shown in  FIGS.  2 A- 5 C , the light guide display systems included in  FIGS.  2 A- 5 C  can provide 2D pupil expansion and output pixel density increase. 
     In some embodiments, when the in-coupled image light  231  is a polarized light, the polarization of the in-coupled image light  231  may change while propagating inside the one or more light guides  210 . A retardation film (e.g., a polarization correction film) may be disposed adjacent or on the respective light guide to compensate for the change in the polarization, thereby preserving the polarization of the in-coupled image light  231  when the in-coupled image light  231  propagates inside the one or more light guide  210 . For discussion purposes, in  FIGS.  2 A- 5 C , when the in-coupled image light (or a TIR propagating light) is a polarized light, the polarization of the in-coupled image light (or the TIR propagating light) is presumed to be unaffected while propagating inside the one or more light guides. 
     In the embodiment shown in  FIG.  2 A , the out-coupling grating  245  may be an active grating that provides a tunable diffraction angle for the in-coupled image light  231 . For example, the controller  215  may change the driving voltage of the out-coupling grating  245 , such that the out-coupling grating  245  operates in different diffraction states to provide different diffraction angles to the in-coupled image light  231 . The in-coupling grating  235  may be an active grating or a passive grating. In some embodiments, a display frame of the virtual image output from the display element  220  may be divided into a plurality of (e.g., two) sub-frames (sub-frames being exemplary two time periods). During each of a first sub-frame (an example of a first time period) and a second sub-frame (an example of a second time period), the controller  215  may control the light source assembly  205  to output the input image light  230  with the input FOV  233 . The in-coupling grating  235  may be configured to couple the image light  230  into the light guide  210  as the in-coupled image light  231 . During the first sub-frame and the second sub-frame, the control  215  may control the driving voltages of the out-coupling grating  245 , such that the out-coupling grating  245  operates in different diffraction states to diffract the same in-coupled image light  231  at different diffraction angles. For discussion purposes,  FIG.  2 A  shows that the in-coupled image light  231  includes three rays. A central ray among the three rays is used as an example. During the first sub-frame and the second sub-frame, the out-coupling grating  245  may diffract the same central ray of the in-coupled image light  231  at two different diffraction angles. 
     For example, during the first sub-frame, the control  215  may control the driving voltage of the out-coupling grating  245  to operate in a first diffraction state to couple, via diffraction, the in-coupled image light  231  out of the light guide  210  as a plurality of first output image lights  232 - 1  towards the plurality of exit pupils  257 . The rays of the first output image lights  232 - 1  are represented by solid lines. The plurality of first output image lights  232 - 1  may correspond to the plurality of exit pupils  257  on a one-to-one basis. Each of the first output image lights  232 - 1  may have the output FOV  234 - 1  that may be substantially the same as the input FOV  233 . The first diffraction state of the out-coupling grating  245  may be configured (e.g., by configuring the grating period or the modulation of the refractive index of the out-coupling grating  245 ), such that the out-coupling grating  245  may diffract the in-coupled image light  231  as the first output image light  232 - 1 , with the axis of symmetry  236 - 1  of the output FOV  234 - 1  perpendicular to the surface of the light guide  210 . That is, the axis of symmetry  236 - 1  of the output FOV  234 - 1  of the first output image light  232 - 1  may be parallel with the surface normal of the light guide  210 . 
     During the second sub-frame, the control  215  may control the driving voltage of the out-coupling grating  245  to be a second driving voltage different from the first driving voltage, such that the out-coupling grating  245  operates in a second diffraction state to couple, via diffraction, the in-coupled image light  231  out of the light guide  210  as a plurality of second output image lights  232 - 2  towards the plurality of exit pupils  257 . The rays of the second output image lights  232 - 2  are represented by dashed lines. The plurality of second output image lights  232 - 2  may correspond to the plurality of exit pupils  257  on a one-to-one basis. Each of the second output image lights  232 - 2  may have the output FOV  234 - 2  that may be substantially the same as the input FOV  233 . The second diffraction state of the out-coupling grating  245  may be configured (e.g., by configuring the grating period or the modulation of the refractive index of the out-coupling grating  245 ), such that the out-coupling grating  245  may diffract the in-coupled image light  231  as the second output image light  232 - 2 , with the axis of symmetry  236 - 2  of the output FOV  234 - 2  being unparallel with the surface normal of the light guide  210 . 
     Referring to  FIG.  2 A , the first and second diffraction states of the out-coupling grating  245  may be configured (e.g., by configuring the grating periods or the modulations of the refractive index of the out-coupling grating  245 ), such that for the first output image light  232 - 1  and the second output image light  232 - 2  propagating toward the same exit pupil  257 , the axis of symmetry  236 - 2  of the output FOV  234 - 2  of the second output image light  232 - 2  may be rotated with respective to the axis of symmetry  236 - 1  of the output FOV  234 - 1  of the first output image light  232 - 1  in a clockwise or counterclockwise direction. For discussion purposes,  FIG.  2 A  shows that the axis of symmetry  236 - 2  of the output FOV  234 - 2  is rotated with respective to the axis of symmetry  236 - 1  of the output FOV  234 - 1  in the counter-clockwise direction. 
     For the first output image light  232 - 1  and the second output image light  232 - 2  propagating toward the same exit pupil  257 , an angle representing the relative rotation between the axis of symmetry  236 - 1  and the axis of symmetry  236 - 2  may be smaller than the angular resolution of the eye  260  at the exit pupil  257 . Thus, the angular separation between the axis of symmetry  236 - 1  and the axis of symmetry  236 - 2  may not be observable by the eye  260 . In some embodiments, an angle representing the relative rotation between the axis of symmetry  236 - 1  and the axis of symmetry  236 - 2  may be smaller than the first predetermined percentage of the output FOV  234 . The output FOV  234 - 1  of the first output image light  232 - 1  and the output FOV  234 - 2  of the second output image light  232 - 2  may have a substantially wide or large overlapping area (or overlapping FOV portion). In some embodiments, an angle representing the overlapping FOV portion may be greater than the second predetermined percentage of the output FOV  234 , and smaller than the full output FOV  234 . 
     Compared to the conventional light guided display system  100  shown in  FIGS.  1 A and  1 B , the light guided display system  200  may provide an increased (e.g., doubled) number of image lights  232  with slightly shifted (e.g., titled) output FOVs  234  propagating through the same exit pupil  257 . Thus, the output pixel density of the light guide display system  200  may be increased (e.g., doubled) as compared to the output pixel density of the conventional light guide display system  100  shown in  FIGS.  1 A and  1 B . The output pixel density of the light guide display system  200  may be increased (e.g., doubled) as compared to the input pixel density at the input side of the light guide  210 . 
       FIG.  2 B  illustrates a schematic diagram of a light guide display system or assembly  250  for providing an increased output pixel density, according to an embodiment of the present disclosure. The light guide display system  250  may include elements that are similar to or the same as those included in the light guide display system  200  shown in  FIG.  2 A . Descriptions of the same or similar elements or features can refer to the above corresponding descriptions, including those rendered in connection with  FIG.  2 A . 
     In the embodiment shown in  FIG.  2 B , the in-coupling grating  235  may be an active grating configured to provide a tunable diffraction angle for the input image light  230 . For example, the controller  215  may control the driving voltage of the in-coupling grating  235  to be different, such that the in-coupling grating  235  may operate in different diffraction states to provide different diffraction angles for the same input image light  230 . The out-coupling grating  245  may be an active grating or a passive grating. In some embodiments, a display frame of the virtual image output from the display element  220  may be divided into a plurality of (e.g., two) sub-frames (sub-frames being exemplary two time periods). During each of a first sub-frame and a second sub-frame, the controller  215  may control the light source assembly  205  to output the input image light  230  with the input FOV  233 . During the first sub-frame and the second sub-frame, the control  215  may control the driving voltages of the in-coupling grating  235  to be different, such that the in-coupling grating  235  operates in different diffraction states to diffract the same input image light  230  at different diffraction angles. For discussion purposes,  FIG.  2 B  shows that the input image light  230  includes three rays. A central ray among the three rays is used as an example. During the first sub-frame and the second sub-frame, the in-coupling grating  235  may diffract the same central ray of the input image light  230  at two different diffraction angles. 
     For example, during the first sub-frame, the control  215  may control the driving voltage of the in-coupling grating  235  to be a first driving voltage, such that the in-coupling grating  235  operates in a first diffraction state. The in-coupling grating  235  may couple, via diffraction, the input image light  230  into the light guide  210  as a first in-coupled image light  231 - 1 . The rays of the first in-coupled image light  231 - 1  are represented by solid lines. The in-coupling grating  235  may diffract the central ray of the input image light  230  as a central ray of the first in-coupled image light  231 - 1  with a first TIR propagating angle inside the light guide  210 . 
     The out-coupling grating  245  may couple, via diffraction, the first in-coupled image light  231 - 1  out of the light guide  210  as a plurality of first output image lights  252 - 1  towards the plurality of exit pupils  257 . The plurality of first output image lights  252 - 1  may correspond to the plurality of exit pupils  257  on a one-to-one basis. Each of the first output image lights  252 - 1  may have an output FOV  254 - 1  that may be substantially the same as the input FOV  233 . The first diffraction state of the in-coupling grating  235  may be configured (e.g., by configuring the grating period or the modulation of the refractive index of the in-coupling grating  235 ), such that the out-coupling grating  245  may diffract the first in-coupled image light  231 - 1  as the first output image light  252 - 1 , with an axis of symmetry  256 - 1  of the output FOV  254 - 1  perpendicular to the surface of the light guide  210 . That is, the axis of symmetry  256 - 1  of the output FOV  254 - 1  of the first output image light  252 - 1  may be parallel with the surface normal of the light guide  210 . 
     During the second sub-frame, the control  215  may control the driving voltage of the in-coupling grating  235  to be a second driving voltage, such that the in-coupling grating  235  operates in a second diffraction state. The in-coupling grating  235  may couple, via diffraction, the input image light  230  into the light guide  210  as a second in-coupled image light  231 - 2 . The rays of the second in-coupled image light  231 - 2  are represented by dashed lines. The in-coupling grating  235  may diffract the central ray of the input image light  230  as a central ray of the second in-coupled image light  231 - 2  with a second TIR propagating angle inside the light guide  210 . The second TIR propagating angle may be different from the first TIR propagating angle. The out-coupling grating  245  may couple, via diffraction, the second in-coupled image light  231 - 2  out of the light guide  210  as a plurality of second output image lights  252 - 2  towards the plurality of exit pupils  257 . The plurality of second output image lights  252 - 2  may correspond to the plurality of exit pupils  257  on a one-to-one basis. Each of the second output image lights  252 - 2  may have an output FOV  254 - 2  that may be substantially the same as the input FOV  233 . The second diffraction state of the in-coupling grating  235  may be configured (e.g., by configuring the grating period or the modulation of the refractive index of the in-coupling grating  235 ), such that the out-coupling grating  245  may diffract the second in-coupled image light  231 - 2  as the second output image light  252 - 2 , with an axis of symmetry  256 - 2  of the output FOV  254 - 2  being unparallel with the surface normal of the light guide  210 . 
     Referring to  FIG.  2 B , the first and second diffraction states of the in-coupling grating  235  may be configured (e.g., by configuring the grating periods or the modulations of the refractive index of the in-coupling grating  235 ), such that for the first output image light  252 - 1  and the second output image light  252 - 2  propagating toward the same exit pupil  257 , the axis of symmetry  256 - 2  of the output FOV  254 - 2  of the second output image light  252 - 2  may be rotated with respective to the axis of symmetry  256 - 1  of the output FOV  254 - 1  of the first output image light  252 - 1  in a clockwise or counterclockwise direction. For discussion purposes,  FIG.  2 B  shows that the axis of symmetry  256 - 2  of the output FOV  254 - 2  is rotated with respective to the axis of symmetry  256 - 1  of the output FOV  254 - 1  in the counter-clockwise direction. In addition, the output image lights  252 - 1  and  252 - 2  may be relatively shifted in the x-axis direction. 
     For the first output image light  252 - 1  and the second output image light  252 - 2  propagating toward the same exit pupil  257 , an angle representing the relative rotation between the axis of symmetry  256 - 1  and the axis of symmetry  256 - 2  may be smaller than the angular resolution of the eye  260  at the exit pupil  257 . Thus, the angular separation between the axis of symmetry  256 - 1  and the axis of symmetry  256 - 2  may not be observable by the eye  260 . In some embodiments, an angle representing the relative rotation between the axis of symmetry  256 - 1  and the axis of symmetry  256 - 2  may be smaller than the first predetermined percentage of the output FOV  254 - 1  or  254 - 2 . The output FOV  254 - 1  of the first output image light  252 - 1  and the output FOV  254 - 2  of the second output image light  252 - 2  may have a substantially wide or large overlapping area (or overlapping FOV portion). In some embodiments, an angle representing the overlapping FOV portion may be greater than the second predetermined percentage of the output FOV  254 - 1  or  254 - 2 , and smaller than the full output FOV  254 - 1  or  254 - 2 . 
     Compared to the conventional light guided display system  100  shown in  FIGS.  1 A and  1 B , the light guided display system  250  may provide an increased (e.g., doubled) number of image lights  252 - 1  and  252 - 2  with slightly shifted (e.g., tilted) output FOVs  254 - 1  and  254 - 2  propagating through the same exit pupil  257 . Thus, the output pixel density of the light guide display system  250  may be increased (e.g., doubled) as compared to the output pixel density of the conventional light guide display system  100  shown in  FIGS.  1 A and  1 B . The output pixel density of the light guide display system  250  may be increased (e.g., doubled) as compared to the input pixel density at the input side of the light guide  210 . 
       FIGS.  2 C- 2 E  illustrate x-z sectional views of a light guide display system or assembly  270  for providing an increased pixel density (pixel per degree), according to an embodiment of the present disclosure. The light guide display system or assembly  270  may include elements that are similar to or the same as those included in the light guide display system  200  shown in  FIG.  2 A , or the light guide display system  250  shown in  FIG.  2 B . Descriptions of the same or similar elements or features can refer to the above corresponding descriptions, including those rendered in connection with  FIG.  2 A or  2 B . 
     In the embodiment shown in  FIGS.  2 C- 2 E , the in-coupling grating  235  may be an active grating that provides a tunable diffraction angle for the input image light  230 . For example, the controller  215  may control the driving voltages of the in-coupling grating  235 , such that the in-coupling grating  235  may operate in different diffraction states to provide different diffraction angles. The out-coupling grating  245  may be an active grating that provides a tunable diffraction angle for the in-coupled image light  231 - 1  or  231 - 2 . For example, the controller  215  may control the driving voltages of the out-coupling grating  245 , such that the out-coupling grating  245  may operate in different diffraction states to provide different diffraction angles. In some embodiments, a display frame of the virtual image output from the display element  220  may be divided into a plurality of (e.g., four) sub-frames (sub-frames being exemplary four time periods). During each of a first sub-frame, a second sub-frame, a third sub-frame, and a fourth sub-frame, the controller  215  may control the light source assembly  205  to output the input image light  230  with the input FOV  233 . 
       FIG.  2 C  illustrates an x-z sectional views of the light guide display system  270  during a first sub-frame and a second sub-frame. As shown in  FIG.  2 C , during the first sub-frame and the second sub-frame, the control  215  may control the driving voltage of the in-coupling grating  235  to be a same first driving voltage, such that the in-coupling grating  235  may operate in a same first diffraction state. During the first sub-frame and the second sub-frame, the in-coupling grating  235  may diffract the input image light  230  to the same diffraction angle. The in-coupling grating  235  may couple, via diffraction, the input image light  230  into the light guide  210  as a first in-coupled image light  231 - 1 . For example, during the first sub-frame and the second sub-frame, the in-coupling grating  235  may diffract the central ray of the input image light  230  as a central ray of the first in-coupled image light  231 - 1  with a first TIR propagating angle inside the light guide  210 . 
     During the first sub-frame and the second sub-frame, the control  215  may control the out-coupling grating  245  to operate in different diffraction states to diffract the first in-coupled image light  231 - 1  at different diffraction angles. For example, during the first sub-frame, the control  215  may control the driving voltage of the out-coupling grating  245  to be a first driving voltage, such that the out-coupling grating  245  may operate in a first diffraction state. The out-coupling grating  245  may couple, via diffraction, the first in-coupled image light  231 - 1  out of the light guide  210  as a plurality of first output image lights  272 - 1  towards the plurality of exit pupils  257 . The plurality of first output image lights  272 - 1  may correspond to the plurality of exit pupils  257  on a one-to-one basis. Each of the first output image lights  272 - 1  may have an output FOV  274 - 1  that may be substantially the same as the input FOV  233 . The first diffraction state of the in-coupling grating  235  may be configured (e.g., by configuring the grating period or the modulation of the refractive index of the in-coupling grating  235 ), and the first diffraction state of the out-coupling grating  245  may be configured (e.g., by configuring the grating period or the modulation of the refractive index of the out-coupling grating  245 ), such that the out-coupling grating  245  may diffract the first in-coupled image light  231 - 1  as the first output image light  272 - 1 , with an axis of symmetry  276 - 1  of the output FOV  274 - 1  being perpendicular to the surface of the light guide  210 . That is, the axis of symmetry  276 - 1  of the output FOV  274 - 1  of the first output image light  272 - 1  may be parallel with the surface normal of the light guide  210 . 
     During the second sub-frame, the control  215  may control the driving voltage of the out-coupling grating  245  to be a second driving voltage, such that the out-coupling grating  245  may operate in a second diffraction state. The out-coupling grating  245  may couple, via diffraction, the first in-coupled image light  231 - 1  out of the light guide  210  as a plurality of second output image lights  272 - 2  towards the plurality of exit pupils  257 . The plurality of second output image lights  272 - 2  may correspond to the plurality of exit pupils  257  on a one-to-one basis. Each of the second output image lights  272 - 2  may have an output FOV  274 - 2  that may be substantially the same as the input FOV  233 . The first diffraction state of the in-coupling grating  235  may be configured (e.g., by configuring the grating period or the modulation of the refractive index of the in-coupling grating  235 ), and the second diffraction state of the out-coupling grating  245  may be configured (e.g., by configuring the grating period or the modulation of the refractive index of the out-coupling grating  245 ), such that the out-coupling grating  245  may diffract the first in-coupled image light  231 - 1  as the second output image light  272 - 2 , with an axis of symmetry  276 - 2  of the output FOV  274 - 2  being unparallel with the surface normal of the light guide  210 . 
     For the first output image light  272 - 1  and the second output image light  272 - 2  propagating toward the same exit pupil  257 , the axis of symmetry  276 - 2  of the output FOV  274 - 2  of the second output image light  272 - 2  may be rotated with respective to the axis of symmetry  276 - 1  of the output FOV  274 - 1  of the first output image light  272 - 1  in a clockwise or counterclockwise direction. For discussion purposes,  FIG.  2 C  shows that the axis of symmetry  276 - 2  of the output FOV  274 - 2  is rotated with respective to the axis of symmetry  276 - 1  of the output FOV  274 - 1  in the counter-clockwise direction. 
     For the first output image light  272 - 1  and the second output image light  272 - 2  propagating toward the same exit pupil  257 , an angle representing the relative rotation between the axis of symmetry  276 - 1  and the axis of symmetry  276 - 2  may be smaller than the angular resolution of the eye  260  at the exit pupil  257 . Thus, the angular separation between the axis of symmetry  276 - 1  and the axis of symmetry  276 - 2  may not be observable by the eye  260 . In some embodiments, an angle representing the relative rotation between the axis of symmetry  276 - 1  and the axis of symmetry  276 - 2  may be smaller than the first predetermined percentage of the output FOV  274 - 1  or  274 - 2 . The output FOV  274 - 1  of the first output image light  272 - 1  and the output FOV  274 - 2  of the second output image light  272 - 2  may have a substantially wide or large overlapping area (or overlapping FOV portion). In some embodiments, an angle representing the overlapping FOV portion may be greater than the second predetermined percentage of the output FOV  274 - 1  or  274 - 2 , and smaller than the full output FOV  274 - 1  or  274 - 2 . 
       FIG.  2 D  illustrates an x-z sectional views of the light guide display system  270  during a third sub-frame and a fourth sub-frame. As shown in  FIG.  2 D , during the third sub-frame and the fourth sub-frame, the control  215  may control the in-coupling grating  235  to operate in the same diffraction state. For example, during the third sub-frame and the fourth sub-frame, the control  215  may control the driving voltage of the in-coupling grating  235  to be a same second driving voltage different from the first driving voltage, such that the in-coupling grating  235  may operate in a second diffraction state to diffract the input image light  230  to the same diffraction angle. The in-coupling grating  235  may couple, via diffraction, the input image light  230  into the light guide  210  as a second in-coupled image light  231 - 2 . For example, during the third sub-frame and the fourth sub-frame, the in-coupling grating  235  may diffract the central ray of the input image light  230  as a central ray of the second in-coupled image light  231 - 2  with a second TIR propagating angle inside the light guide  210 . The second TIR propagating angle may be different from the first TIR propagating angle. 
     During the third sub-frame and the fourth sub-frame, the control  215  may control the out-coupling grating  245  to operate in different diffraction states to diffract the second in-coupled image light  231 - 2  at different diffraction angles. For example, during the third sub-frame, the control  215  may control the driving voltage of the out-coupling grating  245  to be a third driving voltage, such that the out-coupling grating  245  may operate in a third diffraction state. The out-coupling grating  245  may couple, via diffraction, the second in-coupled image light  231 - 2  out of the light guide  210  as a plurality of third output image lights  272 - 3  towards the plurality of exit pupils  257 . The plurality of third output image lights  272 - 3  may correspond to the plurality of exit pupils  257  on a one-to-one basis. Each of the third output image lights  272 - 3  may have an output FOV  274 - 3  that may be substantially the same as the input FOV  233 . The second diffraction state of the in-coupling grating  235  may be configured (e.g., by configuring the grating period or the modulation of the refractive index of the in-coupling grating  235 ), and the third diffraction state of the out-coupling grating  245  may be configured (e.g., by configuring the grating period or the modulation of the refractive index of the out-coupling grating  245 ), such that the out-coupling grating  245  may diffract the second in-coupled image light  231 - 2  as the third output image light  272 - 3 , with an axis of symmetry  276 - 3  of the output FOV  274 - 3  being unparallel with the surface normal of the light guide  210 . 
     Referring to  FIGS.  2 C and  2 D , for the first output image light  272 - 1 , for the second output image light  272 - 2 , and the third output image light  272 - 3  propagating toward the same exit pupil  257 , the axis of symmetry  276 - 3  of the output FOV  274 - 3  of the third output image light  272 - 3  may be rotated with respective to each of the axis of symmetry  276 - 1  of the output FOV  274 - 1  of the first output image light  272 - 1  and the axis of symmetry  276 - 2  of the output FOV  274 - 2  of the second output image light  272 - 2  in a clockwise or counterclockwise direction. For discussion purposes,  FIGS.  2 C and  2 D  show that the axis of symmetry  276 - 3  is rotated with respective to each of the axis of symmetry  276 - 1  (or the surface normal of the light guide  210 ) and the axis of symmetry  276 - 2  in the counter-clockwise direction. 
     For the first output image light  272 - 1 , the second output image light  272 - 2 , and the third output image light  272 - 3  propagating toward the same exit pupil  257 , an angle representing the relative rotation between the axis of symmetry  276 - 3  and each of the axis of symmetry  276 - 1  and the axis of symmetry  276 - 2  may be smaller than the angular resolution of the eye  260  at the exit pupil  257 . Thus, the angular separation between the axis of symmetry  276 - 3  and each of the axis of symmetry  276 - 1  and the axis of symmetry  276 - 2  may not be observable by the eye  260 . 
     In some embodiments, an angle representing the relative rotation between the axis of symmetry  276 - 3  and each of the axis of symmetry  276 - 1  and the axis of symmetry  276 - 2  may be smaller than the first predetermined percentage of the output FOV  274 - 3  (or  274 - 1 , or  274 - 2 ). The output FOV  274 - 3  and the output FOV  274 - 1  (or  274 - 2 ) may have a substantially wide or large overlapping area (or overlapping FOV portion). In some embodiments, an angle representing the overlapping FOV portion may be greater than the second predetermined percentage of the output FOV  274 - 3  (or  274 - 1 , or  274 - 2 ), and smaller than the full output FOV  274 - 3  (or  274 - 1 , or  274 - 2 ). 
     Referring back to  FIG.  2 D , during the fourth sub-frame, the control  215  may control the driving voltage of the out-coupling grating  245  to be a fourth driving voltage, such that the out-coupling grating  245  may operate in a fourth diffraction state. The out-coupling grating  245  may couple, via diffraction, the second in-coupled image light  231 - 2  out of the light guide  210  as a plurality of fourth output image lights  272 - 4  towards the plurality of exit pupils  257 . The plurality of fourth output image lights  272 - 4  may correspond to the plurality of exit pupils  257  on a one-to-one basis. Each of the fourth output image lights  272 - 4  may have an output FOV  274 - 4  that may be substantially the same as the input FOV  233 . The second diffraction state of the in-coupling grating  235  may be configured (e.g., by configuring the grating period or the modulation of the refractive index of the in-coupling grating  235 ), and the fourth diffraction state of the out-coupling grating  245  may be configured (e.g., by configuring the grating period or the modulation of the refractive index of the out-coupling grating  245 ), such that the out-coupling grating  245  may diffract the second in-coupled image light  231 - 2  as the fourth output image light  272 - 4 , with an axis of symmetry  276 - 4  of the output FOV  274 - 4  being unparallel with the surface normal of the light guide  210 . 
     Referring to  FIGS.  2 C and  2 D , for the first output image light  272 - 1 , for the second output image light  272 - 2 , the third output image light  272 - 3 , and the fourth output image light  272 - 4  propagating toward the same exit pupil  257 , the axis of symmetry  276 - 4  of the output FOV  274 - 4  of the fourth output image light  272 - 4  may be rotated with respective to each of the axis of symmetry  276 - 1  of the output FOV  274 - 1  of the first output image light  272 - 1 , the axis of symmetry  276 - 2  of the output FOV  274 - 2  of the second output image light  272 - 2 , and the axis of symmetry  276 - 3  of the output FOV  274 - 3  of the third output image light  272 - 3  in a clockwise or counterclockwise direction. For discussion purposes,  FIGS.  2 C and  2 D  show that the axis of symmetry  276 - 4  is rotated with respective to each of the axis of symmetry  276 - 1  (or the surface normal of the light guide  210 ), the axis of symmetry  276 - 2 , and the axis of symmetry  276 - 3  in the counter-clockwise direction. 
     For the first output image light  272 - 1 , the second output image light  272 - 2 , the third output image light  272 - 3 , and the fourth output image light  272 - 4  propagating toward the same exit pupil  257 , an angle representing the relative rotation between the axis of symmetry  276 - 4  and each of the axis of symmetry  276 - 1 , the axis of symmetry  276 - 2 , and the axis of symmetry  276 - 3  may be smaller than the angular resolution of the eye  260  at the exit pupil  257 . Thus, the angular separation between the axis of symmetry  276 - 4  and each of the axis of symmetry  276 - 1 , the axis of symmetry  276 - 2 , and the axis of symmetry  276 - 3  may not be observable by the eye  260  at the exit pupil  257 . 
     In some embodiments, an angle representing the relative rotation between the axis of symmetry  276 - 4  and each of the axis of symmetry  276 - 1 , the axis of symmetry  276 - 2 , and the axis of symmetry  276 - 3  may be smaller than the first predetermined percentage of the output FOV  274 - 4  (or  274 - 1 , or  274 - 2 , or  274 - 3 ). The output FOV  274 - 4  and the output FOV  274 - 1  (or  274 - 2 , or  274 - 3 ) may have a substantially wide or large overlapping area (or overlapping FOV portion). In some embodiments, an angle representing the overlapping FOV portion may be greater than the second predetermined percentage of the output FOV  274 - 4  (or  274 - 1 , or  274 - 2 , or  274 - 3 ), and smaller than the full output FOV  274 - 4  (or  274 - 1 , or  274 - 2 , or  274 - 3 ). 
       FIG.  2 E  illustrates an x-z sectional view of the light guide display system  270  operating during the first to the fourth sub-frames. As shown in  FIG.  2 E , angles representing the relative rotations between the axis of symmetry  276 - 4  and each of the axis of symmetry  276 - 1 , the axis of symmetry  276 - 2 , and the axis of symmetry  276 - 3  may be different. For example, the angle representing the relative rotation between the axis of symmetry  276 - 4  and the axis of symmetry  276 - 1  may be the greatest, and the angle representing the relative rotation between the axis of symmetry  276 - 2  and the axis of symmetry  276 - 1  may be the smallest. The angle representing the relative rotation between the axis of symmetry  276 - 3  and the axis of symmetry  276 - 1  may be greater than the angle representing of the relative rotation between the axis of symmetry  276 - 2  and the axis of symmetry  276 - 1 , and smaller than the angle representing of the relative rotation between the axis of symmetry  276 - 4  and the axis of symmetry  276 - 1 . 
     Compared to the conventional light guided display system  100  shown in  FIGS.  1 A and  1 B , the light guided display system  270  of the present disclosure may provide an increased (e.g., quadrupled) number of image lights  272 - 1 ,  272 - 2 ,  272 - 3 , and  272 - 4  with slightly shifted output FOVs  274 - 1 ,  274 - 2 ,  274 - 3 , and  274 - 4  propagating through the same exit pupil  257 . Thus, the output pixel density of the light guide display system  270  may be increased (e.g., quadrupled) as compared to the output pixel density of the conventional light guide display system  100  shown in  FIGS.  1 A and  1 B . The output pixel density of the light guide display system  270  may be increased (e.g., quadrupled) as compared to the input pixel density at the input side of the light guide  210 . 
     In some embodiments, an active grating configured to operate in a plurality of (e.g., two) different diffraction states (e.g., at different driving voltages) to diffract the same incident light at a plurality of (e.g., two) different diffraction angles may be replaced by a plurality of (e.g., two) active gratings. Each of the plurality of (e.g., two) active gratings may be controlled or switched, e.g., by the controller  215 , between operating in a diffraction state to diffract an incident light, and operating in a non-diffraction state to transmit the incident light with substantially zero or negligible diffraction. The plurality of (e.g., two) active gratings that operates in the diffraction state may diffract the same incident light at a plurality of (e.g., two) different diffraction angles. 
       FIG.  3 A  illustrates a schematic diagram of a light guide display system or assembly  300  for providing an increased pixel density (pixel per degree), according to an embodiment of the present disclosure. The light guide display system  300  may include elements that are similar to or the same as those included in the light guide display system  200  shown in  FIG.  2 A , the light guide display system  250  shown in  FIG.  2 B , or the light guide display system  270  shown in  FIGS.  2 C- 2 E . Descriptions of the same or similar elements or features can refer to the above corresponding descriptions, including those rendered in connection with  FIG.  2 A ,  FIG.  2 B , or  FIGS.  2 C- 2 E . 
     As shown in  FIG.  3 A , the light guide display system  300  may include an out-coupling element and an in-coupling element coupled with the light guide  210 . For simplicity and convenience, the out-coupling element is labelled as  245 , and the in-coupling element is labelled as  235 , same as those shown in  FIGS.  2 A- 2 E . It is understood that although the same reference numerals for the in-coupling element and the out-coupling element are used in  FIG.  3 A  and other figures, the in-coupling element and the out-coupling element in each embodiment may include different configurations, functions, shapes, sizes, other physical properties and/or optical properties. 
     In the embodiment shown in  FIG.  3 A , the out-coupling element  245  may include a plurality of out-coupling gratings  245 - 1  and  245 - 2 , each of which may be an active grating that is controlled or switched, e.g., by the controller  215 , between operating in a diffraction state to diffract an incident light, and operating in a non-diffraction state to transmit the incident light with substantially zero or negligible diffraction. The plurality of out-coupling gratings  245 - 1  and  245 - 2  may be stacked at the same surface of the light guide  210  or at different surfaces of the light guide  210 . For discussion purposes,  FIG.  3 A  shows that the first out-coupling grating  245 - 1  and the second out-coupling grating  245 - 2  are stacked at the second surface  210 - 2  of the light guide  210 . The in-coupling element  235  may include an in-coupling grating (also referred to as  235 ). 
     In some embodiments, a display frame of the virtual image output from the display element  220  may be divided into a plurality of (e.g., two) sub-frames (sub-frames are example time periods). During the respective sub-frame, the controller  215  may control the light source assembly  205  to output the input image light  230  with the input FOV  233 . The in-coupling grating  235  may be configured to couple the image light  230  into the light guide  210  as the in-coupled image light  231 . During the respective sub-frame, the controller  125  may control one of the plurality of out-coupling gratings  245 - 1  and  245 - 2  to operate in the diffraction state, and the remaining one or more of the plurality of out-coupling gratings  245 - 1  and  245 - 2  to operate in the non-diffraction state. The first out-coupling grating  245 - 1  and the second out-coupling grating  245 - 2  may be configured (e.g., by configuring the grating periods, or modulations of the refractive indices, etc.), such that the first out-coupling grating  245 - 1  and the second out-coupling grating  245 - 2  operating in the diffraction state during different sub-frames may diffract the in-coupled image light  231  at different diffraction angles. 
     As shown in  FIG.  3 A , during the first sub-frame, the control  215  may control the first out-coupling grating  245 - 1  to operate in the diffraction state, and control the second out-coupling grating  245 - 2  to operate in the non-diffraction state. Thus, the second out-coupling grating  245 - 2  operating in the non-diffraction state may transmit the in-coupled image light  231  toward the first out-coupling grating  245 - 1 , with substantially zero or negligible diffraction. The first out-coupling grating  245 - 1  may couple, via diffraction, the in-coupled image light  231  out of the light guide  210  as a plurality of first output image lights  332 - 1  towards the plurality of exit pupils  257 . The rays of the first output image lights  332 - 1  are represented by solid lines. The plurality of first output image lights  332 - 1  may correspond to the plurality of exit pupils  257  on a one-to-one basis. Each of the first output image lights  332 - 1  may have a first output FOV  334 - 1  that may be substantially the same as the input FOV  233 . 
     The diffraction state of the first out-coupling grating  245 - 1  may be configured (e.g., by configuring the grating period or the modulation of the refractive index of the first out-coupling grating  245 - 1 ), such that the first out-coupling grating  245 - 1  may diffract the in-coupled image light  231  as the first output image light  332 - 1 , with the axis of symmetry  336 - 1  of the output FOV  334 - 1  perpendicular to the surface of the light guide  210 . That is, the axis of symmetry  336 - 1  of the output FOV  334 - 1  of the first output image light  332 - 1  may be parallel with the surface normal of the light guide  210 . 
     During the second sub-frame, the control  215  may control the first out-coupling grating  245 - 1  to operate in the non-diffraction state, and control the second out-coupling grating  245 - 2  to operate in the diffraction state. Thus, the out-coupling grating  245  may couple, via diffraction, the in-coupled image light  231  out of the light guide  210  as a plurality of second output image lights  332 - 2  toward the first out-coupling grating  245 - 1 . The first out-coupling grating  245 - 1  operating in the non-diffraction state may transmit the plurality of second output image lights  332 - 2  towards the plurality of exit pupils  257 , with substantially zero or negligible diffraction. The rays of the second output image lights  332 - 2  are represented by dashed lines. The plurality of second output image lights  332 - 2  may correspond to the plurality of exit pupils  257  on a one-to-one basis. Each of the second output image lights  332 - 2  may have a second output FOV  334 - 2  that may be substantially the same as the input FOV  233 . 
     The diffraction state of the second out-coupling grating  245 - 2  may be configured (e.g., by configuring the grating period or the modulation of the refractive index of the second out-coupling grating  245 - 2 ), such that the second out-coupling grating  245 - 2  may diffract the in-coupled image light  231  as the second output image light  332 - 2 , with the axis of symmetry  336 - 2  of the output FOV  334 - 2  being unparallel with the surface normal of the light guide  210 . 
     Referring to  FIG.  3 A , the diffraction states of the first and second out-coupling grating  245 - 1  and  245 - 2  may be configured (e.g., by configuring the grating periods or the modulations of the refractive index of the first and second out-coupling grating  245 - 1  and  245 - 2 ), such that for the first output image light  332 - 1  and the second output image light  332 - 2  propagating toward the same exit pupil  257 , the axis of symmetry  336 - 2  of the output FOV  334 - 2  of the second output image light  332 - 2  may be rotated with respective to the axis of symmetry  336 - 1  of the output FOV  334 - 1  of the first output image light  332 - 1  in a clockwise or counterclockwise direction. For discussion purposes,  FIG.  3 A  shows that the axis of symmetry  336 - 2  of the output FOV  334 - 2  is rotated with respective to the axis of symmetry  336 - 1  of the output FOV  334 - 1  in the counter-clockwise direction. 
     For the first output image light  332 - 1  and the second output image light  332 - 2  propagating toward the same exit pupil  257 , an angle representing the relative rotation between the axis of symmetry  336 - 1  and the axis of symmetry  336 - 2  may be smaller than the angular resolution of the eye  260  at the exit pupil  257 . Thus, the angular separation between the axis of symmetry  336 - 1  and the axis of symmetry  336 - 2  may not be observable by the eye  160 . In some embodiments, an angle representing the relative rotation between the axis of symmetry  336 - 1  and the axis of symmetry  336 - 2  may be smaller than the first predetermined percentage of the output FOV  334 - 1  or  334 - 2 . The output FOV  334 - 1  of the first output image light  332 - 1  and the output FOV  334 - 2  of the second output image light  332 - 2  may have a substantially wide or large overlapping area (or overlapping FOV portion). In some embodiments, an angle representing the overlapping FOV portion may be greater than the second predetermined percentage of the output FOV  334 - 1  or  334 - 2 , and smaller than the full output FOV  334 - 1  or  334 - 2 . 
     Compared to the conventional light guided display system  100  shown in  FIGS.  1 A and  1 B , the light guided display system  300  may provide an increased (e.g., doubled) number of image lights  332 - 1  and  332 - 2  with slightly shifted (e.g., tilted) output FOVs  334 - 1  and  334 - 2  propagating through the same exit pupil  257 . Thus, output pixel density of the light guide display system  300  may be increased (e.g., doubled) as compared to the output pixel density of the conventional light guide display system  100  shown in  FIGS.  1 A and  1 B . The output pixel density of the light guide display system  300  may be increased (e.g., doubled) as compared to the input pixel density at the input side of the light guide  210 . 
       FIG.  3 B  illustrates a schematic diagram of a light guide display system or assembly  350  for providing an increased pixel density (pixel per degree), according to an embodiment of the present disclosure. The light guide display system  350  may include elements that are similar to or the same as those included in the light guide display system  200  shown in  FIG.  2 A , the light guide display system  250  shown in  FIG.  2 B , the light guide display system  270  shown in  FIGS.  2 C- 2 E , or the light guide display system  300  shown in  FIG.  3 A . Descriptions of the same or similar elements or features can refer to the above corresponding descriptions, including those rendered in connection with  FIG.  2 A ,  FIG.  2 B ,  FIGS.  2 C- 2 E , or  FIG.  3 A . 
     As shown in  FIG.  3 B , the light guide display system  300  may include an out-coupling element and an in-coupling element coupled with the light guide  210 . For simplicity and convenience, the out-coupling element is labelled as  245 , and the in-coupling element is labelled as  235 , same as those shown in  FIGS.  2 A- 2 E  and  FIG.  3 A . It is understood that although the same reference numerals for the in-coupling element and the out-coupling element are used in  FIG.  3 B  and other figures, the in-coupling element and the out-coupling element in each embodiment may include different configurations, functions, shapes, sizes, other physical properties and/or optical properties. 
     In the embodiment shown in  FIG.  3 B , the in-coupling element  235  may include a plurality of in-coupling gratings, such as a first in-coupling grating  235 - 1  and a second in-coupling grating  235 - 2 . Each of the first in-coupling grating  235 - 1  and the second in-coupling grating  235 - 2  may be an active grating that is controlled or switched by the controller  215  between operating in a diffraction state to diffract an incident light, and operating in a non-diffraction state to transmit the incident light with substantially zero or negligible diffraction. The in-coupling gratings  235 - 1  and  235 - 2  may be disposed in a stacked configuration at the same surface of the light guide  210  or at different surfaces of the light guide  210 . For discussion purposes,  FIG.  3 B  shows that the first in-coupling grating  235 - 1  and the second in-coupling grating  235 - 2  are stacked at the second surface  210 - 2  of the light guide  210 . 
     In some embodiments, a display frame of the virtual image output from the display element  220  may be divided into a plurality of (e.g., two) sub-frames. During the respective sub-frame, the controller  215  may control the light source assembly  205  to output the input image light  230  with the input FOV  233 . The controller  125  may also control one of the in-coupling gratings  235 - 1  and  235 - 2  to operate in the diffraction state, and the remaining of the in-coupling gratings  235 - 1  and  235 - 2  to operate in the non-diffraction state. When operating in the diffraction state, the first in-coupling grating  235 - 1  and the second in-coupling grating  235 - 2  may be configured (e.g., by configuring the grating periods, or modulations of the refractive indices, etc.,), such that the first in-coupling grating  235 - 1  and the second in-coupling grating  235 - 2  operating in the diffraction state may diffract the input image light  230  at different diffraction angles during different sub-subframes. 
     As shown in  FIG.  3 B , during the first sub-frame, the control  215  may control the first in-coupling grating  235 - 1  to operate in the diffraction state, and the second in-coupling grating  235 - 2  to operate in the non-diffraction state. Thus, the second in-coupling grating  235 - 2  operating in the non-diffraction state may transmit the input image light  230  toward the first out-coupling grating  245 - 1 , with substantially zero or negligible diffraction. The first in-coupling grating  235 - 1  operating in the diffraction state may couple, via diffraction, the input image light  230  into the light guide  210  as a first in-coupled image light  331 - 1 . The rays of the first in-coupled image light  331 - 1  are represented by solid lines. For example, the first in-coupling grating  235 - 1  may diffract the central ray of the input image light  230  as a central ray of the first in-coupled image light  331 - 1  with a first TIR propagating angle inside the light guide  210 . 
     The out-coupling grating  245  may couple, via diffraction, the first in-coupled image light  331 - 1  out of the light guide  210  as a plurality of first output image lights  352 - 1  towards the plurality of exit pupils  257 . The first output image lights  352 - 1  are represented by solid lines. The first output image lights  352 - 1  may correspond to the plurality of exit pupils  257  on a one-to-one basis. Each of the first output image lights  352 - 1  may have a first output FOV  354 - 1  that may be substantially the same as the input FOV  233 . 
     The diffraction state of the first in-coupling grating  235 - 1  may be configured (e.g., by configuring the grating period or the modulation of the refractive index of the first in-coupling grating  235 - 1 ), such that the out-coupling grating  245  may diffract the first in-coupled image light  331 - 1  as the first output image light  352 - 1 , with an axis of symmetry  356 - 1  of the output FOV  354 - 1  being perpendicular to the surface of the light guide  210 . That is, the axis of symmetry  356 - 1  of the output FOV  354 - 1  of the first output image light  352 - 1  may be parallel with the surface normal of the light guide  210 . 
     During the second sub-frame, the control  215  may control the first in-coupling grating  235 - 1  to operate in the non-diffraction state, and the second in-coupling grating  235 - 2  to operate in the diffraction state. Thus, the second in-coupling grating  235 - 2  may couple, via diffraction, the input image light  230  into the light guide  210  as a second in-coupled image light  331 - 2 . The first in-coupling grating  235 - 1  operating in the non-diffraction state may transmit the second in-coupled image light  331 - 2 , with substantially zero or negligible diffraction. The rays of the second in-coupled image light  331 - 2  are represented by dashed lines. The second in-coupling grating  235 - 2  may diffract the central ray of the input image light  230  as a central ray of the second in-coupled image light  331 - 2  with a second TIR propagating angle inside the light guide  210 . The second TIR propagating angle may be different from the first TIR propagating angle. 
     The out-coupling grating  245  may couple, via diffraction, the second in-coupled image light  331 - 2  out of the light guide  210  as a plurality of second output image lights  352 - 2  towards the plurality of exit pupils  257 . The second output image lights  352 - 2  are represented by dashed lines. The plurality of second output image lights  352 - 2  may one-to-one correspond to the plurality of exit pupils  257 . Each of the second output image lights  352 - 2  may have a second output FOV  354 - 2  that is substantially the same as the input FOV  233 . 
     The diffraction state of the second in-coupling grating  235 - 2  may be configured (e.g., by configuring the grating period or the modulation of the refractive index of the second in-coupling grating  235 - 2 ), such that the out-coupling grating  245  may diffract the second in-coupled image light  331 - 2  as the second output image light  352 - 2 , with an axis of symmetry  356 - 2  of the output FOV  354 - 2  being unparallel with the surface normal of the light guide  210 . 
     Referring to  FIG.  3 B , the diffraction states of the first and second in-coupling grating  235 - 1  and  235 - 2  may be configured such that for the first output image light  352 - 1  and the second output image light  352 - 2 , an angle representing the relative rotation between the axis of symmetry  356 - 1  and the axis of symmetry  356 - 2  may be smaller than the angular resolution of the eye  260  at the exit pupil  257 . Thus, the angular separation between the axis of symmetry  356 - 1  and the axis of symmetry  356 - 2  may not be observable by the eye  260 . In some embodiments, an angle representing the relative rotation between the axis of symmetry  356 - 1  and the axis of symmetry  356 - 2  may be smaller than the first predetermined percentage of the output FOV  354 - 1  or  354 - 2 . The output FOV  354 - 1  of the first output image light  352 - 1  and the output FOV  354 - 2  of the second output image light  352 - 2  may have a substantially wide or large overlapping area (or overlapping FOV portion). In some embodiments, an angle representing the overlapping FOV portion may be greater than the second predetermined percentage of the output FOV  354 - 1  or  354 - 2 , and smaller than the full output FOV  354 - 1  or  354 - 2 . 
     Compared to the conventional light guided display system  100  shown in  FIGS.  1 A and  1 B , the light guided display system  350  may provide an increased (e.g., doubled) number of image lights  352 - 1  and  352 - 2  with slightly shifted output FOVs  354 - 1  and  354 - 2  propagating through the same exit pupil  257 . Thus, the output pixel density of the light guide display system  350  may be increased (e.g., doubled) as compared to the output pixel density of the conventional light guide display system  100  shown in  FIGS.  1 A and  1 B . The output pixel density of the light guide display system  350  may be increased (e.g., doubled) as compared to the input pixel density at the input side of the light guide  210 . 
     In some embodiments, although not shown, a light guide display system may include a plurality of in-coupling gratings and a plurality of out-coupling gratings. For example, in an embodiment, the out-coupling gratings  245 - 1  and  245 - 2  in the light guide display system  300  shown in  FIG.  3 A  and the in-coupling gratings  235 - 1  and  235 - 2  in the light guide display system  350  shown in  FIG.  3 B  may be included in a single light guide display system. The display frame of the virtual image output from the display element  220  may be divided into four sub-frames. During the respective sub-frame, the controller  125  may control one of the out-coupling gratings  245 - 1  and  245 - 2  and one of the in-coupling gratings  235 - 1  and  235 - 2  to operate in the diffraction state, and configure the remaining in-coupling and out-coupling gratings to operate in the non-diffraction state. 
     Compared to the conventional light guided display system  100  shown in  FIGS.  1 A and  1 B , a light guided display system of the present disclosure may provide an increased (e.g., quadrupled) number of image lights with slightly shifted output FOVs propagating through the same exit pupil  257 . Thus, the output pixel density of the disclosed light guide display system may be increased (e.g., quadrupled) as compared to the output pixel density of the conventional light guide display system  100  shown in  FIGS.  1 A and  1 B . The output pixel density of the disclosed light guide display system may be increased (e.g., quadrupled) as compared to the input pixel density at the input side of the light guide  210 . 
       FIGS.  4 A and  4 B  illustrate schematic diagrams of a light guide display system or assembly  400  for providing an increased pixel density (pixel per degree), according to an embodiment of the present disclosure. The light guide display system  400  may include elements that are similar to or the same as those included in the light guide display system  200  shown in  FIG.  2 A , the light guide display system  250  shown in  FIG.  2 B , the light guide display system  270  shown in  FIGS.  2 C- 2 E , the light guide display system  300  shown in  FIG.  3 A , or the light guide display system  350  shown in  FIG.  3 B . Descriptions of the same or similar elements or features can refer to the above corresponding descriptions, including those rendered in connection with  FIG.  2 A ,  FIG.  2 B ,  FIGS.  2 C- 2 E ,  FIG.  3 A , or  FIG.  3 B . 
     As shown in  FIG.  4 A , the light guide display system  400  may include a plurality of light guides  410  and  412  stacked together, each of which may be coupled with an in-coupling element and an out-coupling element. For illustrative purposes, two light guides  410  and  412  are shown in  FIG.  4 A . Other suitable number of light guides may be included, such as three, four, five, six, etc. In some embodiments, for a wave guiding to take place in the light guides, the light guides  410  and  412  may be separated by air gaps. In some embodiments, the air gaps between the neighboring light guides  410  and  412  may be at least partially filled with a material (e.g., a liquid glue) having a refractive index lower than that of the light guides  410  and  412 . The light guide  410  or  412  may be coupled with an in-coupling element  435 - 1  or  435 - 2  and an out-coupling element  445 - 1  or  445 - 2 . 
     The in-coupling element  435 - 1  or  435 - 2  may include one or more in-coupling gratings, and the out-coupling element  445 - 1  or  445 - 2  may include one or more out-coupling gratings. For discussion purposes,  FIG.  4 A  shows that the in-coupling element  435 - 1  or  435 - 2  may include an in-coupling grating (also referred to as  435 - 1  or  435 - 2  for discussion purposes), and the out-coupling element  445 - 1  or  445 - 2  may include an out-coupling grating (also referred to as  445 - 1  or  445 - 2  for discussion purposes). At least one (e.g., each) of the in-coupling grating  435 - 1 , the in-coupling grating  435 - 2 , the out-coupling grating  445 - 1 , and the out-coupling grating  445 - 2  may be an active grating, which may be controlled or switched by the controller  215  between operating in a diffraction state to diffract an incident light, and operating in a non-diffraction state to transmit the incident light with substantially zero or negligible diffraction. 
     In some embodiments, at least one of the pair of the in-coupling gratings  435 - 1  and  435 - 2  or the pair of the out-coupling gratings  445 - 1  and  445 - 2  may be configured to diffract an incident light with a fixed incidence angle at different diffraction angles. For example, the in-coupling gratings  435 - 1  and  435 - 2  may be configured with different grating periods, and/or different modulations of refractive index, etc., thereby diffracting an incident light with a fixed incidence angle to different diffraction angles. The out-coupling gratings  445 - 1  and  445 - 2  may be configured with different grating periods, and/or different modulations of refractive index, etc., thereby diffracting an incident light with a fixed incidence angle to different diffraction angles. 
     For discussion purposes, in the embodiment shown in  FIG.  4 A , all of the in-coupling gratings  435 - 1 ,  435 - 2 , the out-coupling gratings  445 - 1 ,  445 - 2  may be active gratings. For discussion purposes, the in-coupling gratings  435 - 1  and  435 - 2  operating in the diffraction state may be configured to diffract an incident light with a fixed incidence angle at the same diffraction angle. For example, the in-coupling gratings  435 - 1  and  435 - 2  may be configured with the same grating period, and/or the same modulation of the refractive index, etc. For discussion purposes, the out-coupling gratings  445 - 1  and  445 - 2  operating in the diffraction state may be configured to diffract an incident light with a fixed incidence angle at different diffraction angles. For example, the out-coupling gratings  445 - 1  and  445 - 2  may be configured with different grating periods, and/or different modulations of the refractive index, etc. 
     In some embodiments, a display frame of the virtual image output from the display element  220  may be divided into a plurality of (e.g., two) sub-frames (sub-frames are example time periods).  FIG.  4 A  illustrates an x-z sectional view of the light guide display system  400  during a first sub-frame. As shown in  FIG.  4 A , during the first sub-frame, the controller  215  may control the light source assembly  205  to output the input image light  230  with the input FOV  233 . The control  215  may control the in-coupling grating  435 - 1  and the out-coupling gratings  445 - 1  coupled with the light guide  410  to operate in the diffraction state, and control the in-coupling grating  435 - 2  and the out-coupling gratings  445 - 2  coupled with the light guide  412  to operate in the non-diffraction state. Thus, the in-coupling grating  435 - 1  may couple, via diffraction, the input image light  230  into the light guide  410  as a first in-coupled image light  431 - 1  with a first TIR propagating angle. The rays of the first in-coupled image light  431 - 1  are represented by solid lines. For example, the in-coupling grating  435 - 1  may diffract the central ray of the input image light  230  as a central ray of the first in-coupled image light  431 - 1  with a first TIR propagating angle inside the light guide  410 . 
     The out-coupling grating  445 - 1  may couple, via diffraction, the first in-coupled image light  431 - 1  out of the light guide  410  as a plurality of first output image lights  432 - 1  towards the plurality of exit pupils  257 . The rays of the first output image lights  432 - 1  are represented by solid lines. The plurality of first output image lights  432 - 1  may one-to-one correspond to the plurality of exit pupils  257 . Each of the first output image lights  432 - 1  may have a first output FOV  434 - 1  that is substantially the same as the input FOV  233 . 
     The diffraction state of the out-coupling grating  445 - 1  may be configured (e.g., the grating period or the modulation of the refractive index of the out-coupling grating  445 - 1  may be configured), such that the out-coupling grating  445 - 1  may diffract the first in-coupled image light  431 - 1  as the first output image light  452 - 1 , with an axis of symmetry  456 - 1  of the output FOV  454 - 1  perpendicular to the surface of the light guide  210 . That is, the axis of symmetry  456 - 1  of the output FOV  454 - 1  of the first output image light  452 - 1  may be parallel with the surface normal of the light guide  410 . 
       FIG.  4 B  illustrates an x-z sectional view of the light guide display system  400  during a second sub-frame. As shown in  FIG.  4 B , during the second sub-frame, the controller  215  may control the light source assembly  205  to output the input image light  230  with the input FOV  233 . The control  215  may control the in-coupling grating  435 - 1  and the out-coupling gratings  445 - 1  coupled with the light guide  410  to operate in the non-diffraction state. The controller  215  may control the in-coupling grating  435 - 2  and the out-coupling gratings  445 - 2  coupled with the light guide  412  to operate in the diffraction state. Thus, the in-coupling grating  435 - 1  operating in the non-diffraction state may transmit the input image light  230  toward the light guide  410  and the light guide  412 , with substantially zero or negligible diffraction. The in-coupling grating  435 - 2  operating in the diffraction state may couple, via diffraction, the input image light  230  into the light guide  412  as a second in-coupled image light  431 - 2 . The rays of the second in-coupled image light  431 - 2  are represented by dashed lines. The in-coupling grating  435 - 2  may diffract the central ray of the input image light  430  as a central ray of the second in-coupled image light  431 - 2  with a second TIR propagating angle inside the light guide  412 . As the in-coupling gratings  435 - 1  and  435 - 2  operating in the diffraction state are configured to diffract the incident light with the same incidence angle at the same diffraction angle, the second TIR propagating angle of the central ray of the second in-coupled image light  431 - 2  in the light guide  412  during the second sub-frame may be the same as the first TIR propagating angle of the central ray of the first in-coupled image light  431 - 1  in the light guide  410  during the first sub-frame. 
     The out-coupling grating  445 - 2  operating in the diffraction state may couple, via diffraction, the second in-coupled image light  431 - 2  out of the light guide  412  as a plurality of second output image lights  432 - 2  toward the light guide  310  and the out-coupling grating  445 - 1 . The rays of the second output image lights  432 - 2  are represented by dashed lines. The out-coupling grating  445 - 1  operating in the non-diffraction state may transmit the second output image lights  432 - 2  towards the plurality of exit pupils  257 , with substantially zero or negligible diffraction. The second output image lights  432 - 2  may correspond to the plurality of exit pupils  257  on a one-to-one basis. Each of the second output image lights  432 - 2  may have a second output FOV  434 - 2  that may be substantially the same as the input FOV  233 . 
     The diffraction state of the out-coupling grating  445 - 2  may be configured (e.g., by configuring the grating period or the modulation of the refractive index of the out-coupling grating  445 - 2 ), such that the out-coupling grating  445 - 2  may diffract the second in-coupled image light  431 - 2  as the second output image light  452 - 2 , with an axis of symmetry  456 - 2  of the output FOV  454 - 2  being unparallel with the surface normal of the light guide  410 . 
     Referring to  FIGS.  4 A and  4 B , the out-coupling gratings  445 - 1  and  445 - 2  may be configured (e.g., by configuring the grating periods or the modulations of the refractive index of the out-coupling gratings  445 - 1  and  445 - 2 ), such that for the first output image light  432 - 1  and the second output image light  432 - 2  propagating toward the same exit pupil  257 , the axis of symmetry  436 - 2  of the output FOV  434 - 2  of the second output image light  432 - 2  may be rotated with respective to the axis of symmetry  436 - 1  of the output FOV  434 - 1  of the first output image light  432 - 1  in a clockwise or counterclockwise direction. For discussion purposes,  FIGS.  4 A and  4 B  show that the axis of symmetry  436 - 2  of the output FOV  434 - 2  is rotated with respective to the axis of symmetry  436 - 1  of the output FOV  434 - 1  in the counter-clockwise direction. 
     For the first output image light  432 - 1  and the second output image light  432 - 2  propagating toward the same exit pupil  257 , an angle representing the relative rotation between the axis of symmetry  436 - 1  and the axis of symmetry  436 - 2  may be smaller than the angular resolution of the eye  260  at the exit pupil  257 . Thus, the angular separation between the axis of symmetry  436 - 1  and the axis of symmetry  436 - 2  may not be observable by the eye  260 . In some embodiments, an angle representing the relative rotation between the axis of symmetry  436 - 1  and the axis of symmetry  436 - 2  may be smaller than the first predetermined percentage of the output FOV  434 - 1  or  434 - 2 . The output FOV  434 - 1  of the first output image light  432 - 1  and the output FOV  434 - 2  of the second output image light  432 - 2  may have a substantially wide or large overlapping area (or overlapping FOV portion). In some embodiments, an angle representing the overlapping FOV portion may be greater than the second predetermined percentage of the output FOV  434 - 1  or  434 - 2 , and smaller than the full output FOV  434 - 1  or  434 - 2 . 
     Compared to the conventional light guided display system  100  shown in  FIGS.  1 A and  1 B , the light guided display system  400  may provide an increased (e.g., doubled) number of image lights  432 - 1  and  432 - 2  with slightly shifted output FOVs  434 - 1  and  434 - 2  propagating through the same exit pupil  257 . Thus, the output pixel density of the light guide display system  400  may be increased (e.g., doubled) as compared to the output pixel density of the conventional light guide display system  100  shown in  FIGS.  1 A and  1 B . The output pixel density of the light guide display system  400  may be increased (e.g., doubled) as compared to the input pixel density at the input side of the light guide  410  or  412 . The 
     In some embodiments, although not shown, the in-coupling gratings  435 - 1  and  435 - 2  operating in the diffraction state may be configured to diffract the incident light with a same incident angle at different diffraction angles. The out-coupling gratings  445 - 1  and  445 - 2  operating in the diffraction state may be configured to diffract the incident light with a same incident angle at the same diffraction angle. Thus, the first TIR propagating angle of the central ray of the first in-coupled image light  432 - 1  in the light guide  410  during the first sub-frame may be different from the second TIR propagating angle of the central ray of the second in-coupled image light  432 - 2  in the light guide  412  during the second sub-frame. Thus, for the first output image light  432 - 1  and the second output image light  432 - 2  propagating toward the same exit pupil, the axis of symmetry  436 - 2  of the second output FOV  434 - 2  of the second output image light  432 - 2  may also be rotated with respective to the axis of symmetry  436 - 1  of the first output FOV  434 - 1  of the first output image light  432 - 1  in a clockwise or counter-clockwise direction. The angle representing the relative rotation between the axis of symmetry  436 - 1  and the axis of symmetry  436 - 2  may be smaller than the angular resolution of the eye  260  at the exit pupil  257 . Thus, the light guide display system may provide an increased (e.g., doubled) pixel density (pixel per degree) at the output side, as compared to the conventional light guide display system  100  shown in  FIGS.  1 A and  1 B . 
     In some embodiments, although not shown, the in-coupling gratings  435 - 1  and  435 - 2  operating in the diffraction state may be configured to diffract the incident light with a same incident angle at different diffraction angles. The out-coupling gratings  445 - 1  and  445 - 2  operating in the diffraction state may be configured to diffract the incident light with a same incident angle at different diffraction angles. The display frame of the virtual image output from the display element  220  may be divided into four sub-frames. Compared to the conventional light guided display system  100  shown in  FIGS.  1 A and  1 B , a light guided display system of the present disclosure may provide an increased (e.g., quadrupled) number of image lights with slightly shifted output FOVs propagating through the same exit pupil  257 . Thus, the output pixel density of the disclosed light guide display system may be increased (e.g., quadrupled) as compared to the output pixel density of the conventional light guide display system  100  shown in  FIGS.  1 A and  1 B . 
       FIGS.  5 A- 5 C  illustrate schematic diagrams of a light guide display system or assembly  500  for providing an increased pixel density (pixel per degree), according to an embodiment of the present disclosure. The light guide display system  500  may be configured to deliver single-color images of different colors in a time-multiplexing manner. The light guide display system  500  may be configured to deliver a polychromatic image (e.g., a full-color image) with an increased pixel density to the eye-box region  259 . The light guide display system  500  may include elements that are similar to or the same as those included in the light guide display system  200  shown in  FIG.  2 A , the light guide display system  250  shown in  FIG.  2 B , the light guide display system  270  shown in  FIGS.  2 C- 2 E , the light guide display system  300  shown in  FIG.  3 A , the light guide display system  350  shown in  FIG.  3 B , or the light guide display system  400  shown in  FIGS.  4 A and  4 B . Descriptions of the same or similar elements or features can refer to the above corresponding descriptions, including those rendered in connection with  FIG.  2 A ,  FIG.  2 B ,  FIGS.  2 C- 2 E ,  FIG.  3 A ,  FIG.  3 B , or  FIGS.  4 A and  4 B . 
     As shown in  FIG.  5 A , the light guide display system  500  may include the light guide  210  coupled with an in-coupling element  535  and an out-coupling element  545 . The in-coupling element  535  may include three in-coupling gratings  535 - 1 ,  535 - 2 , and  535 - 3 , which may be disposed in a stacked configuration at the same surface or different surfaces of the light guide  210 . The out-coupling element  545  may include three out-coupling gratings  545 - 1 ,  545 - 2 , and  545 - 3 , which may be disposed in a stacked configuration at the same surface or different surfaces of the light guide  210 . For discussion purposes,  FIG.  5 A  show that the in-coupling gratings  535 - 1 ,  535 - 2 , and  535 - 3  are stacked at the second surface  210 - 2  of the light guide  210 , and the out-coupling gratings  545 - 1 ,  545 - 2 , and  545 - 3  are stacked at the second surface  210 - 2  of the light guide  210 . 
     The in-coupling gratings  535 - 1 ,  535 - 2 , and  535 - 3  and the out-coupling gratings  545 - 1 ,  545 - 2 , and  545 - 3  may be configured for different operation wavelength ranges. That is, the in-coupling gratings  535 - 1 ,  535 - 2 , and  535 - 3  and the out-coupling gratings  545 - 1 ,  545 - 2 , and  545 - 3  may diffract lights having wavelengths within different wavelength ranges. In some embodiments, the in-coupling gratings  535 - 1 ,  535 - 2 , and  535 - 3  and the out-coupling gratings  545 - 1 ,  545 - 2 , and  545 - 3  may be PVH gratings configured for different operation wavelength ranges. For example, the in-coupling grating  535 - 1  and the out-coupling grating  545 - 1  may be configured for a wavelength range corresponding to a first primary color (e.g., red). The in-coupling grating  535 - 2  and the out-coupling grating  545 - 2  may be configured for a wavelength range corresponding to a second primary color (e.g., green). The in-coupling grating  535 - 3  and the out-coupling grating  545 - 3  may be configured for a wavelength range corresponding to a third primary color (e.g., blue). Each of the in-coupling gratings  535 - 1 ,  535 - 2 , and  535 - 3  and out-the coupling gratings  545 - 1 ,  545 - 2 , and  545 - 3  may diffract an incident light of a corresponding wavelength range, and transmit an incident light outside of the corresponding wavelength range with negligible or zero diffraction. 
     At least one of the group of the in-coupling gratings  535 - 1 ,  535 - 2 , and  535 - 3  or the group of the out-coupling gratings  545 - 1 ,  545 - 2 , and  545 - 3  may be a group having all (three) active gratings. In some embodiments, the active grating may be controlled by the controller  215  to operate in different diffraction states by providing different driving voltages to the active grating. The active grating operating in different diffraction states may diffract the incident light associated with a fixed incidence angle at different diffraction angles. For discussion purposes, the out-coupling gratings  545 - 1 ,  545 - 2 , and  545 - 3  are presumed to be active gratings, and the in-coupling gratings  535 - 1 ,  545 - 2 , and  535 - 3  are presumed to be passive gratings, although the in-coupling gratings  535 - 1 ,  545 - 2 , and  535 - 3  may also be active gratings in some embodiments. Each of the out-coupling gratings  545 - 1 ,  545 - 2 , and  545 - 3  may provide a tunable diffraction angle to an incident light of the respective primary color. The diffraction angles provided by the out-coupling gratings  545 - 1 ,  545 - 2 , and  545 - 3  may be tuned by changing the applied driving voltage. 
     In some embodiments, a display frame of a polychromatic image generated by the light source assembly  205  may include six sub-frames. The polychromatic image may be a virtual image. The polychromatic image may be separated into a plurality of single-color images. The controller  215  may control the display element  220  to display single-color images of different primary colors (e.g., red (“R”), green (“G”), and blue (“B”)) in a time-multiplexing manner (e.g., in consecutive sub-frames). 
       FIG.  5 A  illustrates an x-z sectional view of the light guide display system  500  that operates during a first sub-frame and a second sub-frame of the display frame of a polychromatic image generated by the light source assembly  205 . As shown in  FIG.  5 A , during the first sub-frame and the second sub-frame, the controller  215  may control the display element  220  to display a single-color image of red color. For example, the display element  220  may output an image light  229 R representing the single-color image of red color, and the collimating lens  225  may convert the image light  229 R to an input image light  230 R with the input FOV  233  (e.g., a). The in-coupling grating  535 - 1  may be configured to couple the input image light  230 R into the light guide  210  as an in-coupled image light  531 R inside the light guide  210 . The rays of the in-coupled image light  531 R are represented by solid lines. For example, the in-coupling grating  535 - 1  may diffract the central ray of the input image light  230 R as a central ray of the in-coupled image light  531 R with a first TIR propagating angle inside the light guide  210 . 
     During the first sub-frame and the second sub-frame, the control  215  may control the out-coupling grating  545 - 1  to operate in two diffraction states to diffract the same in-coupled image light  531 R at different diffraction angles. For example, during the first sub-frame, the control  215  may control the out-coupling grating  545 - 1  to operate in a first diffraction state (e.g., at a first driving voltage) to couple, via diffraction, the in-coupled image light  531 R out of the light guide  210  as a plurality of output image lights  532 R- 1  towards the plurality of exit pupils  257 . The rays of the output image lights  532 R- 1  are represented by solid lines. The plurality of output image lights  532 R- 1  may correspond to the plurality of exit pupils  257  on a one-to-one basis. Each of the output image lights  532 R- 1  may have an output FOV  534 R- 1  that may be substantially the same as the input FOV  233 . 
     The first diffraction state of the out-coupling grating  545 - 1  may be configured (e.g., by configuring the grating period or the modulation of the refractive index of the out-coupling grating  545 - 1 ), such that the out-coupling grating  545 - 1  may diffract the in-coupled image light  531 R as the first output image light  532 R- 1 , with the axis of symmetry  536 R- 1  of the output FOV  534 R- 1  perpendicular to the surface of the light guide  210 . That is, the axis of symmetry  536 R- 1  of the output FOV  534 R- 1  of the first output image light  532 R- 1  may be parallel with the surface normal of the light guide  210 . 
     During the second sub-frame, the control  215  may control the out-coupling grating  545 - 1  to operate in a second diffraction state by controlling the driving voltage applied to the out-coupling grating  545 - 1  to be a second driving voltage. The out-coupling grating  545 - 1  may couple, via diffraction, the in-coupled image light  531 R out of the light guide  210  as a plurality of output image lights  532 R- 2  towards the plurality of exit pupils  257 . The rays of the output image lights  532 R- 2  are represented by dashed lines. The plurality of output image lights  532 R- 2  may correspond to the plurality of exit pupils  257  on a one-to-one basis. Each of the output image lights  532 R- 2  may have the output FOV  534 R- 2  that may be substantially the same as the input FOV  233 . The second diffraction state of the out-coupling grating  545 - 1  may be configured (e.g., by configuring the grating period or the modulation of the refractive index of the out-coupling grating  545 - 1 ), such that the out-coupling grating  545 - 1  may diffract the in-coupled image light  531 R as the second output image light  532 R- 2 , with the axis of symmetry  536 R- 2  of the output FOV  534 R- 2  being unparallel with the surface normal of the light guide  210 . 
     Referring to  FIG.  5 A , the first and second diffraction states of the out-coupling grating  545 - 1  may be configured (e.g., by configuring the grating periods or the modulations of the refractive index of the out-coupling grating  545 - 1 ), such that for the output image light  532 R- 2  and the output image light  532 R- 1  propagating toward the same exit pupil  257 , the axis of symmetry  536 R- 2  of the output FOV  534 R- 2  of the output image light  532 R- 2  may be rotated with respective to the axis of symmetry  536 R- 1  of the output FOV  534 R- 1  of the output image light  532 R- 1  in a clockwise or counter-clockwise direction. For discussion purposes,  FIG.  5 A  shows that the axis of symmetry  536 R- 2  is rotated with respective to the axis of symmetry  536 R- 1  in the counter-clockwise direction. An angle representing the relative rotation between the axis of symmetry  536 R- 1  and the axis of symmetry  536 R- 2  may be smaller than the angular resolution of the eye  260  at the exit pupil  257 . 
       FIG.  5 B  illustrates an x-z sectional view of the light guide display system  500  that operates during a third sub-frame and a fourth sub-frame of the display frame of a polychromatic image generated by the light source assembly  205 . As shown in  FIG.  5 B , during the third sub-frame and the fourth sub-frame, the controller  215  may control the display element  220  to display a single-color image of green color. The display element  220  may output an image light  229 G representing the single-color image of green color, and the collimating lens  225  may convert the image light  229 G into an input image light  230 G with the input FOV  233 . The in-coupling grating  535 - 2  may be configured to couple the input image light  230 G into the light guide  210  as an in-coupled image light  531 G. For example, the in-coupling grating  535 - 2  may diffract the central ray of the input image light  230 G as a central ray of the in-coupled image light  531 G with a second TIR propagating angle inside the light guide  210 . In the disclosed embodiments, the in-coupling gratings  535 - 1  and  535 - 2  may be configured, such that the second TIR propagating angle of the in-coupled image light  531 G may be the same as the first TIR propagating angle of the in-coupled image light  531 R shown in  FIG.  5 A . 
     During the third sub-frame and the fourth sub-frame, the control  215  may control the out-coupling grating  545 - 2  to operate in two diffraction states to diffract the same in-coupled image light  531 G at different diffraction angles. For example, during the third sub-frame, the control  215  may control the out-coupling grating  545 - 2  to operate a third diffraction state (e.g., at a third driving voltage) to couple, via diffraction, the in-coupled image light  531 G out of the light guide  210  as a plurality of output image lights  532 G- 1  towards the plurality of exit pupils  257 . The rays of the output image lights  532 G- 1  are represented by solid lines. In the disclosed embodiments, the out-coupling gratings  545 - 1  and  545 - 2  may be configured, such that the respective output image lights  532 G- 1  may substantially overlap with the respective output image lights  532 R- 1  shown in  FIG.  5 A . During the fourth sub-frame, the control  215  may control the out-coupling grating  545 - 2  to operate in a fourth diffraction state (e.g., at a fourth driving voltage) to couple, via diffraction, the in-coupled image light  531 G out of the light guide  210  as a plurality of output image lights  532 G- 2  towards the plurality of exit pupils  257 . The rays of the output image lights  532 G- 2  are represented by dashed lines. In the disclosed embodiments, the out-coupling gratings  545 - 1  and  545 - 2  may be controlled, such that respective output image lights  532 G- 2  may substantially overlap with the respective output image lights  532 R- 2  shown in  FIG.  5 A . 
     FIB.  5 C illustrates an x-z sectional view of the light guide display system  500  that operates during a fifth sub-frame and a sixth sub-frame of the display frame of a polychromatic image generated by the light source assembly  205 . As shown in FIB.  5 C, during the fifth sub-frame and the sixth sub-frame, the controller  215  may control the display element  220  to display a single-color image of blue color. The display element  220  may output an image light  229 B representing the single-color image of blue color, and the collimating lens  225  may convert the image light  229 B to an input image light  230 B with the input FOV  233 . The in-coupling grating  535 - 3  may be configured to couple the input image light  230 B into the light guide  210  as an in-coupled image light  531 B inside the light guide  210 . For example, the in-coupling grating  535 - 3  may diffract the central ray of the input image light  230 G as a central ray of the in-coupled image light  531 G with a third TIR propagating angle inside the light guide  210 . In the disclosed embodiments, the in-coupling gratings  535 - 1  and  535 - 3  may be configured, such that the third TIR propagating angle of the in-coupled image light  531 B may be the same as the first TIR propagating angle of the in-coupled image light  531 R shown in  FIG.  5 A . 
     During the fifth sub-frame and the sixth sub-frame, the control  215  may control the out-coupling grating  545 - 3  to operate in two diffraction states to provide different diffraction angles to the same in-coupled image light  531 B. For example, during the fifth sub-frame, the control  215  may control the driving voltage of the out-coupling grating  545 - 3  to be a fifth driving voltage, such that the out-coupling grating  545 - 3  may operate in a fifth diffraction state to couple, via diffraction, the in-coupled image light  531 B out of the light guide  210  as a plurality of output image lights  532 B- 1  towards the plurality of exit pupils  257 . The rays of the output image lights  532 B- 1  are represented by solid lines. In the disclosed embodiments, the out-coupling gratings  545 - 1  and  545 - 3  may be configured, such that the respective output image lights  532 B- 1  may substantially overlap with the respective output image lights  532 R- 1  shown in  FIG.  5 A . 
     During the sixth sub-frame, the control  215  may control the driving voltage of the out-coupling grating  545 - 3  to be a sixth driving voltage, such that the out-coupling grating  545 - 3  may operate in a sixth diffraction state to couple, via diffraction, the in-coupled image light  531 B out of the light guide  210  as a plurality of output image lights  532 B- 2  towards the plurality of exit pupils  257 . The rays of the output image lights  532 B- 2  are represented by dashed lines. In the disclosed embodiments, the out-coupling gratings  545 - 1  and  545 - 3  may be configured, such that the respective output image lights  532 B- 2  may substantially overlap with the respective output image lights  532 R- 2  shown in  FIG.  5 A . 
     Referring to  FIGS.  5 A- 5 C , during the entire display frame from the first sub-frame to the sixth sub-frame, the light guide display system  500  may provide a sequential transmission of image lights of different colors (e.g., blue, green, red) and an increased pixel density. A final image may be perceived by the eye  260  as a polychromatic image with an increased (e.g., doubled) pixel density. In some embodiments, the operation wavelength spectra of the in-coupling gratings  535 - 1 ,  535 - 2 , and  535 - 3  may be configured to be substantially non-overlapping with one another, and the operation wavelength spectra of the out-coupling gratings  545 - 1 ,  545 - 2 , and  545 - 3  may be configured to be substantially non-overlapping with one another. Thus, the crosstalk between the in-coupling gratings  535 - 1 ,  535 - 2 , and  535 - 3 , and the crosstalk between the out-coupling gratings  545 - 1 ,  545 - 2 , and  545 - 3  may be reduced. That is, in some embodiments, the in-coupling gratings  535 - 1 ,  535 - 2 , and  535 - 3  and the out-coupling gratings  545 - 1 ,  545 - 2 , and  545 - 3  may each have a predetermined wavelength selectivity, e.g., each grating may diffract an incident light within a predetermined wavelength band or range and transmit input lights outside of the predetermined wavelength band with substantially zero or negligible diffraction. For example, each of the in-coupling gratings  535 - 1 ,  535 - 2 , and  535 - 3  and the out-coupling gratings  545 - 1 ,  545 - 2 , and  545 - 3  may be fabricated to operate in a Bragg regime to have a predetermined wavelength selectivity. 
       FIGS.  2 A- 5 C  illustrate the principle for providing an increased output pixel density. For example, the output pixel density at the output side of the light guide display system may be at least two times of the input pixel density at the input side of the light guide display system. The principle is described using doubling the output pixel density as an example. The same principle may be applied to tripling, quadrupling, etc., the output pixel density of the light guide display system. 
       FIG.  6    is a flowchart illustrating a method  600  for providing an increased pixel density, according to an embodiment of the present disclosure. The method  600  may be performed by the controller  215 , along with other devices and/or optical elements included in the light guide display systems disclosed herein. The method  600  may include controlling, by a controller during a first time period, at least one of an in-coupling element or an out-coupling element to couple an input image light into a light guide, and couple the input image light out of the light guide as a first output image light having a first FOV (step  610 ). The method  600  may also include controlling, by the controller during a second time period, at least one of the in-coupling element or the out-coupling element to couple the input image light into the light guide, and couple the input image light out of the light guide as a second output image light having a second FOV, the second FOV substantially overlapping with the first FOV, and an axis of symmetry of the first FOV being rotated from an axis of symmetry of the second FOV (step  620 ). 
     The method  600  may include other steps or processes described above that are not shown in  FIG.  6   . For example, the method  600  may include generating, by a light source assembly, an input image light representing a virtual image during each of the first time period and the second time period. In some embodiments, the first time period and the second time period may be a first sub-frame and a second sub-frame of a display frame of the virtual image. The input image light may have an input FOV, and the first FOV and the second FOV may have a same size as the input FOV. In some embodiments, during the first sub-frame of the display frame of the virtual image, the controller  215  may control at least one of the in-coupling element or the out-coupling element, to couple a first input image light into the light guide and couple the first input image light out of the light guide as a first output image light. During a second sub-frame of the frame of the image, the controller  215  may control at least one of the in-coupling element or the out-coupling element, to couple a second input image light into the light guide and couple the second input image light out of the light guide as a second output image light. The first input image light and the second input image light may have the same input FOV. 
     The first output image light and the second output image light may propagate toward the same exit pupil. The first output image light may have a first FOV, and the second image light may have a second FOV. The first FOV and the second FOV may have the same FOV size. The first FOV and the second FOV may substantially overlap one another, with a slight shift in their respective axes of symmetry. In other words, the second output image light may be considered as a duplicate of the first output image light, and may be slightly rotated for an angle relative to the first output image light. When the sub-frames are sufficiently short, and the relative rotation between the first output image light and the second output image light is smaller than the angular resolution of the eye at the exit pupil, the user may perceive both the first output image light and the second output image light as a single image light with an increased pixel density (or resolution) and an increased brightness. 
     In some embodiments, the in-coupling element may include an in-coupling grating. The controller may control the in-coupling grating to operate in a first diffraction state during the first time period, and to operate in a second diffraction state during the second time period. The first diffraction state may be different from the second diffraction state, such that the in-coupling grating may provide different diffraction angles to a same input image light incident thereonto. 
     In some embodiments, the out-coupling element may include an out-coupling grating. The controller may control the out-coupling grating to operate in a first diffraction state during the first time period, and to operate in a second diffraction state during the second time period. The first diffraction state may be different from the second diffraction state, such that the out-coupling grating may provide different diffraction angles to a same image light incident thereonto. 
     In some embodiments, the in-coupling element may include an in-coupling grating, and the out-coupling element may include an out-coupling grating. In some embodiments, during the first time period, the controller may control both of the in-coupling grating and the out-coupling grating to operate in their respective first diffraction states, and during the second time period, the controller may control both of the in-coupling grating and the out-coupling grating to operate in their respective second diffraction states. 
     In some embodiments, the in-coupling element may include a first in-coupling grating and a second in-coupling grating stacked together. During the first time period, the controller may control the first in-coupling grating to operate in a diffraction state and the second in-coupling grating to operate in a non-diffraction state. During the second time period, the controller may control the first in-coupling grating to operate in the non-diffraction state, and the second in-coupling grating to operate in the diffraction state. The first in-coupling grating operating in the diffraction state and the second in-coupling grating operating in the diffraction state may provide different diffraction angles to image lights with a same incidence angle. 
     In some embodiments, the out-coupling element may include a first out-coupling grating and a second out-coupling grating stacked together. During the first time period, the controller may control the first out-coupling grating to operate in the diffraction state and the second out-coupling grating to operate in the non-diffraction state. During the second time period, the controller may control the first out-coupling grating to operate in the non-diffraction state and the second out-coupling grating to operate in the diffraction state. The first out-coupling grating operating in the diffraction state and the second out-coupling grating operating in the diffraction state may provide different diffraction angles to image lights with a same incidence angle. 
     In some embodiments, the in-coupling element may include a first in-coupling grating and a second in-coupling grating stacked together, and the out-coupling element may include a first out-coupling grating and a second out-coupling grating stacked together. During the respective time period of a first time period, a second time period, a third time period, and a fourth time period, the controller may control different combinations of the in-coupling gratings and the out-coupling gratings to operate in the diffraction state, and control the remaining in-coupling gratings and out-coupling gratings to operate in the non-diffraction state. For example, during each time period, the controller may control one of the first and second in-coupling gratings and one of the first and second out-coupling gratings to operate in the diffraction state, and control the other one of the first and second in-coupling gratings and the other one of the first and second out-coupling gratings to operate in the non-diffraction state. The first in-coupling grating operating in the diffraction state and the second in-coupling grating operating in the diffraction state may provide different diffraction angles to image lights with a same incidence angle. The first out-coupling grating operating in the diffraction state and the second out-coupling grating operating in the diffraction state may provide different diffraction angles to image lights with a same incidence angle. 
     The disclosed optical systems (e.g., light guide display systems) and method for providing an increased output pixel density may be implemented in various systems, e.g., a near-eye display (“NED”), a head-up display (“HUD”), a head-mounted display (“HMD”), smart phones, laptops, or televisions, etc. In addition, the light guide display systems shown in the figures are for illustrative purposes to explain the mechanism for providing an increased output pixel density (pixel per degree) that may be two times, three times, or four times, etc., of an input pixel density (pixel per degree). The mechanism for an increased output pixel density may be applicable to any suitable display systems other than the disclosed light guide display systems. The gratings are for illustrative purposes. Any suitable light deflecting elements (e.g., non-switchable light deflecting elements, indirectly switchable light deflecting elements, and/or directly switchable light deflecting elements) may be used and configured to provide the increased output pixel density, following the same or similar design principles described herein with respect to the gratings. 
     A non-switchable light deflecting element may be a passive light deflecting element. In some embodiments, the passive light deflecting element may be polarization non-selective (or polarization independent). An indirectly switchable light deflecting element may be a passive light deflecting element that is polarization selective. The indirectly switchable light deflecting element may be switchable between different operating states when the polarization of the input light is switched by a polarization switch coupled with the passive light deflecting element. A directly switchable light deflecting element may be switchable between different operating states when a driving voltage applied to the directly switchable light deflecting element is controlled to be different voltages. 
     For example, the light deflecting element may include a polarization selective grating or a holographic element that includes sub-wavelength structures, liquid crystals, a photo-refractive holographic material, or a combination thereof. In some embodiments, the polarization non-selective light deflecting element may also be implemented and configured to provide an increased output pixel density. In some embodiments, the light deflecting elements may include diffraction gratings, cascaded reflectors, prismatic surface elements, an array of holographic reflectors, or a combination thereof. The controller may be configured to configure a light deflecting element to operate at a light deflection state to deflect an input light to change a propagating direction of the input light, or operate at a light non-deflection state in which the light deflecting element may not change the propagating direction of the input light. 
       FIG.  7 A  illustrates a schematic diagram of a near-eye display (“NED”)  700  according to an embodiment of the present disclosure.  FIG.  7 B  is a cross-sectional view of half of the NED  700  shown in  FIG.  7 A  according to an embodiment of the present disclosure. For purposes of illustration,  FIG.  7 B  shows the cross-sectional view associated with a left-eye display system  710 L. The NED  700  may include a controller (not shown), which may be similar to the controller  215 . The NED  700  may include a frame  705  configured to mount to a user&#39;s head. The frame  705  is merely an example structure to which various components of the NED  700  may be mounted. Other suitable type of fixtures may be used in place of or in combination with the frame  705 . The NED  700  may include right-eye and left-eye display systems  710 R and  710 L mounted to the frame  705 . The NED  700  may function as a VR device, an AR device, an MR device, or any combination thereof. In some embodiments, when the NED  700  functions as an AR or an MR device, the right-eye and left-eye display systems  710 R and  710 L may be entirely or partially transparent from the perspective of the user, which may provide the user with a view of a surrounding real-world environment. In some embodiments, when the NED  700  functions as a VR device, the right-eye and left-eye display systems  710 R and  710 L may be opaque to block the light from the real-world environment, such that the user may be immersed in the VR imagery based on computer-generated images. 
     The left-eye and right-eye display systems  710 L and  710 R may include image display components configured to project computer-generated virtual images into left and right display windows  715 L and  715 R in a field of view (“FOV”). The left-eye and right-eye display systems  710 L and  710 R may be any suitable display systems. In some embodiments, the left-eye and right-eye display systems  710 L and  710 R may include one or more optical systems (e.g., light guide display systems) disclosed herein, such as the light guide display system  200  shown in  FIG.  2 A , the light guide display system  250  shown in  FIG.  2 B , the light guide display system  270  shown in  FIGS.  2 C- 2 E , the light guide display system  300  shown in  FIG.  3 A , the light guide display system  350  shown in  FIG.  3 B , the light guide display system  400  shown in  FIGS.  4 A and  4 B , or the light guide display system  500  shown in  FIGS.  5 A- 5 C . For illustrative purposes,  FIG.  7 A  shows that the left-eye display systems  710 L may include a light source assembly (e.g., a projector)  735  coupled to the frame  705  and configured to generate an image light representing a virtual image. 
     As shown in  FIG.  7 B , the left-eye display systems  710 L may also include a viewing optical system  780  and an object tracking system  790  (e.g., eye tracking system and/or face tracking system). The viewing optical system  780  may be configured to guide the image light output from the left-eye display system  710 L to the exit pupil  727 . The exit pupil  257  may be a location where an eye pupil  258  of the eye  260  of the user is positioned in the eye-box region  259  of the left-eye display system  710 L. For example, the viewing optical system  780  may include one or more optical elements configured to, e.g., correct aberrations in an image light output from the left-eye display systems  710 L, magnify an image light output from the left-eye display systems  710 L, or perform another type of optical adjustment of an image light output from the left-eye display systems  710 L. Examples of the one or more optical elements may include an aperture, a Fresnel lens, a convex lens, a concave lens, a filter, any other suitable optical element that affects an image light, or a combination thereof. 
     The object tracking system  790  may include an IR light source  791  configured to illuminate the eye  260  and/or the face, a deflecting element  792  (such as a grating), and an optical sensor  793  (such as a camera). The deflecting element  792  may deflect (e.g., diffract) the IR light reflected by the eye  260  toward the optical sensor  793 . The optical sensor  793  may generate a tracking signal relating to the eye  260 . The tracking signal may be an image of the eye  260 . A controller (not shown), such as the controller  215 , may control various optical elements, such as an active in-coupling element, an active out-coupling element, an active dimming element, etc., based on eye-tracking information obtained from analysis of the image of the eye  260 . 
     In some embodiments, the NED  700  may include an adaptive or active dimming element configured to dynamically adjust the transmittance of lights reflected by real-world objects, thereby switching the NED  700  between a VR device and an AR device or between a VR device and an MR device. In some embodiments, along with switching between the AR/MR device and the VR device, the adaptive dimming element may be used in the AR and/MR device to mitigate differences in brightness of lights reflected by real-world objects and virtual image lights. 
       FIGS.  8 A- 11 H  illustrate exemplary active diffractive optical elements (e.g., active gratings), which may be implemented in various light guide display systems disclosed herein, for example, as gratings described above and shown in other figures for providing an increased output pixel density. The active diffractive optical element (e.g., active grating) may be implemented as an in-coupling element, an out-coupling element, or a redirecting element. 
       FIGS.  8 A and  8 B  illustrate a schematic diagram of an active grating  801  at a diffraction state and a non-diffraction state, respectively, according to an embodiment of the disclosure. The active grating  801  may be implemented into a light guide display system disclosed herein as an in-coupling grating, an out-coupling grating, or a redirecting grating. A power source  840  may be electrically coupled with the active grating  801  via electrodes (not shown) disposed at the active grating  801 . The power source  840  may provide an electric field to the active grating  801  through the electrodes. The controller  215  may be electrically coupled (e.g., through a wired or wireless connection) with the power source  840 , and may control the output voltage and/or current of the power source  840 . The active grating  801  may be switchable between a diffraction state and a non-diffraction state, when the controller  215  controls the power source  840  to generate a suitable electric field in the active grating  801 . As described above, an active grating may be polarization selective or polarization nonselective. For illustrative purposes, the active grating  801  is shown as a polarization selective grating. 
     As shown in  FIGS.  8 A and  8 B , the active grating  801  may include an upper substrate  810  and a lower substrate  815  arranged opposing (e.g., facing) one another. In some embodiments, when the active grating  801  is implemented into a light guide display system disclosed herein, the active grating  801  may be disposed at a surface of the light guide (e.g.,  210 ,  410 , etc.). In some embodiments, one of the upper substrate  810  and the lower substrate  815  may be the light guide or a part of the light guide. In some embodiments, at least one (e.g., each) of the upper substrate  810  or the lower substrate  815  may be provided with a transparent electrode at a surface (e.g., an inner surface) of the substrate for supplying an electric field to the active grating  801 , such as an indium tin oxide (“ITO”) electrode. The power source  840  may be coupled with the transparent electrodes to supply a voltage for providing the electric field to the active grating  801 . 
     In some embodiments, the active grating  801  may include a surface relief grating (“SRG”)  805  disposed at (e.g., bonded to or formed on) a surface of the lower substrate  815  facing the upper substrate  810 . The SRG  805  may include a plurality of microstructures  805   a , with sizes in micron levels or nano levels, which define or form a plurality of grooves  806 . The microstructures  805   a  are schematically illustrated as solid black longitudinal structures, and the grooves  806  are shown as white portions between the solid black portions. The number of the grooves  806  may be determined by the grating period and the size of the SRG  805 . The grooves  806  may be at least partially provided (e.g., filled) with a birefringent material  850 . Optically anisotropic molecules  820  of the birefringent material  850  may have an elongated shape (represented by white rods in  FIGS.  8 A and  8 B ). The optically anisotropic molecules  820  may be aligned within the grooves  806  in any suitable alignment manner, such as homeotropic alignment, or homogeneous alignment, etc. The birefringent material  850  may have a first principal refractive index (e.g., n e   AN ) along a groove direction (e.g., y-axis direction, length direction, or longitudinal direction) of the grooves  806 . The birefringent material  850  may have a second principal refractive index (e.g., n o   AN ) along an in-plane direction (e.g., x-axis direction, width direction, or lateral direction) perpendicular to the groove direction of the SRG  805 . 
     When the grooves  806  have a substantially rectangular prism shape, or a longitudinal shape, the groove direction may be a groove length direction. In some embodiments, the grooves  806  may have other shapes. Accordingly, the groove direction may be other suitable directions. The birefringent material  850  may be an active, optically anisotropic material, such as active liquid crystals (“LCs”) with LC directors reorientable by an external field, e.g., the electric field provided by the power source  840 . The optically anisotropic molecules  820  of the birefringent material  850  may also be referred to as LC molecules  820 . The active LCs may have a positive or negative dielectric anisotropy. 
     The SRG  805  may be fabricated based on an organic material, such as amorphous or liquid crystalline polymers, or cross-linkable monomers including those having LC properties (reactive mesogens (“RMs”)). In some embodiments, the SRG  805  may be fabricated based on an inorganic material, such as metals or oxides used for manufacturing metasurfaces. The materials of the SRG  805  may be isotropic or anisotropic. In some embodiments, the SRG  805  may provide an alignment for the birefringent material  850 . That is, the SRG  805  may function as an alignment layer to align the birefringent material  850 . In some embodiments, the optically anisotropic molecules  820  may be aligned within the grooves  806  by a suitable alignment method, such as by a mechanical force (e.g., a stretch), a light (e.g., through photoalignment), an electric field, a magnetic field, or a combination thereof. 
     For illustrative purposes,  FIGS.  8 A and  8 B  show that the SRG  805  may be a binary non-slanted grating with a periodic rectangular profile. That is, the cross-sectional profile of the grooves  806  of the SRG  805  may have a periodic rectangular shape. In some embodiments, the SRG  805  may be a binary slanted grating, in which the microstructures  805   a  are slanted at a slant angle relative to a surface of the substrate  815 , on which the microstructures  805   a  are disposed. In some embodiments, the slant angle of the SRG  805  may continuously vary in a predetermined direction, such as the x-axis direction in  FIG.  8 A . In some embodiments, the cross-sectional profile of the grooves  806  of the SRG  805  may be non-rectangular, for example, sinusoidal, triangular, parallelogrammic (e.g., when the microstructures  805   a  are slanted), or saw-tooth shaped. 
     In some embodiments, the alignment of the birefringent material  850  may be provided by one or more alignment structures (e.g., alignment layers) other than by the SRG  805 . An alignment structure may be disposed at the substrate  810  and/or  815  (e.g., two alignment layers may be disposed at the respective opposing surfaces of the substrates  810  and  815 ). In some embodiments, the alignment structures provided at both of the substrates  810  and  815  may provide parallel planar alignments or hybrid alignments. For example, the alignment structure disposed at one of the substates  810  and  815  may be configured to provide a planar alignment, and the alignment structure disposed at the other one of the substates  810  and  815  may be configured to provide a homeotropic alignment. In some embodiments, the alignment of the birefringent material  850  may be provided by both the SRG  805  and one or more alignment structures (e.g., alignment layers) disposed at the substrate  810  and/or  815 . 
     In some embodiments, as shown in  FIG.  8 A , the birefringent material  850  may include active LCs having a positive anisotropy, such as nematic liquid crystals (“NLCs”). The LC molecules  820  of the birefringent material  850  may be homogeneously aligned within the grooves  806  in the groove direction (e.g., y-axis direction). The second principal refractive index (e.g., n o   AN ) may substantially match with a refractive index n g  of the SRG  805 , and the first principal refractive index (e.g., n e   AN ) may not match with the refractive index n g  of the SRG  805 . The active grating  801  may be linear polarization dependent. 
     For example, referring to  FIG.  8 A , when a linearly polarized input light  830  polarized in the groove direction (e.g., y-axis direction) is incident onto the active grating  801 , due to the refractive index difference between n e   AN  and n g , the input light  830  may experience a periodic modulation of the refractive index in the active grating  801 . As a result, the active grating  801  may diffract the input light  830  as a light  835 . Due to the substantial match between the refractive indices n o   AN  and n g , the active grating  801  may function as a substantially optically uniform plate for a linearly polarized input light polarized in the in-plane direction (e.g., x-axis direction) perpendicular to the groove direction (e.g., y-axis direction). That is, the active grating  801  may not diffract the input light linearly polarized in the in-plane direction perpendicular to the groove direction. Rather, the active grating  801  may transmit the input light polarized in the in-plane direction with substantially zero or negligible diffraction. 
     In some embodiments, the active grating  801  may be an active grating, which may be directly switchable between a diffraction state (or an activated state) and a non-diffraction state (or a deactivated state) by an external field, e.g., an external electric field provided by the power source  840 . For example, the active grating  801  may include electrodes (not shown) disposed at the upper and lower substrate  810  and  815 , and the power source  840  may be electrically coupled with the electrodes to provide the electric field to the active grating  801 . The controller  215  may control an output (e.g., a voltage and/or current) of the power source  840 . For discussion purposes, the voltage is used as an example output of the power source  840 . By controlling the voltage output by the power source  840 , the controller  215  may control the switching of the active grating  801  between the diffraction state and the non-diffraction state. For example, the controller  215  may control the voltage supplied by the power source  840  to switch the active grating  801  between the diffraction state and the non-diffraction state. When the active grating  801  operates in the diffraction state, the controller  215  may adjust the voltage supplied by the power source  840  to the electrodes to adjust the diffraction efficiency. 
     In some embodiments, the controller  215  may control the voltage supplied by the power source  840  to be lower than or equal to a threshold voltage, thereby configuring the active grating  801  to operate in the diffraction state (or activated state). In some embodiments, the threshold voltage may be determined by physical parameters of the active grating  801 . When the voltage is lower than or equal to the threshold voltage, the electric field generated by the supplied voltage may be insufficient to reorient the LC molecules  820 . When the controller  215  controls the supplied voltage to be higher than the threshold voltage (and sufficiently high) to reorient the LC molecules  820  to substantially follow (e.g., be parallel with) the direction of the electric field, the active grating  801  may operate in the non-diffraction state (or deactivated state). 
     As shown in  FIG.  8 A , when the controller  215  controls the power source  840  to supply a voltage that is lower than or equal to the threshold voltage (e.g., when the power source  840  supplies a substantially zero voltage), for the linearly polarized input light  830  polarized in the groove direction (e.g., y-axis direction) of the SRG  805 , due to the difference between the refractive indices n e   AN  and n g , the light  830  may experience a periodic modulation of the refractive index in the active grating  801  while propagating therethrough. As a result, the active grating  801  may diffract the light  830  as the light  835 . That is, the controller  215  may control the power source  840  to supply a voltage that is lower than or equal to the threshold voltage, thereby configuring the active grating  801  to operate in the diffraction state to diffract the linearly polarized input light  830 . In some embodiments, when the active grating  801  operates in the diffraction state, the diffraction angle of the light  835  may be tunable (or adjustable). For example, the controller  215  may tune (or adjust) a magnitude of the supplied voltage to tune the modulation of the refractive index in the active grating  801 , thereby tuning the diffraction angle of the light  835 . 
     As shown in  FIG.  8 B , when a voltage is supplied to the active grating  801 , an electric field (which may extend in the z-axis direction) may be generated between the parallel substrates  810  and  815 . When the voltage is higher than the threshold voltage and is gradually increased, the LC molecules  820  (of LCs having the positive dielectric anisotropy) may gradually become reoriented by the electric field to align in parallel with the electric field direction. As the voltage changes, for the linearly polarized input light  830  polarized in the groove direction (e.g., y-axis direction), the modulation of the refractive index nm (i.e., the difference between n e   AN  and n g ) provided by the active grating  801  to the light  830  may change accordingly, which in turn may change the diffraction efficiency. 
     When the voltage is sufficiently high, as shown in  FIG.  8 B , directors of the LC molecules  820  (of LCs having the positive dielectric anisotropy) may be reoriented to be parallel with the electric field direction (e.g., z-axis direction). Due to the substantial match between the refractive indices n o   AN  and n g , the active grating  801  may function as a substantially optically uniform plate for the input light  830  polarized in the groove direction. The active grating  801  may operate in a non-diffraction state to transmit the light  830  therethrough as a light  890  with substantially zero or negligible diffraction. 
     In the embodiment shown in  FIGS.  8 A and  8 B , the active grating  801  is configured to operate in the diffraction state when the voltage supplied by the power source  840  is lower than or equal to the threshold voltage, and operate in the non-diffraction state when the voltage is sufficiently higher than the threshold voltage. In other embodiments, by configuring the initial orientations of the LC molecules  820  differently, the active grating  801  may be configured to operate in the diffraction state when the voltage is sufficiently higher than the threshold voltage, and operate in the non-diffraction state when the voltage is lower than or equal to the threshold voltage. 
       FIGS.  9 A- 9 F  illustrate schematic diagrams of an active grating  901 , according to an embodiment of the disclosure. The active grating  901  may be implemented into a light guide display system disclosed herein as an in-coupling grating, an out-coupling grating, or a redirecting grating. As shown in  FIG.  9 A , the power source  840  may be electrically coupled with the active grating  901  to provide an electric field to the active grating  901 . The controller  215  may be electrically coupled (e.g., through wired or wireless connection) with the power source  840 , and may control the output of a voltage and/or current from the power source  840 . The active grating  901  may be switchable between a diffraction state and a non-diffraction state, when the controller  215  controls the power source  840  to generate a suitable electric field. For illustrative purposes, the active grating  901  is shown as an active, polarization selective grating. 
       FIGS.  9 A and  9 D  illustrate schematic diagrams of the active grating  901  in the diffraction state, according to an embodiment of the present disclosure.  FIG.  9 A  illustrates an x-z sectional view of the active grating  901  in the diffraction state, and  FIG.  9 D  illustrates an x-y sectional view of the active grating  901  in the diffraction state. As shown in  FIGS.  9 A and  9 D , the active grating  901  may be an H-PDLC grating  901 , which may be fabricated by polymerizing an isotropic photosensitive liquid mixture of monomers and LCs under a laser interference irradiation. The H-PDLC grating  901  may include layers of LC droplets  902  embedded in a polymer matrix  904  disposed between two substrates  906 . One of the two substrate  906  may be provided with a transparent conductive electrode layer  908 , such as an ITO electrode layer. In some embodiments, the electrode layer  908  may include interdigitated electrodes  909 . In addition, at least one (e.g., each) of the substrates  906  may be provided with an alignment layer (not shown), which may be configured to homogeneously (or horizontally) align LC molecules  920  in a predetermined alignment direction, e.g., an x-axis direction in  FIG.  9 A . 
     The substrate  906  provided with the electrode layer  908  may also be provided with a low refractive index layer  910 . In some embodiments, the low refractive index layer  910  may be configured to have a refractive index that is less than a refractive index n p  of the material of the polymer matrix  904 . For example, the refractive index n p  of the material of the polymer matrix  904  may be about 1.3, and the refractive index of the low refractive index layer  910  may be less than 1.3 and close to the refractive index of air. For discussion purposes,  FIG.  9 A  shows that the upper substate  906  is provided with the electrode layer  908  and the low refractive index layer  910 . The low refractive index layer  910  may be disposed between the electrode layer  908  and the alignment layer of the upper substate  906 . The lower substate  906  may not be provided with an electrode layer  908 . 
     Referring to  FIG.  9 A , an ordinary refractive index n o  of the LCs within the LC droplets  902  may be sufficiently close to the refractive index n p  of the material of the polymer matrix  904 , and an extraordinary refractive index n e  of the LCs within the LC droplets  902  may be substantially different from the refractive index n p  of the material of the polymer matrix  904 . Due to the refractive index difference between the extraordinary refractive index n e  of the LCs and the refractive index n p  of the material of the polymer matrix  904 , the spatial modulation of the LCs may produce a modulation in the average refractive index, resulting in an optical phase grating. When an input light  930  that is linearly polarized in the predetermined alignment direction (e.g., an x-axis direction) is incident onto the active grating  901  from the lower substate  906 , due to the refractive index difference between n e  and n p , the input light  930  may experience a periodic modulation of the refractive index in the active grating  901 . As a result, the active grating  901  may diffract the input light  930  as a light  935 . For illustrative purposes,  FIG.  9 A  shows that the active grating  901  forwardly diffracts the input light  930  as the light  935 . In some embodiments, although not shown, the active grating  901  may backwardly diffract the input light  930  as the light  935 . 
     The LC droplets  902  are usually small (dimensions in sub-wavelength ranges) so that scattering due to refractive index mismatch of the LC and polymer may be minimized, and phase modulation may play a primary role. In other words, H-PDLC may belong to a class of nano-PDLC. The haze of the H-PDLC grating  901  caused by the scattering of the LC droplets  902  may be substantially small. 
     For an input light linearly polarized in a direction (e.g., a y-axis direction) perpendicular to the predetermined alignment direction (e.g., an x-axis direction) of the H-PDLC grating  901 , due to the substantial match between the refractive indices n o  and n g , the H-PDLC grating  901  may function as a substantially optically uniform plate. That is, the H-PDLC grating  901  may not diffract, but may transmit the input light linearly polarized in the direction (e.g., a y-axis direction) perpendicular to the predetermined alignment direction (e.g., an x-axis direction). 
     The controller  215  may control an output (e.g., a voltage and/or current) of the power source  840 . For example, by controlling the voltage output by the power source  840 , the controller  215  may control the switching of the H-PDLC grating  901  between the diffraction state and the non-diffraction state. When the H-PDLC grating  901  operates in the diffraction state, the controller  215  may adjust the voltage supplied by the power source  840  to adjust the diffraction angle. In some embodiments, the controller  215  may configure the active grating  901  to operate in the diffraction state by controlling a voltage supplied by the power source  840  to be lower than or equal to a threshold voltage. When the voltage is lower than or equal to the threshold voltage, the electric field generated by the supplied voltage may be insufficient to reorient the LC molecules  920  in the LC droplets  902 . In some embodiments, the controller  215  may configure the H-PDLC grating  901  to operate in the non-diffraction state by controlling the supplied voltage to be higher than the threshold voltage (and sufficiently high) to reorient the LC molecules  920  to be parallel with the direction of the electric field. 
       FIGS.  9 B and  9 E  illustrate schematic diagrams of the active grating  901  in the non-diffraction state, according to an embodiment of the present disclosure.  FIG.  9 B  illustrates an x-z sectional view of the active grating  901  in the non-diffraction state, and  FIG.  9 E  illustrates an x-y sectional view of the active grating  901  in the non-diffraction state. As shown in  FIGS.  9 B and  9 E , when a voltage is supplied to the H-PDLC grating  901 , an electric field (e.g., along a z-axis direction) may be generated between the interdigitated electrodes  909 . When the voltage is higher than the threshold voltage and is gradually increased, the LC molecules  920  (of LCs having the positive dielectric anisotropy) may gradually become reoriented by the electric field to align in parallel with the electric field direction. Depending on the gap L between the two neighboring interdigitated electrodes and the thickness D of the active grating  901 , the generated electric field may be an in plane electric field that is within a plane (e.g., within the x-y plane) perpendicular to a thickness direction of the active grating  901  or a vertical electric field that is in a thickness direction (e.g., the z-axis direction) of the active grating  901 . 
     In the embodiment shown in  FIGS.  9 B and  9 E , the gap L between the two neighboring interdigitated electrodes and the thickness D of the active grating  901  may be configured, such that the generated electric field may be a vertical electric field that is in a thickness direction (e.g., the z-axis direction) of the active grating  901 . When the voltage is sufficiently high, as shown in  FIGS.  9 B and  9 E , directors of the LC molecules  920  (of LCs having the positive dielectric anisotropy) may be reoriented to be parallel with the electric field direction (e.g., the z-axis direction). Due to the substantial match between the refractive indices n o  and n g , the H-PDLC grating  901  may function as a substantially optically uniform plate for the input light  930 . As shown in  FIG.  9 B , the H-PDLC grating  901  may operate in a non-diffraction state for the light  930  polarized in the predetermined alignment direction (e.g., the x-axis direction), and may transmit the light  930  therethrough as a light  937  with substantially zero or negligible diffraction. 
       FIGS.  9 C and  9 F  illustrate schematic diagrams of the active grating  901  in the non-diffraction state, according to an embodiment of the present disclosure.  FIG.  9 C  illustrates an x-z sectional view of the active grating  901  in the non-diffraction state, and  FIG.  9 F  illustrates an x-y sectional view of the active grating  901  in the non-diffraction state. In the embodiment shown in  FIGS.  9 C and  9 F , the gap L between the two neighboring interdigitated electrodes and the thickness D of the active grating  901  may be configured, such that the generated electric field may be an in-plane electric field that is within a plane (e.g., the x-y plane) perpendicular to a thickness direction of the active grating  901 . When the voltage is sufficiently high, as shown in  FIGS.  9 C and  9 F , directors of the LC molecules  920  (of LCs having the positive dielectric anisotropy) may be reoriented to be parallel with the electric field direction (e.g., the y-axis direction). Due to the substantial match between the refractive indices n o  and n g , the H-PDLC grating  901  may function as a substantially optically uniform plate for the input light  930 . As shown in  FIG.  9 C , the H-PDLC grating  901  may operate in a non-diffraction state for the light  930  polarized in the predetermined alignment direction (e.g., the x-axis direction), and may transmit the light  930  therethrough as a light  939  with substantially zero or negligible diffraction. 
       FIGS.  9 A- 9 C  show that the H-PDLC grating  901  includes layers (e.g., three layers) of LC droplets  902  embedded in the polymer matrix  904 , and the LC droplets  902  in the same layer may be separated from one another. In some embodiments, although not shown, the LC droplets  902  in the same layer may not be separated from one another. Instead, the LC droplets  902  may be in contact with one another to form a continuous LC layer. Two neighboring LC layers may be separated by the polymer matrix  904 . In other words, the active grating  901  may include LC layers and polymer layers alternately arranged. Thus, the scattering of the LC droplets  902  may be reduced and, accordingly, the haze of the H-PDLC grating  901  caused by the scattering of the LC droplets  902  may be reduced. 
     In the embodiment shown in  FIGS.  9 A- 9 E , the H-PDLC grating  901  is configured to operate in the diffraction state when the voltage supplied by the power source  840  is lower than or equal to the threshold voltage, and to operate in the non-diffraction state when the voltage is sufficiently higher than the threshold voltage. In other embodiments, by configuring the initial orientations of the LC molecules  920  differently (e.g., homeotropically aligning LCs having a negative dielectric anisotropy), the H-PDLC grating  901  may be configured to operate in the diffraction state when the voltage supplied by the power source  840  is sufficiently higher than the threshold voltage, and to operate in the non-diffraction state when the voltage supplied by the power source  840  is lower than or equal to the threshold voltage. 
     In some embodiments, when the active grating  901  is implemented in a light guide display system disclosed herein as an in-coupling grating, an out-coupling grating, or a redirecting grating, the lower substrate  906  may be a light guide or a part of the light guide in a light guide display system disclosed herein. That is, the polymer matrix  904  embedded with the LC droplets  902  may be disposed between the upper substate  906  (that is provided with the electrode layer  908  and the low refractive index layer  910 ), and the light guide of the light guide display system.  FIG.  9 G  illustrates an x-z sectional view of the active grating  901  implemented in a light guide display system disclosed herein, such as the light guide display system  200  shown in  FIG.  2 A , the light guide display system  250  shown in  FIG.  2 B , the light guide display system  270  shown in  FIGS.  2 C- 2 E , the light guide display system  300  shown in  FIG.  3 A , the light guide display system  350  shown in  FIG.  3 B , the light guide display system  400  shown in  FIGS.  4 A and  4 B , or the light guide display system  500  shown in  FIGS.  5 A- 5 C   
     For discussion purposes,  FIG.  9 G  shows that the active grating  901  functions as an out-coupling grating in the light guide display system disclosed herein. An input image light output from a light source assembly may be coupled, via an in-coupling element, into the lower substrate  906  (or the light guide  906 ) as an in-coupled image light (or a TIR propagating image light)  931 . The in-coupled image light  931  may propagate toward the active grating  901  (or the out-coupling grating  901 ) via TIR. When the in-coupled image light  931  interacts with the polymer matrix  904  embedded with the LC droplets  902 , the polymer matrix  904  embedded with the LC droplets  902  may diffract a first portion of the in-coupled image light  931  as an output image light  932  out of the active grating  901 . A second portion of the in-coupled image light  931  may propagate toward the upper substrate  906  provided with the low refractive index layer  910  and the electrode layer  908 . As the refractive index of the low refractive index layer  910  is configured to be less than the average refractive index of the polymer matrix  904  embedded with the LC droplets  902 , the second portion of the in-coupled image light  931  may be totally internally reflected at the interface between the polymer matrix  904  embedded with the LC droplets  902  and the low refractive index layer  910  toward the light guide  906 . Thus, the second portion of the in-coupled image light  931  may not be incident onto the electrode layer (e.g., ITO electrode layer)  908 , and may not be absorbed by the electrode layer  908 . Thus, when the in-coupled image light  931  propagating inside the light guide  906  is gradually coupled out of the light guide  906  as the output image lights  932 , the absorption of the in-coupled image light  931  caused by the electrode layer (e.g., ITO electrode layer)  908  may be reduced. For illustrative purposes,  FIG.  9 G  shows that the active grating  901  forwardly diffracts the in-coupled image light  931  as the output image light  932 . In some embodiments, although not shown, the active grating  901  may backwardly diffract the in-coupled image light  931  as the output image light  932 . 
       FIGS.  10 A- 10 D  illustrate schematic diagrams of liquid crystal polarization hologram (“LCPH”) gratings, according to various embodiments of the present disclosure. Liquid crystal polarization holograms (“LCPHs”) refer to the intersection of liquid crystal devices and polarization holograms. LCPH elements have features such as flatness, compactness, high efficiency, high aperture ratio, absence of on-axis aberrations, flexible design, simple fabrication, and low cost, etc. Thus, LCPH elements can be implemented in various applications such as portable or wearable optical devices or systems. Among LCPH elements, liquid crystal (“LC”) based Pancharatnam-Berry phase (“PBP”) elements and polarization volume hologram (“PVH”) elements have been extensively studied. A PBP element may modulate a circularly polarized light based on a phase profile provided through a geometric phase. A PVH element may modulate a circularly polarized light based on Bragg diffraction. 
     An LCPH grating (e.g., a PBP grating, a PVH grating, etc.) may be formed by a thin layer of one or more birefringent materials with intrinsic or induced (e.g., photo-induced) optical anisotropy (referred to as an optically anisotropic layer or a birefringent medium layer). A desirable predetermined grating phase profile may be directly encoded into local orientations of the optic axis of the birefringent medium layer. An LCPH grating described herein may be fabricated based on various methods, such as holographic interference, laser direct writing, ink-jet printing, and various other forms of lithography. Thus, a “hologram” described herein is not limited to creation by holographic interference, or “holography.” 
     An LCPH grating may be switchable between a diffraction state and a non-diffraction state. In some embodiments, an LCPH grating operating in the diffraction state may provide a tunable diffraction angle to an incident light. An LCPH grating may be transmissive or reflective. An LCPH grating may be polarization selective or polarization non-selective. An LCPH grating may be implemented into a light guide display system disclosed herein as an in-coupling grating, an out-coupling grating, or a redirecting grating. 
       FIGS.  10 A and  10 B  illustrate schematic diagrams a transmissive-type LCPH grating  1005  in a diffraction state and a non-diffraction state, respectively, according to an embodiment of the present disclosure. For discussion purposes, the LCPH grating  1005  is polarization selective. As shown in  FIGS.  10 A and  10 B , the power source  840  may be electrically coupled with the LCPH grating  1005  to provide an electric field to the LCPH grating  1005 . The controller  215  may be electrically coupled (e.g., through wired or wireless connection) with the power source  840 , to control an output (e.g., a voltage and/or current) of the power source  840 . For example, by controlling the voltage output by the power source  840 , the controller  215  may control the switching of the LCPH grating  1005  between the diffraction state and the non-diffraction state. 
     In some embodiments, the controller  215  may control the LCPH grating  1005  to operate in the diffraction state by controlling a voltage supplied by the power source  840  to be lower than or equal to a threshold voltage. When the voltage is lower than or equal to the threshold voltage, the electric field generated by the supplied voltage may be insufficient to reorient the LC molecules in the LCPH grating  1005 . As shown in  FIG.  10 A , the LCPH grating  1005  that operates in the diffraction state may substantially forwardly diffract an incident light  1035  with a predetermined polarization (e.g., a circularly polarized light with a predetermined handedness) as a light of a predetermined order, such as, a +1 st  order diffracted light  1040 . In some embodiments, the polarization of the diffracted light  1040  may be opposite or orthogonal to the polarization of the incident light  1035 . For example, the diffracted light  1040  may be a circularly polarized light with handedness that is opposite or orthogonal to the predetermined handedness. In some embodiments, when the LCPH grating  1005  operates in the diffraction state, the controller  215  may adjust the voltage supplied by the power source  840  to adjust the diffraction angle of the diffracted light  1040 . For example, as the voltage supplied by the power source  840  increases, the grating period of the LCPH grating  1005  may increase, and the diffraction angle of the diffracted light  1040  may decrease. 
     In some embodiments, the controller  215  may control the LCPH grating  1005  to operate in the non-diffraction state by controlling the supplied voltage to be higher than the threshold voltage (and sufficiently high) to reorient the LC molecules LCPH grating  1005  to be parallel with the direction of the electric field. As shown in  FIG.  10 B , the LCPH grating  1005  operating in the non-diffraction state may substantially transmit the incident light  1035  as a light  1045 , with negligible or zero diffraction. In some embodiments, transmission of the incident light  1035  as the transmitted light  1045  may be polarization independent. In some embodiments, the LCPH grating  1005  may transmit the incident light  1035  without affecting the polarization thereof. For example, the incident light  1035  and the transmitted light  1045  may have the same polarization. For example, the incident light  1035  and the transmitted light  1045  may be circular polarized lights with the same handedness. In some embodiments, the LCPH grating  1005  may change the polarization of the incident light  1035 , while transmitting the incident light  1035 . For example, the incident light  1035  and the transmitted light  1045  may be circular polarized lights with opposite handednesses. 
       FIGS.  10 C and  10 D  illustrate schematic diagrams a reflective-type LCPH grating  1050  in a diffraction state and a non-diffraction state, respectively, according to an embodiment of the present disclosure. For discussion purposes, the LCPH grating  1050  is presumed to be polarization selective. As shown in  FIGS.  10 C and  10 D , the power source  840  may be electrically coupled with the LCPH grating  1050  to provide an electric field to the LCPH grating  1050 . The controller  215  may be electrically coupled (e.g., through wired or wireless connection) with the power source  840 , to control an output (e.g., a voltage and/or current) of the power source  840 . For example, by controlling the voltage output by the power source  840 , the controller  215  may control the switching of the LCPH grating  1050  between the diffraction state and the non-diffraction state. 
     In some embodiments, the controller  215  may configure the LCPH grating  1050  to operate in the diffraction state by controlling a voltage supplied by the power source  840  to be lower than or equal to a threshold voltage. When the voltage is lower than or equal to the threshold voltage, the electric field generated by the supplied voltage may be insufficient to reorient the LC molecules in the LCPH grating  1050 . As shown in  FIG.  10 C , the LCPH grating  1050  operating in the diffraction state may substantially backwardly diffract an incident light  1035  with a predetermined polarization (e.g., a circularly polarized light with a predetermined handedness) as a light of a predetermined order, such as, a +1 st  order diffracted light  1060 . In some embodiments, the diffracted light  1060  and the incident light  1035  may have the same polarization. For example, the diffracted light  1060  and the incident light  1035  may be circular polarized lights with the same handedness. In some embodiments, when the LCPH grating  1050  operates in the diffraction state, the controller  215  may adjust the voltage supplied by the power source  840  to adjust the diffraction angle of the diffracted light  1060 . For example, as the voltage supplied by the power source  840  increases, the grating period of the LCPH grating  1050  may increase, and the diffraction angle of the diffracted light  1060  may decrease. 
     In some embodiments, the controller  215  may control the LCPH grating  1050  to operate in the non-diffraction state by controlling the supplied voltage to be higher than the threshold voltage (and sufficiently high) to reorient the LC molecules LCPH grating  1050  to be parallel with the direction of the electric field. As shown in  FIG.  10 D , the LCPH grating  1050  operating in the non-diffraction state may substantially transmit the incident light  1035  as a light  1065 , with negligible or zero diffraction. In some embodiments, the LCPH grating  1050  operating in the non-diffraction state may substantially transmit the incident light  1035  as the transmitted light  1065 . The transmission of the incident light  1035  as the light  1065  may be independent of the polarization of the incident light  1035 . In some embodiments, the LCPH grating  1050  may transmit the incident light  1035  without affecting the polarization thereof. For example, the incident light  1035  and the transmitted light  1065  may be circular polarized lights with the same handedness. In some embodiments, the LCPH grating  1050  may change the polarization of the incident light  1035 , while transmitting the incident light  1035 . In some embodiments, the incident light  1035  and the transmitted light  1065  may have opposite or orthogonal polarizations. For example, the incident light  1035  and the transmitted light  1065  may be circular polarized lights with opposite handednesses. 
       FIG.  11 A  illustrates an x-z sectional view of a liquid crystal polarization hologram (“LCPH”) element  1100  with a light  1102  incident onto the LCPH element  1100  along a −z-axis, according to an embodiment of the present disclosure.  FIGS.  11 B- 11 D  schematically illustrate various views of a portion of the LCPH element  1100  shown in  FIG.  11 A , showing in-plane orientations of optically anisotropic molecules in the LCPH element  1100 , according to various embodiments of the present disclosure.  FIGS.  11 E- 11 H  schematically illustrate various views of a portion of the LCPH element  1100  shown in  FIG.  11 A , showing out-of-plane orientations of optically anisotropic molecules in the LCPH element  1100 , according to various embodiments of the present disclosure. The LCPH element  1100  may be an active LCPH grating, such as the LCPH grating  1005  shown in  FIGS.  10 A and  10 B , or the LCPH grating  1050  shown in  FIGS.  10 C and  10 D . 
     As shown in  FIG.  11 A , although the LCPH element  1100  is shown as a rectangular plate shape for illustrative purposes, the LCPH element  1100  may have any suitable shape, such as a circular shape. In some embodiments, one or both surfaces along the light propagating path of the light  1102  may have curved shapes. The LCPH element  1100  may include two opposite substates  1106 , and a thin layer (or film)  1115  of one or more birefringent materials disposed between the two substates  1106 . The one or more birefringent materials may have an intrinsic or induced (e.g., photo-induced) optical anisotropy, such as liquid crystals, liquid crystal polymers, amorphous polymers. Such a thin layer  1115  may also be referred to as a birefringent medium layer (or film)  1115 , or an LCPH layer (or film)  1115 . In some embodiments, the birefringent medium layer  1115  may include active LCs, such as nematic LCs, twist-bend LCs, chiral nematic LCs, smectic LCs, or any combination thereof. 
     In some embodiments, at least one (e.g., each) of the two substates  1106  may be provided with an alignment structure  1107 . The alignment structure  1107  may provide a suitable alignment pattern to optically anisotropic molecules in the birefringent medium layer  1115 . The alignment pattern may correspond to a predetermined in-plane orientation pattern, such as an in-plane orientation pattern with periodic linear orientations. The alignment structure  1107  may include a suitable alignment structure, such as a photo-alignment material (“PAM”) layer, a mechanically rubbed alignment layer, an alignment layer with anisotropic nanoimprint, an anisotropic relief, or a ferroelectric or ferromagnetic material layer, etc. 
     In some embodiments, at least one (e.g., each) of the two substates  1106  may be provided with a transparent conductive electrode layer (e.g., ITO electrode) layer  1108 . One or more power sources (not shown) may be electrically coupled with the LCPH element  1100 . The one or more power sources may provide one or more electric fields to the LCPH element  1100  via the electrode layer  1108 . In some embodiments, the LCPH element  1100  may include two electrode layers  1108 , and a power source may provide an electric field to the LCPH element  1100  via the two electrode layers  1108 . In some embodiments, the two electrode layers  1108  may be disposed at the two substrates  1106 , respectively. In some embodiments, both of the two electrode layers  1108  may include planar continuous electrodes. In some embodiments, both of the two electrode layers  1108  may include patterned electrodes, e.g., slit electrodes. In some embodiments, one of the two electrode layers  1108  may include a planar continuous electrode, and the other one of the two electrode layers  1108  may include patterned electrodes, e.g., slit electrodes. 
     In some embodiments, each electrode layer  1108  may include two sub-electrode layers, and an electrically insulating layer disposed between the two sub-electrode layers. A respective power source may be electrically coupled with the two sub-electrode layers in each electrode layer  1108 , thereby providing a respective electric field to the LCPH element  1100 . In some embodiments, the two sub-electrode layers may include a planar continuous electrode and patterned electrodes. 
     The birefringent medium layer  1115  may have a first surface  1115 - 1  on one side and a second surface  1115 - 2  on an opposite side. The first surface  1115 - 1  and the second surface  1115 - 2  may be surfaces along the light propagating path of the incident light  1102 . The birefringent medium layer  1115  may include optically anisotropic molecules (e.g., LC molecules) configured with a three-dimensional (“3D”) orientational pattern to provide a polarization selective optical response. In some embodiments, an optic axis of the LC material or birefringent medium layer  1115  may be configured with a spatially varying orientation in at least one in-plane direction. The in-plane direction may be an in-plane linear direction (e.g., an x-axis direction, a y-axis direction), an in-plane radial direction, an in-plane circumferential (e.g., azimuthal) direction, or a combination thereof. The LC molecules may be configured with an in-plane orientation pattern, in which the directors of the LC molecules may periodically or non-periodically vary in the at least one in-plane direction. In some embodiments, the optic axis of the LC material may also be configured with a spatially varying orientation in an out-of-plane direction. The directors of the LC molecules may also be configured with spatially varying orientations in an out-of-plane direction. For example, the optic axis of the LC material (or directors of the LC molecules) may twist in a helical fashion in the out-of-plane direction. 
       FIGS.  11 B- 11 D  schematically illustrate x-y sectional views of a portion of the LCPH element  1100  shown in  FIG.  11 A , showing in-plane orientations of the optically anisotropic molecules  1112  in the LCPH element  1100 , according to various embodiments of the present disclosure. The in-plane orientations of the optically anisotropic molecules  1112  in the LCPH element  1100  shown in  FIGS.  11 B- 11 D  are for illustrative purposes. In some embodiments, the optically anisotropic molecules  1112  in the LCPH element  1100  may have other in-plane orientation patterns. For discussion purposes, rod-like LC molecules  1112  are used as examples of the optically anisotropic molecules  1112 . The rod-like LC molecule  1112  may have a longitudinal axis (or an axis in the length direction) and a lateral axis (or an axis in the width direction). The longitudinal axis of the LC molecule  1112  may be referred to as a director of the LC molecule  1112  or an LC director. An orientation of the LC director may determine a local optic axis orientation or an orientation of the optic axis at a local point of the birefringent medium layer  1115 . The term “optic axis” may refer to a direction in a crystal. A light propagating in the optic axis direction may not experience birefringence (or double refraction). An optic axis may be a direction rather than a single line: lights that are parallel with that direction may experience no birefringence. The local optic axis may refer to an optic axis within a predetermined region of a crystal. For illustrative purposes, the LC directors of the LC molecules  1112  shown in  FIGS.  11 B- 11 D  are presumed to be in the surface of the birefringent medium layer  1115  or in a plane parallel with the surface with substantially small tilt angles with respect to the surface. 
       FIG.  11 B  schematically illustrates an x-y sectional view of a portion of the LCPH element  1100 , showing a periodic in-plane orientation pattern of the orientations of the LC directors (indicated by arrows  1188  in  FIG.  11 B ) of the LC molecules  1112  located in a film plane of the birefringent medium layer  1115 , e.g., a plane parallel with at least one of the first surface  1115 - 1  or the second surface  1115 - 2 . The film plane may be perpendicular to the thickness direction of the birefringent medium layer  1115 . The orientations of the LC directors located in the film plane of the birefringent medium layer  1115  may exhibit a periodic rotation in at least one in-plane direction. The at least one in-plane direction is shown as the x-axis direction in  FIG.  11 B . The periodically varying in-plane orientations of the LC directors form a pattern. The in-plane orientation pattern of the LC directors shown in  FIG.  11 B  may also be referred to as an in-plane grating pattern. Accordingly, the LCPH element  1100  may function as a polarization selective grating, e.g., a PVH grating, or a PBP grating, etc. 
     As shown in  FIG.  11 B , the LC molecules  1112  located in the film plane of the birefringent medium layer  1115  may be configured with orientations of LC directors continuously changing (e.g., rotating) in a first predetermined in-plane direction in the film plane. The first predetermined in-plane direction is the shown as the x-axis in-plane direction. The continuous rotation exhibited in the orientations of the LC directors may follow a periodic rotation pattern with a uniform (e.g., same) in-plane pitch P in . It is noted that the first predetermined in-plane direction may be any other suitable direction in the film plane of the birefringent medium layer  1115 , such as the y-axis direction, the radial direction, or the circumferential direction within the x-y plane. The pitch P in  along the first predetermined (or x-axis) in-plane direction may be referred to as an in-plane pitch or a horizontal pitch. In some embodiments, the in-plane pitch or a horizontal pitch P in  may be tunable through adjusting a voltage applied to the LCPH element  1100 . 
     For simplicity of illustration and discussion, the LCPH element  1100  shown in  FIG.  11 B  is presumed to be a 1D grating. Thus, the orientations in the y-axis direction are the same. In some embodiments, the LCPH element  1100  may be a 2D grating, and the orientations in the y-axis direction may also vary. The pattern with the uniform (or same) in-plane pitch P in  may be referred to as a periodic LC director in-plane orientation pattern. The in-plane pitch P in  may be defined as a distance along the first predetermined (or x-axis) in-plane direction over which the orientations of the LC directors exhibit a rotation by a predetermined value (e.g., 180°). In other words, in the film plane of the birefringent medium layer  1115 , local optic axis orientations of the birefringent medium layer  1115  may vary periodically in the first predetermined (or x-axis) in-plane direction with a pattern having the uniform (or same) in-plane pitch P in . 
     In addition, in the film plane of the birefringent medium layer  1115 , the orientations of the directors of the LC molecules  1112  may exhibit a rotation in a predetermined rotation direction, e.g., a clockwise direction or a counter-clockwise direction. Accordingly, the rotation exhibited in the orientations of the directors of the LC molecules  1112  in the film plane of the birefringent medium layer  1115  may exhibit a handedness, e.g., right handedness or left handedness. In the embodiment shown in  FIG.  11 B , in the film plane of the birefringent medium layer  1115 , the orientations of the directors of the LC molecules  1112  may exhibit a rotation in a clockwise direction. Accordingly, the rotation of the orientations of the directors of the LC molecules  1112  in the film plane of the birefringent medium layer  1115  may exhibit a left handedness. In some embodiments, the LCPH element  1100  having the in-plane orientation pattern shown in  FIG.  11 B  may be polarization selective. 
     In the embodiment shown in  FIG.  11 C , in the film plane of the birefringent medium layer  1115 , the orientations of the directors of the LC molecules  1112  may exhibit a rotation in a counter-clockwise direction. Accordingly, the rotation exhibited in the orientations of the directors of the LC molecules  1112  the film plane of the birefringent medium layer  1115  may exhibit a right handedness. In some embodiments, the LCPH element  1100  having the in-plane orientation pattern shown in  FIG.  11 C  may be polarization selective. 
     In the embodiment shown in  FIG.  11 D , in the film plane of the birefringent medium layer  1115 , domains in which the orientations of the directors of the LC molecules  1112  exhibit a rotation in a clockwise direction (referred to as domains DL) and domains in which the orientations of the directors of the LC molecules  1112  exhibit a rotation in a counter-clockwise direction (referred to as domains DR) may be alternatingly arranged in at least one in-plane direction, e.g., a first (or x-axis) in-plane direction and/or a second (or y-axis) in-plane direction. In some embodiments, the LCPH element  1100  having the in-plane orientation pattern shown in  FIG.  11 D  may be polarization non-selective. 
       FIGS.  11 E- 11 H  schematically illustrate y-z sectional views of a portion of the LCPH element  1100 , showing out-of-plane orientations of the LC directors of the LC molecules  1112  in the LCPH element  1100 , according to various embodiments of the present disclosure. The term “out-of-plane” means that a direction or orientation is not parallel with or within the film plane. Rather, the direction or orientation forms an angle with the film plane. In some embodiments, when the angle is 90°, the out-of-plane direction or orientation may be in the thickness direction of the LCPH element  1100 . For discussion purposes,  FIGS.  11 E- 11 H  schematically illustrate out-of-plane (e.g., along z-axis direction) orientations of the LC directors of the LC molecules  1112  when the in-plane orientation pattern is a periodic in-plane orientation pattern shown in  FIG.  11 B . As shown in  FIG.  11 E , within a volume of the birefringent medium layer  1115 , the LC molecules  1112  may be arranged in a plurality of helical structures  1117  with a plurality of helical axes  1118  and a helical pitch P h  along the helical axes. The azimuthal angles of the LC molecules  1112  arranged along a single helical structure  1117  may continuously vary around a helical axis  1118  in a predetermined rotation direction, e.g., clockwise direction or counter-clockwise direction. In other words, the orientations of the LC directors of the LC molecules  1112  arranged along a single helical structure  1117  may exhibit a continuous rotation around the helical axis  1118  in a predetermined rotation direction. That is, the azimuthal angles associated of the LC directors may exhibit a continuous change around the helical axis in the predetermined rotation direction. Accordingly, the helical structure  1117  may exhibit a handedness, e.g., right handedness or left handedness. The helical pitch P h  may be defined as a distance along the helical axis  1118  over which the orientations of the LC directors exhibit a rotation around the helical axis  1118  by 360°, or the azimuthal angles of the LC molecules vary by 360°. 
     In the embodiment shown in  FIG.  11 E , the helical axes  1118  may be substantially perpendicular to the first surface  1115 - 1  and/or the second surface  1115 - 2  of the birefringent medium layer  1115 . In other words, the helical axes  1118  of the helical structures  1117  may extend in a thickness direction (e.g., a z-axis direction) of the birefringent medium layer  1115 . That is, the LC molecules  1112  may have substantially small tilt angles (including zero degree tilt angles), and the LC directors of the LC molecules  1112  may be substantially orthogonal to the helical axis  1118 . The birefringent medium layer  1115  may have a vertical pitch P v , which may be defined as a distance along the thickness direction of the birefringent medium layer  1115  over which the orientations of the LC directors of the LC molecules  1112  exhibit a rotation around the helical axis  1118  by 180° (or the azimuthal angles of the LC directors vary by 180°). In the embodiment shown in  FIG.  11 E , the vertical pitch P v  may be half of the helical pitch P h . 
     As shown in  FIG.  11 E , the LC molecules  1112  from the plurality of helical structures  1117  having a first same orientation (e.g., same tilt angle and azimuthal angle) may form a first series of parallel refractive index planes  1114  periodically distributed within the volume of the birefringent medium layer  1115 . Although not labeled, the LC molecules  1112  with a second same orientation (e.g., same tilt angle and azimuthal angle) different from the first same orientation may form a second series of parallel refractive index planes periodically distributed within the volume of the birefringent medium layer  1115 . Different series of parallel refractive index planes may be formed by the LC molecules  1112  having different orientations. In the same series of parallel and periodically distributed refractive index planes  1114 , the LC molecules  1112  may have the same orientation and the refractive index may be the same. Different series of refractive index planes  1114  may correspond to different refractive indices. When the number of the refractive index planes  1114  (or the thickness of the birefringent medium layer) increases to a sufficient value, Bragg diffraction may be established according to the principles of volume gratings. Thus, the periodically distributed refractive index planes  1114  may also be referred to as Bragg planes  1114 . In some embodiments, as shown in  FIG.  11 E , the refractive index planes  1114  may be slanted with respect to the first surface  1115 - 1  or the second surface  1115 - 2 . In some embodiments, the refractive index planes  1114  may be perpendicular to or parallel with the first surface  1115 - 1  or the second surface  1115 - 2 . Within the birefringent medium layer  1115 , there may exist different series of Bragg planes. A distance (or a period) between adjacent Bragg planes  1114  of the same series may be referred to as a Bragg period PB. The different series of Bragg planes formed within the volume of the birefringent medium layer  1115  may produce a varying refractive index profile that is periodically distributed in the volume of the birefringent medium layer  1115 . The birefringent medium layer  1115  may diffract an input light satisfying a Bragg condition through Bragg diffraction. 
     As shown in  FIG.  11 E , the birefringent medium layer  1115  may also include a plurality of LC molecule director planes (or molecule director planes)  1116  arranged in parallel with one another within the volume of the birefringent medium layer  1115 . An LC molecule director plane (or an LC director plane)  1116  may be a plane formed by or including the LC directors of the LC molecules  1112 . In the example shown in  FIG.  11 E , the LC directors in the LC director plane  1116  have different orientations, i.e., the orientations of the LC directors vary in the x-axis direction. The Bragg plane  1114  may form an angle θ with respect to the LC molecule director plane  1116 . In the embodiment shown in  FIG.  11 E , the angle θ may be an acute angle, e.g., 0°&lt;θ&lt;90°. The LCPH element  1100  including the birefringent medium layer  1115  shown in  FIG.  11 B  may function as a transmissive PVH element, e.g., a transmissive PVH grating. 
     In the embodiment shown in  FIG.  11 F , the helical axes  1118  of helical structures  1117  may be tilted with respect to the first surface  1115 - 1  and/or the second surface  1115 - 2  of the birefringent medium layer  1115  (or with respect to the thickness direction of the birefringent medium layer  1115 ). For example, the helical axes  1118  of the helical structures  1117  may have an acute angle or obtuse angle with respect to the first surface  1115 - 1  and/or the second surface  1115 - 2  of the birefringent medium layer  1115 . In some embodiments, the LC directors of the LC molecule  1112  may be substantially orthogonal to the helical axes  1118  (i.e., the tilt angle may be substantially zero degree). In some embodiments, the LC directors of the LC molecule  1112  may be tilted with respect to the helical axes  1118  at an acute angle. The birefringent medium layer  1115  may have a vertical periodicity (or pitch) P v . In the embodiment shown in  FIG.  11 F , an angle θ (not shown) between the LC director plane  1116  and the Bragg plane  1114  may be substantially 0° or 180°. That is, the LC director plane  1116  may be substantially parallel with the Bragg plane  1114 . In the example shown in  FIG.  11 F , the orientations of the directors in the molecule director plane  1116  may be substantially the same. The LCPH element  1100  including the birefringent medium layer  1115  shown in  FIG.  11 F  may function as a reflective PVH element, e.g., a reflective PVH grating. 
     In the embodiment shown in  FIG.  11 G , the birefringent medium layer  1115  may also include a plurality of LC director planes  1116  arranged in parallel within the volume of the birefringent medium layer  1115 . In the embodiment shown in  FIG.  11 F , an angle θ between the LC director plane  1116  and the Bragg plane  1114  may be a substantially right angle, e.g., θ=90°. That is, the LC director plane  1116  may be substantially orthogonal to the Bragg plane  1114 . In the example shown in  FIG.  11 F , the LC directors in the LC director plane  1116  may have different orientations. In some embodiments, the LCPH element  1100  including the birefringent medium layer  1115  shown in  FIG.  11 F  may function as a transmissive PVH element, e.g., a transmissive PVH grating. 
     In the embodiment shown in  FIG.  11 H , in a volume of the birefringent medium layer  1115 , along the thickness direction (e.g., the z-axis direction) of the birefringent medium layer  1115 , the directors (or the azimuth angles) of the LC molecules  1112  may remain in the same orientation (or same angle value) from the first surface  1115 - 1  to the second surface  1115 - 2  of the birefringent medium layer  1115 . In some embodiments, the thickness of the birefringent medium layer  1115  may be configured as d=λ/(2*Δn), where λ is a design wavelength, Δn is the birefringence of the LC material of the birefringent medium layer  1115 , and Δn=n e −n o , where n e  and n o  are the extraordinary and ordinary refractive indices of the LC material, respectively. In some embodiments, the LCPH element  1100  including the birefringent medium layer  1115  shown in  FIG.  11 F  may function as a PBP element, e.g., a PBP grating. 
     In some embodiments, the present disclosure provides a device. The device includes a light guide. The device includes an in-coupling element coupled with the light guide and configured to couple an input image light into the light guide. The device includes an out-coupling element coupled with the light guide and configured to couple the input image light out of the light guide as an output image light propagating toward an exit pupil. The device includes a controller configured to control at least one of the in-coupling element or the out-coupling element during a first time period and a second time period. The out-coupling element is configured to output a first output image light during the first time period to the exit pupil, and a second output image light during the second time period to the exit pupil. The first output image light is shifted from the second output image light for an angle. 
     In some embodiments, the present disclosure provides a method. The method includes generating an input image light. The method includes during a first time period, controlling, by a controller, at least one of an in-coupling element or an out-coupling element to couple the input image light into a light guide, and couple the input image light out of the light guide as a first output image light. The method includes during a second time period, controlling, by the controller, at least one of the in-coupling element or the out-coupling element to couple the input image light into the light guide, and couple the input image light out of the light guide as a second output image light. The first output image light and the second output image light propagate from the light guide toward a same exit pupil. The second output image light is rotated from the first output image light. 
     In some embodiments, the present disclosure provides a device, such as an optical device. The device includes a light guide. The device also includes an in-coupling element coupled with the light guide and configured to couple an input image light into the light guide. The device also includes an out-coupling element coupled with the light guide and configured to couple the input image light out of the light guide as an output image light. The device also includes a controller configured to control at least one of the in-coupling element or the out-coupling element during a first time period and a second time period. The out-coupling element is configured to output a first output image light having a first field of view (“FOV”) during the first time period, and a second output image light having a second FOV during the second time period. The first FOV substantially overlaps with the second FOV, and an axis of symmetry of the first FOV is rotated relative to an axis of symmetry of the second FOV. 
     In some embodiments, the input image light has an input FOV, and the first FOV and the second FOV have a same size as the input FOV. In some embodiments, an overlapping portion of the first FOV and the second FOV is within a range of from 80% to 95% of the first FOV. In some embodiments, a relative rotation between the axis of symmetry of the first FOV and the axis of symmetry of the second FOV is within a range of from 5% to 20% of the first FOV. In some embodiments, the in-coupling element includes an in-coupling grating, and the controller is configured to control the in-coupling grating to operate in a first diffraction state during the first time period and a second diffraction state during the second time period. In some embodiments, the in-coupling grating operating in the first diffraction state and the second diffraction state have different grating periods or different modulations of refractive index. In some embodiments, the out-coupling element includes an out-coupling grating, and the controller is configured to control the out-coupling grating to operate in a first diffraction state during the first time period and a second diffraction state during the second time period. In some embodiments, the out-coupling grating operating in the first diffraction state and the second diffraction state have different grating periods or different modulations of refractive index. In some embodiments, the in-coupling element includes a first in-coupling grating and a second in-coupling grating. The controller is configured to: control the first in-coupling grating to operate in a diffraction state and the second in-coupling grating to operate in a non-diffraction state during the first time period, and control the first in-coupling grating to operate in the non-diffraction state and the second in-coupling grating to operate in the diffraction state during the second time period. In some embodiments, the first in-coupling grating operating in the diffraction state and the second in-coupling grating operating in the diffraction state have different grating periods or different modulations of refractive index. 
     In some embodiments, the out-coupling element includes a first out-coupling grating and a second out-coupling grating. The controller is configured to: control the first out-coupling grating to operate in a diffraction state and the second out-coupling grating to operate in a non-diffraction state during the first time period, and control the first out-coupling grating to operate in the non-diffraction state and the second out-coupling grating to operate in the diffraction state during the second time period. In some embodiments, the first out-coupling grating operating in the diffraction state and the second out-coupling grating operating in the diffraction state have different grating periods or different modulations of refractive index. 
     In some embodiments, at least one of the in-coupling element or the out-coupling element includes one or more active gratings. In some embodiments, the one more active gratings include one or more holographic polymer-dispersed liquid crystal gratings, one or more surface relief gratings including active liquid crystals (“LCs”), one or more Pancharatnam-Berry phase gratings based on active LCs, or one or more polarization volume hologram gratings based on active LCs. 
     In some embodiments, the present disclosure provides a method. The method includes controlling, by a controller during a first time period, at least one of an in-coupling element or an out-coupling element to couple an input image light into a light guide, and couple the input image light out of the light guide as a first output image light having a first FOV. The method also includes controlling, by the controller during a second time period, at least one of the in-coupling element or the out-coupling element to couple the input image light into the light guide, and couple the input image light out of the light guide as a second output image light having a second FOV. The second FOV substantially overlaps with the first FOV. An axis of symmetry of the first FOV is rotated from an axis of symmetry of the second FOV. In some embodiments, the input image light has an input FOV, and the first FOV and the second FOV have a same size as the input FOV. In some embodiments, an overlapping portion of the first FOV and the second FOV is within a range of from 80% to 95% of the first FOV. In some embodiments, a relative rotation between the axis of symmetry of the first FOV and the axis of symmetry of the second FOV is within a range of from 5% to 20% of the first FOV. In some embodiments, a relative rotation between the axis of symmetry of the first FOV and the axis of symmetry of the second FOV is between 0.5°-10°. In some embodiments, the first output image light having the first FOV and the second output image light having the second FOV propagate toward a same eye pupil. 
     The foregoing description of the embodiments of the present disclosure have been presented for the purpose of illustration. It is not intended to be exhaustive or to limit the disclosure to the precise forms disclosed. Persons skilled in the relevant art can appreciate that modifications and variations are possible in light of the above disclosure. 
     Some portions of this description may describe the embodiments of the present disclosure in terms of algorithms and symbolic representations of operations on information. These operations, while described functionally, computationally, or logically, may be implemented by computer programs or equivalent electrical circuits, microcode, or the like. Furthermore, it has also proven convenient at times, to refer to these arrangements of operations as modules, without loss of generality. The described operations and their associated modules may be embodied in software, firmware, hardware, or any combinations thereof. 
     Any of the steps, operations, or processes described herein may be performed or implemented with one or more hardware and/or software modules, alone or in combination with other devices. In one embodiment, a software module is implemented with a computer program product including a computer-readable medium containing computer program code, which can be executed by a computer processor for performing any or all of the steps, operations, or processes described. In some embodiments, a hardware module may include hardware components such as a device, a system, an optical element, a controller, an electrical circuit, a logic gate, etc. 
     Embodiments of the present disclosure may also relate to an apparatus for performing the operations herein. This apparatus may be specially constructed for the specific purposes, and/or it may include a general-purpose computing device selectively activated or reconfigured by a computer program stored in the computer. Such a computer program may be stored in a non-transitory, tangible computer readable storage medium, or any type of media suitable for storing electronic instructions, which may be coupled to a computer system bus. The non-transitory computer-readable storage medium can be any medium that can store program codes, for example, a magnetic disk, an optical disk, a read-only memory (“ROM”), or a random access memory (“RAM”), an Electrically Programmable read only memory (“EPROM”), an Electrically Erasable Programmable read only memory (“EEPROM”), a register, a hard disk, a solid-state disk drive, a smart media card (“SMC”), a secure digital card (“SD”), a flash card, etc. Furthermore, any computing systems described in the specification may include a single processor or may be architectures employing multiple processors for increased computing capability. The processor may be a central processing unit (“CPU”), a graphics processing unit (“GPU”), or any processing device configured to process data and/or performing computation based on data. The processor may include both software and hardware components. For example, the processor may include a hardware component, such as an application-specific integrated circuit (“ASIC”), a programmable logic device (“PLD”), or a combination thereof. The PLD may be a complex programmable logic device (“CPLD”), a field-programmable gate array (“FPGA”), etc. 
     Embodiments of the present disclosure may also relate to a product that is produced by a computing process described herein. Such a product may include information resulting from a computing process, where the information is stored on a non-transitory, tangible computer readable storage medium and may include any embodiment of a computer program product or other data combination described herein. 
     Further, when an embodiment illustrated in a drawing shows a single element, it is understood that the embodiment or an embodiment not shown in the figures but within the scope of the present disclosure may include a plurality of such elements. Likewise, when an embodiment illustrated in a drawing shows a plurality of such elements, it is understood that the embodiment or an embodiment not shown in the figures but within the scope of the present disclosure may include only one such element. The number of elements illustrated in the drawing is for illustration purposes only, and should not be construed as limiting the scope of the embodiment. Moreover, unless otherwise noted, the embodiments shown in the drawings are not mutually exclusive, and they may be combined in any suitable manner. For example, elements shown in one figure/embodiment but not shown in another figure/embodiment may nevertheless be included in the other figure/embodiment. In any optical device disclosed herein including one or more optical layers, films, plates, or elements, the numbers of the layers, films, plates, or elements shown in the figures are for illustrative purposes only. In other embodiments not shown in the figures, which are still within the scope of the present disclosure, the same or different layers, films, plates, or elements shown in the same or different figures/embodiments may be combined or repeated in various manners to form a stack. 
     Various embodiments have been described to illustrate the exemplary implementations. Based on the disclosed embodiments, a person having ordinary skills in the art may make various other changes, modifications, rearrangements, and substitutions without departing from the scope of the present disclosure. Thus, while the present disclosure has been described in detail with reference to the above embodiments, the present disclosure is not limited to the above described embodiments. The present disclosure may be embodied in other equivalent forms without departing from the scope of the present disclosure. The scope of the present disclosure is defined in the appended claims.