Display device having a grating with gradient edges

Abstract

The display may include a waveguide and an optical coupler. The coupler may include one or more surface relief gratings (SRGs) in a substrate above the waveguide. The SRG(s) may have a central region and gradient lateral edges separating the central region from a non-diffractive region of the substrate. The SRG(s) may exhibit peak diffraction efficiency in the central region and gradient diffraction efficiency across the gradient lateral edges from the central region toward the non-diffractive region. The gradient diffraction efficiency may be created across the gradient lateral edges by varying the amplitude of the SRG(s), the phase of the SRG(s), the duty cycle of the SRG(s), the blaze angle of the SRG(s), and / or the thickness of a high-index or low-index coating layered on the SRG(s). This may serve to prevent the coupler from being undesirably visible and minimize perturbation of the replicated pupil.

Description

[Technical Field]

[0001] FIELD OF THE DISCLOSURE The present disclosure relates to optical systems, such as optical systems in electronic devices having displays. (CROSS-REFERENCE TO RELATED APPLICATIONS) This application claims priority to U.S. Patent Application No. 18 / 414,126, filed January 16, 2024, and U.S. Provisional Patent Application No. 63 / 483,152, filed February 3, 2023, both of which are incorporated by reference in their entireties. [Background technology]

[0002] Electronic devices can include displays that present images near a user's eyes. Such electronic devices often include virtual reality or augmented reality headsets in which the displays have optical elements that allow the user to view the display. If care is not taken, the components used to display the images can be bulky and not exhibit the desired level of optical performance. For example, boundaries between optical elements can cause unsightly visual artifacts. Summary of the Invention

[0003] The electronic device may have a display system for providing image light to an eyebox. The display system may include a waveguide. An input coupler may couple light into the waveguide. A cross coupler may perform pupil expansion on the light. An output coupler may couple light exiting the waveguide toward the eyebox. Alternatively, the cross coupler and output coupler may be replaced by an interleaved coupler that combines and expands light exiting the waveguide.

[0004] Any of the couplers may include one or more surface relief gratings (SRGs) in a substrate above the waveguide. The SRG(s) may have a central region and gradient lateral edges separating the central region from non-diffracting regions of the substrate. The SRG(s) may exhibit peak diffraction efficiency in the central region. The SRG(s) may exhibit gradient diffraction efficiency across the gradient lateral edges from the central region toward the non-diffracting regions. The gradient diffraction efficiency may be created across the gradient lateral edges by varying the amplitude of the SRG(s), the phase of the SRG(s), the duty cycle of the SRG(s), the blaze angle of the SRG(s), and / or the thickness of a high-index or low-index coating layered on the SRG(s).

[0005] The sloped lateral edges may function to prevent a sharp boundary between the coupler and the non-diffractive regions of the substrate. This may prevent the coupler from being undesirably visible, noticeable, and / or distracting to the user of the system and / or others facing the user. This may also function to minimize perturbation of the replicated pupil, thereby improving the modulation transfer function (MTF) and reducing visible image artifacts such as bleeding and double images. [Brief explanation of the drawings]

[0006] [Figure 1] FIG. 1 is a diagram of an exemplary system having a display, according to some embodiments.

[0007] [Figure 2] FIG. 1 is a top view of an exemplary optical system for a display having a waveguide with an optical coupler, according to some embodiments.

[0008] [Figure 3A] FIG. 2 is a top view of an exemplary waveguide provided with a surface relief grating, according to some embodiments. [Figure 3B] FIG. 2 is a top view of an exemplary waveguide provided with a surface relief grating, according to some embodiments. [Figure 3C] FIG. 2 is a top view of an exemplary waveguide provided with a surface relief grating, according to some embodiments.

[0009] [Figure 4] FIG. 1 is a front view of an exemplary waveguide having an optical coupler formed from a surface relief grating, according to some embodiments.

[0010] [Figure 5] FIG. 1 illustrates a front view of an exemplary waveguide having an optical coupler with overlapping first and second surface relief gratings oriented in different directions, according to some embodiments.

[0011] [Figure 6] 1 is a front view of an exemplary optical coupler having one or more surface relief gratings with sloped lateral edges, according to some embodiments.

[0012] [Figure 7] 1A-1C are cross-sectional top views of exemplary surface relief gratings having gradient lateral edges formed by varying the thickness of a coating on the surface relief grating, according to some embodiments.

[0013] [Figure 8] 1A-1C are cross-sectional top views of exemplary surface relief gratings having gradient lateral edges formed by varying grating depths, according to some embodiments.

[0014] [Figure 9] 1A-1C are cross-sectional top views of exemplary surface relief gratings having gradient lateral edges formed by varying duty cycles, according to some embodiments. DETAILED DESCRIPTION OF THE INVENTION

[0015] System 10 of FIG. 1 may be a head-mounted device having one or more displays. The display in system 10 may include a near-eye display 20 mounted within a support structure (housing) 14. Support structure 14 may have the shape of glasses or goggles (e.g., a support frame), may form a helmet-shaped housing, or may have other configurations useful for mounting and securing the components of near-eye display 20 near a user's head or eyes. Near-eye display 20 may include one or more display projectors (sometimes referred to herein as display modules 26), such as projector 26, and one or more optical systems, such as optical system 22. Projectors 26 may be mounted within a support structure, such as support structure 14. Each projector 26 may use an associated one of optical systems 22 to emit image light 30 that is redirected toward a user's eye at eyebox 24. Image light 30 may be, for example, light including and / or representing something visible, such as a scene or object (e.g., modulated onto the image light using image data provided to the display module by control circuitry).

[0016] The operation of system 10 may be controlled using control circuitry 16. Control circuitry 16 may include storage and processing circuitry for controlling the operation of system 10. Circuitry 16 may include storage such as, for example, hard disk drive storage, non-volatile memory (e.g., electrically programmable read-only memory configured to form a solid-state drive), and volatile memory (e.g., static or dynamic random access memory). The processing circuitry of control circuitry 16 may be based on one or more microprocessors, microcontrollers, digital signal processors, baseband processors, power management units, audio chips, graphics processing units, application-specific integrated circuits, and other integrated circuits. Software code may be stored in the storage of circuitry 16 and run on the processing circuitry within circuitry 16 to perform the operations of system 10 (e.g., data collection operations, operations involving coordination of components using control signals, image rendering operations to produce image content to be displayed to a user, etc.).

[0017] System 10 may include input / output circuitry, such as input / output device 12. Input / output device 12 may be used to allow system 10 to receive data from external devices (e.g., a tethered computer, a portable device such as a handheld or laptop computer, or other electronic device) and to allow a user to provide user input to head-mounted device 10. Input / output device 12 may also be used to collect information about the environment in which system 10 (e.g., head-mounted device 10) is operating. Output components within device 12 may allow system 10 to provide output to the user and may also be used to communicate with external electronic devices. Input / output device 12 may include sensors and other components 18 (e.g., image sensors for collecting images of real-world objects to be digitally merged with virtual objects on the display of system 10, accelerometers, depth sensors, light sensors, haptic output devices, speakers, batteries, wireless communication circuitry for communicating between system 10 and external electronic devices, etc.).

[0018] Projector 26 may include a liquid crystal display, an organic light emitting diode display, a laser-based display, or other types of displays. Projector 26 may include a light source, an emissive display panel, a transmissive display panel illuminated with illumination light from the light source to create image light, a reflective display panel such as a digital micromirror display (DMD) panel and / or a liquid crystal on silicon (LCOS) display panel illuminated with illumination light from the light source to create image light 30, etc.

[0019] The optical system 22 may form lenses that allow a viewer (e.g., see the viewer's eyes in eyebox 24) to see images on the display(s) 20. There may be two optical systems 22 associated with each of the user's eyes (e.g., to form a left lens and a right lens). A single display 20 may produce images for both eyes, or a pair of displays 20 may be used to display images. In a configuration with multiple displays (e.g., a left-eye display and a right-eye display), the focal lengths and positions of the lenses formed by the systems 22 may be selected so that any gaps between the displays are invisible to the user (i.e., so that the image on the left display overlaps or seamlessly merges with the image on the right display).

[0020] Optionally, optical system 22 may include components (e.g., an optical combiner, etc.) to enable real-world light 31 (sometimes referred to herein as world light 31 or ambient light 31) produced and / or reflected from real-world objects 28 (sometimes referred to herein as external objects 28) to be optically combined with virtual (computer-generated) images, such as the virtual images in image light 30. In this type of system, sometimes referred to as an augmented reality system, a user of system 10 can view both real-world content and computer-generated content that is overlaid on top of the real-world content. Camera-based augmented reality systems may also be used within device 10 (e.g., in an arrangement in which a camera captures real-world images of external objects, and this content is digitally merged with the virtual content in optical system 22).

[0021] System 10 may include wireless and / or other circuitry, as needed, to support communication with a computer or other external device (e.g., a computer providing image content to display 20). In operation, control circuitry 16 may provide image content to display 20. The content may be received remotely (e.g., from a computer or other content source coupled to system 10) and / or generated by control circuitry 16 (e.g., text, other computer-generated content, etc.). A viewer may view the content provided to display 20 by control circuitry 16 at eyebox 24.

[0022] Figure 2 is a top view of an exemplary display 20 that may be used in system 10 of Figure 1. As shown in Figure 2, display 20 may include a projector, such as projector 26, and an optical system, such as optical system 22. Optical system 22 may include optical elements, such as one or more waveguides 32. Waveguide 32 may include one or more laminated substrates (e.g., laminated planar layers and / or laminated curved layers, sometimes referred to herein as waveguide substrates) of optically transmissive material, such as plastic, polymer, glass, or the like.

[0023] Optionally, the waveguide 32 may also include one or more layers of a holographic recording medium (sometimes referred to herein as a holographic medium, grating medium, or grating medium) having one or more diffraction gratings recorded therein (e.g., a holographic phase grating, sometimes referred to herein as a hologram, surface relief grating, etc.). The holographic recording may be stored as an optical interference pattern (e.g., alternating regions of different refractive index) within a photosensitive optical material such as a holographic medium. The optical interference pattern may produce a holographic phase grating that, when illuminated with a given light source, diffracts light to produce a three-dimensional reconstruction of the holographic recording. The holographic phase grating may be a non-switchable diffraction grating encoded with a persistent interference pattern, or a switchable diffraction grating that can modulate the diffracted light by controlling the electric field applied to the holographic recording medium. Optionally, multiple holographic phase gratings (holograms) may be recorded within (e.g., superimposed within) the same volume of the holographic medium. The holographic phase grating may be, for example, a volume hologram or a thin-film hologram within the grating medium. The grating medium may include photopolymer, gelatin such as dichromated gelatin, silver halide, holographic polymer dispersed liquid crystal, or other suitable holographic medium.

[0024] The diffraction grating on the waveguide 32 may include a holographic phase grating, such as a volume hologram or a thin-film hologram, a metagrating, or any other desired diffraction grating structure. The diffraction grating on the waveguide 32 may also include surface relief gratings (SRGs) formed on one or more surfaces of a substrate within the waveguide 32 (e.g., as a modulation in the thickness of an SRG medium layer), a grating formed from a pattern of a metal structure, etc. The diffraction grating may include, for example, multiple multiplexed gratings (e.g., holograms) that at least partially overlap within the same volume of the grating medium (e.g., to diffract light of different colors and / or light from different ranges of input angles to one or more corresponding output angles). If desired, other light redirection elements, such as louver mirrors, may be used in place of a diffraction grating within the waveguide 32.

[0025] As shown in FIG. 2 , projector 26 may generate (produce and emit) image light 30 related to image content to be displayed in eyebox 24 (e.g., image light 30 may carry a series of image frames for display in eyebox 24). Image light 30 may be collimated, if desired, using a collimating lens within projector 26. Optical system 22 may be used to present image light 30 output from projector 26 to eyebox 24. If desired, projector 26 may be mounted within support structure 14 of FIG. 1 , while optical system 22 may be mounted between components of support structure 14 (e.g., to form a lens that aligns with eyebox 24). Other mounting arrangements may be used, if desired.

[0026] Optical system 22 may include one or more optical couplers (e.g., optical redirection elements), such as input coupler 34, cross coupler 36, and output coupler 38. In the example of Figure 2, input coupler 34, cross coupler 36, and output coupler 38 are formed in or on waveguide 32. Input coupler 34, cross coupler 36, and / or output coupler 38 can be completely embedded within a substrate layer of waveguide 32, partially embedded within a substrate layer of waveguide 32, or attached to waveguide 32 (e.g., attached to an outer surface of waveguide 32).

[0027] The waveguide 32 may guide the image light 30 down its length by total internal reflection. The input coupler 34 may be configured to couple the image light 30 from the projector 26 into the waveguide 32 (e.g., within the total-internal reflection (TIR) ​​range of the waveguide, where the light propagates within the waveguide via TIR), and the output coupler 38 may be configured to couple the image light 30 from within the waveguide 32 (e.g., propagating within the TIR range) out of the waveguide 32 toward the eyebox 24 (e.g., at an angle outside the TIR range). The input coupler 34 may include an input coupling prism, an edge or face of the waveguide 32, a lens, a steering mirror or liquid crystal steering element, a diffraction grating structure (e.g., a volume hologram, SRG, etc.), a partially reflective structure (e.g., a louvered mirror), or any other desired input coupling element.

[0028] For example, projector 26 may emit image light 30 toward optical system 22 in the +Y direction. When image light 30 hits input coupler 34, input coupler 34 may redirect image light 30 such that the light propagates within waveguide 32 via total internal reflection (e.g., in direction +X within the TIR range of waveguide 32) toward output coupler 38. When image light 30 hits output coupler 38, output coupler 38 may redirect image light 30 from waveguide 32 toward eyebox 24 (e.g., back along the Y axis). In implementations in which cross coupler 36 is formed on waveguide 32, cross coupler 36 may redirect image light 30 in one or more directions (e.g., from the propagation direction coupled into the waveguide by the input coupler toward output coupler 38) as image light 30 propagates along the length of waveguide 32. In redirecting the image light 30, the cross coupler 36 may also perform pupil expansion in one or more directions on the image light 30. In expanding the pupil of the image light, the cross coupler 36 may serve to reduce the vertical size (e.g., in the Z direction) of the waveguide 32, for example, relative to an implementation in which the cross coupler 36 is omitted. Accordingly, the cross coupler 36 is sometimes referred to herein as a pupil expander 36 or an optical expander 36. Optionally, the output coupler 38 may also expand the image light 30 when coupling the image light out of the waveguide 32.

[0029] The input coupler 34, cross coupler 36, and / or output coupler 38 can be based on reflective and refractive optics or diffractive (e.g., holographic) optics. In arrangements where couplers 34, 36, and 38 are formed from reflective and refractive optics, couplers 34, 36, and 38 may include one or more reflectors (e.g., arrays of micromirrors, partial mirrors, louvered mirrors, or other reflectors). In arrangements where couplers 34, 36, and 38 are based on diffractive optics, couplers 34, 36, and 38 may include diffraction gratings (e.g., volume holograms, surface relief gratings, etc.).

[0030] The embodiment of FIG. 2 is merely illustrative. Optical system 22 may include multiple waveguides stacked laterally and / or vertically relative to one another. Each waveguide may include one, two, all, or none of couplers 34, 36, and 38. Waveguide 32 may be at least partially curved or bent as desired. One or more of couplers 34, 36, and 38 may be omitted. Optionally, optical system 22 may include a single optical coupler (sometimes referred to herein as an interleaved coupler, diamond coupler, or diamond expander) that performs the functions of both cross coupler 36 and output coupler 38, or cross coupler 36 may be separate from output coupler 38. Implementations in which cross coupler 36, or a single optical coupler that performs the functions of both cross coupler 36 and output coupler 38 (e.g., receiving light from an input coupler) includes surface relief gratings (SRGs), are described herein by way of example.

[0031] FIG. 3A is a top view illustrating one example of how a surface relief grating may be formed on a waveguide 32. As shown in FIG. 3A, the waveguide 32 may have a first lateral surface 70 and a second lateral surface 72 opposite the lateral surface 70 (sometimes referred to herein as a waveguide surface). The waveguide 32 may include any desired number of one or more stacked waveguide substrates. Optionally, the waveguide 32 may also include a layer of grating medium sandwiched between a first waveguide substrate and a second waveguide substrate (e.g., the first waveguide substrate includes the lateral surface 70 and the second waveguide substrate includes the lateral surface 72).

[0032] The waveguide 32 may be provided with a surface relief grating (SRG), such as a surface relief grating 74. The SRG 74 may be included within the cross coupler 36 or, for example, as part of an optical coupler (e.g., a diamond expander or interleaved coupler) that performs the functions of both the cross coupler 36 and the output coupler 38. The SRG 74 may be formed within a substrate, such as a layer of an SRG substrate 76 (sometimes referred to herein as a medium 76, medium layer 76, SRG medium 76, or SRG medium layer 76). For clarity, FIG. 3A shows only a single SRG 74 in the SRG substrate 76, but the SRG substrate 76 may include two or more SRGs 74 (e.g., SRGs with different respective lattice vectors). If desired, at least a portion of each of the SRGs may be superimposed within the same volume of the SRG substrate 76. In the example of FIG. 3A, the SRG substrate 76 is layered on a lateral surface 70 of the waveguide 32. This is merely an example; if desired, the SRG substrate 76 can be deposited on a lateral surface 72 (eg, the surface of the waveguide 32 facing the eyebox).

[0033] The SRG 74 may include peaks 78 and troughs 80 within the thickness of the SRG substrate 76. The peaks 78 may also be referred to herein as ridges 78 or maxima 78. The troughs 80 may also be referred to herein as notches 80, slots 80, grooves 80, or minima 80. In the example of FIG. 3A , the SRG 74 is shown for clarity as a binary structure, where the SRG 74 is defined by either a first thickness associated with the ridges 78 or a second thickness associated with the troughs 80. This is merely exemplary. Optionally, the SRG 74 may be non-binary (e.g., include any desired number of thicknesses following any desired profile, include ridges 78 angled at fringe angles non-parallel to the Y-axis, etc.), include ridges 78 with sloped surfaces (e.g., oriented out of the XZ plane), include sloped troughs 80 (e.g., oriented out of the XZ plane), include ridges 78 and / or troughs 80 with heights and / or depths following a modulation envelope, etc. If desired, the SRG substrate 76 may be adhered to the lateral surfaces 70 of the waveguide 32 using a layer of optically clear adhesive (not shown). The SRG 74 may also be fabricated separately from the waveguide 32 and adhered to the waveguide 32 after fabrication, or may be etched into the SRG substrate 76 after the SRG substrate 76 has already been layered on the waveguide 32, for example.

[0034] The example of FIG. 3A is merely illustrative. In another implementation, the SRG 74 may be located at a location inside the waveguide 32, as shown in the example of FIG. 3B. As shown in FIG. 3B, the waveguide 32 may include a first waveguide substrate 84, a second waveguide substrate 86, and a medium layer 82 interposed between the waveguide substrates 84 and 86. The medium layer 82 may be a diffraction grating or holographic recording medium, a layer of adhesive, a layer of polymer, a layer of the waveguide substrate, or any other desired layer within the waveguide 32. The SRG substrate 76 may be layered on the surface of the waveguide substrate 84 facing the waveguide substrate 86. Alternatively, the SRG substrate 76 may be layered on the surface of the waveguide substrate 86 facing the waveguide substrate 84.

[0035] If desired, multiple SRGs 74 may be distributed across multiple layers of an SRG substrate, as shown in the example of FIG. 3C. As shown in FIG. 3C, the optical system may include multiple stacked waveguides, such as at least a first waveguide 32 and a second waveguide 32′. A first SRG substrate 76 may be layered on one of the lateral surfaces of the waveguide 32, and a second SRG substrate 76′ may be layered on one of the lateral surfaces of the waveguide 32′. The first SRG substrate 76 may include one or more of the SRGs 74. The second SRG substrate 76′ may include one or more of the SRGs 74. This example is merely illustrative. If desired, the optical system may include three or more stacked waveguides. In an example where the optical system includes three or more waveguides, each waveguide provided with an SRG substrate may include one or more SRGs 74. Although described herein as separate waveguides, waveguides 32 and 32' in Figure 3C may also be formed from the same waveguide substrate, if desired. The arrangements of Figures 3A, 3B, and / or 3C may be combined if desired.

[0036] Optionally, waveguide 32 may include one or more substrates having regions containing the gratings of input coupler 34, cross coupler 36, and / or output coupler 38, and having regions without gratings. Figure 4 is a front view illustrating one example of how waveguide 32 may include one or more substrates having regions containing the gratings of input coupler 34, cross coupler 36, and / or output coupler 38, and having regions without gratings.

[0037] As shown in FIG. 4, the waveguide 32 may include one or more substrates 89 (e.g., a single substrate 89 or multiple stacked substrates 89) on one or more waveguides 32 (e.g., a single waveguide 32 or multiple stacked waveguides 32). The substrate(s) 89 may include one or more layers of a grating medium, such as an SRG substrate 76 (FIGS. 3A-3B). One or more grating structures 88 used to form optical couplers for the waveguide 32 may be disposed or formed on the substrate(s) 89. Each grating structure 88 may include one or more SRGs 74 (FIGS. 3A-3C).

[0038] For example, substrate(s) 89 may include a first grating structure 88A (sometimes referred to herein as grating structure 88A or grating(s) 88A) formed from a first set of one or more overlapping SRGs 74 ( FIGS. 3A-3C ) in a first region of the substrate(s) 89. Optionally, substrate(s) 89 may also include a second grating structure 88B (sometimes referred to herein as grating structure 88B or grating(s) 88B) formed from a second set of one or more overlapping SRGs 74 in a second region of the substrate(s) 89 laterally separated from the first grating structure 88A. Optionally, the substrate(s) 89 may further include a third diffraction grating structure 88C (sometimes referred to herein as grating structure 88C or grating(s) 88C) formed from a third set of one or more overlapping SRGs 74 in a third region of the substrate(s) 89 laterally separated from the first diffraction grating structure 88A and the second diffraction grating structure 88B.

[0039] Each grating structure 88A, 88B, and 88C may form a respective optical coupler for the waveguide 32. For example, grating structure 88A may form an input coupler 34 for the waveguide 32. Grating structure 88B may form a cross coupler (e.g., a pupil expander) 36 on the waveguide 32. Grating structure 88C may form an output coupler 38 for the waveguide 32. Thus, grating structure 88A may couple a beam 92 of image light 30 into the waveguide 32 toward grating structure 88B. Grating structure 88B may redirect the image light 30 toward grating structure 88C and, optionally, perform pupil expansion on the image light 30 (e.g., split the image light 30 into multiple paths to form a larger beam that covers the eye's pupil and forms a more uniform image). Grating structure 88C may couple the image light 30 exiting the waveguide 32 toward the eyebox. If desired, the grating structure 88C can also perform pupil expansion on the image light 30.

[0040] The substrate(s) 89, and thus the waveguide 32, may also include one or more regions 90 that are free of a grating structure 88, a diffraction grating, or an optical coupler. Regions 90 may be, for example, free of any of the ridges 78 and troughs 80 of the SRG (FIGS. 3A-3C) and, if desired, free of any of the refractive index modulations of the VPH. Regions 90 may separate grating structure 88A from grating structure 88B, grating structure 88B from grating structure 88C, grating structure 88C from grating structure 88A, and / or may laterally surround one or all of the grating structures 88A-88C. Regions 90 may be referred to herein as grating-free regions 90, intergrating regions 90, non-grating regions 90, or non-diffracting regions 90. Non-diffracting regions 90 may include, for example, all of the lateral area of ​​the substrate(s) 89 that does not include a diffraction grating.

[0041] Each grating structure 88 of substrate(s) 89 may span a corresponding lateral area of ​​substrate(s) 89. The lateral area spanned by each grating structure 88 is defined (bounded) by lateral edge(s) 94 of that grating structure 88. The lateral edge 94 may separate or divide the portion of substrate(s) 89 containing the thickness modulation used to form one or more SRG(s) within the grating structure 88 from the non-diffracting region 90 on the substrate(s) 89. In other words, the lateral edge 94 may define the boundary between the grating structure 88 and the non-diffracting region 90. The grating structures 88A, 88B, and 88C may have any desired lateral shape (e.g., as defined by the lateral edge 94).

[0042] 4 is merely illustrative; in general, the input coupler 34, cross coupler 36, and output coupler 38 may have any desired lateral contour or shape (e.g., as defined by lateral edges 94). If desired, the waveguide 32 may include optical couplers that redirect and expand / duplicate the image light 30 (e.g., to fill as much of the eyebox 24 as possible with uniform intensity image light 30). Such optical couplers, sometimes referred to herein as diamond expanders or interleaved couplers, are capable of performing the functionality of both the cross coupler 36 and the output coupler 38. Using an optical coupler as both a cross coupler and an output coupler may save space within the display (e.g., space that would otherwise be occupied by separate cross couplers and output couplers).

[0043] FIG. 5 is a front view of one such optical coupler 109 on waveguide 32. Optical coupler 109 may, for example, replace cross coupler 36 and output coupler 38 on waveguide 32 of FIG. 4. As shown in FIG. 5, optical coupler 109 may include a grating structure 88D on substrate(s) 89 having at least a first SRG 74A and a second SRG 74B (e.g., superimposed on one another within the same volume of a single substrate 89). SRGs 74A and 74B may each include a respective set of ridges 78 and troughs 80 ( FIGS. 3A-3C ) extending in different respective directions in substrate 89. For example, SRG 74A may be characterized by a first grating vector K1 (e.g., oriented orthogonal to the direction of the peaks, troughs, or lines of constant median thickness of SRG 74A). Similarly, SRG 74B may be characterized by a second lattice vector K2 (e.g., oriented perpendicular to the direction of the peaks, troughs, or lines of constant median thickness of SRG 74B). Lattice vector K2 may be oriented non-parallel to lattice vector K1.

[0044] The magnitude of the grating vector K1 corresponds to the width and spacing (e.g., period) of the ridges 78 and troughs 80 (fringes) of SRG 74A and the wavelength of light diffracted by the SRG. The magnitude of the grating vector K2 corresponds to the width and spacing (e.g., period) of the ridges 78 and troughs 80 of SRG 74B and the wavelength of light diffracted by the SRG. Surface relief gratings generally have broad bandwidths. The bandwidths of SRGs 74A and 74B may, for example, encompass each of the wavelengths of the image light 30 (e.g., the entire visible spectrum, a portion of the visible spectrum, a portion of the infrared or near-infrared spectrum, some or all of the visible spectrum, and a portion of the infrared or near-infrared spectrum, etc.). The magnitude of the grating vector K2 may be equal to or different from the magnitude of the grating vector K1. While shown in the plane of the page in FIG. 5 for clarity, the grating vectors K1 and / or K2 may have non-zero vector components parallel to the Y-axis (e.g., the grating vectors K1 and K2 may be tilted into or out of the page).

[0045] SRG 74A at least partially overlaps SRG 74B within optical coupler 109 (e.g., at least some of the ridges and troughs of each SRG spatially overlap or are superimposed within the same volume of the SRG substrate). Optionally, the intensity of SRG 74A and / or SRG 74B may be modulated vertically (e.g., along the Z axis) and / or horizontally (e.g., along the X axis). Optionally, one or both of SRGs 74A and 74B may have a magnitude that decreases to zero in peripheral regions 108A and 108B of the field of view, which may help mitigate the production of rainbow artifacts.

[0046] Image light 30 may be conveyed through waveguide 32 (e.g., via total internal reflection) to optical coupler 89. SRGs 74A and 74B may diffract the incident image light 30 in two different directions, thereby replicating the pupil of the image light. SRGs 74A and 74B may additionally or alternatively widen the pupil of the image light. This creates multiple optical paths for image light 30 within optical coupler 89, allowing for uniform intensity image light 30 to fill as much of the eyebox as possible.

[0047] As shown in FIG. 5 , the grating structure 88D may span a corresponding lateral area of ​​the substrate(s) 89. The lateral area spanned by the grating structure 88D is defined (bounded) by lateral edge(s) 94 of the grating structure 88D. The lateral edge 94 may separate or divide the portion of the substrate(s) 89 containing the thickness modulation used to form one or more SRG(s) in the grating structure 88D from the non-diffracting region 90 on the substrate(s) 89. In other words, the lateral edge 94 may define the boundary between the grating structure 88D and the non-diffracting region 90. The grating structure 88D may have any desired lateral shape (e.g., as defined by the lateral edge 94).

[0048] While optical couplers on waveguide 32 (e.g., optical couplers 34, 36, or 38 in FIG. 4 or optical coupler 109 in FIG. 5) redirect image light 30 for display at eyebox 24, diffraction grating structures 88 within each optical coupler (e.g., diffraction grating structures 88A-88C in FIG. 4 or diffraction grating structure 88D in FIG. 5) may also accidentally diffract ambient light from the environment (e.g., world light 31 in FIG. 1) in different directions. In some implementations, lateral edges 94 are precisely defined sharp boundaries between the SRGs of diffraction grating structures 88 within optical couplers and non-diffracting regions 90 of substrate(s) 89. In these implementations, the diffraction intensity (e.g., diffraction efficiency) of substrate(s) 89 changes abruptly at lateral edges 94 from peak intensity within diffraction grating structures 88 to zero intensity within non-diffracting regions 90. Thus, the amount of ambient light diffracted by the SRG(s) in the grating structure 88 changes abruptly from the peak amount to zero on either side of the lateral edge 94. A sharp boundary can cause the grating structure 88 and corresponding optical coupler to be undesirably visible, noticeable, and / or distracting to a user of the system 10 and / or others facing the system 10 (e.g., as an iridescent region or visual artifact on the waveguide 32 surrounded by a transmissive non-diffracting region 90 that does not diffract ambient light) while the system 10 is worn by the user. The boundary can also undesirably disrupt pupil replication by the grating structure, which can create undesirable visual artifacts such as bleeding or double images.

[0049] To mitigate these problems, the grating structure 88 may be provided with one or more gradient lateral edges 94 (sometimes referred to herein as blurred, transitional, diffused, fuzzy, or unsharp lateral edges 94). FIG. 6 is a front view of a waveguide 32 having an exemplary grating structure 88 with gradient lateral edges 94. As shown in FIG. 6, the grating structure 88 (e.g., grating structure 88A of the input coupler 34 of FIG. 4, grating structure 88B of the cross coupler 36 of FIG. 4, grating structure 88C of the output coupler 38 of FIG. 4, and / or grating structure 88D of the optical coupler 109 of FIG. 5) may include one or more SRGs 74 in a substrate(s) 89 on the waveguide 32.

[0050] The grating structure 88 may be laterally bounded (e.g., in the XZ plane) on the substrate(s) 89 by sloped lateral edges 94. In the example of FIG. 6, all of the lateral edges of the grating structure 88 are sloped lateral edges. This is merely exemplary; sloped lateral edges may be used to form some, but not all, of the lateral edges of the grating structure 88, if desired. The sloped lateral edges 94 may be formed by gradually decreasing the intensity (and thus the diffraction efficiency of the SRG(s) 74) in the grating structure 88 from a peak intensity (peak diffraction efficiency) within the sloped lateral edges 94 to zero intensity (diffraction efficiency) in the non-diffracting regions 90 on the substrate(s) 89. The direction or gradient of the intensity decrease may be oriented orthogonal (in the XZ plane) to the direction of the sloped lateral edges 94, as indicated by arrow 110.

[0051] In other words, rather than being a one-dimensional line, gradient lateral edge 94 may instead be formed from a two-dimensional (peripheral) region or area of ​​substrate(s) 89 that laterally surrounds central region 136 of grating structure 88 and extends in the direction of arrow 110 from central region 136 to non-diffracting region 90. At gradient lateral edge 94, the intensity (diffraction efficiency) of the SRG(s) in grating structure 88 may decrease in the direction of arrow 110 (e.g., radially outward from central region 136) from the intensity of the SRG(s) in central region 136 to zero intensity in non-diffracting region 90. At the gradient lateral edge 94, the intensity of the SRG(s) in the diffraction grating structure 88 can be configured to decrease in the direction of arrow 110 across the gradient lateral edge 94 by varying the amplitude of the SRG(s) (e.g., the height of the ridge 78 in Figures 3A-3C and / or the depth of the trough 80 in Figures 3A-3C), the phase of the SRG(s), the duty cycle of the SRG(s), the blaze angle of the SRG(s), the thickness of a coating deposited on the SRG(s), and / or any other desired property of the SRG(s).

[0052] FIG. 7 is a cross-sectional top view illustrating one example of how the sloped lateral edges 94 of a grating structure 88 can be formed by varying the thickness of a coating on the SRG(s) within the grating structure 88 in the direction of arrow 110. As shown in FIG. 7, the grating structure 88 can include at least one SRG 74 formed in a substrate 89 above a waveguide 32. The waveguide 32 can be formed from a high refractive index material, such as glass. The refractive index of the waveguide 32 can be greater than 1.5, greater than 1.7, greater than 1.8, greater than 1.9, greater than 2.0, greater than 2.2, greater than 2.4, greater than 2.5, between 1.9 and 2.1, etc. The SRG 74 can include a ridge 78 formed from a high refractive index material. The material used for the ridge 78 can be, for example, silicon nitride, titanium dioxide, or another desired high refractive index material. The refractive index of the ridge 78 can be greater than 1.5, greater than 1.8, greater than 2.0, greater than 2.2, greater than 2.4, greater than 2.5, and the like.

[0053] In the example of Figure 7, the SRG 74 is a blazed grating having ridges 78 with non-parallel sidewalls. This is merely an example, and if desired, one or more (e.g., all) of the ridges 78 can have sidewalls that are parallel or nearly parallel (e.g., within 5 degrees, within 3 degrees, within 1 degree, etc.). In the blazed grating of Figure 7, each ridge 78 is defined by a first surface 132 and an opposite second surface 134.

[0054] The surface 132 of each ridge 78 may be oriented at an angle 128 relative to the top lateral surface of the waveguide 32 (or the bottom surface of the substrate 89). The angle 128 (sometimes referred to as the blaze angle) may have any desired magnitude (e.g., between 10 and 40 degrees, between 15 and 40 degrees, between 25 and 35 degrees, between 25 and 30 degrees, greater than 10 degrees, greater than 20 degrees, greater than 30 degrees, greater than 40 degrees, less than 10 degrees, less than 20 degrees, less than 30 degrees, less than 40 degrees, etc.).

[0055] A surface 134 of each ridge 78 may be oriented at an angle 130 relative to an upper lateral surface of the waveguide 32 (or the bottom surface of the substrate 89). The angle 130 (sometimes referred to as the anti-blaze angle) may have any desired magnitude (e.g., greater than 75 degrees, greater than 85 degrees, greater than 90 degrees, greater than 100 degrees, greater than 110 degrees, between 85 degrees and 110 degrees, less than 90 degrees, less than 110 degrees, etc.).

[0056] Each trough 80 can have an opening angle given by the difference between angle 130 and angle 128. The opening angle can be between 60 degrees and 120 degrees, between 70 degrees and 110 degrees, between 80 degrees and 100 degrees, between 75 degrees and 85 degrees, between 85 degrees and 95 degrees, greater than 60 degrees, greater than 70 degrees, greater than 80 degrees, greater than 90 degrees, greater than 100 degrees, greater than 110 degrees, less than 60 degrees, less than 70 degrees, less than 80 degrees, less than 90 degrees, less than 100 degrees, less than 110 degrees, etc.

[0057] Each ridge 78 may have a height measured parallel to the Y-axis from the waveguide 32 to the maximum thickness of the ridge. The height of the ridge 78 may be greater than 50 nanometers, greater than 100 nanometers, greater than 200 nanometers, greater than 300 nanometers, greater than 500 nanometers, less than 50 nanometers, less than 100 nanometers, less than 200 nanometers, less than 300 nanometers, less than 500 nanometers, between 50 nanometers and 300 nanometers, etc. Each ridge 78 may also have a width measured parallel to the X-axis across its base at the waveguide 32. The width of the ridge 78 may be greater than 50 nanometers, greater than 100 nanometers, greater than 200 nanometers, greater than 300 nanometers, greater than 500 nanometers, less than 50 nanometers, less than 100 nanometers, less than 200 nanometers, less than 300 nanometers, less than 500 nanometers, between 50 nanometers and 300 nanometers, between 300 nanometers and 400 nanometers, etc.

[0058] A coating 124 may be deposited on the ridges 78 of the grating structure 88. If desired, the coating 124 may be directionally deposited on surfaces 132 of the ridges 78, but not on surfaces 134. The coating 124 may be a high-index coating (e.g., having a refractive index greater than the refractive index of the substrate 89 and / or waveguide 32 by more than 0.1, more than 0.3, more than 0.5, more than 0.7, more than 1.0, etc.) or a low-index coating (e.g., having a refractive index less than the refractive index of the substrate 89 and / or waveguide 32 by more than 0.1, more than 0.2, more than 0.5, more than 0.7, more than 1.0, etc.). The coating 124 may include titanium dioxide (TiO) or silicon dioxide (SiO), as two examples. If desired, an encapsulation layer (not shown) may be deposited on the coated ridges 78. Coating 124 may help to increase the contrast between waveguide 32 and the material above substrate 89 (e.g., air or an encapsulation layer), which may help maximize the diffraction efficiency of the grating and / or help reduce unwanted reflections. If desired, a residual or sacrificial substrate (not shown) may be interposed between substrate 89 and waveguide 32. The residual substrate may be formed from the same material as ridge 78 or may be left over from the nanoimprint process in which ridge 78 is formed.

[0059] 7 , the coating 124 may have a corresponding thickness 126 on the ridge 78. The coating 124 may exhibit a peak thickness in a central region 136 of the grating structure 88. The coating 124 may exhibit a variable thickness within the sloped lateral edges 94 of the grating structure 88. For example, the thickness of the coating 124 may decrease across the sloped lateral edges 94 in the direction of arrow 110 from a maximum thickness in the central region 136 to zero thickness outside the sloped lateral edges 94. This decrease in coating thickness across the sloped lateral edges 94 may serve to reduce the strength and diffraction efficiency of the SRG(s) 74 within the grating structure 88 across the sloped lateral edges 94 (in the direction of arrow 110) and prevent a sharp boundary between the grating structure 88 and the surrounding portions of the substrate 89.

[0060] Fabrication equipment 112 may be used to form the SRG 74 on the substrate 89 and deposit a coating 124 on the SRG 74. After the SRG 74 is etched or cut into the substrate 89, the fabrication equipment 112 may deposit the coating 124 on the SRG 74. The fabrication equipment 112 may include a coating deposition device that directionally deposits the coating 124 onto the surface 132 of the SRG 74 through an opening 120 in a mask 118, as indicated by arrow 114. The coating material may be scattered or diffracted at the edges of the opening 120, as indicated by arrow 116. This diffraction may cause the coating 124 to be deposited with a decreasing thickness 126 in the direction of arrow 110 within the sloped lateral edges 94 of the grating structure 88. At the same time, the portion of the coating material that passes through the opening 120 without diffracting at the edges of the opening 120 is deposited with a peak thickness 126 in a central region 136. By adjusting the distance 122 between the mask 118 and the SRG 74, the fabrication equipment 112 can vary the gradient of the thickness of the coating 124 and, therefore, the width of the sloped lateral edges 94. In the example of Figure 7, the substrate 89 includes additional ridges 78 and troughs 80 outside the sloped lateral edges 94 of the diffraction grating structure 88. This is merely an example; if desired, the substrate 89 may be free of the ridges 78 and troughs 80 outside the sloped lateral edges 94 (e.g., to form non-diffractive regions 90). Other deposition equipment or techniques may be used to form the coating 124.

[0061] 8 is a cross-sectional top view illustrating one example of how sloped lateral edges 94 of a grating structure 88 may be formed by varying the depth of the troughs 80 (sometimes referred to herein as the grating depth) in the SRG(s) 74 of the grating structure 88 (or equivalently by varying the height of the ridges 78 relative to the bottom of the troughs 80). In the example of FIG. 8, the ridges 78 have parallel sidewalls oriented at a non-perpendicular angle to the lateral surfaces of the waveguide 32. This is merely an example; in general, the sidewalls can be in any desired orientation, and the SRG 74 can be a blazed grating, etc.

[0062] In FIG. 8 , the substrate 89 has a flat top surface opposite the waveguide 32. Each ridge 78 has a top surface separated from the waveguide 32 (or residual underlying substrate, not shown) by the same distance across the grating structure 88. Each trough 80 may have a corresponding depth 142 (sometimes referred to herein as the height 142 or thickness 142 of the trough 80). The trough 80 may have a first depth (e.g., maximum depth) 142 in the central region 136 of the grating structure 88. The trough 80 may have a variable depth 142 within the sloped lateral edges 94 of the grating structure 88. The depth 142 of the trough 80 may decrease across the sloped lateral edges 94 in the direction of arrow 110, from the first depth 142 in the central region 136 to a depth of zero outside the sloped lateral edges 94 (e.g., within the non-diffracting regions 90).

[0063] In general, the decrease in trough depth can follow any desired function 146 (in the direction of arrow 110) that decreases from the central region 136 across the sloped lateral edge 94 toward the non-diffracting region 90. For example, as shown in FIG. 8 , the depth modulation (e.g., function 146) of the ridge of the SRG 74 can be characterized by a line or plane having a slope angle 144. This angle characterizes how the depth of the trough 80 changes across the sloped lateral edge 94. The angle 144 can be less than 10 degrees, less than 1 degree, less than 0.1 degrees, less than 0.01 degrees, less than 0.001 degrees, less than 0.0001 degrees, less than 30 degrees, less than 45 degrees, less than 60 degrees, etc. The bottom of the trough 80 can be oriented parallel to the lateral surface of the waveguide 32 or non-parallel to the lateral surface of the waveguide 32. For example, as shown in FIG. 8 , the bottom of the trough 80 can be oriented parallel to the function 146. This is merely exemplary.

[0064] The depth 142 of each trough can be greater than 50 nanometers, greater than 100 nanometers, greater than 200 nanometers, greater than 300 nanometers, greater than 500 nanometers, greater than 750 nanometers, greater than 1000 nanometers, less than 50 nanometers, less than 100 nanometers, less than 200 nanometers, less than 300 nanometers, less than 500 nanometers, less than 750 nanometers, less than 1000 nanometers, between 200 nanometers and 400 nanometers, between 100 nanometers and 750 nanometers, between 50 nanometers and 1000 nanometers, etc. The depth of the trough is generally proportional to the diffraction efficiency. Reducing the grating depth across the sloped lateral edge 94 in this manner serves to reduce the strength and diffraction efficiency of the SRG(s) 74 within the grating structure 88 across the sloped lateral edge 94 (in the direction of arrow 110) and can prevent a sharp boundary between the grating structure 88 and the surrounding portion of the substrate 89.

[0065] Fabrication equipment 112 may be used to form SRGs 74 in substrate 89 (e.g., by etching or cutting troughs 80 in substrate 89). As shown in FIG. 8 , fabrication equipment 112 may include etching elements 140 (e.g., laser light or other optical emitters, lithography equipment, etc.) that pass through openings 120 in mask 118. The etching elements 140 may scatter or diffract at the edges of opening 120, as indicated by arrows 116. This diffraction may cause the etching elements 140 to form troughs 80 in substrate 89 that decrease in depth 142 in the direction of arrow 110 within sloped lateral edges 94 of grating structure 88. At the same time, the portions of etching elements 140 that pass through opening 120 without diffracting at the edges of opening 120 form troughs 80 with a uniform depth in central region 136. By adjusting the distance 122 between the mask 118 and the substrate 89 , the fabrication equipment 112 can vary the gradient of the depth of the trough 80 and, therefore, the width of the gradient lateral edge 94 .

[0066] Each ridge 78 in the grating structure 88 may have a corresponding width 152 (sometimes referred to herein as ridge width 152). Width 152 may be greater than 50 nanometers, greater than 100 nanometers, greater than 200 nanometers, greater than 300 nanometers, greater than 500 nanometers, less than 50 nanometers, less than 100 nanometers, less than 200 nanometers, less than 300 nanometers, less than 500 nanometers, between 50 nanometers and 300 nanometers, between 300 nanometers and 400 nanometers, etc.

[0067] The center-to-center spacing between the ridges 78 (sometimes referred to herein as pitch 150 or ridge pitch 150) can be any desired size (e.g., greater than 50 nanometers, greater than 100 nanometers, greater than 200 nanometers, greater than 300 nanometers, greater than 500 nanometers, greater than 750 nanometers, greater than 1000 nanometers, less than 50 nanometers, less than 100 nanometers, less than 200 nanometers, less than 300 nanometers, less than 500 nanometers, less than 750 nanometers, less than 1000 nanometers, between 200 nanometers and 400 nanometers, between 300 nanometers and 400 nanometers, between 100 nanometers and 750 nanometers, etc.).

[0068] The duty cycle of the ridges (defined as the ridge width 152 divided by the ridge pitch 150) can be greater than 60%, greater than 70%, greater than 80%, greater than 90%, greater than 95%, less than 99%, less than 70%, less than 80%, less than 90%, less than 95%, between 60% and 99%, etc. In the examples of Figures 7 and 8, the grating structure 88 exhibits a uniform duty cycle across its lateral area (e.g., across both the central region 136 and the sloped lateral edges 94). If desired, the duty cycle of the ridges 78 can be varied to form sloped lateral edges 94.

[0069] Figure 9 is a cross-sectional top view showing one example of how sloped lateral edges 94 of a grating structure 88 can be formed by varying the duty cycle of the SRG(s) 74 within the grating structure 88. In the example of Figure 9, the ridges 78 have parallel sidewalls oriented at an angle perpendicular to the lateral surfaces of the waveguide 32. This is merely an example; in general, the sidewalls can be in any desired orientation, and the SRGs 74 can be a blazed grating, etc.

[0070] 9 , the grating structure 88 may have a first ridge width 152 and a first ridge pitch 150, and thus a first (constant) duty cycle, in the central region 136. The width 152 of the ridges 78 and / or the pitch 150 of the ridges 78 may be varied to thereby vary the duty cycle of the SRG(s) in the sloped lateral edges 94 of the grating structure 88. The duty cycle may increase or decrease in the direction of arrow 110 across the sloped lateral edges 94 from a first duty cycle in the central region 136 to a second duty cycle in the non-diffracting regions 90. In other words, the ridge width 152 and / or the ridge pitch 150 may increase and / or decrease in the direction of arrow 110 across the sloped lateral edges 94.

[0071] Varying the duty cycle of the SRG(s) 74 across the sloped lateral edge 94 in this manner serves to reduce the strength and diffraction efficiency of the SRGs 74 in the grating structure 88 across the sloped lateral edge 94 (in the direction of arrow 110), and can prevent a sharp boundary between the grating structure 88 and the surrounding portions of the substrate 89. The fabrication equipment used to form the grating structure 88 of Figure 9 may include a mask (not shown for clarity) through which the etching elements 140 pass to cause the etching elements 140 to form in the substrate 89 the SRG(s) 74 of the grating structure 88 that vary with the desired duty cycle within the sloped lateral edge 94.

[0072] 7-9 are merely illustrative. Any desired combination of varying coating thickness (FIG. 7), varying grating depth (FIG. 8), and varying duty cycle (FIG. 9) may be used to configure the SRG(s) 74 in the grating structure 88 to exhibit decreasing intensity (diffraction efficiency) across the sloped lateral edge 94 in the direction of arrow 110. For example, the SRG(s) 74 in the grating structure 88 may have a variable duty cycle, a decreasing trough depth, and / or a coating 124 that decreases in thickness across the sloped lateral edge 94 in the direction of arrow 110. More generally, any desired combination of modulation of the amplitude of the SRG(s) (e.g., the height of the ridges 78 in FIGS. 3A-3C and / or the depth of the troughs 80 in FIGS. 3A-3C), the phase of the SRG(s), the duty cycle of the SRG(s), the blaze angle of the SRG(s), the thickness of a coating deposited on the SRG(s), and / or any other desired property of the SRG(s) may be used to form the sloped lateral edge 94.

[0073] The sloped lateral edges 94 may function to prevent sharp boundaries that would cause the diffraction grating structure 88 and corresponding optical coupler to be undesirably visible, noticeable, and / or distracting to a user of the system 10 and / or others facing the system 10 while the system 10 is being worn by the user (e.g., may reduce the formation of rainbow-colored areas or visual artifacts on the waveguide 32), and / or may minimize perturbations of the replicated pupil, thereby improving the modulation transfer function (MTF) and reducing visual image artifacts such as bleeding and double images.

[0074] According to one embodiment, an electronic device is provided that includes a waveguide, a substrate on the waveguide, and a surface relief grating (SRG) on the substrate, the SRG having sloped lateral edges.

[0075] According to another embodiment, an electronic device includes a coating on the SRG, the coating having a thickness that decreases across the sloped lateral edge.

[0076] According to another embodiment, the SRG has grooves that decrease in depth across the sloping lateral edges.

[0077] According to another embodiment, the SRG has a duty cycle that varies across the gradient lateral edge.

[0078] According to another embodiment, the SRG has a duty cycle that varies across the gradient lateral edge.

[0079] According to another embodiment, the SRG has a duty cycle that varies across the gradient lateral edge.

[0080] According to another embodiment, the SRG has grooves that decrease in depth across the sloping lateral edges.

[0081] According to another embodiment, the SRG has grooves that decrease in depth across the sloping lateral edges.

[0082] According to another embodiment, an electronic device includes an SRG and includes an input coupler configured to couple light into a waveguide, an output coupler configured to couple light out of the waveguide, and a cross coupler configured to redirect light from the input coupler towards the output coupler.

[0083] According to another embodiment, an electronic device includes an input coupler configured to couple light into a waveguide, an output coupler including an SRG and configured to couple light out of the waveguide, and a cross coupler configured to redirect light from the input coupler towards the output coupler.

[0084] According to another embodiment, an electronic device includes an input coupler configured to couple light into a waveguide, an output coupler configured to couple light out of the waveguide, and a cross coupler including an SRG and configured to redirect light from the input coupler towards the output coupler.

[0085] According to another embodiment, an electronic device includes an input coupler configured to couple light into a waveguide and an interleaved coupler including an SRG and an additional SRG overlapping the SRG, the interleaved coupler configured to expand the light and couple the light out of the waveguide, the SRG having a first grating vector and the additional SRG having a second grating vector non-parallel to the first grating vector.

[0086] According to one embodiment, there is provided an electronic device including a waveguide, an input coupler configured to couple light into the waveguide, a substrate over the waveguide, and a surface relief grating (SRG) on the substrate configured to redirect light coupled into the waveguide by the input coupler, the SRG including a central region and a peripheral region laterally separating the central region from a non-diffracting portion of the substrate, the peripheral region having a diffraction efficiency that decreases from the central region towards the non-diffracting portion of the substrate.

[0087] According to another embodiment, the SRG has a peak diffraction efficiency in a central region, and a peripheral region laterally surrounds the central region.

[0088] According to another embodiment, the SRG has grooves whose depth decreases in the peripheral region from the central region towards the non-diffracting portion of the substrate.

[0089] According to another embodiment, the SRG has a duty cycle in the peripheral region that varies from the central region towards the non-diffracting portion of the substrate.

[0090] According to another embodiment, an electronic device includes a coating on an SRG, wherein the substrate has a first refractive index, the coating has a second refractive index different from the first refractive index, and the coating has a thickness in a peripheral region that decreases from a central region toward a non-diffracting portion of the substrate.

[0091] According to another embodiment, the SRG has a non-perpendicular blaze angle in the peripheral region that varies from the central region towards the non-diffracting portion of the substrate.

[0092] According to one embodiment, an electronic device is provided that includes a waveguide, a substrate on the waveguide, a first surface relief grating (SRG) on the substrate, and a second SRG on the substrate, wherein the second SRG overlaps the first SRG in a first region and a second region of the substrate, the first SRG is oriented non-parallel to the second SRG, the first SRG and the second SRG have a first gradient diffraction efficiency in the first region of the substrate, the substrate has a second diffraction efficiency in the second region of the substrate, and the first SRG and the second SRG have a gradient diffraction efficiency in a third region of the substrate, the third region of the substrate laterally surrounding the first region of the substrate and laterally separating the first region of the substrate from the second region of the substrate, and the gradient diffraction efficiency decreases from the first diffraction efficiency in the first region to the second diffraction efficiency in the second region.

[0093] According to another embodiment, the second diffraction efficiency is zero.

[0094] The above is merely exemplary and various modifications may be made to the described embodiments. The foregoing embodiments may be implemented individually or in any combination.

Claims

1. A waveguide; a substrate on the waveguide; a surface relief grating (SRG) in the substrate, the surface relief grating (SRG) having sloped lateral edges; Electronic devices.

2. a coating on the SRG, the coating having a thickness that decreases over the sloped lateral edge. The electronic device of claim 1 .

3. The electronic device of claim 2 , wherein the SRG has a groove with a decreasing depth across the sloped lateral edge.

4. The electronic device of claim 3 , wherein the SRG has a duty cycle that varies across the gradient lateral edge.

5. The electronic device of claim 2 , wherein the SRG has a duty cycle that varies across the gradient lateral edge.

6. The electronic device of claim 1 , wherein the SRG has a duty cycle that varies across the gradient lateral edge.

7. The electronic device of claim 6 , wherein the SRG has a groove with a decreasing depth across the sloped lateral edge.

8. The electronic device of claim 1 , wherein the SRG has a groove with a decreasing depth across the sloped lateral edge.

9. an input coupler comprising the SRG and configured to couple light into the waveguide; an output coupler configured to couple the light out of the waveguide; a cross coupler configured to redirect the light from the input coupler towards the output coupler. The electronic device of claim 1 .

10. an input coupler configured to couple light into the waveguide; an output coupler comprising the SRG and configured to couple the light out of the waveguide; a cross coupler configured to redirect the light from the input coupler towards the output coupler. The electronic device of claim 1 .

11. an input coupler configured to couple light into the waveguide; an output coupler configured to couple the light out of the waveguide; a cross coupler comprising the SRG and configured to redirect the light from the input coupler towards the output coupler. The electronic device of claim 1 .

12. an input coupler configured to couple light into the waveguide; an interleaved coupler comprising the SRG and an additional SRG overlapping the SRG, configured to expand the light and couple the light out of the waveguide, the SRG having a first grating vector and the additional SRG having a second grating vector non-parallel to the first grating vector; The electronic device of claim 1 .

13. A waveguide; an input coupler configured to couple light into the waveguide; a substrate on the waveguide; a surface relief grating (SRG) in the substrate and configured to redirect the light coupled into the waveguide by the input coupler; a central region; a peripheral region laterally separating the central region from a non-diffracting portion of the substrate, the peripheral region having a diffraction efficiency that decreases from the central region toward the non-diffracting portion of the substrate; Electronic devices.

14. The electronic device of claim 13 , wherein the SRG has a peak diffraction efficiency in the central region, and the peripheral region laterally surrounds the central region.

15. 15. The electronic device of claim 14, wherein the SRG has grooves, the depth of the grooves decreasing in the peripheral region from the central region toward the non-diffracting portion of the substrate.

16. The electronic device of claim 14 , wherein the SRG has a duty cycle in the peripheral region that varies from the central region towards the non-diffracting portion of the substrate.

17. a coating on the SRG, the substrate having a first refractive index, the coating having a second refractive index different from the first refractive index, the coating having a thickness in the peripheral region that decreases from the central region toward the non-diffracting portion of the substrate.

15. The electronic device of claim 14.

18. The electronic device of claim 14 , wherein the SRG has a non-perpendicular blaze angle in the peripheral region that varies from the central region toward the non-diffracting portion of the substrate.

19. A waveguide; a substrate on the waveguide; a first surface relief grating (SRG) on the substrate; a second SRG on the substrate; the second SRG overlaps the first SRG in the first and second regions of the substrate; The first SRG is oriented non-parallel to the second SRG. the first SRG and the second SRG have a first diffraction efficiency within a first region of the substrate; the substrate has a second diffraction efficiency in a second region of the substrate; the first SRG and the second SRG have gradient diffraction efficiency within a third region of the substrate; the third region of the substrate laterally surrounds and laterally separates the first region of the substrate from the second region of the substrate; the gradient diffraction efficiency decreasing from the first diffraction efficiency in the first region to the second diffraction efficiency in the second region. Electronic devices.

20. 20. The electronic device of claim 19, wherein the second diffraction efficiency is zero.

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