Grating with spatially varying refractive index and grating modulation

Abstract

Holographic devices and more particularly holographic gratings with spatially varying average refractive index and grating modulation are provided. Various waveguides provided include: a grating including an input coupler for coupling light into a TIR path within the waveguide; and at least one grating for providing beam expansion and extraction of light from the waveguide. Gratings can have an input face and an output face and a principal input beam direction from the input face and a principal diffraction direction passing through the output face. The average grating refractive index may decrease along the principal input beam direction and the grating modulation increases along the principal input beam direction. The grating modulation may comprise refractive index modulation or surface amplitude modulation.

Description

GRATING WITH SPATIALLY VARYING REFRACTIVE INDEX AND GRATINGMODULATIONFIELD OF THE INVENTION

[0001] The present disclosure relates to holographic devices and more particularly to a holographic grating with spatially varying average refractive index and grating modulation.BACKGROUND

[0002] Waveguides can be referred to as structures with the capability of confining and guiding waves (i.e., restricting the spatial region in which waves can propagate). One subclass includes optical waveguides, which are structures that can guide electromagnetic waves, typically those in the visible spectrum. Waveguide structures can be designed to control the propagation path of waves using a number of different mechanisms. For example, planar waveguides can be designed to utilize diffraction gratings to diffract and couple incident light into the waveguide structure such that the incoupled light can proceed to travel within the planar structure via total internal reflection (TIR).

[0003] Fabrication of waveguides can include the use of material systems that allow for the recording of holographic optical elements within the waveguides. One class of such material includes polymer dispersed liquid crystal (PDLC) mixtures, which are mixtures containing photopolymerizable monomers and liquid crystals. A further subclass of such mixtures includes holographic polymer dispersed liquid crystal (HPDLC) mixtures. Holographic optical elements, such as volume phase gratings, can be recorded in such a liquid mixture by illuminating the material with two mutually coherent laser beams. During the recording process, the monomers polymerize, and the mixture undergoes a photopolymerization-induced phase separation, creating regions densely populated by liquid crystal micro-droplets, interspersed with regions of clear polymer. The alternating liquid crystal-rich and liquid crystal-depleted regions form the fringe planes of the grating. The resulting grating, which is commonly referred to as a switchable Bragg grating (SBG), has all the properties normally associated with volume or Bragg gratings but with muchhigher refractive index modulation ranges combined with the ability to electrically tune the grating over a continuous range of diffraction efficiency (the proportion of incident light diffracted into a desired direction). The latter can extend from non-diffracting (cleared) to diffracting with close to 100% efficiency.

[0004] Waveguide optics, such as those described above, can be considered for a range of display and sensor applications. In many applications, waveguides containing one or more grating layers encoding multiple optical functions can be realized using various waveguide architectures and material systems, enabling new innovations in neareye displays for augmented reality (AR) and virtual reality (VR), compact head-up displays (HUDs) and helmet-mounted displays or head-mounted displays (HMDs) for road transport, aviation, and military applications, and sensors for biometric and laser radar (LIDAR) applications.SUMMARY OF THE INVENTION

[0005] The present disclosure relates to holographic devices and more particularly to a holographic grating with spatially varying average refractive index and grating modulation.

[0006] Many embodiments are directed to a waveguide including:• a grating including an input coupler for coupling light into a TIR path within the waveguide; and• at least one grating for providing beam expansion and extraction of light from the waveguide;• wherein the grating has an input face and an output face and a principal input beam direction from the input face and a principal diffraction direction passing through the output face;• wherein the average grating refractive index decreases along the principal input beam direction;wherein the grating modulation increases along the principal input beam direction;• wherein the grating is recorded in a holographic recording material mixture including a first monomer for forming polymer of a first refractive index and a mixture of a second monomer for forming polymer of a second refractive index, and• wherein the second refractive index is higher than the first refractive index.

[0007] In still many embodiments, the spatial distribution of the first refractive index material and the second refractive index material result in non-binary refractive index profile along at least a portion of the perimeter of the grating.

[0008] In yet many embodiments, the second refractive index exceeds the first refractive index by at least 0.02 or a gradual increase to the required index by varying concentrations.

[0009] In still yet many embodiments, the spatial distribution of the first refractive index material and the second refractive index material reduce the average refractive index variation across the grating

[0010] In yet still many embodiments, the polymerof a second refractive index reduces image splitting resulting from rays skirting edge of the grating during expansion.

[0011] In still yet many embodiments, the grating is surrounded by uniform polymer formed from a mixture comprising a first monomer for forming polymer of a first refractive index and a mixture of a second monomer for forming polymer of a second refractive index.

[0012] In yet still many embodiments, the second monomer has a spatial varying concentration prior to the recording of the grating.

[0013] In still yet many embodiments, the grating is a fold grating for expanding and deflecting the total internal reflection beam within the waveguide plane, wherein the input face and the output face are cross sections of the grating.

[0014] In yet still many embodiments, the grating is an output grating for expanding and deflecting the total internal reflection beam out of the waveguide, wherein the inputface is a cross section of grating layer and the output face is formed by a surface of the grating parallel to the waveguide plane.

[0015] In still yet many embodiments, a grating high grating modulation region is abutted by a portion of the output edge and an edge of the grating at the extremity of the principal beam direction optical path.

[0016] In yet still many embodiments, a grating high average refractive index region is abutted by the input edge and a portion of the output edge.

[0017] In still yet many embodiments, the refractive index spatial gradient decreases along principal beam direction.

[0018] In yet still many embodiments, the gradient modulation spatial gradient increases along the principal beam direction.

[0019] In still yet many embodiments, the grating modulation comprises refractive index modulation.

[0020] In yet still many embodiments, the grating modulation comprises surface amplitude modulation.

[0021] In still yet many embodiments, the grating has average refractive index in the range from 1.3 to 2.6.

[0022] In yet still many embodiments, the grating has average refractive index in the range from 1.5 to 2.1.

[0023] In still yet many embodiments, the grating has a grating modulation defined by a refractive index modulation in the range from 0.001 to 0.1.

[0024] In yet still many embodiments, the grating has a grating modulation defined by surface relief depth in the range from 20nm to 1000nm.

[0025] In still yet many embodiments, the grating is a dual interaction fold.

[0026] In yet still many embodiments, the grating has a spatial variation of at least one selected from the group comprising: K-vector, grating thickness, birefringence, polarization rotation, bias layer thickness, duty cycle, backfill material composition, backfill material thickness, and refractive index additive concentration.

[0027] In still yet many embodiments the waveguide includes a layer for controlling polarization.

[0028] In yet still many embodiments the input coupler is a grating or a prism.

[0029] Additional embodiments and features are set forth in part in the description that follows, and in part will become apparent to those skilled in the art upon examination of the specification or may be learned by the practice of the disclosure. A further understanding of the nature and advantages of the present disclosure may be realized by reference to the remaining portions of the specification and the drawings, which forms a part of this disclosure.BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The description will be more fully understood with reference to the following figures, which are presented as embodiments of the invention and should not be construed as a complete recitation of the scope of the invention, wherein:

[0031] FIG.1 provides a plan view of a grating structure in accordance with various embodiments.

[0032] FIG.2 provides a plan view of a grating structure showing the spatial variation of average refractive index in accordance with various embodiments.

[0033] FIG.3 provides a plan view of a grating structure showing the spatial variation of average refractive index in accordance with various embodiments.

[0034] FIG.4 provides a cross-section view of a portion of a waveguide in accordance with various embodiments.

[0035] FIG.5 provides a plan view of a grating in accordance with various embodiments.

[0036] FIG.6 provides a plan view of a grating showing the principal propagation direction in accordance with various embodiments.

[0037] FIG.7a provides average index fields of a waveguide in accordance with various embodiments.

[0038] FIG.7b provides the refractive index modulation field for the waveguide of FIG.7a in accordance with various embodiments.

[0039] FIG.7c provides a plot of minimal refractive index for the waveguide of FIG.7a.

[0040] FIGs. 8a-8c provide plots for diagonal fields of view of 25° (15°x 20°) in accordance with various embodiments.

[0041] FIGs. 9a-9c provide plots for diagonal fields of view of 30° (18°x 24°) in accordance with various embodiments.

[0042] FIGs. 10a-10c provide plots for diagonal fields of view of 35° (21 °x 28°) in accordance with various embodiments.

[0043] FIGs. 11 a-11 c provide illustrative examples of minimum red (FIG.11a), green (FIG.11 b) and blue (FIG.11 c) minimum refractive index requirements for a color waveguide in accordance with various embodiments.

[0044] FIGs.12a-12c illustrate the stages in the refractive index mapping of the fold and output gratings in accordance with various embodiments.

[0045] FIG. 13 provides average refractive index requirements (blue) for fold gratings (continuous line) and output gratings (dashed line) for the fields of view and refractive indices in accordance with various embodiments.

[0046] FIGs. 14-15 provide comparisons of grating material design spaces VHG (FIG.14) and SRG (FIG.15) in accordance with various embodiments.

[0047] FIGs.16a-16d provide plots of average refractive index and index modulation in accordance with various embodiments.

[0048] FIG.17 provides a plot of the relationship of dn versus Rl in gratings in accordance with various embodiments.

[0049] FIGs. 18 and 19 illustrate a cross section of a two waveguide stack in accordance with various embodiments.

[0050] FIGs. 20 and 21 illustrate a single waveguide substrate supporting multiplexing gratins in accordance with various embodiments.

[0051] FIG. 22 illustrates a single waveguide substrate supporting a grating including an input coupler, a fold grating, and an output coupler in accordance with various embodiments.DETAILED DESCRIPTION

[0052] The present disclosure relates to holographic devices and more particularly to a holographic grating with spatially varying average refractive index and grating modulation. The gratings used in various embodiments may include volume holographicgrating (VHGs) and surface relief gratings. Volume holographic gratings can include Bragg gratings and Raman-Nath gratings (often referred to as thick and thin gratings in the literature). VHGs can be formed by monomer to polymer photoconversion in a holographic photopolymer. Higher efficiency VHGs are formed by phase separation of a monomer and an inert material, such as a liquid crystal (LC), an inert fluid or nanoparticles. Where LC is used the material system used to form the hologram is referred to a holographic polymer dispersed liquid crystal (HPDLC). Conventionally, the regime for Bragg and Raman Nath can be defined using criteria based on the Kogelnik theory, making the assumption that all higher diffraction orders are very small. Where a grating falls within the Bragg regime according to the above theory it may be referred to as a Volume Bragg Grating (VBG). Volume holographic gratings may exist in an intermediate region lying between the Bragg and Raman-Nath regime boundaries. Precise definitions of boundaries are given in our co-pending application [U.S. Provisional Application No. 63 / 744,738 entitled “Waveguide Based Display with Reduced Eyeglow”]. A surface relief grating may be formed using well known NIL processes. As discussed in our prior applications [US 11 ,4422,222 Evacuated grating and methods of manufacturing], A SRG+ grating can be made by first forming a volume holographic grating by phase separation of monomer and inert component and then removing the inert material to form air separated polymer diffracting features. The embodiments to be discussed may use any of the above grating types.

[0053] Fold gratings and output gratings are used for beam expansion and light extraction in waveguides. There is a requirement for these functions to be performed with high efficiency and high uniformity with the latter being characterized by one or more of luminance uniformity, field uniformity, eye box uniformity, color uniformity, etc. The challenge is how to overcome the non-uniformities that can arise from the many beam / grating interactions and that result in many different optical paths for different field angle and pupil positions.

[0054] Various embodiments will now be described by way of example only with reference to the accompanying drawings.

[0055] High average refractive index and high refractive index modulation has, to date, been a goal of waveguide grating materials design. The insight underlying the presentdisclosure is that greater holographic materials design freedom can be achieved where lower refractive index can be tolerated where high dn is required and vice versa. This is particularly true of VHG materials but can also apply to SRG+ type gratings (i.e. , SRGs formed by phase separation and inert material extraction), and to SRG gratings (e.g., gratings formed using NIL / resin etch / glass etch, etc.). In many of these cases there is no need for both high average index and high refractive index modulation.

[0056] Various embodiments of the disclosure recognize that higher Diffraction Efficiency (DE) is generally required at the end of the beam paths through each of the fold grating and the output grating. Likewise, modulation of refractive index (dn) needs to be higher at these locations to support the high DE. At the same time, various embodiments recognize that high refractive index is generally required in the region where the beam enters the fold grating and in the portion of the output grating that is closest to the fold. This corresponds to the locations where rays travelling at the highest angles in total internal reflection (TIR) need to be diffracted to support ray paths to the design eyebox.

[0057] In many embodiments, a waveguide comprises: a grating including an input coupler for coupling light into a TIR path within the waveguide; and at least one grating for providing beam expansion and extraction of light from the waveguide. The grating has an input face and an output face and a principal input beam direction from the input face and a principal diffraction direction passing through the output face. In accordance with many embodiments, the average grating refractive index decreases along the principal input beam direction and the grating modulation increases along the principal input beam direction. In such embodiments, the grating modulation may comprise refractive index modulation or surface amplitude modulation.

[0058] In many cases, the grating is a fold grating for expanding and deflecting the total internal reflection beam within the waveguide plane where the input face and the output face are cross sections of the grating.

[0059] FIG.1 shows a plan view of a fold grating 100 comprising a grating structure (101 ) bounded by an input edge (102), an output edge (103), a first edge (104) and a second edge (105). In many cases, a fold may be a higher order polygon with a geometry configured to manage unwanted ray paths and achieve a more compact gratingconfiguration within the waveguide. A beam propagating through the grating comprising rays parallel to and coplanar with the principal ray (106) is multiply diffracted to provide an expanded beam comprising parallel rays (107,108) within the waveguide plane. Typically, the fold will operate over an angular space resulting from the collimation and projection of light from an input image coupled into the waveguide by an input coupler. The coupler may be a grating or a prism. In many cases the grating is a dual interaction fold grating as disclosed in US 9,632,22 Waveguide grating device.

[0060] In many embodiments, a fold grating requires high index at the beam input region (i.e. , the portion of the fold nearest the waveguide input coupler) and low index in the output region of the fold grating. FIG.2 is a plan view (110) of the fold grating of FIG.1 showing the spatial variation of average refractive index which extends from a high value (light shaded) in a region (111 A) near the input edge to a low value (dark shaded) in a region (111 B) near the first edge. FIG.3 is a plan view (112) of the grating of FIG.1 showing the spatial variation of average refractive index which extends from a low value (dark shaded) in a region (113A) near the input edge to a high value (light shaded) in a region (113B) near the first edge.

[0061] In many cases, the high grating modulation region of the grating is abutted by a portion of the output edge and an edge of the grating at the extremity of the principal beam direction optical path. In many cases the high average refractive index region if the grating is abutted by the input edge and a portion of the output edge. In many cases, the refractive index spatial gradient of the grating decreases along principal beam direction while the modulation spatial gradient of the grating increases along the principal beam direction.

[0062] The behavior of gratings requiring higher refractive index but lower index modulation, versus gratings requiring lower refractive index but higher index modulation becomes easier to understand if the optical paths are considered. Fold gratings tend to be further from the eyebox than output gratings. This additional optical path allows the field angles to be spatially more discrete. The separation of high average index / low modulation vs low index / high modulation regions in the output grating is improved when the eye relief (ER) is large and the eyebox (EB) size is small. Reducing the ER decreasesthe separation of fields projected from the EB onto the output grating. Similarly, a smaller EB for a given ER will allow fields from the EB to the output grating to better separate.

[0063] Embodiments recognize that the highest refractive index values are required to extract the highest propagation angles within the waveguide. In waveguide displays, these highest angles occur spatially at the start of the fold and output gratings. At this point the modulation profile is at its lowest. Moving spatially across the waveguide, the modulation requirement increases, but the maximum angle with which the grating needs to interact to direct light towards the eyebox reduces, i.e. , the minimum refractive index requirement falls off as the minimum index modulation requirement increases. Note, however, that where a high modulation value is required the refractive index modulation does not need to be lower; where a high modulation is needed it may be acceptable to provide a high refractive index. However, in many embodiments, having a lower refractive index where high modulation is needed provides greater materials design freedom.

[0064] In many embodiments, the grating may have an average refractive index in the range from 1.3 to 2.1 , and in still many embodiments in the range from 1.5 to 2.6. In many embodiments, the grating modulation may be defined by a refractive index modulation in the range from 0.001 to 0.05, as an example, in the case of a VHG, or a surface relief depth in the range from 20nm to 1000nm., in the cases of a SRG.

[0065] Spatial variation of index and modulation may be used in other types of gratings such as output gratings, according to some embodiments. In many embodiments, the grating is an output grating for expanding and deflecting the total internal reflection beam out of the waveguide, where the input face is a cross section of grating layer and the output face is formed by a surface of the grating parallel to the waveguide plane. FIG.4 shows a cross-section view (120) of a portion of a waveguide comprising an output grating (121 ) sandwiched by upper (122A) and lower (122B) substrates, in accordance with an example embodiment. A TIR path (123) is partially diffracted out of the waveguide in an extraction direction at each beam grating interaction providing the expanded output beam represented by the rays 124A,124B. FIG.5 is a plan view (125) of the grating showing the principal propagation direction (126) and the refractive index scale (127) shown the spatial variation of average refractive index. FIG.6 is a plan view (128) of the grating showing the principal propagation direction (126) and the refractive modulation scale(127) showing the spatial variation of refractive index modulation. As discussed above, the effect of spatial average index is stronger in fold gratings than in output gratings dure the higher field separation that exists in a fold grating.

[0066] Various embodiments incorporate a variety of grating average index and index modulation fields for different waveguide fields of view. Various embodiments also incorporate a variety of material requirements for both VHG and SRG+ gratings. SRG+ gratings seek to offer refractive index and grating modulation capabilities beyond those achievable with VHG. In many embodiments, SRG+ gratings may incorporate a refractive index of up to 1 .85.

[0067] In the following embodiments, diagonal fields of view (3:4 portrait aspect ratio) of 20°, 25°, 30°, and 35°, where a single waveguide is supporting full color (R,G,B) are considered. In such embodiments, the red light will propagate at the highest angles within the waveguide (furthest from TIR). The red field is therefore the most limited by refractive index in these embodiments. Accordingly, in various embodiments a minimum refractive index of as low as 1.3 or 1.5 may be used to prevent Fresnel reflections within a high refractive glass waveguide from becoming too high; strong reflections within the waveguide can cause noticeable interference based image artifacts (such as “herring bone”) which may be avoided by having better index match between the grating material and the waveguide glass substrates. The principles disclosed may apply to embodiments incorporating smaller or higher FoV waveguides and are not necessarily limited to the material refractive indices discussed.

[0068] Fig.7a shows the average index fields of a waveguide in accordance with various embodiments comprising a fold grating (131 A) with a principal beam direction (132A and an output grating (133A) with a principal beam direction (134A) configured for a diagonal FOV of 20° (12°x16°) waveguide. Fig.7B shows the refractive index modulation field for the same waveguide embodiment. Fig.7c is a plot of minimal refractive index and the refractive index modulation plot against the waveguide x coordinate which relates to the x-coordinate of Fig.7a. The green lines relate to the range of refractive index modulation and the blue lines to the minimum average refractive index, with the continuous line each case relating to the fold grating and the dashed lines to the output grating. Figs.8a-8c, 9a-9c and 10a-10c show similar plots for diagonal fields of view of25° (15°x20°), 30° (18°x24°), and 35° (21 °x28°), respectively, in accordance with many embodiments.

[0069] In Figs. 5, 6, 7a-7b, 8a-8b,9a-9b and 10a-1 Ob, the vertical (y) coordinate extends from 0-37.5 mm. and the horizontal (x) coordinate from 0-50 mm. The graphical scale for refractive index extends from 1.0 to 2.0 and for index modulation from 0 to 0.05. In Figs. 7c, 8c, 9c and 10c the low Rl value may be as low as 1 .3 to 1 .5 and the high Rl value may be 2.05 and the dn value may extend from 0 to 0.05. Note that these scales and limits are merely exemplary and do not reflect the maximum or minimum values of either Rl or dn available in accordance with the various embodiments of the invention.

[0070] Figs. 11a-11c show illustrative examples of minimum red (Fig.11a), green (Fig.11 b) and blue (Fig.11 c) minimum refractive index requirements for a color waveguide in accordance with some embodiments. Note that longer wavelengths (red light) have the highest angles of propagation within a single waveguide, and so the corner of the red display drives the maximum refractive index requirement in many embodiments. The start position of the fold and output gratings have the highest refractive index requirement, and lowest index modulation requirement in accordance with various embodiments. Figs.12a- 12c show stages in the refractive index mapping of the fold and output gratings in accordance with various embodiments.

[0071] In an example embodiment shown in Figs. 11a, 11 b and 11c, the vertical (y) coordinate extends from -30 to 10 mm. and the horizontal (x) coordinated from -50 to 0 mm. The graphical scale for refractive index extends from 1 .0 to 2.0.

[0072] Fig. 13 shows average refractive index requirements (blue) for fold gratings (continuous line) and output gratings (dashed line) for the fields of view and refractive indices discussed above. The range of grating modulation (green) is show by green lines and green shaded area.

[0073] Fig. 13 is an example embodiment demonstrating a design space (200) comprising minimum refractive index requirement (left hand side vertical axis) and dn requirement ( right hand side vertical axis) plotted against the x-coordinate of the waveguide, as defined in the above paragraphs. The vertical axis regions labelled by 201A-201 D correspond to different Rl and field of view combinations with region 201 A corresponding to a high index and high field of view, for example, one providing a field ofview of 20° for an index of 2.06 and a field of view of 35 deg. The lower region 201 D may correspond to a low index and low field of view design, for example, one providing a field of view of 20° for an index of 1.76 and a field of view of 20 deg. The region 201 B and 201 C are for intermediate Rl and field of view values. The design space for dn is represented by the shaded area (202) which is bounded by the upper curve (203A) and a lower curve (203B). The intercept of the upper curved with the refractive index axis gives an estimate of the target minimum dn value. Ideally the preferred minimum dn value should lie on the lower curve. In many cases the upper curve may target a dn in the range 0.02 to 0.05 and the upper curve may target a minimum value for the max dn of around 0.045. The waveguide path length as represented by the horizontal axis may extend from 0 to 30 mm. The dn requirement in embodiments exemplified in FIG.13 may range from 0 to 0.05 corresponding to a minimum refractive index requirement ranging from 1.50- 2.06.

[0074] FIGs. 14-15 compare grating material design spaces VHG (Fig.14) and SRG (Fig.15) in accordance with many embodiments. In each case the grating modulation is plotted against average refractive index with fold grating data shown in blue and output grating data shown in green. The shaded areas represent the design spaces for fold and output gratings. In FIG.14 the dn values may range from 0.01 to 0.05 and the Rl values from 1.5 to 1.8. In FIG.15 the dn values may range from 0.01 to 0.05 and the Rl values from 1.5 to 2.1.

[0075] FIG.16 shows plots for of average refractive index and index modulation for red diffracting fold grating and output grating configured to provide a full color 30 degree field of view in accordance with various embodiments. In Figs.16a and 16d (red fold gratings), the vertical (y) and horizontal (x) coordinates extends from 0 to 30 mm. In Figs.16a and 16d (red output gratings), the vertical (y) and horizontal (x) coordinates extends from 0 to 20 mm. The graphical scale for refractive index extends from 1 .0 to 2.0 and for modulation from 0 to 0.6.

[0076] FIG.17 shows the relationship of dn versus Rl in gratings like those discussed. The Rl scale in this plot may extend from 1 .3 to 1 .9 and the dn scale may extend from 0 to 0.06 in accordance with some embodiments. FIG.17 shows the results of a Pareto analysis of the index and modulation data of Fig.16 illustrating how consideration of therelationship of index modulation to refractive index design requirements may open up the material design space in many embodiments. The analysis demonstrates that in various embodiments the maximum refractive index and maximum refractive index modulation are not required at the same physical locations for the gratings considered. Note that the index modulation is limited to a maximum of 0.06, which is set as a current practical materials and hence design limitation. In the case of the output grating, the Pareto boundary is essentially a vertical line at this maximum dn condition. With a different material system (higher index modulation) this relationship would change to have a curved Pareto boundary similar to the fold grating, although the gradient of the boundary would be steeper owing to the closer proximity of the output grating to the EB than is the case with the fold grating. Note that materials used in the output grating in accordance with various embodiments require an SRG structure because the highest index modulation and refractive index requirements cannot be met with VHGs.

[0077] For a single substrate full color waveguide, in accordance with some embodiments, the max grating modulation required is dictated by the longest wavelength present in the image. The refractive index is required for that wavelength so care is required to measure or otherwise convert a measured refractive index value at another wavelength to the refractive index at the maximum wavelength. In many embodiments, refractive index values for green need to be at least 0.02 greater than the corresponding index for red. It is found that, in accordance with many embodiments, reducing the maximum wavelength reduces the peak refractive index by approximately 0.02 per 10 nm of wavelength reduction. Reduction of the maximum field angle in various embodiments reduces the peak refractive index requirement by approx. 0.02 per degree of field of view or more. In some embodiments, rake angles on the waveguide may have a similar effect on the peak angle (i.e., about a reduction in the index of 0.02 or more per degree of waveguide rake where the maximum TIR angle is reduced). However, rake angle changes can cut the shortest supported wavelengths by a similar amount. The values quoted here are approximate and will depend on the waveguide design of the subject embodiments.

[0078] In many embodiments spatial varying refractive index may be used in conjunction with other spatially varying parameters including slant angle, index modulation, duty cycle and feature height.

[0079] In various embodiments, the grating may have a spatial variation of at least one selected from the group comprising: K-vector, grating thickness, birefringence, polarization rotation, bias layer thickness, duty cycle, backfill material composition, backfill material thickness, and refractive index additive concentration. The waveguide may further comprise a layer for controlling polarization. In many embodiments the spatial variation of refractive index and modulation may be determined using reverse ray tracing procedures disclosed in our earlier filings

[0080] In various embodiments, a spatially varying average refractive index may be provided using various methods.

[0081] In many embodiments the grating is recorded in a holographic recording material mixture including a first monomer for forming polymer of a first refractive index and a mixture of a second monomer for forming polymer of a second refractive index, where the second refractive index is higher than the first refractive index. In many embodiments the second refractive index exceeds the first refractive index by at least 0.02 or a gradual increase to the required index by varying concentrations. In many embodiments the spatial distribution of the first refractive index material and the second refractive index material reduce the average refractive index variation across the grating. In many embodiments, the polymer of a second refractive index reduces image splitting resulting from rays skirting edge of the grating during expansion. In many embodiments the grating is surrounded by a uniform polymer formed from a mixture comprising a first monomer for forming polymer of a first refractive index and a mixture of a second monomer for forming polymer of a second refractive index. In many embodiments the second monomer has a spatial varying concentration prior to the recording of the grating. In many embodiments the spatial distribution of the first refractive index material and the second refractive index material result in non-binary refractive index profile along at least a portion of the perimeter of the grating.

[0082] In many embodiments refractive index dopants (such as nanoparticles) suspended in a solvent may be added to regions of a holographic recording mixturecoated on a substrate. The coating and the dopants may be deposited using an inkjet process using a moving printhead. The solvent may be removed by evaporation or some other process.

[0083] In many embodiments, a spatial variation of average index may be provided by spatially varying the effective refractive index of the grating using one or more grating parameters including duty cycle, feature height and refractive index modulation. In some embodiments the grating may include a bias layers having a spatially varying index.

[0084] In many embodiments, a spatial variation of refractive index modulation may be providing as part of the grating exposure process by perturbation of the recording wavefronts to from a grating of a required modulation and spatial frequency with a spatially varying average index.

[0085] In many embodiments, refractive index dopants may be added to the holographic recording mixture such that they participate in the phase separation process. In some embodiments refractive index dopants may be added to an exposed grating that is still in the process of curing. In such embodiments, the dopants may be introduced via vertical diffusion into the partially cured structure using a spraying process. In some embodiments the dopants may be introduced or by suffusion from an overlaying solution comprising refractive index dopants having an initial spatial concentration and a removable or evaporable solvent. In many embodiments, the refractive index dopants may be nanoparticles with magnetic or electrical properties that allow the spatial redistribution of the dopant using electromagnetic fields.

[0086] In many embodiments, a spatially varying refractive index may result from selective coating backfilling or immersion processed applied to one of a cured VHG structure, a SRG formed using phases separation and etching or a surface grating formed by a NIL process.

[0087] Decoupling spatial refractive index and spatial grating modulation as described in the various embodiments allows for higher fields of view to be achieved. The basic principle described in accordance with embodiments is not limited to any particular type of grating, any particular definition of grating refractive index and rating modulation, or any particular ranges of values of refractive index or grating modulation. The discussionapplies to both VHGs and SRGs (including SRG+). The only proviso is that the definition of modulation will differ between VHGs and SRGs. In embodiments employing an SRG, refractive index is the average of the refractive indices of polymer and air. In embodiments where gratings are coated, backfilled or immersed, an effective index needs to be defined. Grating modulation in embodiments employing SRG+ is given by the difference between the polymer and the air index and is thus much higher than the modulations achievable in VHGs. Note that in Kogelnik theory, refractive index modulation is defined as the amplitude of a sinusoidal index variation (not the difference in index measured from peak to trough). In most embodiments, even for perfectly sinusoidal intensity exposure, the non-linearity of photopolymerization results in non-sinusoidal grating modulation, which can be represented as a Fourier sum of harmonics of the recording spatial frequency. In embodiments in which the SRG is deep, the Kogelnik theory gives a good approximation of DE if the refractive index modulation is defined as (polymer refractive index - air refractive index) / 2. In general, the DE must be computed by solving Maxwell’s equations applied to a grating structure defined in terms of the geometry of the diffracting features (e.g., height, shape, duty cycle, etc.). In embodiments employing VHGs where the grating modulation comprises refractive index modulation, the grating modulation may lie in the range from 0.001 to 0.05 for holographic photopolymers. However, in embodiments employing an HPDLC-type VHG the grating modulation (which will be highly polarization dependent) may be much higher. In various embodiments, LC birefringence (‘typically in excess of 0.2) may result in an index modulation higher than 0.1. In many embodiments, the average refractive index of a VHG may lie in the range from 1.5 to 2.6. The upper index is chosen to include embodiments employing Silicon Carbide. Higher index may be also be achieved in accordance with various embodiments using a doped polymer, which will typically have index of 1.8. In an example embodiment in which the doped polymer grating has a duty cycle of 20% and a Titanium Dioxide coat of index 2.25 (at 550 nm.) is employed an effective refractive index in the range 2.35-2.4 may be achieved. In embodiments employing a SRG where the grating modulation comprises surface amplitude modulation, the grating modulation may be defined as a surface relief depth in the range from 20nm to 1000nm.

[0088] Spatially varying index and modulation gratings in accordance with the various embodiments discussed above may also be implemented using overlapping and multiplexed gratings. Overlapping gratings, with respect to such embodiments, refers to gratings formed on separated substrates that are overlapped that may be air spaced or laminated with or without spacer layers. In such embodiments, separate propagation within the substrates may be considered with respect to each grating having a unique average index and modulation spatial variation. According to various embodiments, the layers may be used to propagate different angular bandwidths or different spectral bandwidths. In some embodiments the beam propagation may be occurring in both overlapping substrates with the index and modulation fields of each substrate being optimized to provide a net beam effect. In some embodiments two gratings may be combined using multiplexing into a single grating layer. Multiplexing may be implemented using overlap of the two grating structures in the recording material layer either by simultaneous or sequential exposure, as is well known in holography. In some embodiments, spatial multiplexing in which the two or more gratings are spatially sampled and elements of different prescriptions are interspersed within a layer may be used. Fig. 18 shows in cross section a two waveguide stack (220) comprising a first waveguide substrate (221) supporting a first grating (222) and a second waveguide (223) supporting a second grating (224). The waveguides are each configured to propagate TIR light (225,226) over defined angular and / or spectral ranges. The waveguides may be separated by an air gap (227) or, alternatively, by a layer of material of a low refractive index to satisfy TIR at the lowest guided ray angle in each waveguide. The first grating (222) has a first spatial variation of refractive index and a first spatial variation of grating modulation. In the case of a surface grating, the modulation will be determined by the grating feature height above the substrate (or bias layer, if one is present). The second grating (224) provides a second spatial variation of refractive index and second spatial variation of grating modulation. The indices and modulation are specified such that each waveguide can propagate light of a particular wavelength range and / or angular bandwidth.

[0089] Fig. 19 shows an embodiment (230) in which two overlaid waveguides (231 ,232) supporting gratings (233,234) are configured to propagate TIR light (235) in both substrates.

[0090] Fig. 20 shows an embodiment (240) in which a single waveguide substrate (241 ) supports a grating (242) multiplexing gratings that diffract in one or more wavelength bands and / or one or more angular bands. The waveguide light is propagated along one or more TIR paths in the substrate.

[0091] In general, consideration of eyebox projection, longer eye relief / wider FoV, permits more design freedom in the design of any of the above waveguide embodiments. The first order geometry for describing eyebox projection is shown in Fig. 21. A waveguide portion comprises a substrate (251 ) supporting a grating (252). TIR light (253) propagating in the substrate expands and extracts light into a beam bounded by rays 255,254 to form an eyebox (EB) at an eye relief (ER). For eye relief greater than the waveguide thickness (d), that is, ER»d, the eye box projection (D) onto the waveguide, for eyebox (EB), eye relief (ER), and field of view (0FOV ) is given by the equation:D = EB + 2ER tan(0Fov / 2) (EQ. 1)

[0092] In further embodiments a waveguide comprising: a grating including an input coupler for coupling light into a TIR path within the waveguide; and at least one grating for providing beam expansion and extraction of light from the waveguide is considered. The grating in such embodiments may have an input face and an output face. The input face and output face may be defined in different ways. In the case of a fold grating for expanding and deflecting the total internal reflection beam within the waveguide plane, the input face and the output face are cross sections of the grating. In the case of an output grating for expanding and deflecting the total internal reflection beam out of the waveguide, the input face is a cross section of grating layer and the output face is formed by a surface of the grating parallel to the waveguide plane. The grating has a principal input beam direction from the input face and a principal diffraction direction passing through the output face. Fig. 22 provides an embodiment (260) in which a single waveguide substrate (261 ) supports a grating including an input coupler (262), a fold grating (263), and an output coupler (264). The input coupler (262) couples the input light (265) into a TIR path (266) within the waveguide substrate (261 ). The output coupler (264)expands and deflects the light (267) out of the waveguide substrate (261). Again, following the earlier described embodiments, the grating is configured such that the average grating refractive index decreases along the principal input beam direction whereas the grating modulation increases along the principal input beam direction. In other words, the refractive index spatial gradient decreases along principal beam direction while the grating modulation spatial gradient increases along the principal beam direction. However, in embodiments where the grating is recorded in a holographic recording material mixture including: a first monomer for forming polymer of a first refractive index, and a mixture of a second monomer for forming polymer of a second refractive index, the second refractive index is higher than the first refractive index.

[0093] In many embodiments, the spatial distribution of the first refractive index material and the second refractive index material may result in non-binary refractive index profile along at least a portion of the perimeter of the grating. In many embodiments, the second refractive index may exceed the first refractive index by at least 0.02. In many embodiments, the spatial distribution of the first refractive index material and the second refractive index material modifies the average refractive index and modulation fields in ways that might be advantageous for waveguide beam propagation. For example, two materials may be optimized to reduce the average refractive index variation across the grating. In many embodiments, having a polymer of a second refractive index may be advantageous in terms of reducing the image splitting resulting from rays skirting edge of the grating during expansion.

[0094] In many embodiments, the grating is surrounded by a uniform polymer formed from a mixture comprising a first monomer for forming polymer of a first refractive index and a mixture of a second monomer for forming polymer of a second refractive index. The second monomer may be deposited onto the recording substrate with a spatial varying concentration prior to the recording of the grating.

[0095] In many embodiments, a waveguide grating may include a high grating modulation region abutted by a portion of the output edge and an edge of the grating at the extremity of the principal beam direction optical path. In many embodiments, a grating having a high average refractive index region is abutted by the input edge and a portion of the output edge.

[0096] In any of the embodiments considered, the grating may be a dual interaction fold. In any of the embodiments considered, the grating may have a spatial variation of at least one selected from the group comprising: K-vector, grating thickness, birefringence, polarization rotation, bias layer thickness, duty cycle, backfill material composition, backfill material thickness, and refractive index additive concentration. The waveguides considered may further comprise a layer for controlling polarization. The input coupler may be a grating or a prism.DOCTRINE OF EQUIVALENTS

[0097] This description of the invention has been presented for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form described, and many modifications and variations are possible in light of the teaching above. The embodiments were chosen and described in order to best explain the principles of the invention and its practical applications. This description will enable others skilled in the art to best utilize and practice the invention in various embodiments and with various modifications as are suited to a particular use. The scope of the invention is defined by the following claims.

[0098] As used herein, the singular terms "a," "an," and "the" may include plural referents unless the context clearly dictates otherwise. Reference to an object in the singular is not intended to mean "one and only one" unless explicitly so stated, but rather "one or more."

[0099] As used herein, the terms "approximately" and "about" are used to describe and account for small variations. When used in conjunction with an event or circumstance, the terms can refer to instances in which the event or circumstance occurs precisely as well as instances in which the event or circumstance occurs to a close approximation. When used in conjunction with a numerical value, the terms can refer to a range of variation of less than or equal to ± 10% of that numerical value, such as less than or equal to ±5%, less than or equal to ±4%, less than or equal to ±3%, less than or equal to ±2%, less than or equal to ±1 %, less than or equal to ±0.5%, less than or equal to ±0.1 %, or less than or equal to ±0.05%.

[0100] Additionally, amounts, ratios, and other numerical values may sometimes be presented herein in a range format. It is to be understood that such range format is used for convenience and brevity and should be understood flexibly to include numerical values explicitly specified as limits of a range, but also to include all individual numerical values or sub-ranges encompassed within that range as if each numerical value and sub-range is explicitly specified. For example, a ratio in the range of about 1 to about 200 should be understood to include the explicitly recited limits of about 1 and about 200, but also to include individual ratios such as about 2, about 3, and about 4, and sub-ranges such as about 10 to about 50, about 20 to about 100, and so forth.

Claims

WHAT IS CLAIMED IS:

1. A waveguide comprising: a grating including an input coupler for coupling light into a TIR path within the waveguide; and at least one grating for providing beam expansion and extraction of light from the waveguide; wherein the grating has an input face and an output face and a principal input beam direction from the input face and a principal diffraction direction passing through the output face; wherein the average grating refractive index decreases along the principal input beam direction; wherein the grating modulation increases along the principal input beam direction; wherein the grating is recorded in a holographic recording material mixture including a first monomer for forming polymer of a first refractive index and a mixture of a second monomer for forming polymer of a second refractive index, and wherein the second refractive index is higher than the first refractive index.

2. The waveguide of claim 1 , wherein the spatial distribution of the first refractive index material and the second refractive index material result in non-binary refractive index profile along at least a portion of the perimeter of the grating.

3. The waveguide of claim 1 , wherein the second refractive index exceeds the first refractive index by at least 0.02 or a gradual increase to the required index by varying concentrations.

4. The waveguide of claim 1 , wherein the spatial distribution of the first refractive index material and the second refractive index material reduces the average refractive index variation across the grating.

5. The waveguide of claim 1 , wherein the polymer of a second refractive index reduces image splitting resulting from rays skirting edge of the grating during expansion.

6. The waveguide of claim 1 , wherein the grating is surrounded by uniform polymer formed from a mixture comprising a first monomer for forming polymer of a first refractive index and a mixture of a second monomer for forming polymer of a second refractive index.

7. The waveguide of claim 1 , wherein the second monomer has a spatial varying concentration prior to the recording of the grating.

8. The waveguide of claim 1 , wherein the grating is a fold grating for expanding and deflecting the total internal reflection beam within the waveguide plane, wherein the input face and the output face are cross sections of the grating.

9. The waveguide of claim 1 , wherein the grating is an output grating for expanding and deflecting the total internal reflection beam out of the waveguide, wherein the input face is a cross section of grating layer and the output face is formed by a surface of the grating parallel to the waveguide plane.

10. The waveguide of claim 1 , wherein a grating high grating modulation region is abutted by a portion of the output edge and an edge of the grating at the extremity of the principal beam direction optical path.

11. The waveguide of claim 1 , wherein a grating high average refractive index region is abutted by the input edge and a portion of the output edge.

12. The waveguide of claim 1 , wherein the refractive index spatial gradient decreases along principal beam direction.

13. The waveguide of claim 1 , wherein the gradient modulation spatial gradient increases along the principal beam direction.

14. The waveguide of claim 1 , wherein the grating modulation comprises refractive index modulation.

15. The waveguide of claim 1 , wherein the grating modulation comprises surface amplitude modulation.

16. The waveguide of claim 1 , wherein the grating has average refractive index in the range from 1.3 to 2.1.

17. The waveguide of claim 1 , wherein the grating has average refractive index in the range from 1.5 to 2.6.

18. The waveguide of claim 1 , wherein the grating has a grating modulation defined by a refractive index modulation in the range from 0.001 to 0.1.

19. The waveguide of claim 1 , wherein the grating has a grating modulation defined by surface relief depth in the range from 20nm to 1000nm.

20. The waveguide of claim 1 , wherein the grating is a dual interaction fold.

21. The waveguide of claim 1 , wherein the grating has a spatial variation of at least one selected from the group comprising: K-vector, grating thickness, birefringence, polarization rotation, bias layer thickness, duty cycle, backfill material composition, backfill material thickness, and refractive index additive concentration.

22. The waveguide of claim 1 , further comprising a layer for controlling polarization.

23. The waveguide of claim 1 , wherein the input coupler is a grating or a prism.

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