Facebook Patent | High-index waveguide for conveying images

Patent: High-index waveguide for conveying images

Drawings: Click to check drawins

Publication Number: 20210141130

Publication Date: 20210513

Applicant: Facebook

Abstract

A waveguide display includes an image light source for emitting polychromatic image light, and a waveguide of high-index material for transmitting polychromatic image light to an eyebox. The waveguide has an input grating and an offset output grating. The output grating is configured so that ambient light diffracted by the output grating is directed away from the eyebox or out of at least a central portion of the field of view so as to lessen the appearance of visual artifacts.

Claims

1. A waveguide for conveying image light from an image light source to an eyebox with a target field of view (FOV) spanning an angular range .GAMMA., the waveguide comprising: a substrate for propagating the image light therein by total internal reflection; an input coupler supported by the substrate and configured to couple the image light into the waveguide; and, an output coupler supported by the substrate and configured to couple the image light out of the waveguide for propagating toward the eyebox; wherein the output coupler comprises a first output grating having a pitch p.sub.1 that does not exceed .lamda. 1 + sin .function. ( 0.8 .GAMMA. .times. / .times. 2 ) , ##EQU00021## wherein .lamda. is a wavelength of blue light.

2. The waveguide of claim 1, wherein p 1 .ltoreq. .lamda. 1 + sin .function. ( .GAMMA. .times. / .times. 2 ) . ##EQU00022##

3. The waveguide of claim 1, wherein the substrate has a refractive index of at least 2.3.

4. The waveguide of claim 1, wherein the output coupler further comprises a second output grating configured to cooperate with the first output grating to diffract the image light out of the waveguide, and wherein the second output grating has a pitch p.sub.2 that does not exceed p.sub.1.

5. The waveguide of claim 4, wherein the input coupler comprises an input grating having a pitch p.sub.0 that does not exceed p.sub.1.

6. The waveguide of claim 4, wherein the first output grating and the second output grating cooperate for diffracting the image light out of the waveguide at an output angle equal to an angle of incidence thereof upon the waveguide.

7. The waveguide of claim 4, wherein the first and second output gratings are disposed at opposite faces of the waveguide.

8. The waveguide of claim 1, wherein the waveguide is configured for conveying to the eyebox at least one of a red color (R) channel and a green color (G) channel.

9. The waveguide of claim 1, wherein .lamda. is equal or smaller than 450 nm.

10. The waveguide of claim 1, wherein p.sub.1.ltoreq.300 nm.

11. The waveguide of claim 1, wherein the eyebox extends over a length 2a in a first direction, wherein the first output grating extends over a length 2b in the first direction and is disposed at a distance d from the eyebox; and wherein the pitch p.sub.1 does not exceed .lamda. 1 + sin .function. ( .theta. m ) ##EQU00023## wherein .theta..sub.m=atan[(b+a)/d].

12. A near-eye display (NED) device comprising: a light source configured to emit image light comprising a plurality of color channels; and, a waveguide optically coupled to the light source and configured to convey a portion of the image light from the light source to an eyebox within a target field of view (FOV) spanning an angular range .GAMMA., the waveguide comprising: an input coupler for receiving the portion of the image light; and, an output coupler for coupling the portion out of the waveguide toward the eyebox; wherein the output coupler comprises a first output grating having a pitch p.sub.1 that does not exceed .lamda. 1 + sin .function. ( 0.8 .GAMMA. .times. / .times. 2 ) , ##EQU00024## wherein .lamda. is a wavelength of blue light.

13. The NED device of claim 12, wherein the waveguide comprises dielectric material with an index of refraction of at least 2.3.

14. The NED device of claim 13, wherein the output coupler further comprises a second output grating configured to cooperate with the first output grating to diffract the image light out of the waveguide at an output angle equal to an incidence angle of the image light upon the input coupler, wherein the second output grating has a pitch not exceeding p.sub.1.

15. The NED device of claim 14, wherein .lamda. is a wavelength of blue light, and wherein the waveguide is configured to convey to the eyebox at least one of a red color channel of the image light or a green color channel of the image light.

16. The NED device of claim 14, wherein .lamda..ltoreq.500 nm, and wherein the waveguide is configured to convey to the eyebox a red color channel of the image light with wavelengths equal or longer than 600 nm.

17. The NED device of claim 14, comprising a waveguide stack including the waveguide, wherein each waveguide of the waveguide stack comprises an output grating with a pitch of at most p.sub.1.

18. A waveguide for conveying image light comprising a plurality of color channels from an image light source to an eyebox, the waveguide comprising: a substrate for propagating the image light therein by total internal reflection; an input coupler supported by the substrate for receiving the image light; and, an output coupler supported by the substrate for coupling the image light out of the waveguide toward the eyebox; wherein the output coupler comprises a first output grating having a pitch p that does not exceed 300 nm.

19. The waveguide of claim 18, wherein the substrate has an index of refraction of at least 2.3.

20. The waveguide of claim 19, wherein the waveguide is configured for conveying to the eyebox at least one of a red color (R) channel of the image light and a green color (G) channel of the image light.

Description

TECHNICAL FIELD

[0001] The present disclosure generally relates to optical display systems and devices, and in particular to waveguide displays and components therefor.

BACKGROUND

[0002] 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.

[0003] 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.

[0004] 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

[0005] 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:

[0006] FIG. 1A is a schematic isometric view of a waveguide display system using a waveguide assembly for transmitting images to a user;

[0007] FIG. 1B is a schematic block diagram of a display projector of the waveguide display of FIG. 1A;

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

[0009] FIG. 2B is a schematic diagram illustrating the coupling of a second color channel into the display waveguide of FIG. 2A and an input FOV of the second color channel;

[0010] FIG. 3A is a schematic diagram illustrating input and output FOVs of a display waveguide for a selected color channel;

[0011] FIG. 3B is a schematic side cross-section of a display waveguide with two out-coupler gratings at opposing faces;

[0012] FIG. 4 is a schematic plan view of a pupil-expanding waveguide illustrating an example layout of output-coupler gratings and an in-coupler aligned therewith;

[0013] FIG. 5 is a schematic k-space diagram illustrating the formation of a 2D FOV in an example embodiment of the waveguide of FIG. 4;

[0014] FIG. 6 is a graph illustrating the 2D FOV of the waveguide of FIG. 5 in the angle space;

[0015] FIG. 7 is a schematic side cross-sectional view of a display waveguide of FIG. 3B or 4 illustrating diffraction of ambient light into an eyebox by an output grating;

[0016] FIG. 8 is a schematic k-space diagram illustrating the diffraction of ambient light into a display FOV by an output grating of the display waveguide;

[0017] FIG. 9 is a schematic k-space diagram illustrating a condition when once-diffracted ambient light is captured by the waveguide;

[0018] FIG. 10 is a schematic k-space diagram illustrating a condition when an output grating diffracts ambient light outside of a central FOV;

[0019] FIG. 11 is a schematic side cross-sectional view of a display waveguide illustrating a maximum-angle ray capable of entering an eyebox from an output grating;

[0020] FIG. 12 is a k-space diagram illustrating the operation of a display waveguide of FIG. 4 for two different color channels;

[0021] FIG. 13A is a k-space diagram illustrating the formation of a FOV of an example display waveguide with the refraction index 2.6(?) for red light;

[0022] FIG. 13B is a k-space diagram illustrating the formation of a FOV of the example display waveguide of FIG. 13A for green light;

[0023] FIG. 13C is a k-space diagram illustrating the formation of a FOV of the example display waveguide of FIG. 13A for blue light;

[0024] FIG. 14 is a schematic side cross-sectional view of a two-waveguide stack with color-optimized waveguides;

[0025] FIG. 15A 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. 15B is a schematic vector diagram illustrating grating vectors for the example layout of FIG. 15A;

[0027] FIG. 16A is an isometric view of a head-mounted display of the present disclosure; and

[0028] FIG. 16B is a block diagram of a virtual reality system including the headset of FIG. 16A.

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). 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 nanometers (nm) or shorter, the red light or color channel may correspond to wavelength about 600 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 non-overlapping 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 waveguide may be configured to prevent undesired ambient light from being directed into the eye of the user. The term “field of view” (FOV), when used in relation to a display system, may define 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 from an image light source to an eyebox with a target FOV spanning an angular range .GAMMA.. The waveguide may comprise a substrate for propagating the image light therein by total internal reflection, an input coupler supported by the substrate and configured to couple the image light into the waveguide, and an output coupler supported by the substrate and configured to couple the image light out of the waveguide for propagating toward the eyebox. The output coupler may comprise a first output grating having a pitch p.sub.1 that does not exceed

.lamda. 1 + sin .function. ( 0.8 .GAMMA. .times. / .times. 2 ) , ##EQU00001##

where .lamda. may be a shortest wavelength of a visible light.

[0035] In some implementations the input coupler comprises an input grating having a pitch that does not exceed p.sub.1.

[0036] In some implementations p.sub.1 may be equal or smaller than

.lamda. 1 + sin .function. ( .GAMMA. .times. / .times. 2 ) . ##EQU00002##

[0037] In some implementations the substrate may have a refractive index of at least 2.3. In some implementations the substrate may have a refractive index of at least 2.4. In some implementations the substrate may have a refractive index of at least 2.5.

[0038] In some implementations the output coupler may further comprise a second output grating configured to cooperate with the first output grating to diffract the image light out of the waveguide, wherein the second output grating may have a pitch that does not exceed p. In some implementations the first output grating and the second output grating cooperate for diffracting the image light out of the waveguide at an output angle equal to an angle of incidence thereof upon the waveguide. In some implementations the first and second output gratings may be disposed at opposite faces of the waveguide.

[0039] In some implementations the waveguide may be configured for conveying to the eyebox at least one of a red color (R) channel and a green color (G) channel, and the pitch p may be equal or smaller than

.lamda. 1 + sin .function. ( 0.8 .GAMMA. .times. / .times. 2 ) ##EQU00003##

where .lamda. may be a wavelength of blue light. In some implementations the wavelength .lamda. may be smaller than 500 nm.

[0040] In some implementations the pitch p may be equal or less than 300 nm. In some implementations the pitch p may be equal or less than 280 nm.

[0041] In some implementations wherein the eyebox extends over a length 2a in a first direction, and wherein the first output grating extends over a length 2b in the first direction and is disposed at a distance d from the eyebox; the pitch p may satisfy the condition

p .ltoreq. .lamda. 1 + sin .function. ( .alpha. ) ##EQU00004##

wherein .alpha.=atan[(b+a)/d].

[0042] An aspect to the present disclosure relates to a near-eye display (NED) device comprising: a light source configured to emit image light comprising a plurality of color channels, and a first waveguide optically coupled to the light source and configured to convey a portion of the image light from the light source to an eyebox within a target field of view (FOV) spanning an angular range .GAMMA.. The first waveguide may comprise an input coupler for receiving the portion of the image light, and an output coupler for coupling said portion out of the first waveguide toward the eyebox. The output coupler may comprise a first output grating having a pitch p.sub.1 that does not exceed

.lamda. 1 + sin .function. ( 0.8 .GAMMA. .times. / .times. 2 ) , ##EQU00005##

where .lamda. is a wavelength of a shortest-wavelength color channel of the image light.

[0043] In some implementations of the NED device, the first waveguide may comprise dielectric material with an index of refraction of at least 2.3. In some implementations of the NED device, the first waveguide may comprise dielectric material with an index of refraction of at least 2.4. In some implementations of the NED device, the waveguide may comprise dielectric material with an index of refraction of at least 2.5.

[0044] In some implementations of the NED device, the output coupler may further comprise a second output grating configured to cooperate with the first output grating to diffract the image light out of the first waveguide at an output angle equal to an incidence angle of the image light upon the input coupler, wherein the second output grating has a pitch not exceeding p.sub.1.

[0045] In some implementations of the NED device, .lamda. is a wavelength of blue light, and the first waveguide may be configured to convey to the eyebox at least one of a red color channel of the image light or a green color channel of the image light.

[0046] In some implementations of the NED device, .lamda..ltoreq.500 nm, and the first waveguide may be configured to convey to the eyebox a red color channel of the image light with wavelengths equal or longer than 600 nm.

[0047] In some implementations the NED device may comprise a waveguide stack including the first waveguide, wherein each waveguide of the waveguide stack comprises an output grating with a pitch of at most p.sub.1.

[0048] In some implementations the image light may comprise RGB light comprising a red color channel, a green color channel, and a red color channel, and the first waveguide is configured to convey to the eyebox each of the red, green, and blue color channels.

[0049] An aspect of the disclosure relates to a waveguide for conveying image light comprising a plurality of color channels from an image light source to an eyebox, the waveguide comprising: a substrate for propagating the image light therein by total internal reflection; an input coupler supported by the substrate for receiving the image light; and, an output coupler supported by the substrate for coupling the image light out of the waveguide toward the eyebox. The output coupler may comprise a first output grating having a pitch p that does not exceed 300 nm. In some implementations the substrate may have an index of refraction of at least 2.3. In some implementations the substrate may have an index of refraction of at least 2.4. In some implementations the substrate may have an index of refraction of at least 2.5. In some implementations the waveguide may be configured for conveying to the eyebox at least one of a red color (R) channel of the image light and a green color (G) channel of the image light.

[0050] An aspect of the present disclosure relates to a waveguide for conveying image light from an image light source to an eyebox with a target field of view (FOV) spanning an angular range .GAMMA.. The waveguide may comprise a substrate for propagating the image light therein by total internal reflection, an input coupler supported by the substrate and configured to couple the image light into the waveguide, and an output coupler supported by the substrate and configured to couple the image light out of the waveguide for propagating toward the eyebox. The output coupler may comprise a first output grating having a pitch p.sub.1 does not exceed

.lamda. 1 + sin .function. ( 0.8 .GAMMA. .times. / .times. 2 ) ##EQU00006##

where .lamda. is a wavelength of blue light. In some implementations the pitch p.sub.1 does not exceed

.lamda. 1 + sin .function. ( .GAMMA. .times. / .times. 2 ) . ##EQU00007##

In some implementations .lamda. may be 500 nm. In some implementations .lamda. may be 450 nm.

[0051] 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 an electronic display assembly, a controller, and an optical waveguide configured to transmit image light from the electronic display assembly 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 that may incorporate a waveguide display, and 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.

[0052] With reference to FIGS. 1A and 1B, 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 assembly 120, and may further include a display controller 155. The image light source 110 is configured to generate image light 111. In some embodiments the image light source 110 may be in the form of, or include, a scanning projector.

[0053] In some embodiments the image light source 110 may include a pixelated electronic display 114 that may be optically followed by an optics block 116. The electronic display 114 may be any suitable electronic display configured to display images, 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 electronic display 114 may be in the form of a linear array of light sources, such as light-emitting diodes (LED), laser diodes (LDs), or the like, with each light source configured to emit polychromatic light. In some embodiments it may include a two-dimensional (2D) pixel array, with each pixel configured to emit polychromatic light.

[0054] The optics block 116 may include one or more optical components configured to suitably condition the image light emitted by the electronic display 114. This may include, without limitation, expanding, collimating, correcting for aberrations, and/or adjusting the direction of propagation of the image light emitted by the electronic display 114, 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 116 may include, without limitations, one or more lenses, mirrors, apertures, gratings, or a combination thereof. In some embodiments the optics block 116 may include one or more adjustable elements operable to scan the beam of light emitted by the electronic display 114 with respect to it propagation angle.

[0055] The waveguide assembly 120 may be in the form of, or include, a waveguide 123 comprising an in-coupler 130 and an out-coupler 140. In some embodiments a waveguide stack composed of two or more waveguides stacked one over another may be used in place of the waveguide 123. 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 123, 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 123 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 image light source 110. In some embodiments the waveguide assembly 120 may be partially transparent to outside light, and may be used in AR applications. The waveguide 123 may be configured to convey a 2D FOV from an input coupler 130 to the output coupler 140, and ultimately to the eye 166 of the user. Here and in the following description a Cartesian coordinate system (x,y,z) is used for convenience, in which the (x,y) plane is parallel to the main faces of the waveguide assembly 120 through which the assembly receives and/or outputs the image light, and the z-axis is orthogonal thereto. The 2D FOV of waveguide 123 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.

[0056] Referring now to FIGS. 2A and 2B, they schematically illustrate the coupling of light of two different wavelengths into a waveguide 210, which may represent the waveguide 123 of waveguide assembly 120, or any waveguide of a waveguide stack that may be used in place of the waveguide 123. The wavelength .lamda. of incident light in FIG. 2A may be different, for example smaller, than the wavelength of incident light in FIG. 2B. FIG. 2A may represent, for example, the operation of waveguide 210 for green light, while FIG. 2B may for example represent the operation of waveguide 210 for red light.

[0057] Waveguide 210 may be a slab waveguide formed of a substrate 205, which may be for example in the form of 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. Opposing main 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 may be for example in the range of 1.4 to 2.6. In some embodiments, high-index materials having an index of refraction equal or greater than about 2.3 may be used for the substrate 205. In some embodiments these materials may have an index of refraction n greater than about 2.4. 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 (LiNbO3), titanium dioxide (TiO2), galium nitirde (GaN), aluminum nitiride (AlN), silicon carbide (SiC), CVD diamond, zinc sulfide (ZnS).

[0058] An in-coupler 230 may be provided in or upon 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, is 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 opposing faces 211, 212 of the waveguide, and/or two output gratings that may be disposed at opposing faces 211, 212 of 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. In the example embodiment illustrated in FIGS. 2A and 2B, the in-coupler 230 is embodied with a diffraction grating operating in transmission, while the out-coupler 240 is embodied with a diffraction grating operating in reflection.

[0059] The in-coupler 230 may be configured to provide the waveguide 210 with an input FOV 234, which may also be referred to herein as the acceptance angle. The input FOV 234, which depends on the wavelength, defines a range of angles of incidence a 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, so that light coupled into the waveguide becomes trapped therein by total internal reflection (TIR), and propagates within the waveguide with suitably low attenuation until it is engaged 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 .alpha. 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 corresponding rays are on the same side from the normal 207 to the opposing faces 211, 212 of the waveguide and is negative otherwise. Equation (1) may be easily modified for embodiments in which the waveguide 210 is surrounded by cladding 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 grating vector of the in-coupler grating lies within the plane of incidence of image light.

[0060] The TIR condition for the diffracted light within the waveguide, referred hereinafter as the in-coupled light, is defined by the TIR equation (2):

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

where the equality corresponds to a critical TIR angle .beta..sub.c=asin(1/n). The input FOV 234 of the waveguide 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 edge angles. The first FOV angle of incidence .alpha..sub.1 corresponding to the right-most incident ray 111b in FIG. 2A is defined by the critical TIR angle .beta..sub.c of the in-coupled light, i.e. light trapped within the waveguide:

.alpha. 1 = a .times. sin .function. ( .lamda. p - 1 ) , ( 3 ) ##EQU00008##

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

.alpha. 2 = ( .lamda. p - n sin .function. ( .beta. max ) ) , ( 4 ) ##EQU00009##

[0061] 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 FOV of the waveguide is about 26.degree. for n=1.5, about 43.degree. for n=1.8, and is about 107.degree. for n=2.4.

[0062] 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.

[0063] Referring to FIG. 3A, 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 at least 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.

[0064] 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 k.sub.g is equal to substantially zero:

|.SIGMA.k.sub.g|.apprxeq.0. (5)

Here the summation in the left hand side (LHS) of equation (5) is performed over grating vectors k.sub.g of all gratings that 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 k.sub.g 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, |k.sub.g|=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 opposing 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 one-dimensional (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.

[0065] FIG. 3B illustrates an embodiment in which the out-coupler 240 includes two diffraction gratings 241, 242 that are disposed at opposing faces of the waveguide. In such embodiments the in-coupled light 211a may exit the waveguide as output light 221 after being sequentially diffracted by the diffraction gratings 241 and 242. 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.

[0066] FIG. 4 illustrates, in a plan view, a display waveguide 410 with an in-coupler 430 and an out-coupler 440. 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 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 opposing faces of the waveguide. In some embodiments they may 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 area 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 an eyebox projection area 450, is an area where the out-coupled light has optimal characteristics for viewing, for example where it has desired dimensions. The eyebox projection area 450 may be located at some distance from the in-coupler 430.

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