Meta Patent | Low stress loca additive and loca processing for bonding optical substrates

where R₁, R₂, and R₃ may include methoxide, ethoxide, propoxide, or a mixture of these materials, and R₄ may be an alkyl chain that is linear or branched and is composed of 2-8 carbons, such as linear C₆H₁₂. R₁, R₂, and R₃ may improve the adhesion strength of the LOCA, whereas R₄ may help to reduce stress of the LOCA during the curing and thermal treatment. Thus, the siloxane additive of Structure 1 may allow the LOCA to have reduced internal stress, such that the bowing of the bonded substrate stack may be minimized and the optical performance of the waveguide display may not be compromised. For example, when the optical substrates include 6-inch wafers, the bow of the bonded substrate stack may be below about 20 μm, and the performance of the waveguide display may not be degraded or may only be minimally degraded. Upon curing, the mixture of the LOCA and the siloxane additive of Structure 1 may result in a permanently bonded layer with stable mechanical properties, a refractive index about 1.6 or higher at 450 nm, an absorption below about 0.1%/μm, and an adhesion strength to glass greater than about 1.5 MPa.

According to certain embodiments, an optically clear, siloxane-containing epoxy adhesive mixture for bonding two optical substrates may be cured via UV, thermal, or both UV and thermal processes to produce a high refractive index, high transparency, and low bowing bonding layer that can provide high adhesion for the bonded substrate stack. The adhesive mixture may include, for example, siloxane and epoxy-containing oligomers, a UV-activated photo-acid generator, a crosslinker additive, a solvent, and an additive of Structure 1, where the additive of Structure 1 may constitute about 1-7% of the total mass of the adhesive mixture (excluding the solvent). In the additive of Structure 1, R₁, R₂, and R₃ may include methoxide, ethoxide, propoxide, or a mixture of these materials, and R₄ may include an alkyl chain that is linear or branched and includes 2-8 carbons. The adhesive mixture, when cured, may have a refractive index between about 1.6 and about 1.7 at 450 nm, and an optical absorption below 0.1% per micrometer of the adhesive mixture. The adhesive mixture, when applied onto 4-8 inch wafers and cured, may yield a bonded wafer stack with a bow below about 20 micrometers.

According to certain embodiments, a method of bonding two optical substrates may include spin-coating, spraying, ink-jet printing, screen-printing, needle dispensing, or otherwise dispensing an adhesive layer including a siloxane-containing epoxy adhesive mixture onto a first substrate, and bonding the adhesive layer to a second substrate by curing the adhesive mixture via a combination of UV curing and thermal curing. The adhesive mixture may include an additive of Structure 1, where the additive of Structure 1 may constitute about 1-7% of the total mass of the mixture (excluding the solvent). The adhesive mixture may be applied onto the first substrate to form an adhesive layer with a thickness about 1-100 microns. The adhesive mixture may be cured to generate a mechanically stable adhesive layer with a refractive index between about 1.6 and about 1.7 at 450 nm, and an optical absorption below about 0.1% per micrometer of the adhesive mixture. The bonded substrate stack may have a lap shear strength of at least 2.0 MPa, and a low degree of bowing. In some embodiments, the first substrate and the second substrate may be transparent substrates with diameters about 4 to 8 inches, and the bonded substrate stack may have a bow below 20 micrometers. In some embodiments, at least one of the first substrate or the second substrate may be a lens with an arbitrary shape and a length about 1 to 4 inches, and the bow of the bonded substrate stack may be below about 10 micrometers.

According to certain embodiments, two transparent substrates may be bonded together by a siloxane-containing epoxy adhesive layer created from a mixture including an additive of Structure 1, where the additive of Structure 1 may constitute about 1-7% of the total mass of the mixture excluding the solvent. The adhesive layer may be mechanically stable, and may have a refractive index between about 1.6 and about 1.7 at 450 nm and an optical absorption below about 0.1% per micrometer of the adhesive layer. The substrate stack bonded by the adhesive layer may have a lap shear strength of at least 2.0 MPa, and may have a low degree of bowing. In one example, the two transparent substrates may be wafers with diameters about 4 to 8 inches, and the bonded substrate stack may have a bow below 20 micrometers. In some embodiments, at least one of the two transparent substrates is a lens having an arbitrary shape and a length about 1 to 4 inches, and the bow of the bonded substrate stack is below 10 micrometers.

Unless defined otherwise, all technical and scientific terms used herein have the same meaning as is commonly understood by one of ordinary skill in the art to which this disclosure belongs.

As used herein, the term “about” means that dimensions, sizes, formulations, parameters, shapes and other quantities and characteristics are not and need not be exact, but may be approximate and/or larger or smaller, as desired, reflecting tolerances, conversion factors, rounding off, measurement error and the like, and other factors known to those of skill in the art. In general, a dimension, size, formulation, parameter, shape or other quantity or characteristic is “about” or “approximate” whether or not expressly stated to be such. It is noted that embodiments of different sizes, shapes and dimensions may employ the described arrangements.

In the following description, for the purposes of explanation, specific details are set forth in order to provide a thorough understanding of examples of the disclosure. However, it will be apparent that various examples may be practiced without these specific details. For example, devices, systems, structures, assemblies, methods, and other components may be shown as components in block diagram form in order not to obscure the examples in unnecessary detail. In other instances, well-known devices, processes, systems, structures, and techniques may be shown without necessary detail in order to avoid obscuring the examples. The figures and description are not intended to be restrictive. The terms and expressions that have been employed in this disclosure are used as terms of description and not of limitation, and there is no intention in the use of such terms and expressions of excluding any equivalents of the features shown and described or portions thereof. The word “example” is used herein to mean “serving as an example, instance, or illustration.” Any embodiment or design described herein as “example” is not necessarily to be construed as preferred or advantageous over other embodiments or designs.

FIG. 1 is a simplified block diagram of an example of an artificial reality system environment 100 including a near-eye display 120 in accordance with certain embodiments. Artificial reality system environment 100 shown in FIG. 1 may include near-eye display 120, an optional external imaging device 150, and an optional input/output interface 140, each of which may be coupled to an optional console 110. While FIG. 1 shows an example of artificial reality system environment 100 including one near-eye display 120, one external imaging device 150, and one input/output interface 140, any number of these components may be included in artificial reality system environment 100, or any of the components may be omitted. For example, there may be multiple near-eye displays 120 monitored by one or more external imaging devices 150 in communication with console 110. In some configurations, artificial reality system environment 100 may not include external imaging device 150, optional input/output interface 140, and optional console 110. In alternative configurations, different or additional components may be included in artificial reality system environment 100.

Near-eye display 120 may be a head-mounted display that presents content to a user. Examples of content presented by near-eye display 120 include one or more of images, videos, audio, or any combination thereof. In some embodiments, audio may be presented via an external device (e.g., speakers and/or headphones) that receives audio information from near-eye display 120, console 110, or both, and presents audio data based on the audio information. Near-eye display 120 may include one or more rigid bodies, which may be rigidly or non-rigidly coupled to each other. A rigid coupling between rigid bodies may cause the coupled rigid bodies to act as a single rigid entity. A non-rigid coupling between rigid bodies may allow the rigid bodies to move relative to each other. In various embodiments, near-eye display 120 may be implemented in any suitable form-factor, including a pair of glasses. Some embodiments of near-eye display 120 are further described below with respect to FIGS. 2 and 3. Additionally, in various embodiments, the functionality described herein may be used in a headset that combines images of an environment external to near-eye display 120 and artificial reality content (e.g., computer-generated images). Therefore, near-eye display 120 may augment images of a physical, real-world environment external to near-eye display 120 with generated content (e.g., images, video, sound, etc.) to present an augmented reality to a user.

In various embodiments, near-eye display 120 may include one or more of display electronics 122, display optics 124, and an eye-tracking unit 130. In some embodiments, near-eye display 120 may also include one or more locators 126, one or more position sensors 128, and an inertial measurement unit (IMU) 132. Near-eye display 120 may omit any of eye-tracking unit 130, locators 126, position sensors 128, and IMU 132, or include additional elements in various embodiments. Additionally, in some embodiments, near-eye display 120 may include elements combining the function of various elements described in conjunction with FIG. 1.

Display electronics 122 may display or facilitate the display of images to the user according to data received from, for example, console 110. In various embodiments, display electronics 122 may include one or more display panels, such as a liquid crystal display (LCD), an organic light emitting diode (OLED) display, an inorganic light emitting diode (ILED) display, a micro light emitting diode (μLED) display, an active-matrix OLED display AMOLED), a transparent OLED display (TOLED), or some other display. For example, in one implementation of near-eye display 120, display electronics 122 may include a front TOLED panel, a rear display panel, and an optical component (e.g., an attenuator, polarizer, or diffractive or spectral film) between the front and rear display panels. Display electronics 122 may include pixels to emit light of a predominant color such as red, green, blue, white, or yellow. In some implementations, display electronics 122 may display a three-dimensional (3D) image through stereoscopic effects produced by two-dimensional panels to create a subjective perception of image depth. For example, display electronics 122 may include a left display and a right display positioned in front of a user's left eye and right eye, respectively. The left and right displays may present copies of an image shifted horizontally relative to each other to create a stereoscopic effect (i.e., a perception of image depth by a user viewing the image).

In certain embodiments, display optics 124 may display image content optically (e.g., using optical waveguides and couplers) or magnify image light received from display electronics 122, correct optical errors associated with the image light, and present the corrected image light to a user of near-eye display 120. In various embodiments, display optics 124 may include one or more optical elements, such as, for example, a substrate, optical waveguides, an aperture, a Fresnel lens, a convex lens, a concave lens, a filter, input/output couplers, or any other suitable optical elements that may affect image light emitted from display electronics 122. Display optics 124 may include a combination of different optical elements as well as mechanical couplings to maintain relative spacing and orientation of the optical elements in the combination. One or more optical elements in display optics 124 may have an optical coating, such as an antireflective coating, a reflective coating, a filtering coating, or a combination of different optical coatings.

Magnification of the image light by display optics 124 may allow display electronics 122 to be physically smaller, weigh less, and consume less power than larger displays. Additionally, magnification may increase a field of view of the displayed content. The amount of magnification of image light by display optics 124 may be changed by adjusting, adding, or removing optical elements from display optics 124. In some embodiments, display optics 124 may project displayed images to one or more image planes that may be further away from the user's eyes than near-eye display 120.

Display optics 124 may also be designed to correct one or more types of optical errors, such as two-dimensional optical errors, three-dimensional optical errors, or any combination thereof. Two-dimensional errors may include optical aberrations that occur in two dimensions. Example types of two-dimensional errors may include barrel distortion, pincushion distortion, longitudinal chromatic aberration, and transverse chromatic aberration. Three-dimensional errors may include optical errors that occur in three dimensions. Example types of three-dimensional errors may include spherical aberration, comatic aberration, field curvature, and astigmatism.

Locators 126 may be objects located in specific positions on near-eye display 120 relative to one another and relative to a reference point on near-eye display 120. In some implementations, console 110 may identify locators 126 in images captured by external imaging device 150 to determine the artificial reality headset's position, orientation, or both. A locator 126 may be a light-emitting diode (LED), a corner cube reflector, a reflective marker, a type of light source that contrasts with an environment in which near-eye display 120 operates, or any combination thereof. In embodiments where locators 126 are active components (e.g., LEDs or other types of light emitting devices), locators 126 may emit light in the visible band (e.g., about 380 nm to 750 nm), in the infrared (IR) band (e.g., about 750 nm to 1 mm), in the ultraviolet band (e.g., about 10 nm to about 380 nm), in another portion of the electromagnetic spectrum, or in any combination of portions of the electromagnetic spectrum.

External imaging device 150 may include one or more cameras, one or more video cameras, any other device capable of capturing images including one or more of locators 126, or any combination thereof. Additionally, external imaging device 150 may include one or more filters (e.g., to increase signal to noise ratio). External imaging device 150 may be configured to detect light emitted or reflected from locators 126 in a field of view of external imaging device 150. In embodiments where locators 126 include passive elements (e.g., retroreflectors), external imaging device 150 may include a light source that illuminates some or all of locators 126, which may retro-reflect the light to the light source in external imaging device 150. Slow calibration data may be communicated from external imaging device 150 to console 110, and external imaging device 150 may receive one or more calibration parameters from console 110 to adjust one or more imaging parameters (e.g., focal length, focus, frame rate, sensor temperature, shutter speed, aperture, etc.).

Position sensors 128 may generate one or more measurement signals in response to motion of near-eye display 120. Examples of position sensors 128 may include accelerometers, gyroscopes, magnetometers, other motion-detecting or error-correcting sensors, or any combination thereof. For example, in some embodiments, position sensors 128 may include multiple accelerometers to measure translational motion (e.g., forward/back, up/down, or left/right) and multiple gyroscopes to measure rotational motion (e.g., pitch, yaw, or roll). In some embodiments, various position sensors may be oriented orthogonally to each other.

IMU 132 may be an electronic device that generates fast calibration data based on measurement signals received from one or more of position sensors 128. Position sensors 128 may be located external to IMU 132, internal to IMU 132, or any combination thereof. Based on the one or more measurement signals from one or more position sensors 128, IMU 132 may generate fast calibration data indicating an estimated position of near-eye display 120 relative to an initial position of near-eye display 120. For example, IMU 132 may integrate measurement signals received from accelerometers over time to estimate a velocity vector and integrate the velocity vector over time to determine an estimated position of a reference point on near-eye display 120. Alternatively, IMU 132 may provide the sampled measurement signals to console 110, which may determine the fast calibration data. While the reference point may generally be defined as a point in space, in various embodiments, the reference point may also be defined as a point within near-eye display 120 (e.g., a center of IMU 132).

Eye-tracking unit 130 may include one or more eye-tracking systems. Eye tracking may refer to determining an eye's position, including orientation and location of the eye, relative to near-eye display 120. An eye-tracking system may include an imaging system to image one or more eyes and may optionally include a light emitter, which may generate light that is directed to an eye such that light reflected by the eye may be captured by the imaging system. For example, eye-tracking unit 130 may include a non-coherent or coherent light source (e.g., a laser diode) emitting light in the visible spectrum or infrared spectrum, and a camera capturing the light reflected by the user's eye. As another example, eye-tracking unit 130 may capture reflected radio waves emitted by a miniature radar unit. Eye-tracking unit 130 may use low-power light emitters that emit light at frequencies and intensities that would not injure the eye or cause physical discomfort. Eye-tracking unit 130 may be arranged to increase contrast in images of an eye captured by eye-tracking unit 130 while reducing the overall power consumed by eye-tracking unit 130 (e.g., reducing power consumed by a light emitter and an imaging system included in eye-tracking unit 130). For example, in some implementations, eye-tracking unit 130 may consume less than 100 milliwatts of power.

Near-eye display 120 may use the orientation of the eye to, e.g., determine an inter-pupillary distance (IPD) of the user, determine gaze direction, introduce depth cues (e.g., blur image outside of the user's main line of sight), collect heuristics on the user interaction in the VR media (e.g., time spent on any particular subject, object, or frame as a function of exposed stimuli), some other functions that are based in part on the orientation of at least one of the user's eyes, or any combination thereof. Because the orientation may be determined for both eyes of the user, eye-tracking unit 130 may be able to determine where the user is looking. For example, determining a direction of a user's gaze may include determining a point of convergence based on the determined orientations of the user's left and right eyes. A point of convergence may be the point where the two foveal axes of the user's eyes intersect. The direction of the user's gaze may be the direction of a line passing through the point of convergence and the mid-point between the pupils of the user's eyes.

Input/output interface 140 may be a device that allows a user to send action requests to console 110. An action request may be a request to perform a particular action. For example, an action request may be to start or to end an application or to perform a particular action within the application. Input/output interface 140 may include one or more input devices. Example input devices may include a keyboard, a mouse, a game controller, a glove, a button, a touch screen, or any other suitable device for receiving action requests and communicating the received action requests to console 110. An action request received by the input/output interface 140 may be communicated to console 110, which may perform an action corresponding to the requested action. In some embodiments, input/output interface 140 may provide haptic feedback to the user in accordance with instructions received from console 110. For example, input/output interface may provide haptic feedback when an action request is received, or when console 110 has performed a requested action and communicates instructions to input/output interface 140. In some embodiments, external imaging device 150 may be used to track input/output interface 140, such as tracking the location or position of a controller (which may include, for example, an IR light source) or a hand of the user to determine the motion of the user. In some embodiments, near-eye display 120 may include one or more imaging devices to track input/output interface 140, such as tracking the location or position of a controller or a hand of the user to determine the motion of the user.

Console 110 may provide content to near-eye display 120 for presentation to the user in accordance with information received from one or more of external imaging device 150, near-eye display 120, and input/output interface 140. In the example shown in FIG. 1, console 110 may include an application store 112, a headset tracking module 114, an artificial reality engine 116, and an eye-tracking module 118. Some embodiments of console 110 may include different or additional modules than those described in conjunction with FIG. 1. Functions further described below may be distributed among components of console 110 in a different manner than is described here.

In some embodiments, console 110 may include a processor and a non-transitory computer-readable storage medium storing instructions executable by the processor. The processor may include multiple processing units executing instructions in parallel. The non-transitory computer-readable storage medium may be any memory, such as a hard disk drive, a removable memory, or a solid-state drive (e.g., flash memory or dynamic random access memory (DRAM)). In various embodiments, the modules of console 110 described in conjunction with FIG. 1 may be encoded as instructions in the non-transitory computer-readable storage medium that, when executed by the processor, cause the processor to perform the functions further described below.

Application store 112 may store one or more applications for execution by console 110. An application may include a group of instructions that, when executed by a processor, generates content for presentation to the user. Content generated by an application may be in response to inputs received from the user via movement of the user's eyes or inputs received from the input/output interface 140. Examples of the applications may include gaming applications, conferencing applications, video playback application, or other suitable applications.

Headset tracking module 114 may track movements of near-eye display 120 using slow calibration information from external imaging device 150. For example, headset tracking module 114 may determine positions of a reference point of near-eye display 120 using observed locators from the slow calibration information and a model of near-eye display 120. Headset tracking module 114 may also determine positions of a reference point of near-eye display 120 using position information from the fast calibration information. Additionally, in some embodiments, headset tracking module 114 may use portions of the fast calibration information, the slow calibration information, or any combination thereof, to predict a future location of near-eye display 120. Headset tracking module 114 may provide the estimated or predicted future position of near-eye display 120 to artificial reality engine 116.

Artificial reality engine 116 may execute applications within artificial reality system environment 100 and receive position information of near-eye display 120, acceleration information of near-eye display 120, velocity information of near-eye display 120, predicted future positions of near-eye display 120, or any combination thereof from headset tracking module 114. Artificial reality engine 116 may also receive estimated eye position and orientation information from eye-tracking module 118. Based on the received information, artificial reality engine 116 may determine content to provide to near-eye display 120 for presentation to the user. For example, if the received information indicates that the user has looked to the left, artificial reality engine 116 may generate content for near-eye display 120 that mirrors the user's eye movement in a virtual environment. Additionally, artificial reality engine 116 may perform an action within an application executing on console 110 in response to an action request received from input/output interface 140, and provide feedback to the user indicating that the action has been performed. The feedback may be visual or audible feedback via near-eye display 120 or haptic feedback via input/output interface 140.

Eye-tracking module 118 may receive eye-tracking data from eye-tracking unit 130 and determine the position of the user's eye based on the eye tracking data. The position of the eye may include an eye's orientation, location, or both relative to near-eye display 120 or any element thereof. Because the eye's axes of rotation change as a function of the eye's location in its socket, determining the eye's location in its socket may allow eye-tracking module 118 to more accurately determine the eye's orientation.

FIG. 2 is a perspective view of an example of a near-eye display in the form of an HMD device 200 for implementing some of the examples disclosed herein. HMD device 200 may be a part of, e.g., a VR system, an AR system, an MR system, or any combination thereof. HMD device 200 may include a body 220 and a head strap 230. FIG. 2 shows a bottom side 223, a front side 225, and a left side 227 of body 220 in the perspective view. Head strap 230 may have an adjustable or extendible length. There may be a sufficient space between body 220 and head strap 230 of HMD device 200 for allowing a user to mount HMD device 200 onto the user's head. In various embodiments, HMD device 200 may include additional, fewer, or different components. For example, in some embodiments, HMD device 200 may include eyeglass temples and temple tips as shown in, for example, FIG. 3 below, rather than head strap 230.

HMD device 200 may present to a user media including virtual and/or augmented views of a physical, real-world environment with computer-generated elements. Examples of the media presented by HMD device 200 may include images (e.g., two-dimensional (2D) or three-dimensional (3D) images), videos (e.g., 2D or 3D videos), audio, or any combination thereof. The images and videos may be presented to each eye of the user by one or more display assemblies (not shown in FIG. 2) enclosed in body 220 of HMD device 200. In various embodiments, the one or more display assemblies may include a single electronic display panel or multiple electronic display panels (e.g., one display panel for each eye of the user). Examples of the electronic display panel(s) may include, for example, an LCD, an OLED display, an ILED display, a μLED display, an AMOLED, a TOLED, some other display, or any combination thereof. HMD device 200 may include two eye box regions.

In some implementations, HMD device 200 may include various sensors (not shown), such as depth sensors, motion sensors, position sensors, and eye tracking sensors. Some of these sensors may use a structured light pattern for sensing. In some implementations, HMD device 200 may include an input/output interface for communicating with a console. In some implementations, HMD device 200 may include a virtual reality engine (not shown) that can execute applications within HMD device 200 and receive depth information, position information, acceleration information, velocity information, predicted future positions, or any combination thereof of HMD device 200 from the various sensors. In some implementations, the information received by the virtual reality engine may be used for producing a signal (e.g., display instructions) to the one or more display assemblies. In some implementations, HMD device 200 may include locators (not shown, such as locators 126) located in fixed positions on body 220 relative to one another and relative to a reference point. Each of the locators may emit light that is detectable by an external imaging device.

FIG. 3 is a perspective view of an example of a near-eye display 300 in the form of a pair of glasses for implementing some of the examples disclosed herein. Near-eye display 300 may be a specific implementation of near-eye display 120 of FIG. 1, and may be configured to operate as a virtual reality display, an augmented reality display, and/or a mixed reality display. Near-eye display 300 may include a frame 305 and a display 310. Display 310 may be configured to present content to a user. In some embodiments, display 310 may include display electronics and/or display optics. For example, as described above with respect to near-eye display 120 of FIG. 1, display 310 may include an LCD display panel, an LED display panel, or an optical display panel (e.g., a waveguide display assembly).

Near-eye display 300 may further include various sensors 350a, 350b, 350c, 350d, and 350e on or within frame 305. In some embodiments, sensors 350a-350e may include one or more depth sensors, motion sensors, position sensors, inertial sensors, or ambient light sensors. In some embodiments, sensors 350a-350e may include one or more image sensors configured to generate image data representing different fields of views in different directions. In some embodiments, sensors 350a-350e may be used as input devices to control or influence the displayed content of near-eye display 300, and/or to provide an interactive VR/AR/MR experience to a user of near-eye display 300. In some embodiments, sensors 350a-350e may also be used for stereoscopic imaging.

In some embodiments, near-eye display 300 may further include one or more illuminators 330 to project light into the physical environment. The projected light may be associated with different frequency bands (e.g., visible light, infra-red light, ultra-violet light, etc.), and may serve various purposes. For example, illuminator(s) 330 may project light in a dark environment (or in an environment with low intensity of infra-red light, ultra-violet light, etc.) to assist sensors 350a-350e in capturing images of different objects within the dark environment. In some embodiments, illuminator(s) 330 may be used to project certain light patterns onto the objects within the environment. In some embodiments, illuminator(s) 330 may be used as locators, such as locators 126 described above with respect to FIG. 1.

In some embodiments, near-eye display 300 may also include a high-resolution camera 340. High-resolution camera 340 may capture images of the physical environment in the field of view. The captured images may be processed, for example, by a virtual reality engine (e.g., artificial reality engine 116 of FIG. 1) to add virtual objects to the captured images or modify physical objects in the captured images, and the processed images may be displayed to the user by display 310 for AR or MR applications.

FIG. 4 illustrates an example of an optical see-through augmented reality system 400 including a waveguide display according to certain embodiments. Augmented reality system 400 may include a projector 410 and a combiner 415. Projector 410 may include a light source or image source 412 and projector optics 414. In some embodiments, light source or image source 412 may include one or more micro-LED devices described above. In some embodiments, image source 412 may include a plurality of pixels that displays virtual objects, such as an LCD display panel or an LED display panel. In some embodiments, image source 412 may include a light source that generates coherent or partially coherent light. For example, image source 412 may include a laser diode, a vertical cavity surface emitting laser, an LED, and/or a micro-LED described above. In some embodiments, image source 412 may include a plurality of light sources (e.g., an array of micro-LEDs described above), each emitting a monochromatic image light corresponding to a primary color (e.g., red, green, or blue). In some embodiments, image source 412 may include three two-dimensional arrays of micro-LEDs, where each two-dimensional array of micro-LEDs may include micro-LEDs configured to emit light of a primary color (e.g., red, green, or blue). In some embodiments, image source 412 may include an optical pattern generator, such as a spatial light modulator. Projector optics 414 may include one or more optical components that can condition the light from image source 412, such as expanding, collimating, scanning, or projecting light from image source 412 to combiner 415. The one or more optical components may include, for example, one or more lenses, liquid lenses, mirrors, apertures, and/or gratings. For example, in some embodiments, image source 412 may include one or more one-dimensional arrays or elongated two-dimensional arrays of micro-LEDs, and projector optics 414 may include one or more one-dimensional scanners (e.g., micro-mirrors or prisms) configured to scan the one-dimensional arrays or elongated two-dimensional arrays of micro-LEDs to generate image frames. In some embodiments, projector optics 414 may include a liquid lens (e.g., a liquid crystal lens) with a plurality of electrodes that allows scanning of the light from image source 412.

Combiner 415 may include an input coupler 430 for coupling light from projector 410 into a substrate 420 of combiner 415. Input coupler 430 may include a volume Bragg grating (VBG), a diffractive optical element (DOE) (e.g., a surface-relief grating (SRG)), a slanted surface of substrate 420, or a refractive coupler (e.g., a wedge or a prism). For example, input coupler 430 may include a reflective volume Bragg grating or a transmissive volume Bragg grating. Input coupler 430 may have a coupling efficiency of greater than 30%, 50%, 75%, 90%, or higher for visible light. Light coupled into substrate 420 may propagate within substrate 420 through, for example, total internal reflection (TIR). Substrate 420 may be in the form of a lens of a pair of eyeglasses. Substrate 420 may have a flat or a curved surface, and may include one or more types of dielectric materials, such as glass, quartz, plastic, polymer, poly(methyl methacrylate) (PMMA), crystal, or ceramic. A thickness of the substrate may range from, for example, less than about 1 mm to about 10 mm or more. Substrate 420 may be transparent to visible light.

Substrate 420 may include or may be coupled to a plurality of output couplers 440, each configured to extract at least a portion of the light guided by and propagating within substrate 420 from substrate 420, and direct extracted light 460 to an eyebox 495 where an eye 490 of the user of augmented reality system 400 may be located when augmented reality system is in use. The plurality of output couplers 440 may replicate the exit pupil to increase the size of eyebox 495 such that the displayed image is visible in a larger area. As input coupler 430, output couplers 440 may include grating couplers (e.g., volume holographic gratings or surface-relief gratings), other diffraction optical elements, prisms, etc. For example, output couplers 440 may include reflective volume Bragg gratings or transmissive volume Bragg gratings. Output couplers 440 may have different coupling (e.g., diffraction) efficiencies at different locations. Substrate 420 may also allow light 450 from the environment in front of combiner 415 to pass through with little or no loss. Output couplers 440 may also allow light 450 to pass through with little loss. For example, in some implementations, output couplers 440 may have a very low diffraction efficiency for light 450 such that light 450 may be refracted or otherwise pass through output couplers 440 with little loss, and thus may have a higher intensity than extracted light 460. In some implementations, output couplers 440 may have a high diffraction efficiency for light 450 and may diffract light 450 in certain desired directions (i.e., diffraction angles) with little loss. As a result, the user may be able to view combined images of the environment in front of combiner 415 and images of virtual objects projected by projector 410.

In some embodiments, projector 410, input coupler 430, and output coupler 440 may be on any side of substrate 420. Input coupler 430 and output coupler 440 may be reflective gratings (also referred to as reflective gratings) or transmissive gratings (also referred to as transmissive gratings) to couple display light into or out of substrate 420.

FIG. 5 illustrates an example of an optical see-through augmented reality system 500 including a waveguide display for exit pupil expansion according to certain embodiments. Augmented reality system 500 may be similar to augmented reality system 500, and may include the waveguide display and a projector that may include a light source or image source 510 and projector optics 520. The waveguide display may include a substrate 530, an input coupler 540, and a plurality of output couplers 550 as described above with respect to augmented reality system 500. While FIG. 5 only shows the propagation of light from a single field of view, FIG. 5 shows the propagation of light from multiple fields of view.

FIG. 5 shows that the exit pupil is replicated by output couplers 550 to form an aggregated exit pupil or eyebox, where different regions in a field of view (e.g., different pixels on image source 510) may be associated with different respective propagation directions towards the eyebox, and light from a same field of view (e.g., a same pixel on image source 510) may have a same propagation direction for the different individual exit pupils. Thus, a single image of image source 510 may be formed by the user's eye located anywhere in the eyebox, where light from different individual exit pupils and propagating in the same direction may be from a same pixel on image source 510 and may be focused onto a same location on the retina of the user's eye. FIG. 5 shows that the image of the image source is visible by the user's eye even if the user's eye moves to different locations in the eyebox.

FIG. 6A illustrates an example of a waveguide display 600 including volume Bragg grating couplers. Waveguide display 600 may include a VBG layer 620 within a substrate 610 or between two substrate that are bonded together. For example, VBG layer 620 may be formed on one substrate and the substrate with VBG layer 620 may be bonded to another substrate, such that VBG layer 620 may be sandwiched by the two substrates to form a waveguide display, where display light may be reflected by a top surface 612 and a bottom surface 614. VBG layer 620 may include an input VBG 622 and an output VBG 624. In the illustrated example, input VBG 622 may reflectively diffract incident light, and thus may function as a reflective VBG. Output VBG 624 may partially reflectively diffract the light from input VBG 622 out of substrate 610 towards an eyebox of waveguide display 600. Input VBG 622 and output VBG 624 may function as multiple reflectors that strongly reflect light of a specific wavelength and/or from a specific angle that satisfies the Bragg condition. In various embodiments, depending on the slant angle of the multiple reflectors in the VBG, input VBG 622 and output VBG 624 may be transmissive VBGs or reflective VBGs, where the reflected light may or may not pass through the VBG such that the VBG may transmissively or reflectively diffract the incident light. The reflectivity of each of the multiple reflectors may depend on the polarization state, the wavelength, and the incident angle of the incident light, and the period, the base refractive index, and the refractive index modulation (Δn) of the VBG.

FIG. 6B illustrates an example of a grating-based waveguide display 602 including multiple grating layers for different fields of view according to certain embodiments. In waveguide display 602, gratings may be spatially multiplexed along the z direction. For example, waveguide display 602 may include multiple substrates, such as substrates 630, 632, 634, and the like. The substrates may include a same material or materials having similar refractive indexes. One or more gratings 640, 642, 644, and the like (e.g., VBGs or SRGs) may be made on each substrate, such as recorded in a holographic material layer formed on the substrate or etched in the substrate. The gratings may be reflective gratings or transmissive gratings. The substrates with the gratings may be arranged in a substrate stack along the z direction for spatial multiplexing. In some embodiments, each grating 640, 642, or 644 may be a multiplexed VBG that includes multiple gratings designed for different Bragg conditions to couple display light in different wavelength ranges and/or different FOVs into or out of waveguide display 602. In the example shown in FIG. 6B, grating 640 may couple light 654 from a positive field of view into the waveguide as shown by a light ray 664 within the waveguide. Grating 642 may couple light 650 from around 0° field of view into the waveguide as shown by a light ray 660 within the waveguide. Grating 644 may couple light 652 from a negative field of view into the waveguide as shown by a light ray 662 within the waveguide.

In many waveguide-based near-eye display systems, in order to expand the eyebox of the waveguide-based near-eye display in two dimensions, two or more output gratings may be used to expand the display light in two dimensions or along two axes (which may be referred to as dual-axis pupil expansion). The two gratings may have different grating parameters, such that one grating may be used to replicate the exit pupil in one direction and the other grating may be used to replicate the exit pupil in another direction.

FIG. 7A is a top view of an example of a grating-based (e.g., volume Bragg grating or surface-relief grating -based) waveguide display 700 with exit pupil expansion and dispersion reduction according to certain embodiments. Waveguide display 700 may be an example of augmented reality system 400 or 500, and may include a waveguide 705, an input grating 710, a first middle grating 720, a second middle grating 730, and an output grating 740 formed on or in waveguide 705. Each of input grating 710, first middle grating 720, second middle grating 730, and output grating 740 may be a transmissive grating or a reflective grating. Display light from a light source (e.g., one or more micro-LED arrays) may be coupled into waveguide 705 by input grating 710. The in-coupled display light may be reflected by surfaces of waveguide 705 through total internal reflection as shown in FIG. 4, such that the display light may propagate within waveguide 705. Input grating 710 may include VBGs or SRGS. In one example, input grating 710 may include multiplexed VBGs and may couple display light of different colors and from different fields of view into waveguide 705 at corresponding diffraction angles.

First middle grating 720 and second middle grating 730 may be in different regions of a same holographic material layer or may be on different holographic material layers. In some embodiments, first middle grating 720 may be spatially separate from second middle grating 730. First middle grating 720 and second middle grating 730 may each include multiplexed VBGs or SRGs. In some embodiments, first middle grating 720 and second middle grating 730 may be recorded in a same number of exposures and under similar recording conditions, such that each VBG in first middle grating 720 may match a respective VBG in second middle grating 730 (e.g., having the same grating vector in the x-y plane and having the same and/or opposite grating vectors in the z direction). For example, in some embodiments, a VBG in first middle grating 720 and a corresponding VBG in second middle grating 730 may have the same grating period and the same grating slant angle (and thus the same grating vector), and the same thickness. In one example, first middle grating 720 and second middle grating 730 may have a thickness about 20 μm and may each include about 20 or more VBGs recorded through about 20 or more exposures.

Output grating 740 may be formed in the see-through region of waveguide display 700 and may include an exit region 750 that overlaps with the eyebox of waveguide display 700 when viewed in the z direction (e.g., at a distance about 18 mm from output grating 740 in +z or −z direction). Output grating 740 may include SRGs or multiplexed VBG gratings that include many VBGs. In some embodiments, output grating 740 and second middle grating 730 may at least partially overlap in the x-y plane, thereby reducing the form factor of waveguide display 700. Output grating 740, in combination with first middle grating 720 and second middle grating 730, may perform the dual-axis pupil expansion described above to expand the incident display light beam in two dimensions to fill the eyebox with the display light.

Input grating 710 may couple the display light from the light source into waveguide 705. The display light may reach first middle grating 720 directly or may be reflected by surfaces of waveguide 705 to first middle grating 720, where the size of the display light beam may be slightly larger than the size of the display light beam at input grating 710. Each VBG in first middle grating 720 may diffract a portion of the display light within a FOV range and a wavelength range that approximately satisfies the Bragg condition of the VBG to second middle grating 730. While the display light diffracted by a VBG in first middle grating 720 propagates within waveguide 705 (e.g., along a direction shown by a line 722) through total internal reflection, a portion of the display light may be diffracted by the corresponding VBG in second middle grating 730 towards output grating 740 each time the display light propagating within waveguide 705 reaches second middle grating 730, as shown by lines 732. Output grating 740 may then expand the display light from second middle grating 730 in a different direction by diffracting a portion of the display light to the eyebox each time the display light propagating within waveguide 705 reaches exit region 750 of output grating 740.

As described above, each VBG in first middle grating 720 may match a respective VBG in second middle grating 730 (e.g., having the same grating vector in the x-y plane and having the same and/or opposite grating vector in the z direction). The two matching VBGs may work under opposite Bragg conditions (e.g., +1 order diffraction versus −1 order diffraction) due to the opposite propagation directions of the display light at the two matching VBGs. For example, as shown in FIG. 7A, the VBG in first middle grating 720 may change the propagation direction of the display light from a downward direction to a rightward direction, while the matching VBG in second middle grating 730 may change the propagation direction of the display light from a rightward direction to a downward direction. Thus, the dispersion caused by second middle grating 730 may be opposite to the dispersion caused by first middle grating 720, thereby reducing or minimizing the overall dispersion.

Similarly, each VBG in input grating 710 may match a respective VBG in output grating 740 (e.g., having the same grating vector in the x-y plane and having the same and/or opposite grating vector in the z direction). The two matching VBGs may also work under opposite Bragg conditions (e.g., +1 order diffraction versus −1 order diffraction) due to the opposite propagation directions of the display light (e.g., into and out of waveguide 705) at the two matching VBGs. Therefore, the dispersion caused by input grating 710 may be opposite to the dispersion caused by output grating 740, thereby reducing or minimizing the overall dispersion.

FIG. 7B is a side view of the example of waveguide display 700 including grating couplers. As illustrated, waveguide display 700 may include a first assembly 760 and a second assembly 770 that may be separated by a spacer 780. First assembly 760 may include a first substrate 762, a second substrate 766, and one or more grating layers 764 between first substrate 762 and second substrate 766. First substrate 762 and second substrate 766 may each be a thin transparent substrate, such as a glass substrate having a thickness about 100 μm or few hundred micrometers. Grating layers 764 may include multiplexed reflective VBGs, transmissive VBGs, SRGs, or a combination. Similarly, second assembly 770 may include a first substrate 772, a second substrate 776, and one or more grating layers 774 between first substrate 772 and second substrate 776. Grating layers 774 may include multiplexed reflective VBGs, transmissive VBGs, SRGs, or a combination. In one example, first assembly 760 may be used to couple display light in red, green, and blue colors from certain fields of view to user's eyes, and second assembly 770 may be used to couple display light in red, green, and blue colors from other fields of view to user's eyes.

FIG. 8A illustrates an example of a layer stack 800 formed by bonding two substrates 810 and 820 using a bonding layer 830. Layer stack 800 may be used as a waveguide for guiding display light, and may include one or more optical elements formed on one or both substrates, as described above. In the illustrated example, an output grating coupler 840 may be formed on substrate 820. Substrate 810 may or may not include a grating formed thereon. A light beam 850 coupled into the waveguide may propagate within the waveguide through total internal reflection. Each time the guided light beam reaches output grating coupler 840, a portion 860 of the guided light beam may be coupled out of the waveguide by output grating coupler 840. In layer stack 800, the top surface of substrate 820 and the bottom surface of substrate 810 may be parallel to each other. Therefore, the incident angle of the guided light beam incident on the top surface of substrate 820 and the incident angle of the guided light beam incident on the bottom surface of substrate 810 may remain constant, and the portions 860 of the guided light beam coupled out of the waveguide at different locations may have the same diffraction angle.

FIG. 8B illustrates another example of a waveguide display 802. Waveguide display 802 may include a substrate 812, which may be similar to substrate 420 or 530. Substrate 812 may include, for example, glass, silicon, silicon nitride, silicon carbide, LiNbO₃, TiO₂, GaN, AlN, SiC, CVD diamond, ZnS, or any other suitable material. An input grating 822 and one or more output gratings 832 and 842 may be etched in substrate 812 or in a grating material layer formed on substrate 812. In some embodiments, input gratings 822 and output gratings 832 and 842 may be holographic gratings recorded in holographic material layers coated on substrate 812. In some embodiments, input grating 822 and output gratings 832 and 842 may include slanted or vertical surface-relief gratings etched in substrate 812 or imprinted in nanoimprint material layers deposited on substrate 812, and may include an overcoat layer filling the grating grooves. Output gratings 832 and 842 may be etched on opposite surfaces of substrate 812. In some embodiments, only one output grating 832 or 842 may be used. Input grating 822 may couple display light of different colors (e.g., red, green, and blue) from different view angles (or within different fields of view (FOVs)) into substrate 812, which may guide the in-coupled display light through total internal reflection. A portion of the in-coupled display light propagating within substrate 812 may be coupled out of substrate 812 towards an eyebox of waveguide display 802 by output grating 832 or 842 each time the in-coupled display light reaches output grating 832 or 842.

To satisfy the grating equation, a diffraction grating may diffract incident light of different colors (wavelengths) and/or from different view angles to different diffraction angles. For example, in the example illustrated in FIG. 8B, two light beams having different colors (e.g., red and blue) and the same incidence angle (e.g., about 0°) may be diffracted by input grating 822 to different directions within substrate 812. More specifically, the light beam having a shorter wavelength (e.g., blue light) may have a smaller diffraction angle. Two light beams having the same color but different incidence angles may also be diffracted by input grating 822 to two different directions within substrate 812. Due to the different propagation directions, the two in-coupled light beams may reach the surfaces of substrate 812 and be diffracted out of substrate 812 after propagating different distances in the x direction. A light beam having a smaller angle with respect to the surface-normal direction of substrate 812 may reach output grating 832 or 842 for a larger number of times than a light beam having a larger angle with respect to the surface-normal direction of substrate 812. In addition, a grating may not have a flat diffraction efficiency for incident light of different colors or different incidence angles. For at least these reasons, display light of different colors or from different FOVs may be directed to the eyebox at different densities, and may also form ghost images on the retina of user's eyes.

FIG. 8C illustrates an example of a multi-layer waveguide display 804 according to certain embodiments. Multi-layer waveguide display 804 may include a first waveguide layer 814 that includes one or more input gratings 824 and 826 and one or two output gratings 834 and 844 formed thereon as in waveguide display 802 described above. First waveguide layer 814 may include, for example, glass, silicon, silicon nitride, silicon carbide, LiNbO₃, TiO₂, GaN, AlN, CVD diamond, ZnS, and the like. Input gratings 824 and 826 and output gratings 834 and 844 may be slanted or vertical holographic or surface-relief gratings and may include an overcoat layer filling the grating grooves. In some embodiments, one or more of input gratings 824 and 826 and output gratings 834 and 844 may each have a variable grating period, a variable duty cycle, a variable slant angle, and/or a variable etch depth. In some embodiments, one or more of the input gratings and output gratings may each include a two-dimensional grating that has a variable grating period, a variable duty cycle, a variable slant angle, and/or a variable etch depth along two directions of the two-dimensional grating.

Multi-layer waveguide display 804 may include a second waveguide layer 854 and a third waveguide layer 864 on opposing sides of first waveguide layer 814. Second waveguide layer 854 and third waveguide layer 864 may each be a thin layer (e.g., a few hundred micrometers, such as between about 100 μm and about 600 μm) of a transparent material having a lower refractive index than the refractive index of first waveguide layer 814. For example, the difference between the refractive index of first waveguide layer 814 and the refractive index of second waveguide layer 854 or third waveguide layer 864 may be about 0.01, 0.02, 0.05, 0.1, 0.2, 0.25, 0.3, or larger. Second waveguide layer 854 and third waveguide layer 864 may have a same refractive index or different refractive indices.

In addition, a fourth waveguide layer 870 may be formed on second waveguide layer 354, and a fifth waveguide layer 880 may be formed on third waveguide layer 864. Fourth waveguide layer 870 and fifth waveguide layer 880 may each be a thin layer (e.g., a few hundred micrometers, such as between about 100 μm and about 600 μm) of a transparent material having a lower refractive index than the refractive indices of second waveguide layer 854 and third waveguide layer 864, respectively. For example, the difference between the refractive index of second waveguide layer 854 and the refractive index of fourth waveguide layer 870 and the difference between the refractive index of third waveguide layer 864 and the refractive index of fifth waveguide layer 880 may be about 0.01, 0.02, 0.05, 0.1, 0.2, 0.25, 0.3, or larger. Fourth waveguide layer 870 and fifth waveguide layer 880 may have a same refractive index or different refractive indices.

Multi-layer waveguide display 804 may achieve a more uniform replication of light having different colors and from different FOVs. For example, a first light beam 890 (e.g., having a longer wavelength or from a larger view angle) may be coupled into first waveguide layer 814 by input grating 824 and may propagate within first waveguide layer 814 with a large angle with respect to a surface-normal direction of first waveguide layer 814. Therefore, first light beam 890 may be reflected at the interface between first waveguide layer 814 and second waveguide layer 854 through total internal reflection, due to the large incidence angle and the large difference between the refractive indices of first waveguide layer 814 and second waveguide layer 854.

A second light beam 892 (e.g., having a shorter wavelength and/or from a smaller view angle) may be coupled into first waveguide layer 814 by input grating 824 and may propagate within first waveguide layer 814 with a smaller angle with respect to the surface-normal direction of first waveguide layer 814. Therefore, second light beam 892 may not be reflected at the interface between first waveguide layer 814 and second waveguide layer 854 through total internal reflection, because the incidence angle may be smaller than the critical angle at the interface. Thus, second light beam 892 may instead be refracted at the interface with a larger refraction angle into second waveguide layer 854, and may then be reflected at the bottom surface of second waveguide layer 854 through total internal reflection due to the increased incidence angle and the difference between the refractive indices of second waveguide layer 854 and fourth waveguide layer 870. Therefore, even though second light beam 892 may have a smaller propagation angle with respect to the surface-normal direction of first waveguide layer 814 than first light beam 890, second light beam 892 may travel a longer distance in the z direction before being reflected through total internal reflection, and thus may travel a similar distance in the x direction as first light beam 890 before being reflected through total internal reflection. In this way, first light beam 890 and second light beam 892 may be diffracted by output grating 834 or 844 at about the same locations (or same interval) and/or for about the same number of times.

Similarly, a third light beam 894 (e.g., having an even shorter wavelength and/or from an even smaller view angle) may be coupled into first waveguide layer 814 by input grating 824 and may propagate within first waveguide layer 814 with a smaller angle with respect to the surface-normal direction of first waveguide layer 814. Third light beam 894 may be refracted at the interface between first waveguide layer 814 and second waveguide layer 854 and the interface between second waveguide layer 854 and fourth waveguide layer 870, but may be reflected at the bottom surface of fourth waveguide layer 870 through total internal reflection due to the increased incidence angle and the difference between the refractive indices of fourth waveguide layer 870 and air. Therefore, even though third light beam 894 may have a small propagation angle with respect to the surface-normal direction of first waveguide layer 814 than first light beam 890, third light beam 894 may travel a longer distance in the z direction before being reflected through total internal reflection, and thus may travel a similar distance in the x direction as first light beam 890 before being reflected through total internal reflection. In this way, first light beam 890 and third light beam 894 may be diffracted by output grating 834 or 844 at about the same locations (or same interval) and/or for about the same number of times.

The thicknesses and the refractive indices of first waveguide layer 814, second waveguide layer 854, third waveguide layer 864, fourth waveguide layer 870, and fifth waveguide layer 880 may be selected based on the desired performance. In various embodiments, the multi-layer waveguide displays herein may include two or more waveguide layers, such as three, four, five, or more layers. In some embodiments, the low-index waveguide layers may be on a same side of the input and output gratings, and the refractive indices of the two or more waveguide layers may be the highest at one side of the layer stack and then gradually decrease towards the other side of the layer stack. In some embodiments, the low-index waveguide layers may be on opposing sides of the input and output gratings, and the refractive indices of the two or more waveguide layers may be the highest at the center of the layer stack and may gradually decrease towards two opposite sides of the layer stack. In some embodiments, the refractive index profile of the waveguide layer stack may be symmetrical and have the highest value at the center as shown in FIG. 8C. In some embodiments, the refractive index profile of the waveguide layer stack may not be symmetrical with respect to the center of the waveguide layer stack. In some embodiments, one or more gratings or other optical elements may be formed in or on waveguide layer 854, 864, 870, or 880.

In some embodiments, optical substrates (e.g., including one or more optical waveguide layers, such as waveguide layer 814, 854, 864, 870, or 880) may be bonded using a liquid optically clear adhesive (LOCA). In order for the LOCA to be compatible with the optical substrates for waveguide display applications, the LOCA needs to be transparent to visible light (e.g., with an absorption less than about 0.1%/μm), have a high refractive index (e.g., greater than about 1.6), and can fully crosslink via curing, without inducing a large internal stress. The high transparency and high refractive index can be achieved by utilizing, for example, siloxane-containing epoxy-based LOCAs. These materials can have refractive indices about 1.6 or higher at 450 nm, their absorption can be below about 0.1%/μm of the LOCA materials, and their adhesion strength to glass may typically be above 1.5 Mpa. Therefore, these LOCA materials can be used to form permanent bonds between two optical substrates, and the bonds may be able to survive device processing and reliability testing.

FIG. 9A illustrates an example of a process 900 for bonding two optical substrates using a LOCA layer. As illustrates, a LOCA layer 920 (e.g., including siloxane-containing epoxy-based LOCA) may be applied onto a first optical substrate 910 by, for example, spin-coating, spraying, ink-jet printing, screen-printing, or otherwise dispensing techniques. Any residual solvent may be evaporated thermally, for example, by post apply bake (PAB). The LOCA may be partially cured via UV treatment. A second optical substrate 930 may then be placed above LOCA layer 920 and first optical substrate 910, and the substrate stack may optionally undergo a compression bonding process by a compressor. The substrate stack including LOCA layer 920 between first optical substrate 910 and second optical substrate 930 may be cured via UV curing and/or thermal curing (e.g., post exposure bake (PEB)), which may transform the LOCA material from its initial liquid state into an intermediate thermoplastic state. The substrate stack may then be baked or otherwise thermally cured to transform the LOCA material from the thermoplastic state into a final thermoset state, where the adhesion strength of the bonded stack may be maximized and the LOCA mechanical properties may be stable against further thermal processing. Compression may be applied to the optical substrates in any or all of the curing steps.

FIG. 9B illustrates an example of the polymerization of a LOCA material upon UV curing. The LOCA material may include monomers or oligomers 950, such as siloxane and epoxy-containing oligomers, which may be small molecules. The LOCA material may also include a UV-activated photo-acid generator, a crosslinker additive, and a solvent. At a molecular level, the curing process may lead to polymerization and crosslinking of the LOCA material. More specifically, upon exposure to UV light, the UV-activated photo-acid generator may generate photo-acids, which may cause the crosslinking of oligomers 950. Any thermal treatment may then produce further cross-linking of the adhesive components. The crosslinked oligomers 950 may form polymers 960. Polymers 960 may include a long chain of oligomers or polymers and thus may have a large molecular weight. As the chains grow, the LOCA layer may shrink. As shown in FIG. 9B, polymers 960 may include some sites 970 that are not fully reacted. Therefore, polymers 960 may continue to grow at sites 970, which may crosslink the chains and build bridges between the chains. The crosslinking process of siloxane epoxy-based LOCAs may lead to significant shrinkage that may build up internal stress within the LOCA layer, because it is difficult for the large molecules to rearrange and relax as the LOCA layer shrinks or contracts. The build-up of the internal stress may lead to deformation (e.g., bowing) of the bonded substrate stack as shown in FIG. 9A. If the internal stress is too high, delamination may occur during normal processing and/or reliability testing.

During the thermal curing, the LOCA material may continue to polymerize and crosslink to form larger molecules with long chains of atoms, and thus LOCA layer 920 may continue to shrink during the thermal curing. For example, polymers 960 may continue to grow at sites 970, which may crosslink the chains and build bridges between the chains to form larger molecules, and thus may cause further shrinkage of the LOCA layer. The large molecules may need a large amount of energy to rearrange and relax while the LOCA layer shrinks or contracts. Thus, the internal stress may continue to build up as the LOCA layer continues to crosslink and shrink. The more crosslinks between the chains, the harder it is for the large molecules to rearrange and fully relax in order to reduce the internal stress while the LOCA layer shrinks. Therefore, the internal stress of the LOCA layer and the bowing of the bonded substrate stack may increase during the thermal curing as shown in FIG. 9A. In cases where the two optical substrates may have different thermal expansion coefficients (CTEs), the bonded substrate stack may experience further deformation during the thermal curing of the LOCA material, due to the CTE mismatch and the heating/cooling of the bonded substrate stack, which may increase the bowing of the bonded substrate stack and even result in permeant deformation of the bonded substrate stack.

When at least one of the bonded optical substrates is used as an optical waveguide, the deformation of the substrate stack due to LOCA internal stress may lead to aberrations and other optical artifacts, such as chief ray angle shift, modulation transfer function degradation, lateral color aberration, pupil swim, text breaks, and double images, thereby degrading the optical performance of the waveguide display. When 6-inch wafers are used as the substrates and the bowing of the bonded substrate stack is above 20 μm, the optical performance of the waveguide display may not be acceptable.

FIG. 10A illustrates an example of a waveguide display 1000 including a waveguide layer 1030 having a wedge shape due to, for example, substrate bowing caused by bonding waveguide layer 1030 to a waveguide layer 1010 using a LOCA material (not shown in FIG. 10A). Waveguide layer 1010 may include one or more input gratings 1020 and 1022, and one or more output gratings 1024 and 1026 to form waveguide display 1000. In the example shown in FIG. 10A, a first light beam 1040 (e.g., having a longer wavelength or from a larger view angle) may be coupled into waveguide layer 1010 by input grating 1022 at a large angle with respect to a surface-normal direction of waveguide layer 1010. Therefore, first light beam 1040 may be reflected at the interface between waveguide layer 1010 and waveguide layer 1030 through total internal reflection, due to the large incidence angle and the difference between the refractive indices of waveguide layer 1010 and waveguide layer 1030. A second light beam 1042 (e.g., having a shorter wavelength and/or from a smaller view angle) may be coupled into waveguide layer 1010 by input grating 1022 and may propagate within waveguide layer 1010 at a smaller angle with respect to the surface-normal direction of waveguide layer 1010. Therefore, second light beam 1042 may not be reflected at the interface between waveguide layer 1010 and waveguide layer 1030 through total internal reflection, because the incidence angle may be smaller than the critical angle at the interface. Thus, second light beam 1042 may instead be refracted at the interface with a larger refraction angle into waveguide layer 1030, and may then be reflected at the top surface of waveguide layer 1030 through total internal reflection due to the increased incidence angle and the larger difference (e.g., about 0.5) between the refractive indices of waveguide layer 1030 and air. When waveguide layer 1030 has a low (e.g., close to zero) TTV or a small wedge angle (e.g., having an ideal flat top surface as shown by a plane 1034), second light beam 1042 may be reflected at plane 1034 as shown by a light ray 1043. Even though second light beam 1042 may have a smaller propagation angle with respect to the surface-normal direction of waveguide layer 1010 than first light beam 1040, second light beam may travel a longer distance in the z direction before being reflected through total internal reflection, and thus may travel a similar distance in the x direction as first light beam 1040 before being reflected through total internal reflection (e.g., as shown by light ray 1043). In this way, first light beam 1040 and second light beam 1042 may be diffracted by output grating 1024 or 1026 at about the same locations (or about the same interval) and for about the same number of times. The thicknesses and refractive indices of waveguide layer 1010 and waveguide layer 1030 may be selected based on the desired performance.

However, due to substrate bowing caused by curing the LOCA bonding layer using UV light and/or heat, waveguide layer 1030 may have a wedge shape (e.g., having a wedge angle larger than 1 arcsec). Because of the wedge shape, the incident angle of second light beam 1042 (after being refracted into waveguide layer 1030) incident on a top surface 1032 of waveguide layer 1030 and the incident angle of the guided light beam incident on the bottom surface of waveguide layer 1010 may gradually change (e.g., gradually decrease in the illustrated example). For example, due to the unevenness of waveguide layer 1030, second light beam 1042 may instead be reflected by top surface 1032 of waveguide layer 1030 to a direction as shown by a light ray 1045. As such, first light beam 1040 and second light beam 1042 may be coupled out of waveguide display 1000 (e.g., diffracted by output grating 1024 or 1026) at different locations. In addition, the distance between two adjacent reflection locations at top surface 1032 may gradually decrease. As such, the exit pupil may not be evenly replicated.

Since the incident angles of the light beam incident on different locations of output gratings 1024 and 1026 may be different, the diffraction angles of the light beam diffracted at different locations of output gratings 1024 and 1026 may also be different. As such, display light from a same FOV angle may be diffracted at different locations of the output gratings towards l different directions. As a results, optical artifacts such as double images may occur and the quality of the displayed images may be poor. In some cases, since the incident angle of second light beam 1042 incident on top surface 1032 and the incident angle of second light beam 1042 incident on the bottom surface of waveguide layer 1010 may gradually decrease as second light beam 1042 propagates in waveguide display 1000, at some locations, the incident angle of second light beam 1042 incident on top surface 1032 or the incident angle of second light beam 1042 incident on the bottom surface of waveguide layer 1010 may be smaller than the critical angle, and thus may no longer be guided in waveguide display 1000 through total internal reflection.

FIG. 10B illustrates an example of a layer stack 1005 formed by bonding two flat substrates 1050 and 1060 using a liquid optically clear adhesive. In the illustrated example, an output grating coupler 1062 may be formed on substrate 1060. A LOCA layer 1070 may be dispensed between substrate 1050 and substrate 1060. Substrates 1050 and 1060 may be pushed together by applying a pressure (e.g., mechanical pressure or vacuum pressure) to the bottom surface of substrate 1050 and/or the top surface of substrate 1060. The LOCA material in LOCA layer 1070 may be allowed to flow without the pressure or in response to the pressure. After applying the pressure for a certain period of time, the LOCA material may be cured using, for example, UV light and/or heat (e.g., exposed to UV light in a chamber or baked in an oven) as described above.

Due to substrate bowing caused by curing LOCA layer 1070 using UV light and/or heat, layer stack 1005 may have a wedge shape. The angle of the wedge may not be precisely controlled, and may be large, such as larger than about 1×10⁻⁴ rad. A light beam 1080 coupled into a waveguide formed by the bonded layer stack 1005 may need to propagate within the waveguide through total internal reflection. Each time the guided light beam reaches output grating coupler 1062, a portion 1082 of the guided light beam may be coupled out of the waveguide by output grating coupler 1062. Since layer stack 1005 may have a wedge shape, the incident angle of the guided light beam incident on the top surface of substrate 1060 and the incident angle of the guided light beam incident on the bottom surface of substrate 1050 may gradually change (e.g., gradually decrease in the illustrated example). For example, if the top surface of substrate 1060 is parallel to the bottom surface of substrate 1050, the guided light beam may be reflected by the top surface of substrate 1060 (e.g., through TIR) to a direction as shown by a light ray 1084. Due to the wedge shape of layer stack 1005, the guided light beam may instead be reflected by the top surface of substrate 1060 to a direction as shown by a light ray 1086. As such, the directions of the portions 1082 of the guided light beam coupled out of the waveguide at different locations may be different as shown in FIG. 10B. In addition, the distance between two adjacent reflection locations at the top surface of substrate 1060 may gradually decrease. As such, the exit pupil may not be evenly replicated.

Moreover, since the incident angle of the guided light beam incident on the top surface of substrate 1060 and the incident angle of the guided light beam incident on the bottom surface of substrate 1050 may gradually decrease as the guided light beam propagates in the waveguide, at some locations, the incident angle of the guided light beam incident on the top surface of substrate 1060 or the incident angle of the guided light beam incident on the bottom surface of substrate 1050 may be smaller than the critical angle, and thus may no longer be guided in the waveguide through total internal reflection. Instead, as shown by a light ray 1090, the guided light beam may be refracted out of the waveguide.

Therefore, the variation of the thickness of the waveguide for waveguide display may lead to aberrations and other optical artifacts, such as chief ray angle shift, modulation transfer function degradation, lateral color aberration, pupil swim, text breaks, and double images, thereby degrading the optical performance of the waveguide display. To achieve a better optical performance, the waveguide including two or more waveguide layers bonded together may need to be flat, for example, having a low TTV and a low surface roughness. For example, the two opposing external surfaces of a substrate stack including two substrates bonded together may need to maintain a high degree of parallelism, and the substrate stack may need to have a minimal total thickness variation (TTV) and bowing (e.g., with a very small wedge angle). Thus, it is desirable that the LOCA materials utilized in the process of bonding two optical substrates for waveguide display (e.g., siloxane epoxy-based LOCA with high refractive index and low optical absorption) do not build significant internal stress that may deform the bonded substrate stack via bowing, during the curing and crosslinking and upon thermal treatment.

According to certain embodiments, two optical substrates, where at least one of them may be used as an optical waveguide layer, can be bonded using a siloxane epoxy-based LOCA that also includes a reactive plasticizer, such as a siloxane additive of Structure 1: