Facebook Patent | Display waveguide with a high-index layer

Patent: Display waveguide with a high-index layer

Drawings: Click to check drawins

Publication Number: 20210124108

Publication Date: 20210429

Applicant: Facebook

Abstract

A display waveguide configured for conveying polychromatic image light to a viewer includes a substrate and a higher-index layer supported by the substrate. The high-index layer supports the transmission of the longer-wavelength color channel of the image light in at least a portion of the field of view.

Claims

  1. A waveguide for conveying image light to an eyebox, the waveguide comprising: a substrate of a first refractive index n.sub.1; a high-index layer of a second refractive index n.sub.2 supported by the substrate without an air gap therebetween, wherein n.sub.2 is greater than n.sub.1; an input coupler configured to couple the image light into the high-index layer; and, an output coupler configured to couple the image light out of the waveguide toward the eyebox, the output coupler comprising a first grating and a second grating, wherein at least one of the first and second gratings is configured to redirect light propagating in the high-index layer.

  2. The waveguide of claim 1 wherein each one of the first and the second gratings is disposed in the high-index layer or at a surface thereof to diffract light propagating in the high-index layer.

  3. The waveguide of claim 2 wherein the first grating is disposed at a surface of the high-index layer, and the second grating is disposed at an interface between the substrate and the high-index layer.

  4. The waveguide of claim 2 wherein the output coupler further comprises a third grating configured to redirect light propagating in the substrate.

  5. The waveguide of claim 4 wherein the third grating is disposed at a surface of the substrate opposite of the high-index layer.

  6. The waveguide of claim 1 wherein the input coupler comprises an input grating disposed to couple at least a portion of the image light into the high-index layer.

  7. The waveguide of claim 1 wherein the second refractive index is at least 2.2.

  8. The waveguide of claim 1 wherein (n.sub.1-n.sub.2) is equal to or greater than 0.3.

  9. The waveguide of claim 1 wherein the high-index layer is at least 150 microns thick.

  10. The waveguide of claim 1 wherein the image light comprises a first color channel and a second color channel, wherein the second color channel comprises longer wavelengths than the first color channel, and wherein the input coupler is configured to trap at least a portion of the second color channel in the high-index layer by means of total internal reflection (TIR) at an interface between the high-index layer and the substrate.

  11. The waveguide of claim 10 wherein the waveguide provides a field of view (FOV) shared by the first and second color channels, the FOV having an angular FOV width .THETA. in at least one direction, and wherein the high-index layer supports at least 50% of the angular FOV width .THETA. of at least one of the first and second color channels.

  12. The waveguide of claim 10 wherein the first color channel comprises one of green or blue light and the second color channel comprises red light, and wherein the input coupler is configured to trap at least a portion of the red light in the high-index layer by means of TIR at the interface between the high-index layer and the substrate.

  13. The waveguide of claim 10 wherein the first color channel comprises blue light and the second color channel comprises green light, and wherein the input coupler is configured to trap at least a portion of the green light in the high-index layer by means of TIR at the interface between the high-index layer and the substrate.

  14. The waveguide of claim 10 wherein the image light further comprises a third color channel, and wherein the input coupler is configured to couple all three color channels into the waveguide for propagating toward the output coupler.

  15. The waveguide of claim 10 wherein the input coupler is configured to direct at least a portion of the first color channel into the substrate through the interface of the high-index layer with the substrate.

  16. The waveguide of claim 1 wherein the first grating and the second grating cooperate for diffracting the image light trapped in the high-index layer out of the waveguide at an output angle equal to an angle of incidence thereof upon the waveguide.

  17. The waveguide of claim 16 comprising a third grating disposed in the substrate or at a surface thereof, wherein at least one of the first grating or the second grating cooperate with the third grating for diffracting the image light propagating in the substrate out of the waveguide at an output angle equal to an angle of incidence thereof upon the waveguide.

  18. A near-eye display (NED) device comprising: a support structure for wearing on a head of a user; a light projector carried by the support structure and configured to emit image light comprising a plurality of color channels; and, a first waveguide carried by the support structure and configured to convey at least a first color channel and a second color channel of the image light from the light projector to an eyebox, the first waveguide comprising: a substrate of a first refractive index n.sub.1; a high-index layer of a second refractive index n.sub.2 supported by the substrate, wherein n.sub.2 is greater than n.sub.1; an input coupler configured to couple the image light into the first waveguide; and, an output coupler configured to couple the image light out of the first waveguide toward the eyebox, the output coupler comprising a first grating configured to redirect light propagating in the high-index layer and a second grating configured to redirect light propagating in the high-index layer.

  19. The NED device of claim 18 wherein the first waveguide is further configured to convey a third color channel of the image light from the light projector to an eyebox.

  20. The NED device of claim 18 further comprising a second waveguide configured to convey a third color channel of the image light from the light projector to an eyebox.

Description

REFERENCE TO RELATED APPLICATION

[0001] This application claims priority to U.S. Provisional Application No. 62/926,053 entitled “Display Waveguide with a High-Index Layer” filed on Oct. 25, 2019 and incorporated herein by reference in its entirety.

TECHNICAL FIELD

[0002] The present disclosure generally relates to optical display systems and devices, and in particular to waveguide displays and components therefor.

BACKGROUND

[0003] Head mounted displays (HMD), helmet mounted displays, near-eye displays (NED), and the like are being used increasingly for displaying virtual reality (VR) content, augmented reality (AR) content, mixed reality (MR) content, etc. Such displays are finding applications in diverse fields including entertainment, education, training and biomedical science, to name just a few examples. The displayed VR/AR/MR content can be three-dimensional (3D) to enhance the experience and to match virtual objects to real objects observed by the user. Eye position and gaze direction, and/or orientation of the user may be tracked in real time, and the displayed imagery may be dynamically adjusted depending on the user’s head orientation and gaze direction, to provide a better experience of immersion into a simulated or augmented environment.

[0004] Compact display devices are desired for head-mounted displays. Because a display of HMD or NED is usually worn on the head of a user, a large, bulky, unbalanced, and/or heavy display device would be cumbersome and may be uncomfortable for the user to wear.

[0005] Projector-based displays provide images in angular domain, which can be observed by a user’s eye directly, without an intermediate screen or a display panel. An imaging waveguide may be used to carry the image in angular domain to the user’s eye. The lack of a screen or a display panel in a projector display enables size and weight reduction of the display.

BRIEF DESCRIPTION OF THE DRAWINGS

[0006] Embodiments disclosed herein will be described in greater detail with reference to the accompanying drawings which represent example embodiments thereof, in which like elements are indicated with like reference numerals, and wherein:

[0007] FIG. 1 is a schematic isometric view of a waveguide display system using a waveguide assembly for transmitting images to a user;

[0008] FIG. 2 is a schematic diagram illustrating the coupling of a color channel into a display waveguide and an input FOV therefor;

[0009] FIG. 3 is a schematic diagram illustrating input and output FOVs of a display waveguide for a selected color channel;

[0010] FIG. 4 is a schematic side cross-section of a display waveguide with two out-coupler gratings at main outer faces;

[0011] FIG. 5 is a schematic plan view of a pupil-expanding waveguide illustrating an example layout of output-coupler gratings and an in-coupler aligned therewith;

[0012] FIG. 6A is a schematic k-space diagram illustrating the formation of a 2D FOV in an example embodiment of the waveguide of FIG. 5;

[0013] FIG. 6B is a graph illustrating the 2D FOV of the waveguide of FIG. 6A in the angle space;

[0014] FIG. 7 is a normalized K-space diagram illustrating an estimation of a symmetric 1D FOV shared by two different color channels for a display waveguide of FIG. 5;

[0015] FIG. 8 is a schematic side cross-sectional view of a display waveguide illustrating the divergence of two different color channels therein;

[0016] FIG. 9A is a schematic side cross-sectional view of a display waveguide having a top high-index layer illustrating the coupling of different color channels in to the waveguide;

[0017] FIG. 9B is a schematic side cross-sectional view of the display waveguide of FIG. 9A illustrating example propagation trajectories in the waveguide of in-coupled rays of a selected wavelength in dependence on the angle of incidence upon the waveguide;

[0018] FIG. 10 is a K-space diagram illustrating the coupling of a wavelength of image light into the two-layer display waveguide of FIGS. 9A and 9B;

[0019] FIG. 11 is a graph illustrating critical angles of incidence for in-coupling of red and blue wavelengths into the two-layer waveguide of FIGS. 9A and 9B in dependence on the pitch of the input grating;

[0020] FIG. 12 is a schematic side cross-sectional view of a two-layer display waveguide with a capping layer over the interface grating;

[0021] FIG. 13 is a schematic side cross-sectional view of a three-layer display waveguide illustrating the coupling of rays of image light at opposite ends of the FOV;

[0022] FIG. 14 is a schematic side cross-sectional view of a multi-layer display waveguide with five layers of different refractive indices;

[0023] FIG. 15 is a schematic side cross-sectional view of a gradient-index display waveguide;

[0024] FIG. 16 is a schematic side cross-sectional view of a two-waveguide stack including a two-layer waveguide;

[0025] FIG. 17A is a schematic plan view of a binocular NED with two pupil-expanding waveguides and in-couplers diagonally offset from exit pupils of the out-couplers;

[0026] FIG. 17B is a schematic vector diagram illustrating grating vectors for the example layout of FIG. 17A;

[0027] FIG. 18A is an isometric view of a head-mounted display of the present disclosure;

[0028] FIG. 18B is a block diagram of a virtual reality system including the headset of FIG. 18A.

DETAILED DESCRIPTION

[0029] In the following description, for purposes of explanation and not limitation, specific details are set forth, such as particular optical and electronic circuits, optical and electronic components, techniques, etc. in order to provide a thorough understanding of the present invention. However, it will be apparent to one skilled in the art that the present invention may be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known methods, devices, and circuits are omitted so as not to obscure the description of the example embodiments. All statements herein reciting principles, aspects, and embodiments, as well as specific examples thereof, are intended to encompass both structural and functional equivalents thereof. Additionally, it is intended that such equivalents include both currently known equivalents as well as equivalents developed in the future, i.e., any elements developed that perform the same function, regardless of structure.

[0030] Note that as used herein, the terms “first”, “second”, and so forth are not intended to imply sequential ordering, but rather are intended to distinguish one element from another, unless explicitly stated. Similarly, sequential ordering of method or process steps does not imply a sequential order of their execution, unless explicitly stated.

[0031] Furthermore, the following abbreviations and acronyms may be used in the present document: HMD (Head Mounted Display); NED (Near Eye Display); VR (Virtual Reality); AR (Augmented Reality); MR (Mixed Reality); LED (Light Emitting Diode); FOV (Field of View); TIR (Total Internal Reflection); HI (High Index). The terms “NED” and “HMD” may be used herein interchangeably.

[0032] Example embodiments may be described hereinbelow with reference to polychromatic light that is comprised of three distinct color channels. The color channel with the shortest wavelengths may be referred to as the blue (B) channel or color, and may represent the blue channel of an RGB color scheme. The color channel with the longest wavelengths may be referred to as the red (R) channel or color and may represent the red channel of the RGB color scheme. The color channel with wavelengths between the red and blue color channels may be referred to as the green (G) channel or color, and may represent the green channel of the RBG color scheme. The blue light or color channel may correspond to wavelength about 500 nm or shorter, the red light or color channel may correspond to wavelength about 625 nm or longer, and the green light or color channel may correspond to a wavelength range 500 nm to 565 nm. It will be appreciated however that the embodiments described herein may be adapted for use with polychromatic light comprised of any combination of two or more, or preferably three or more color channels, which may represent different portions of a relevant optical spectrum.

[0033] An aspect of the present disclosure relates to a display system comprising a waveguide and an image light source coupled thereto, wherein the waveguide is configured to receive image light emitted by the image light source and to convey the image light received in a field of view (FOV) of the waveguide to an eyebox for presenting to a user. The term “field of view” (FOV), when used in relation to a display system, may relate to an angular range of light propagation supported by the system or visible to the user. A two-dimensional (2D) FOV may be defined by angular ranges in two orthogonal planes. For example, a 2D FOV of a NED device may be defined by two one-dimensional (1D) FOVs, which may be a vertical FOV, for example +/-20.degree. relative to a horizontal plane, and a horizontal FOV, for example +/-30.degree. relative to the vertical plane. With respect to a FOV of a NED, the “vertical” and “horizontal” planes or directions may be defined relative to the head of a standing person wearing the NED. Otherwise the terms “vertical” and “horizontal” may be used in the present disclosure with reference to two orthogonal planes of an optical system or device being described, without implying any particular relationship to the environment in which the optical system or device is used, or any particular orientation thereof to the environment.

[0034] An aspect of the present disclosure relates to a waveguide for conveying image light to an eyebox, the waveguide comprising a substrate of a first refractive index n.sub.1, and a high-index layer of a second refractive index n.sub.2 supported by the substrate without an air gap therebetween, wherein n.sub.2 is greater than n.sub.1. The waveguide may further comprise an input coupler configured to couple the image light into the high-index layer, and an output coupler configured to couple the image light out of the waveguide toward the eyebox. The output coupler may comprise a first grating and a second grating, at least one of which configured to redirect light propagating in the high-index layer.

[0035] In some implementations the input coupler may comprise an input grating disposed to couple at least a portion of the image light into the high-index layer. In some implementations each one of the first and the second gratings may be disposed in the high-index layer or at a surface thereof to diffract light propagating in the high-index layer. In some implementations the first grating may be disposed at a surface of the high-index layer, and the second grating may be disposed at an interface between the substrate and the high-index layer. In some implementations the output coupler may comprise a third grating configured to redirect light propagating in the substrate. In some implementations the third grating may be disposed at a surface of the substrate opposite of the high-index layer.

[0036] In some implementations, the second refractive index is at least 2.2. In some implementations, an index difference (n.sub.1-n.sub.2) may be equal to or greater than 0.3. In some implementations, an index difference (n.sub.1-n.sub.2) may be at least 0.4. In some implementations, an the high-index layer may be at least 150 microns thick.

[0037] In some implementations, the waveguide may be configured for the image light comprising a first color channel and a second color channel, wherein the second color channel comprises longer wavelengths than the first color channel, and the input coupler may be configured to trap at least a portion of the second color channel in the high-index layer by means of total internal reflection (TIR) at an interface between the high-index layer and the substrate.

[0038] In some implementations, the waveguide is configured to provide a field of view (FOV) shared by the first and second color channels, the FOV having an angular FOV width .THETA. in at least one direction, and wherein the high-index layer supports at least 50% of the angular FOV width .THETA. of at least one of the first and second color channels.

[0039] In some implementations, the first color channel comprises one of green or blue light and the second color channel comprises red light, and the input coupler may be configured to trap at least a portion of the red light in the high-index layer by means of TIR at the interface between the high-index layer and the substrate. In some implementations the first color channel may comprise blue light and the second color channel comprises green light, and the input coupler may be configured to trap at least a portion of the green light in the high-index layer by means of TIR at the interface between the high-index layer and the substrate. In some implementations the input coupler may be configured to direct at least a portion of the first color channel into the substrate through the interface of the high-index layer with the substrate.

[0040] In some implementations, the image light may further comprise a third color channel, and the input coupler may be configured to couple all three color channels into the waveguide for propagating toward the output coupler.

[0041] In some implementations, the first grating and the second grating may cooperate for diffracting the image light trapped in the high-index layer out of the waveguide at an output angle equal to an angle of incidence thereof upon the waveguide.

[0042] In some implementations, the waveguide may comprise a third grating disposed in the substrate or at a surface thereof, and at least one of the first grating or the second grating may cooperate with the third grating for diffracting the image light propagating in the substrate out of the waveguide at an output angle equal to an angle of incidence thereof upon the waveguide.

[0043] An aspect of the present disclosure relates to a near-eye display (NED) device comprising: a support structure for wearing on a head of a user; a light projector carried by the support structure and configured to emit image light comprising a plurality of color channels; and, a first waveguide carried by the support structure and configured to convey at least a first color channel and a second color channel of the image light from the light projector to an eyebox. The first waveguide may comprise a substrate of a first refractive index n.sub.1 and a high-index layer of a second refractive index n.sub.2 supported by the substrate, wherein n.sub.2 is greater than n.sub.1. The waveguide may further comprise an input coupler configured to couple the image light into the first waveguide, and an output coupler configured to couple the image light out of the first waveguide toward the eyebox. The output coupler may comprise a first grating configured to redirect light propagating in the high-index layer and a second grating configured to redirect light propagating in the high-index layer.

[0044] In some implementations of the NED device, the first waveguide may be further configured to convey a third color channel of the image light from the light projector to an eyebox. Some implementations of the NED device may include a second waveguide configured to convey a third color channel of the image light from the light projector to an eyebox.

[0045] An aspect of the present disclosure provides a waveguide for conveying image light in a display system, the waveguide comprising: a waveguide body having two outer surfaces and a thickness therebetween, the waveguide body comprising an input area and an output area, the waveguide body configured to guide the image light received at the input area toward the output area, wherein the waveguide body has a refractive index that varies in a direction of the thickness. An input coupler may be disposed in the input area and configured to couple the image light into the waveguide body for propagating toward the output area. An output coupler may be disposed in the output area and configured to couple the image light out of the waveguide body for propagating toward a viewing area.

[0046] In some implementations the refractive index may be greater at one of the outer surfaces than at the other of the outer surfaces. In some implementations the refractive index may be greater in a middle portion of the waveguide body between the outer surfaces than in portions of the waveguide body adjacent to the outer surfaces.

[0047] Example embodiments of the present disclosure will now be described with reference to a waveguide display. Generally a waveguide display may include an image light source such as a pixelated electronic display or a scanning projector assembly, a controller, and an optical waveguide configured to transmit image light from the image light source to an exit pupil for presenting images to a user. The image light source may also be referred to herein as a display projector, an image projector, or simply as a projector. Example display systems incorporating a display waveguide wherein features and approaches disclosed here may be used, include, but not limited to, a near-eye display (NED), a head-up display (HUD), a head-down display, and the like.

[0048] With reference to FIG. 1, there is illustrated a waveguide display 100 in accordance with an example embodiment. The waveguide display 100 includes an image light source 110, a waveguide 120, and may further include a display controller 155.

[0049] The image light source 110, which may be referred to herein as projector 110, is configured to emit image light 111. In some embodiments the image light source 110 may be in the form of, or include, a scanning projector. In some embodiments the scanning projector may include a light source, such as but not limited to a laser diode (LD) or a light-emitting diode (LED), and one or more scanning reflectors. In some embodiments the scanning projector may include a scanning light source. In some embodiments the image light source 110 may include a pixelated micro-display, such as for example but not limited to a liquid crystal display (LCD), an organic light emitting display (OLED), an inorganic light emitting display (ILED), an active-matrix organic light-emitting diode (AMOLED) display, or a transparent organic light emitting diode (TOLED) display. In some embodiment the image light source 110 may include a linear array of light sources, such LEDs, LDs, or the like. In some embodiments it may include a 2D pixel array, and each pixel may be configured to emit polychromatic light. The image light source 110 may further include one or more optical components configured to suitably condition the image light. This may include, without limitation, expanding, collimating, correcting for aberrations, and/or adjusting the direction of propagation of the image light, or any other suitable conditioning as may be desired for a particular system and electronic display. The one or more optical components in the optics block may include, without limitations, one or more lenses, mirrors, apertures, gratings, or a combination thereof. In some embodiments the optics block of the image light source 110 may include one or more adjustable elements operable to scan the beam of light with respect to its propagation angle.

[0050] The waveguide 120 may comprise a waveguide body 123, an input coupler 130 in an input area of the waveguide, and an output coupler 140 in an output area of the waveguide. In some embodiments a waveguide stack composed of two or more waveguides that are stacked one over another may be used in place of the waveguide 120. The input coupler 130 may be disposed at a location where it can receive the image light 111 from the image light source 110. The input coupler 130, which may also be referred to herein as the in-coupler 130, is configured to couple the image light 111 into the waveguide 120, where it propagates toward the output coupler 140. The output coupler 140, which may also be referred to herein as the out-coupler, may be offset from the input coupler 130 and configured to de-couple the image light from the waveguide 120 for propagating in a desired direction, such as for example toward a user’s eye 166. The out-coupler 140 may be greater in size than the in-coupler 130 to expand the image beam in size as it leaves the waveguide, and to support a larger exit pupil than that of the projector 110. In some embodiments the waveguide body 123 may be partially transparent to outside light, and may be used in AR applications. The waveguide 120 may be configured to convey a two-dimensional (2D) FOV from the input coupler 130 to the output coupler 140, and ultimately to the eye 166 of the user. Here and in the following description the display waveguide 120 and embodiments thereof may be described with reference to a Cartesian coordinate system (x,y,z), in which the (x,y) plane is parallel to the outer faces of the waveguide through which the waveguide receives and/or outputs the image light, and the z-axis is orthogonal thereto. In some embodiments the 2D FOV of waveguide 120 may be defined by a 1D FOV in the (y,z) plane and a 1D FOV in the (x,z) plane, which may also be referred to as the vertical and horizontal FOVs, respectively.

[0051] FIG. 2 schematically illustrates the coupling of light of a wavelength .lamda. into a waveguide 210 for a range of incidence angles .alpha.. Waveguide 210 may represent the waveguide 120 of display 100, or any waveguide of a waveguide stack that may be used in place of the waveguide 120. Waveguide 210 may be a slab waveguide with a waveguide body that may be for example in the form of, or include, a substrate 205. The substrate 205 may be a thin plate of an optical material that is transparent in visible light, such as glass or suitable plastic or polymer as non-limiting examples. Main outer faces 211, 212 of waveguide 210, through which image light may enter or leave the waveguide, may be nominally parallel to each other. The refractive index n of the substrate material may be greater than that of surrounding media, and in some embodiments may be for example in the range of 1.4 to 2.0. In some embodiments, high-index materials may be used for the substrate 205 or a portion thereof. In some embodiments these materials may have an index of refraction n greater than about 2.2. In some embodiments these materials may have an index of refraction n greater than about 2.3. In some embodiments these materials may have an index of refraction n greater than about 2.5. Non-limiting examples of such materials are lithium niobate (LiNbO.sub.3), titanium dioxide (TiO.sub.2), gallium nitride (GaN), aluminum nitride (AlN), silicon carbide (SiC), CVD diamond, zinc sulfide (ZnS).

[0052] An in-coupler 230 may be provided in an input area 203 of the waveguide 210 and may be in the form of one or more diffraction gratings. An out-coupler 240, which may also be in the form of one or more diffraction gratings, may be disposed in an output area 209 of the waveguide, and may be laterally offset from the in-coupler 230, for example along the y-axis. In the illustrated embodiment the out-coupler 240 is located at the same face 211 of the waveguide 210 as the in-coupler 130, but in other embodiments it may be located at the opposite face 212 of the waveguide. Some embodiments may have two input gratings that may be disposed at main outer faces 211, 212 of the waveguide, and/or two output gratings that may be disposed at main outer faces 211, 212 of the waveguide, or superimposed at a same face or at a same plane within the waveguide. The gratings embodying couplers 230, 240 may be any suitable diffraction gratings, including volume and surface-relief gratings, such as for example blaze gratings. The gratings may also be volume holographic gratings. In some embodiments they may be formed in the material of the waveguide itself. In some embodiments they may be fabricated in a different material or materials that may be affixed to a face or faces of the waveguide at desired locations.

[0053] The in-coupler 230 may be configured to support an input FOV 234, which may also be referred to herein as the acceptance angle. The input FOV 234, which depends on wavelength, defines a range of angles of incidence .alpha. for which the light incident upon the in-coupler 230 is coupled into the waveguide and propagates toward the out-coupler 240. In the context of this specification, “coupled into the waveguide” means coupled into the guided modes of the waveguide or modes that have suitably low radiation loss. Light coupled into the waveguide that experiences total internal reflection (TIR) upon the waveguide’s outer surfaces 211 and 212 may propagate within the waveguide with suitably low attenuation until it is redirected by an out-coupler. Thus waveguide 210 may trap light of a particular wavelength .lamda. by means of TIR, and guide the trapped light toward the out-coupler 240, provided that the angle of incidence of the light upon the in-coupler 230 from the outside of the waveguide is within the input FOV 234 of the waveguide 210. The input FOV 234 of the waveguide is determined at least in part by a pitch p of the in-coupler grating 230 and by the refractive index n of the waveguide. For a given grating pitch p, the first-order diffraction angle .beta. of the light incident upon the grating 230 from the air at an angle of incidence a in the (y, z) plane may be found from a diffraction equation (1):

nsin(.beta.)-sin(.alpha.)=.lamda./p. (1)

Here the angle of incidence .alpha. and the diffraction angle .beta. are positive if the corresponding wavevectors have components directed toward the out-coupler 240. Diffraction angle .beta. defines the angle of propagation of the diffracted ray of the image light in the waveguide, and may also be referred to herein as the propagation angle. Equation (1) may be easily modified for embodiments in which light enters the waveguide 210 from a material with refractive index n.sub.c>1. Equation (1) holds for rays of image light with a plane of incidence normal to the groves of the in-coupler grating, i.e. when the plane of incidence of image light includes the grating vector of the in-coupler. In the illustrated example, the grating vector of the in-coupler may be directed along the y-axis.

[0054] Light experiencing TIR in a waveguide or a layer may be referred to herein as the in-coupled light or trapped light. The TIR condition for the diffracted light within the waveguide may be defined by equation (2):

nsin(.beta.).gtoreq.1, (2)

where the equality corresponds to a TIR angle .beta..sub.c=a sin (1/n). The input FOV 234 of waveguide 210 spans between a first FOV angle of incidence .alpha..sub.1 and a second FOV angle of incidence .alpha..sub.2, which may be referred to herein as the FOV angles. The first FOV angle of incidence .alpha..sub.1 corresponding to the right-most incident ray 111b in FIG. 2A may be defined by the TIR angle .beta..sub.c, of the in-coupled light, i.e. light trapped within the waveguide:

.alpha. 1 = asin .function. ( 1 – .lamda. p ) , ( 3 ) ##EQU00001##

The second FOV angle of incidence .alpha..sub.2, corresponding to the left-most incident ray 111a in FIG. 2A, may be defined by a limitation on a maximum angle .beta..sub.max of the in-coupled light:

.alpha. 2 = asin .function. ( n sin .function. ( .beta. max ) – .lamda. p ) , ( 4 ) ##EQU00002##

[0055] The width w=|.alpha..sub.1-.alpha..sub.2| of the input 1D FOV of the waveguide 210 at a particular wavelength can be estimated from equations (3) and (4). Generally the input FOV of a waveguide increases as the refractive index of the waveguide increases relative to that of the surrounding media. By way of example, for a substrate of index n surrounded by air and for .beta..sub.max=75.degree., .lamda./p=1.3, the width w of the input 1D FOV of the waveguide for monochromatic light may be about 26.degree. for n=1.5, about 43.degree. for n=1.8, and about 107.degree. for n=2.4.

[0056] As can be seen from equations (3) and (4), the input FOV 234 of waveguide 210 is a function of the wavelength .lamda. of input light, so that the input FOV 234 shifts its position in the angle space as the wavelength changes; for example, it shifts towards the out-coupler 240 as the wavelength increases. Thus it can be challenging to provide a sufficiently wide FOV for polychromatic image light with a single waveguide.

[0057] Referring to FIG. 3, light coupled into the waveguide 210 by the in-coupler 230 propagates in the waveguide toward the out-coupler 240. The out-coupler 240 is configured to re-direct at least a portion of the in-coupled light out of the waveguide 210 at an angle or angles within an output FOV 244 of the waveguide, which is defined in part by the out-coupler 240. An overall FOV of the waveguide, i.e. the range of incidence angles .alpha. that may be conveyed to the viewer by the waveguide, may be affected by both the in-coupler 230 and the out-coupler 240.

[0058] In some embodiments the gratings embodying the in-coupler 230 and the out-coupler 240 may be configured so that the vector sum of their grating vectors g.sub.i is equal to substantially zero:

|.SIGMA.g.sub.i|=0 (5)

Here the summation in the left hand side (LHS) of equation (5) is performed over grating vectors g.sub.i of all gratings that cooperate to diffract the input light traversing the waveguide, including the one or more gratings of the in-coupler 230, and the one or more gratings of the out-coupler 230. A grating vector g.sub.i is a vector that is directed normally to the equal-phase planes of the grating, i.e. its “grooves”, and which magnitude is inversely proportional to the grating pitch p, |g.sub.i|=2.pi./p. Under conditions of equation (5), rays of the image light exit the waveguide by means of the out-coupler 240 at the same angle at which they entered the in-coupler 230, provided that the waveguide 210 is an ideal slab waveguide with parallel outer faces 211, 212, and the FOV of the waveguide is defined by its input FOV. In practical implementations the equation (5) will hold with some accuracy, within an error threshold that may be allowed for a particular display system. In an example embodiment with a single 1D input grating and a 1D output grating, the grating pitch of the out-coupler 240 may be substantially equal to the grating pitch of the in-coupler 230.

[0059] FIG. 4 illustrates an embodiment in which the out-coupler 240 includes two diffraction gratings 241, 242, which may be disposed for example at main outer faces of the waveguide. The diffraction gratings 241 and 242 may be configured so that the in-coupled light 211a exits the waveguide as output light 221 after being sequentially diffracted once by each of these gratings. In some embodiments, the grating vectors g.sub.1 and g.sub.2 of the diffraction gratings 241, 242 may be directed at an angle to each other. In at least some embodiments they may be selected so that (g.sub.0+g.sub.1+g.sub.2)=0, where g.sub.0 is the grating vector of the in-coupler 230.

[0060] FIG. 5 illustrates, in a plan view, a display waveguide 410 with an in-coupler 430 disposed in an input area 403 of the waveguide, and an out-coupler 440 disposed in an output area 407 of the waveguide. The in-coupler 430 may be in the form of an input diffraction grating with a grating vector g.sub.0 directed generally toward the out-coupler 440. The out-coupler 440 is comprised of two output linear diffraction gratings 441 and 442 with grating vectors g.sub.1 and g.sub.2 oriented at an angle to each other. In some embodiments gratings 441 and 442 may be linear diffraction gratings formed at main outer faces of the waveguide. In some embodiments they may be superimposed upon each other at either face of the waveguide, or in the volume thereof, to form a 2D grating. Light 401 incident upon the in-coupler 430 within a FOV of the waveguide may be coupled by the in-coupler 430 into the waveguide to propagate toward the out-coupler 440, expanding in size in the plane of the waveguide, as illustrated by in-coupled rays 411a and 411b. The gratings 441, 442 are configured so that consecutive diffractions off each of them re-directs the in-coupled light out of the waveguide. Rays 411a may be rays of in-coupled light that, upon entering the output area 407 of the waveguide where the out-coupler 440 is located, are first diffracted by the first grating 441, and then are diffracted out of the waveguide by the second grating 442 after propagating some distance within the waveguide. Rays 411b may be rays of the in-coupled light that are first diffracted by the second grating 442, and then are diffracted out of the waveguide by the first grating 441. An exit pupil 450 of the waveguide, which may also be referred to as the eyebox projection area 450, is indicated where the out-coupled light has optimal characteristics for viewing, for example where it has desired dimensions. The exit pupil 450 may be located at some distance from the in-coupler 430.

[0061] FIG. 6A illustrates aspects of operation of the display waveguide 410 with reference to a (K.sub.x, K.sub.y) plane, where K.sub.x and K.sub.y denote x and y coordinates of a projection of a normalized k-vector K=k2.pi./.lamda. of the image light upon the plane of the waveguide:

K.sub.x=n sin(.theta..sub.x), and K.sub.y=n sin(.theta..sub.y). (6)

Here n is the refractive index of the substrate where in-coupled light is propagating, and the angles .theta..sub.x and .theta..sub.y define the direction of light propagation in the plane of the waveguide (x,y) in projection on the x-axis and y-axis, respectively. These angles may also represent the coordinates of angle space in which a 2D FOV of the waveguide may be defined. The (K.sub.x, K.sub.y) plane may be referred to herein as the K-space, and the normalized wavevector K=(K.sub.x, K.sub.y) as the in-plane K-vector or simply as the K-vector.

[0062] In the K-space, the in-coupled light may be graphically represented by a TIR ring 500. The TIR ring 500 is an area of the K-space bounded by a TIR circle 501 and a maximum-angle circle 502, both circles centered at K.sub.0=(0, 0) corresponding to the normal incidence upon the waveguide. The TIR circle 501 corresponds to the TIR angle .beta..sub.c. The maximum-angle circle 502 corresponds to a maximum propagation angle .beta..sub.max for in-coupled light. States within the TIR circle 501 represent uncoupled light, i.e. the in-coming light that is incident upon the in-coupler 430, or the light coupled out of the waveguide by the out-coupler gratings 441 and/or 442. With the normalization, the radius r.sub.TIR of the TIR circle 501 and the radius r.sub.max of the outer circle 502 may be defined by the following equations:

r.sub.TIR=1,r.sub.max=nsin(.beta..sub.max) (7)

The greater the refractive index n, the wider is the TIR ring 500 and the broader is the angular range of input light of a wavelength .lamda. that can be coupled into the waveguide.

[0063] Arrows labeled g.sub.0, g.sub.1, and g.sub.2 in FIG. 6A represent the normalized grating vectors of the in-coupler 430, the first out-coupler grating 441, and the second out-coupler grating 442, respectively, for a particular wavelength .lamda., with grating lengths g.sub.i=.lamda./p.sub.i, where p.sub.i is the pitch of i-th grating, i=0, 1, or 2. In the figure these grating vectors form two closed triangles describing two possible paths in the K-space along which the incoming light may return to the same K-space state after being diffracted once by each of the three gratings, thereby preserving the direction of propagation in the angle space from the input to the output of the waveguide. Each diffraction may be represented as a shift in the (K.sub.x, K.sub.y) plane by a corresponding grating vector. Areas 520, 530 in combination represent the FOV of the waveguide in the (K.sub.x, K.sub.y) plane, and may be referred to as the first and second partial FOV areas, respectively. They are defined by the in-coupler and out-coupler gratings and the refractive index of the waveguide, and represent all k-vectors of light stays trapped within the waveguide (the TIR ring 500) after consecutive diffractions upon the input grating 430 and one of the output gratings 441, 442, and returns to a same (K.sub.x, K.sub.y) location in the interior of the TIR circle 501 after a subsequent diffraction upon the other of the two output gratings. The first partial FOV area 520 may be determined by identifying all (K.sub.x, K.sub.y) states which are imaged to itself by consecutive diffractions upon the input grating 430, the first output grating 441, and the second output grating 442, each of which may be represented as a shift in the (K.sub.x, K.sub.y) plane by a corresponding grating vector. The second partial FOV area 530 may be determined by identifying all (K.sub.x, K.sub.y) states which are imaged to itself by consecutive diffractions upon the input grating 430, the second output grating 442, and the first output grating 441.

[0064] FIG. 6B illustrates the first and second partial FOVs 520, 530 in a 2D angle space, with the horizontal and vertical axes representing the angles of incidence .theta..sub.x and .theta..sub.y of input light in the x-axis and y-axis directions, respectively, both in degrees. The (0,0) point corresponds to normal incidence upon the in-coupler. In combination, partial FOVs 520, 530 define a full FOV 550 of the waveguide at the wavelength k, which encompasses all incident rays of input light of the selected color or wavelength that may be conveyed to a user. A rectangular area 555 which fits within the full FOV 550 may define a monochromatic FOV of the waveguide that may be useful in a display.

[0065] The position, size, and shape of each partial FOV 520, 530 in the angle space, and thus the full 2D FOV of the waveguide, depends on the wavelength .lamda. of the input light, on the ratios of pitches p.sub.0, p.sub.1, and p.sub.2 of the input and output gratings to the wavelength of incoming light .lamda., and on the relative orientation of the gratings. Thus, the 2D FOV of the waveguide may be suitably shaped and positioned in the angle space for a particular color channel or channels by selecting the pitch sizes and the relative orientation of the gratings. In some embodiments of waveguide 410, the output gratings 441, 442 may have the same pitch, p.sub.1=p.sub.2 and be symmetrically oriented relative to the input grating. In such embodiments the grating vectors g.sub.1, g.sub.2 of the first and second output gratings may be oriented at angles of +/-.PHI. relative to the grating vector g.sub.0 of the in-coupler. By way of non-limiting example, the grating orientation angle .PHI. may be in the range of 50 to 70 degrees, for example 60 to 66 degrees, and may depend on the refractive index of the waveguide. FIG. 6B illustrates the FOV of an example waveguide with the refractive index n=1.8, .PHI..apprxeq.60.degree., and p.sub.1=p.sub.2=p.sub.3=p, with p/.lamda. selected to center the FOV 555 at normal incidence.

[0066] In some embodiments, a single waveguide formed of an optically transparent high-index substrate may be used in a display system to convey multiple color channels of RGB light from an image source to a viewing area of a waveguide display, such as an eyebox of a, NED. In some embodiments the same input and output gratings may be used for at least two color channels of the image light, for example for at least two of the Red, Green, and Blue RGB color channels, or for all three RGB color channels. The desirability of having a high refractive index n may be understood by noting that in the wavelength-normalized K-space the length of each grating vector scales with the wavelength, i.e. g.sub.i=.lamda./p.sub.i, where p.sub.i is the pitch of the i-th grating, i=0, 1, or 2. As the width of the TIR ring 500 is proportional to the refractive index n, greater values of the refractive index enable broader polychromatic FOV, i.e. the common FOV that is shared by two or more color channels of the image light.

[0067] FIG. 7 illustrates the wavelength-scaled grating vectors 531, 532 of the in-coupler 430 for two different wavelength .lamda..sub.1 and .lamda..sub.2>.lamda..sub.1 in the K-space diagram of FIG. 6A. In the illustrated example the grating vector of the in-coupler is directed along the y-axis. The normalized grating vector 531 for the first wavelength .lamda..sub.1 has a length .lamda..sub.1/p.sub.0, while the longer normalized grating vector 532 has a length of .lamda..sub.2/p.sub.0. The first wavelength .lamda..sub.1 may be, for example, a peak wavelength of the blue color channel, while the second wavelength .lamda..sub.2 may be, for example, a peak wavelength of the red color channel.

[0068] In some embodiments a maximum y-axis width (2.alpha.) of a symmetrical FOV shared by the two wavelengths, FOV.sub.y=(-.alpha.,+.alpha.), may be estimated from equations (8) and (9).

1+sin(.alpha.)=.lamda..sub.1/p.sub.0 (8)

nsin(.beta..sub.max)-sin(.alpha.)=.lamda..sub.2/p.sub.0 (9)

Equation (8) represents a condition that the shorter of the grating vectors 531, 532 is long enough to reach the TIR circle 501 from a state A1 of the FOV that is farthest from the TIR circle 501 in the direction of the grating vector. Equation (9) represents a condition that a K-state A2 at an opposite end of the FOV is far enough from the outer boundary 502 of the TIR ring 500 that the longer of the two grating vectors 531, 532 doesn’t extend beyond it. These conditions provide an estimate for the pitch p.sub.0 of the in-coupler grating (equation (10)) and an estimate of the corresponding half-width .alpha. of the common FOV of the two wavelengths along the y-axis (equation 11):

p 0 = .lamda. 2 + .lamda. 1 n sin .function. ( .beta. max ) + 1 ( 10 ) .alpha. = asin .function. ( .lamda. 1 n sin .function. ( .beta. max ) – .lamda. 2 .lamda. 2 + .lamda. 1 ) ( 11 ) ##EQU00003##

[0069] An estimated width 2.alpha. of the shared 1D FOV for wavelengths .lamda..sub.1 and .lamda..sub.2 increases as the refractive index n of the waveguide increases above a minimum value n.sub.min, which in some embodiments may be estimated as n.sub.min=.lamda..sub.2/.lamda..sub.1 sin(.beta..sub.max). By way of example the longer wavelength .lamda.2 may correspond to red light, with the wavelength e.g. of 635 nm, while the shorter wavelength .lamda..sub.1 may correspond to blue light, with the wavelength e.g. of 465 nm, resulting in a minimal value of n of about 1.4 for a waveguide configured to transmit all three color channels of RGB light. According to Equation (11), in one embodiment an estimated width 2.alpha. of a symmetrical 1D FOV of a single one-layer waveguide that may be shared by all three channels of RGB light may be about 30 degrees for n=2.0, about 40 degrees for n=2.2, and about 63 degrees for n=2.6.

[0070] Equation (11) provides an estimate of a 1D FOV that is centered at normal incidence and may be supported by a single waveguide for polychromatic light with wavelengths from .lamda..sub.1 to .lamda..sub.2. A 2D FOV that the waveguide supports for polychromatic light at its output, e.g. at the eyebox, may further depend on the out-coupler, such as the number and configuration of the output gratings.

[0071] In some embodiments, a single waveguide made of optically transparent high-index material with the refractive index of about 2.3, or preferably 2.4 or greater may be used in a display system to convey RGB light from an image source to an eyebox of a NED. In some embodiments, a NED may transmit image light with a single waveguide made of optically transparent high-index material with the refractive index of at least 2.5. In some embodiments, a NED may transmit image light with a single waveguide made of optically transparent high-index material with the refractive index of at least 2.6.

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