Patent Publication Number: US-2023152500-A1

Title: Apodization of refractive index profile in volume gratings

Description:
REFERENCE TO RELATED APPLICATIONS 
     The present application is a divisional of U.S. application Ser. No. 17/176,964 entitled “APODIZATION OF REFRACTIVE INDEX PROFILE IN VOLUME GRATINGS”, filed Feb. 16, 2021, which claims priority from U.S. Provisional Application No. 63/092,288 filed on Oct. 15, 2020 and entitled “Photoinduced Apodization of Refractive Index Profile in Volume Bragg Gratings”, and from U.S. Provisional Application No. 63/114,226 filed on Nov. 16, 2020 and entitled “Chemical Diffusion Treated Volume Holograms and Methods for Making the Same”, all of which being incorporated herein by reference in their entireties. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates to optical devices, and in particular to optical gratings and lightguides using optical gratings. 
     BACKGROUND 
     An artificial reality system may include a near-eye display (e.g., a headset or a pair of glasses) configured to present content to a user. The near-eye display 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 seeing through a “combiner” component, which is a physical structure where display light and environmental light merge as one within the user&#39;s field of view. The combiner of a wearable heads-up display is typically transparent to environmental light but includes some light routing optic to direct the display light into the user&#39;s field of view. 
     Wearable heads-up displays may employ lightguides as transparent or translucent combiners. Lightguides typically consist of plates of a transparent material with a higher refractive index then the surrounding medium, usually air. Light input into the plate propagates along the length of the plate as long as the light continues to be incident at boundaries between the plate and the surrounding medium at an angle above the critical angle. Lightguides employ in-coupling and out-coupling elements to ensure that light follows a specific path along the waveguide and then exits the waveguide at specific location(s) to create an image visible to the user. The in-coupling and out-coupling elements need to accurately convey the angular distribution of brightness of the in-coupled light beam to the user&#39;s eyes to prevent distortion and splitting of the displayed images. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Exemplary embodiments will now be described in conjunction with the drawings, in which: 
         FIGS.  1 A and  1 B  are side cross-sectional views of pupil-replicating lightguides having input and output volume gratings, the pupil-replicating lightguide of  FIG.  1 A  being configured to provide a different portion of field of view (FOV) than the pupil-replicating lightguide of  FIG.  1 B ; 
         FIG.  2    is a side cross-sectional views of a pupil-replicating lightguide having multiplexed volume gratings of  FIGS.  1 A and  1 B  for a broader overall FOV; 
         FIG.  3 A  is an angular dependence of diffraction wavelengths of a plurality of sparsely spaced volume gratings usable in the pupil-replicating lightguide of  FIG.  2   ; 
         FIG.  3 B  is an angular dependence of diffraction efficiency of the plurality of volume gratings of  FIG.  3 A ; 
         FIG.  3 C  is an angular dependence of diffraction wavelengths of a plurality of densely spaced volume gratings usable in the pupil-replicating lightguide of  FIG.  2   ; 
         FIG.  3 D  is an angular dependence of diffraction efficiency of the plurality of volume gratings of  FIG.  3 C ; 
         FIG.  3 E  is a magnified view of the angular dependence of  FIG.  3 C  superimposed with local diffraction efficiency plots for two neighboring volume gratings; 
         FIG.  3 F  is a side cross-sectional view of a pupil-replicating lightguide illustrating optical crosstalk; 
         FIG.  4 A  is an angular reflectivity plot of two non-apodized volume gratings in the pupil-replicating lightguide of  FIG.  2   ; 
         FIG.  4 B  is an angular reflectivity plot of two apodized volume gratings in the pupil-replicating lightguide of  FIG.  2   ; 
         FIG.  4 C  is a combined angular reflectivity plot of volume gratings with different refractive index contrast Δn; 
         FIG.  5    is a three-dimensional view of an optical coupler including a photopolymer layer and a volume grating written in the photopolymer layer; 
         FIG.  6    shows example apodization profiles of volume gratings in the optical coupler of  FIG.  5   ; 
         FIG.  7 A  is a schematic diagram of exposing a photopolymer layer with apodization light and grating forming light where the apodization exposure precedes the grating forming exposure; 
         FIG.  7 B  is a schematic diagram of exposing a photopolymer layer with apodization light and grating forming light where the apodization exposure and the grating forming exposure are performed concurrently; 
         FIG.  7 C  is a schematic diagram of exposing a photopolymer layer with apodization light and grating forming light where the apodization exposure is performed after the grating forming exposure; 
         FIG.  8    is a chart showing a relationship between various embodiments of a method for providing volume grating refractive index contrast apodization in accordance with this disclosure; 
         FIG.  9    is a schematic diagram of exposing a photopolymer layer sandwiched between layers facilitating a chemically induced apodization; 
         FIG.  10    is an example chemical structure of the photopolymer layer of  FIG.  9   ; 
         FIG.  11    is a flow chart of a method of fabrication of a grating coupler of this disclosure; and 
         FIG.  12    is schematic a view of an augmented reality (AR) display of this disclosure having a form factor of a pair of eyeglasses. 
     
    
    
     DETAILED DESCRIPTION 
     While the present teachings are described in conjunction with various embodiments and examples, it is not intended that the present teachings be limited to such embodiments. On the contrary, the present teachings encompass various alternatives and equivalents, as will be appreciated by those of skill in the art. All statements herein reciting principles, aspects, and embodiments of this disclosure, as well as specific examples thereof, are intended to encompass both structural and functional equivalents thereof. Additionally, it is intended that such equivalents include both currently known equivalents as well as equivalents developed in the future, i.e., any elements developed that perform the same function, regardless of structure. 
     As used herein, the terms “first”, “second”, and so forth are not intended to imply sequential ordering, but rather are intended to distinguish one element from another, unless explicitly stated. Similarly, sequential ordering of method steps does not imply a sequential order of their execution, unless explicitly stated. 
     Lightguides are used in optical devices to carry light from one location to another. Pupil-replicating lightguides are used in near-eye displays for providing multiple laterally offset copies of a fan of light beams carrying an image in angular domain for observation by a user of a near-eye display. The multiple offset copies of the beam fan are spread over an eyebox of the display, making observation of the image less dependent on the eye position in the eyebox. 
     Pupil-replicating lightguides may use diffraction gratings for in-coupling and out-coupling image light. Volume gratings, such as volume Bragg gratings (VBGs) or volume holograms, for example, can in-couple and out-couple image light with high efficiency. VBGs however typically operate in a rather narrow angular range. To increase the overall angular range, multiple pairs of in-coupling and out-coupling VBGs may be provided in a pupil-replicating lightguide. VBGs of different pairs may have optical crosstalk. When the image light is reflected by an out-coupling VBG after being in-coupled by an in-coupling VBG of a different VBGs pair, a ghost image may appear. 
     In accordance with this disclosure, optical crosstalk and resulting image ghosting and contrast/clarity reduction may be lessened by apodizing the refractive index profile of volume gratings in a direction of thickness of the pupil-replicating lightguide. Such apodization may be achieved chemically and/or photochemically. In a photochemical apodization process, one or both surfaces of a photopolymer layer are exposed to apodization light for reducing an amplitude of the periodic refractive index variations. Since most light is present proximate to the surface(s) being illuminated, the grating gets apodized in the direction of grating thickness. In a chemical apodization process, one or both surfaces of the photopolymer layer are exposed to a reactant that reduces an amplitude of the periodic refractive index variations near the one or both surfaces. In some embodiments, both the chemical and photochemical apodization processes may be used to achieve the required grating apodization profiles. 
     In accordance with this disclosure, there is provided a method of fabrication of a grating coupler. The method comprises exposing a photopolymer layer having a thickness between opposed first and second surfaces to grating forming light for forming periodic refractive index variations in the photopolymer layer. The first surface of the photopolymer layer is exposed to apodization light for reducing an amplitude of the periodic refractive index variations proximate the first surface. The method may include exposing the second surface of the photopolymer layer to apodization light for reducing an amplitude of the periodic refractive index variations proximate the second surface. The first surface of the photopolymer layer may be exposed to the apodization light before the photopolymer layer is exposed to the grating forming light. 
     In embodiments where a wavelength of the grating forming light is different from a wavelength of the apodization light, the apodization light may be absorbed in the photopolymer layer stronger than the grating forming light. For example, a transmittance of the photopolymer layer at the wavelength of the apodization light may no greater than 5%. The periodic refractive index variations in the photopolymer layer may be formed due to a photoreactive agent of the photopolymer layer being sensitive to illumination with the grating forming light. The amplitude of the periodic refractive index variations may be reduced due to the photoreactive agent being sensitive to illumination with the apodization light. A duration of the exposure of the photopolymer layer to the apodization light may be shorter than a duration of the exposure of the photopolymer layer to the grating forming light. 
     In some embodiments, the exposure of the photopolymer layer to the apodization light is performed concurrently with the exposure of the photopolymer layer to the grating forming light. The photopolymer layer may include a photoreactive agent for forming the periodic refractive index variations by a photoreaction to the grating forming light, and a photoinhibitor agent for impeding the photoreaction when illuminated with the apodization light. A wavelength of the grating forming light may be different from a wavelength of the apodization light. The grating forming light may substantially not activate the photoinhibitor agent, and the apodization light may substantially not activate the photoreactive agent. The photoreaction may include photopolymerization, and the photoinhibitor agent may undergo photolysis when illuminated with the apodization light to produce a radical for impeding the photopolymerization. The photoinhibitor agent may include e.g. at least one of butyl nitrite, hexaarylbiimidazole, or tetraethylthiuram disulfide. 
     In some embodiments, the exposure of the photopolymer layer to the apodization light is performed after the exposure of the photopolymer layer to the grating forming light. The photopolymer layer may include a photoreactive group that reduces the amplitude of the periodic refractive index variations upon illumination with the apodization light by at least one of photoisomerization, photoelimination, photopolymerization, or photolocking. For example, photoreactive group may include at least one of azobenzene, stilbene, spiropyran, diarylethene, a diazo group, or an azido group. The photoreactive group may be on a polymer backbone of the photopolymer layer. 
     In accordance with this disclosure, there is provided a method of fabrication of a grating coupler. The method includes exposing a photopolymer layer having a thickness between opposed first and second surfaces to grating forming light for forming periodic refractive index variations in the photopolymer layer, and exposing at least the first surface of the photopolymer layer to a reactive agent for reducing an amplitude of the periodic refractive index variations proximate the first surface. 
     In embodiments where a photopolymer of the photopolymer layer comprises a photopolymerizable group connected to an end group by an acid-cleavable linker group, and where a local refractive index is defined, at least in part, by the end group, the reactive agent may include an acid for separating the end group from the photopolymerizable group. In operation, the end group diffuses away upon being separated from the corresponding photopolymerizable group by application of the acid to the at least first surface, thereby reducing the amplitude of the periodic refractive index variations proximate the at least first surface. 
     In accordance with this disclosure, there is further provided a grating coupler for a waveguide. The grating coupler includes a photopolymer layer having a thickness between opposed first and second surfaces, the photopolymer layer comprising periodic refractive index variations due to exposure to grating forming light. An amplitude of the periodic refractive index variations proximate the first surface and/or the second surface may be reduced by at least one of: exposing the first surface the photopolymer layer to apodization light; or exposing the first surface the photopolymer layer to a reactive agent. The periodic refractive index variations in the photopolymer layer may be formed due to a photoreactive agent of the photopolymer layer being sensitive to illumination with the grating forming light. The amplitude of the periodic refractive index variations may be reduced due to the photoreactive agent being sensitive to illumination with the apodization light. 
     Examples of lightguides with apodized gratings will now be presented. Referring first to  FIG.  1 A , a pupil-replicating lightguide  100 A includes a substrate  110  and an in-coupling grating  102 A in the substrate  110  for in-coupling image light  104 A into the pupil-replicating lightguide  100 A, and an out-coupling grating  106 A in the substrate  110  for out-coupling portions  108 A of the image light  104 A along a length direction of the pupil-replicating lightguide  100 A (X-direction in  FIG.  1 A ). The image light  104 A propagates in the substrate by series of reflections from opposed top  121  and bottom  122  surfaces of the substrate  110 . The image light  104 A carries a portion of an image in angular domain, corresponding to a narrow cone of rays oriented approximately perpendicular to the pupil-replicating lightguide  100 A, as shown in  FIG.  1 A . In this example, the in-coupling grating  102 A and the out-coupling grating  106 A have a same pitch, such that the out-coupled portions  108 A retain the beam angles of the impinging image light  104 A. 
     Referring to  FIG.  1 B , a pupil-replicating lightguide  100 B is similar to the pupil-replicating lightguide  100 A of  FIG.  1 A . The pupil-replicating lightguide  100 B of  FIG.  1 B  includes an in-coupling grating  102 B in the substrate  110  for in-coupling image light  104 B and an out-coupling grating  106 B in the substrate  110  for out-coupling portions  108 B of the image light  104 A along a length direction of the pupil-replicating lightguide  100 B (X-direction in  FIG.  1 B ). The image light  104 B propagates in the substrate by series of reflections from opposed top  121  and bottom  122  surfaces of the substrate  110 . The image light  104 B carries a different portion of the image in angular domain, corresponding to a narrow cone of rays oriented at an acute, i.e. non-perpendicular, angle to the pupil-replicating lightguide  100 B. The in-coupling grating  102 B and the out-coupling grating  106 B have a same pitch, such that the out-coupled portions  108 B retain the beam angles of the impinging image light  104 B. 
     Referring now to  FIG.  2   , a pupil-replicating lightguide  200  includes an in-coupler  202  in a substrate  210 . The in-coupler  202  includes a plurality of multiplexed in-coupling gratings, e.g. the in-coupling grating  102 A of  FIG.  1 A , the in-coupling grating  102   b  of  FIG.  1 B , and other in-coupling gratings of different pitches or periods, superimposed in the pupil-replicating lightguide  200 . The volume gratings may occupy a same volume area of the substrate  210 , and/or may be disposed at different depths in the substrate  210 . Different gratings of the plurality of in-coupling gratings are configured to in-couple the image light  204  impinging onto the substrate  210  at different angles of incidence. Together, the in-coupling gratings in-couple image light  204  covering an entire field of view (FOV) of an image in angular domain to be carried by the pupil-replicating lightguide  200  and displayed to a user. The in-coupled image light  204  propagates in the substrate by series of reflections from opposed top  221  and bottom  222  surfaces of the substrate  210 . 
     An out-coupler  206  in the substrate  210  includes a plurality of multiplexed out-coupling gratings, e.g. the out-coupling grating  106 A of  FIG.  1 A , the out-coupling grating  106   b  of  FIG.  1 B , and other out-coupling gratings, superimposed in the pupil-replicating lightguide  200 . Different gratings of the plurality of out-coupling gratings are configured to out-couple the image light  204  propagating in the substrate  210  at different angles of diffraction. Together, the out-coupling volume gratings out-couple portions  208  of the image light  204  covering the entire FOV. Different portions of the FOV are being conveyed by the pupil-replicating lightguide  200  by different matching pairs of gratings. It is further noted that one out-coupling grating per an in-coupling grating is only meant as an example. Two or more out-coupling gratings may be provided per each in-coupling grating. Various lightguide types, including straight lightguides, curved lightguides,1D/2D lightguides, etc., may be configured to have matching grating pairs. 
     For the pupil-replicating lightguide  200  to operate as intended, the image light  204  portions should be redirected only by gratings of a same in-coupling and out-coupling volume grating pair, corresponding to a same particular FOV portion. If a portion of the image light  204  is in-coupled into the pupil-replicating lightguide  200  by a volume grating from one in-coupling/out-coupling volume grating pair, and is out-coupled by a grating from another in-coupling/out-coupling volume grating pair, an offset image (ghosting) will result. 
     Origins of the optical crosstalk between different volume grating pairs are further illustrated in  FIGS.  3 A to  3 F . Referring first to  FIGS.  3 A and  3 B , a grating coupler may include a plurality of volume gratings having angular dependencies  312  of diffraction wavelength λ ( FIG.  3 A ) offset relative to one another along an axis of the diffraction angle Θ, due to the volume gratings having different pitches. The angular dependencies  312  are shown for a bandwidth  314  of illuminating light. The angular dependencies  312  are sparsely spaced in the diffraction angle Θ in this example, which results in gaps  315  between plots  316  of angular dependence of diffraction efficiency η of the individual volume gratings ( FIG.  3 B ). When such grating coupler is used in a pupil-replicating lightguide, the gaps  315  will result in FOV gaps in the displayed image. 
     The gaps  315  may be avoided by providing tighter spacing between the pitch values of the gratings multiplexed in a grating coupler, which will cause the angular dependencies  312  to be spaced closer together. Referring to  FIGS.  3 C and  3 D , the angular dependencies  312  are densely spaced in angle ( FIG.  3 C ), eliminating gaps between angular efficiency plots  316 . The angular efficiency plots  316  “coalesce” in a continuous, gap-free angular efficiency curve  317  ( FIG.  3 D ). The grating coupler with the densely spaced (in angular domain) volume gratings will result in a continuous, gap-free FOV. 
     Too close a spacing of the grating pitches and resulting gap-free FOV may result in optical crosstalk, which manifests itself in image contrast loss and/or the appearance of ghost images. Referring to  FIG.  3 E  for example, angular dependencies  312 ,  312 * of first and second diffraction wavelengths of neighboring gratings (i.e. neighboring in pitch) are shown superimposed with corresponding magnified first and second diffraction efficiency curves  316 ,  316 * for these gratings. When the first and second diffraction efficiency curves  316 ,  316 * are disposed too close to each other, crosstalk may result causing the light to be diffracted by a “wrong” grating. 
     The latter point is illustrated in  FIG.  3 F  showing a pupil-replicating lightguide  300 . A light beam  304  impinges onto an in-coupler comprising a plurality of in-coupling gratings, including a first in-coupling volume grating  302 , in a substrate  310 . The other in-coupling gratings are not shown for clarity. The in-coupling grating  302  redirects the light beam  304  to propagate in the pupil-replicating lightguide  300  towards an out-coupler comprising a plurality of out-coupling gratings in the substrate  310 . The out-coupler includes a first out-coupling grating  306  matching the first in-coupling grating  302  and having the first angular dependence  316  ( FIG.  3 E ) of diffraction efficiency η, and a second out-coupling grating  306 * ( FIG.  3 F ) having the second angular dependence  316 * of diffraction efficiency η. Only two out-coupling gratings are shown in  FIG.  3 F  for clarity. The fringes of the in-coupling and out-coupling gratings may form an acute angle with the substrate  310 , as shown in  FIG.  3 F . 
     In operation, a first output light beam  308  diffracts from a “correct”, i.e. the matching first out-coupling grating  306 . A second output light beam  308 * diffracts from a “wrong” grating, i.e. the second out-coupling grating  306 *. The second output light beam  308 * propagates in a different direction than the first output light beam  308  because the second out-coupling grating has a slightly different pitch than the first out-coupling grating. The second output light beam  308 * carries an incorrect image, i.e. a ghost image. 
     The origins of the “incorrect” reflection are further illustrated in  FIG.  4 A , where reflectivity R of two adjacent volume gratings is plotted against an angle of reflective diffraction θ in degrees. The reflectivity R corresponds to the diffraction efficiency η in a reflective volume grating configuration. For each grating, the reflectivity dependence on the angle of diffraction R(θ) includes a central peak  401 A and sidelobes  402 A on both sides of the central peak  401 A. It is seen that the sidelobes  402 A of one grating may overlap with an area of the central peak  401 A of the other grating. The overlap means that, while most of the image light is reflected by the central reflectivity peak  401 A of the “correct” grating as the first output light beam  308  ( FIG.  3 F ), a small portion of the image light may be reflected by a sidelobe of the “incorrect” grating producing the second output light beam  308 *. It is the diffraction on the “incorrect” output gratings that causes the contrast loss/image ghosting to occur. Therefore, the sidelobes  402 A of the reflectivity dependences R(θ) are undesirable, because they degrade the image quality. 
     In accordance with this disclosure, sidelobes of an angular reflectivity plot of a volume grating and associated image ghosting may be suppressed by apodizing the grating along a thickness dimension of the substrate hosting the grating, i.e. generally in a direction substantially perpendicular to a pitch direction of the array of fringes of the grating. In  FIG.  4 B , a reflectivity R of apodized gratings from two adjacent grating pairs is plotted against an angle of reflective diffraction θ in degrees. Only central peaks  401 B are present, without any sidelobes. Accordingly, the image light may not reflect from an “incorrect” grating of a grating pair, resulting in a ghost-free image. At least, image ghosts may be considerably suppressed. It is noted that gratings in grating couplers considered herein may also operate in transmission instead of reflection. 
     Referring to  FIG.  4 C , an angular dependence of reflectivity R of a volume grating is plotted for non-apodized gratings with different grating strength, i.e. with different amplitude of the refractive index variation Δn. For an optimal performance, an apodized volume grating should have as high as possible refractive index contrast in a central peak area  411 , and as low as possible refractive index contrast in sidelobe areas  412 . 
     Referring now to  FIG.  5   , an optical coupler  500  may be a part of the pupil-replicating lightguide  100 A of  FIG.  1 A , the pupil-replicating lightguide  100 B of  FIG.  1 B , the pupil-replicating lightguide  200  of  FIG.  2   , and the pupil-replicating lightguide  300  of  FIG.  3 F . The optical coupler  500  includes a photopolymer (PP) layer  510  having opposed first  521  and second  522  surfaces parallel to XY plane. The direction of thickness t of the substrate is Z-direction in  FIG.  5   . The PP layer  510  may, but does not have to be, flat. The optical coupler  500  represents an in-coupler for in-coupling an impinging light beam, as well as an out-coupler for out-coupling portions of the light beam at different locations along the PP layer  510 . The optical coupler  500  may include a plurality of volume gratings  520 , e.g. at least 10, 20, 50, 100, or more volume gratings having different grating pitches, written in the photopolymer material of the PP layer  510 . 
     The volume gratings  520  may be formed by exposing the PP layer  510  to grating forming light e.g. an interference pattern of two coherent light beams illuminating opposed top  521  and bottom  522  surfaces with oblique coherent beams light. Other configurations, e.g. non-oblique beams, non-opposing beams, are also possible. The photopolymer material of the PP layer  510  changes its refractive index in areas of high intensity of the grating forming light, while in areas of low intensity of the grating forming light the refractive index remains unchanged, or changes very little. 
     Turning to  FIG.  6    with further reference to  FIG.  5   , a profile  601  of a refractive index contrast, that is, a difference between a refractive index of the volume grating fringes and a refractive index of the PP layer  510 , is plotted as a function of the thickness coordinate Z. The first profile  601  is described by a Gaussian function in this example. Non-Gaussian function may also be used. More generally, the refractive index contrast variation of each volume grating of the plurality of volume gratings may have a bell-shaped or a similar function. The bell-shaped function may have the tip of the bell inside the PP layer  510  and the lip of the bell at outer surfaces of the PP layer  510 . In other words, the bell-shaped function may monotonically increase towards a center thickness of the PP layer  510  from both outer surfaces (i.e. top and bottom surfaces in  FIG.  5   ) of the PP layer  510 . The maximum may, but does not have to, be disposed proximate a middle of the thickness t of the PP layer  510 . For example, in some embodiments the bell-shaped profile may be skewed toward one side, such as a second profile  602 . The fringes of the grating couplers disposed in the PP layer  510  may form an acute angle with the PP layer  510 , while their refractive index contrast varies according to the first  601  or second  602  profiles. A uniform profile  603 , i.e. that of a non-apodized grating, is also shown for a comparison. Different volume gratings may spatially overlap in the PP layer  510  while having a same or a different z-profile of the refractive index contrast. 
     The grating apodization may be achieved by illuminating at least one of the top  521  and bottom surfaces  522  of the PP layer  510  with apodization light beams, which may be oriented e.g. along Z-direction. A wavelength or wavelengths of the apodization light may be selected such that at least a major portion of the apodization light is absorbed before reaching the middle of the photopolymer layer. The illumination of the PP layer  510  with the apodization light may facilitate the reduction of the refractive index contrast near the top  521  and bottom  522  surfaces of the PP layer  510 , which causes the grating to be apodized. 
     Referring now to  FIGS.  7 A,  7 B, and  7 C , example exposure sequences and geometries of the photopolymer layer or film are presented as a non-limiting illustration. In  FIG.  7 A , the PP layer  510  is first exposed to apodization light  702 , and is then exposed to grating forming light  704 . The apodization light  702  at a wavelength λ apodization  may uniformly illuminate the PP layer  510  from top and/or bottom, with illuminating light beams oriented along Z-direction. The illuminating beams may be coherent or non-coherent. 
     The grating forming light  704  at a grating forming wavelength λ grating  may include coherent first  711  and second  712  collimated light beams illuminating the PP layer  510  at an acute angle, such that the interference pattern formed by the first  711  and second  712  beams includes a periodic pattern of high and low intensity areas (i.e. optical interference fringes) in the PP layer  510 . A variety of grating configurations, e.g. ones with curved, tilted grating fringes, 2D grating, etc., or any other grating configuration may be provided. 
       FIG.  7 B  corresponds to a situation where the PP layer  510  is concurrently exposed to the apodization light  702  and the grating forming light  704 . 
       FIG.  7 C  illustrates a situation where the PP layer  510  is first exposed to grating forming light  704 , and then is exposed to the apodization light  702 . 
     In the embodiments of  FIGS.  7 A,  7 B, and  7 C , the exposure of the PP layer  510  to the apodization light  702  may be single-sided, such that only one of the top  521  or bottom  522  surfaces ( FIG.  5   ) are exposed. The exposure may also be double-sided, such that both the top  521  and bottom  522  surfaces are exposed. The top  521  and bottom  522  surfaces may be exposed simultaneously or sequentially, i.e. one after another. In embodiments where the wavelength λ apodization  of the apodization light  702  is different from the grating forming wavelength λ grating  of the grating forming light  704 , the apodization light  702  may be absorbed by the PP layer  510  more strongly than the grating forming light  704 . Strong absorption of the apodization light  702  causes the refractive index contrast of the volume gratings  520  to be reduced at the top  521  and bottom  522  surfaces as compared to the refractive index contrast within the PP layer  510 , e.g. at a middle thickness of the PP layer  510 . A duration of exposure of the PP layer  510  to the apodization light  702  may be shorter than a duration of exposure of the PP layer  510  to the grating forming light  704 . 
     Several non-limiting embodiments of a method of forming an apodized volume grating in the PP layer  510  of  FIG.  5    are illustrated in  FIG.  8    with further reference to  FIGS.  7 A to  7 C . A volume grating may be apodized by photoinducing ( FIG.  8   ;  802 ) a dependence of the refractive index contrast Δn of a volume grating on a thickness coordinate z. The refractive index variation is obtained by exposing a photopolymer layer to grating forming light. 
     The specific chemical process(es) utilized to achieve the required degree of apodization Δn(z) of a volume grating may depend on the order of application of the apodization exposure relative to the grating forming exposure. For example, in a first embodiment  811 , the apodization exposure is applied before the grating forming exposure. This corresponds to  FIG.  7 A . The periodic refractive index variations in the PP layer  510  may be formed due to a photoreactive agent of the photopolymer being sensitive to illumination with the grating forming light  704 . The amplitude of the periodic refractive index variations may be reduced due to the photoreactive agent being also sensitive to illumination with the apodization light  702 . The apodization exposure may selectively consume some of the Δn writing chemistry, i.e. the capacity of the photopolymer to undergo a photochemically induced change of the refractive index. 
     The writing chemistry does not necessarily need to be consumed, it could also be inhibited or otherwise have its overall sensitivity reduced, such that the refractive index variation Δn is less proximate the opposed surfaces of the PP layer  510  as compared to the value of Δn at the center of the PP layer  510 , e.g. at Z-coordinate of half the thickness t. In the first embodiment  811 , the apodization wavelength λ apodization  may be different than the grating wavelength λ grating , and may even be outside of the wavelength range of the grating forming light  704  altogether. For example, the apodization wavelength λ apodization  may be selected to be within a strong absorption band of the photoreactive agent of the PP layer  510 . 
     In a second embodiment  812 , the apodization exposure is applied concurrently with the grating forming exposure. This corresponds to the previously considered  FIG.  7 B . In the second embodiment  812 , the photopolymer recording material formulation may be modified to incorporate not only a photoreactive agent for forming the periodic refractive index variations by a photoreaction (i.e. photopolymerization) to the grating forming light, but also an additional component such as, for example, a photoinhibitor agent for impeding the photoreaction when illuminated with the apodization light. The “inhibiting” exposure wavelength λ inhibit  may be different from the grating forming wavelength λ grating  In some variants of the second embodiment  812 , the material formulation for the PP layer  510  may be designed to be wavelength-orthogonal, in other words, the apodization light  702  at the wavelength λ inhibit  substantially does not activate the photoreactive agent, i.e. does not induce polymerization, and the grating forming light  704  at the grating forming wavelength λ grating  substantially does activate the photoinhibitor agent, i.e. does not induce inhibition of the photopolymerization reaction. In some variants, the photochemical process and material composition are selected such that no other reactions may occur. The light exposure may be synchronized, and a relative irradiation may be varied to fine tune the depth of refractive index modulation, Δn(z). Photoinhibitor additive materials may undergo photolysis to produce a radical for polymerization termination. Non-limiting examples of such materials include butyl nitrite, hexaarylbiimidazole, and tetraethylthiuram disulfide (TED). 
     In a third embodiment  813 , the apodization exposure is applied after the grating forming exposure, as illustrated in  FIG.  7 C . The purpose of the apodization exposure in this case is to locally induce a change the refractive index n and/or the refractive index variation Δn of the formed grating. The photopolymer material formulation may include photoreactive groups whereby the photoreaction results in a change in refractive index variation Δn, and/or photoreactive groups causing increase or decrease of the refractive index n. This may be achieved by a reversible photopolymerization in such groups as azobenzene, stilbene, spiropyran, diarylethene; by photoelimination in diazo and/or azido groups; an additional step of photopolymerization/crosslinking independent of the photopolymerization for the volume grating exposure; photoisomerization; and/or by photolocking. In some embodiments, the apodization exposure may initiate depolymerization/decrosslinking reactions that allow high/low refractive index moieties in bright/dark fringes to diffuse and become spatially uniform. In some embodiments, isomerization reactions such as Photo-Fries rearrangement disclosed in Optical Materials 35 (2013) 2283-2289 incorporated herein by reference, and/or Calixarene isomerization disclosed in Bull. Chem. Soc. Jpn., 77, 1415-1422 (2004)) incorporated herein by reference, may be used. 
     For any of the embodiments considered herein, the apodization wavelength λ apodization  of the apodization light  702  may be selected for the apodization light  702  to be strongly absorbed by the recording material of the PP layer  510 . For example, no more than 5% of the optical power of the apodization light  702  may be transmitted through the PP layer  510  in some embodiments. The absorption of the apodization light  702  ensures that the refractive index contrast Δn is reduced only at the opposed surfaces of the PP layer  510  where the exposure of the PP layer  510  to the apodization light  702  is high. The apodization light  702  may be provided for a short amount of time, e.g. less than 1 second. The apodization exposure energy may be controlled with high precision and spatial uniformity, e.g. less than 5% non-uniformity of the apodization light  702  exposure. In embodiments where the apodization and exposure wavelengths are different, the PP layer  510  can be optimized for holographic recording with a low absorption at λ grating  and high absorption at apodization wavelength λ apodization . 
     In some embodiments, the apodization light  702  exposure does not consume the dynamic range of the PP layer  510  considerably, e.g. the dynamic range reduction due to the apodization light  702  exposure may be less than 10-20%. For example and without limitation, the number of groups photopolymerized by the apodization light may be kept to a minimum while providing apodization of the refractive index contrast Δn. The apodization light  702  may be provided immediately before, or within a pre-defined time interval, of the intended exposure of the PP layer  510  with the grating forming light  704 . 
     The wavelength at which photoreactive groups absorb may be outside of the visible light spectrum, typically in ultraviolet wavelength range. In some embodiments, the photoreactive groups are located on the photopolymer backbone. Photoinduced apodization methods disclosed herein may induce strong Δn modulation without significantly changing the base refractive index, shrinkage properties, or other factors which may affect a Bragg reflection condition through the thickness of the PP layer  510 , before, during, or after the exposure(s). Otherwise, a complementary method for modifying these may be used to obtain the desired grating response. 
     In some embodiments, the grating apodization is chemically induced, or a chemical apodization of the grating complement the photoinduced apodization considered above. An overall geometry of a chemical apodization embodiment is presented in  FIG.  9   , where chemically active layers  920 , or inhibitor layers, are provided on opposed parallel sides of the PP layer  510 . At least one active layer  920  may be provided. The volume gratings, e.g. VBGs or volume holograms, may be formed by illuminating the PP layer  510  with the grating forming light. The grating formation may be impeded by a reactive agent present in the chemically active layers  920 , e.g. by controllably suppressing the photopolymerization process to reduce an amplitude of the periodic refractive index variations of the grating  520 . 
     The amplitude of the periodic refractive index variations of the grating  520  may be reduced using a variety of chemical processes. For example, after the grating forming photopolymerization, end groups of a polymerized photopolymer may be separated chemically and/or photochemically, followed by a diffusion of the separated end groups away from their original locations, causing the formed grating to be washed out. Referring to  FIG.  10   , a photopolymer  1000  includes a photopolymerizable group  1002  connected to an end group  1004  by an acid-cleavable linker group  1006 . The end group  1004  may be a high refractive index moiety, such that the local refractive index is defined, at least in part, by the end group  1004 . The reactive agent in the chemically active layer(s)  920  ( FIG.  9   ) may include an acid for separating the end group  1004  ( FIG.  10   ) from the photopolymerizable group  1002  by reacting with the acid-cleavable linker group  1006 . The end group  1004  may be separated from the corresponding photopolymerizable group by application of the acid to at least one of the outer surfaces  521 ,  522  of the PP layer  510  ( FIG.  9   ). The separated end groups  1004  ( FIG.  10   ) diffuse away after separation, thereby reducing the amplitude of the periodic refractive index variations proximate the surface where the acid was applied. The acid may enter the PP layer  510  by diffusion from the chemically active layer(s)  920 , and/or may be photochemically generated in the PP layer  510 . 
     Turning to  FIG.  11   , a general method  1100  of fabrication a grating coupler includes forming ( 1102 ) a plurality of volume gratings of an in-coupler or an out-coupler. The volume gratings may be apodized ( 1104 ) to achieve a desired spatial profile of the refractive index contrast Δn(z). Steps  1102  and  1104  may be performed in any order. The order of performing the steps  1102  and  1104  may depend on the chemistry used to achieve the grating apodization. In some embodiments, the forming step  1102  includes exposing a photopolymer layer to grating forming light, and the apodization step  1104  includes exposing at least one surface of the photopolymer layer to apodization light, and/or exposing the at least one surface to a reactive agent, as explained above with reference to  FIGS.  7 A,  7 B,  7 C ,  FIG.  8   , and  FIG.  9   . 
     Referring to  FIG.  12   , an augmented reality (AR) near-eye display  1200  includes a frame  1201  having a form factor of a pair of eyeglasses. The frame  1201  supports, for each eye: a projector  1208  including a laser light source described herein, a pupil-replicating lightguide  1210  optically coupled to the projector  1208 , an eye-tracking camera  1204 , and plurality of illuminators  1206 . The pupil-replicating lightguide  1210  may include any of the grating-based in-couplers and/or out-couplers including the volume gratings as described herein. The illuminators  1206  may be supported by the pupil-replicating lightguide  1210  for illuminating an eyebox  1212 . The projector  1208  provides a fan of light beams carrying an image in angular domain to be projected into a user&#39;s eye. The pupil-replicating lightguide  1210  receives the fan of light beams and provides multiple laterally offset parallel copies of each beam of the fan of light beams, thereby extending the projected image over the eyebox  1212 . 
     The purpose of the eye-tracking cameras  1204  is to determine position and/or orientation of both eyes of the user. Once the position and orientation of the user&#39;s eyes are known, a gaze convergence distance and direction may be determined. The imagery displayed by the projectors  1208  may be adjusted dynamically to account for the user&#39;s gaze, for a better fidelity of immersion of the user into the displayed augmented reality scenery, and/or to provide specific functions of interaction with the augmented reality. 
     In operation, the illuminators  1206  illuminate the eyes at the corresponding eyeboxes  1212 , to enable the eye-tracking cameras to obtain the images of the eyes, as well as to provide reference reflections i.e. glints. The glints may function as reference points in the captured eye image, facilitating the eye gazing direction determination by determining position of the eye pupil images relative to the glints images. To avoid distracting the user with illuminating light, the latter may be made invisible to the user. For example, infrared light may be used to illuminate the eyeboxes  1212 . 
     Embodiments of the present disclosure may include, or be implemented in conjunction with, an artificial reality system. An artificial reality system adjusts sensory information about outside world obtained through the senses such as visual information, audio, touch (somatosensation) information, acceleration, balance, etc., in some manner before presentation to a user. By way of non-limiting examples, artificial reality may include virtual reality (VR), augmented reality (AR), mixed reality (MR), hybrid reality, or some combination and/or derivatives thereof. Artificial reality content may include entirely generated content or generated content combined with captured (e.g., real-world) content. The artificial reality content may include video, audio, somatic or haptic feedback, or some combination thereof. Any of this content may be presented in a single channel or in multiple channels, such as in a stereo video that produces a three-dimensional effect to the viewer. 
     Furthermore, in some embodiments, artificial reality may also be associated with applications, products, accessories, services, or some combination thereof, that are used to, for example, create content in artificial reality and/or are otherwise used in (e.g., perform activities in) artificial reality. The artificial reality system that provides the artificial reality content may be implemented on various platforms, including a wearable display such as an HMD connected to a host computer system, a standalone HMD, a near-eye display having a form factor of eyeglasses, a mobile device or computing system, or any other hardware platform capable of providing artificial reality content to one or more viewers. 
     The present disclosure is not to be limited in scope by the specific embodiments described herein. Indeed, other various embodiments and modifications, in addition to those described herein, will be apparent to those of ordinary skill in the art from the foregoing description and accompanying drawings. Thus, such other embodiments and modifications are intended to fall within the scope of the present disclosure. Further, although the present disclosure has been described herein in the context of a particular implementation in a particular environment for a particular purpose, those of ordinary skill in the art will recognize that its usefulness is not limited thereto and that the present disclosure may be beneficially implemented in any number of environments for any number of purposes. Accordingly, the claims set forth below should be construed in view of the full breadth and spirit of the present disclosure as described herein.