Output diffraction grating, diffractive waveguide combiner, and augmented reality or virtual reality display

Abstract

Output diffraction gratings, diffractive waveguide combiners, and augmented reality or virtual reality displays are disclosed. An output diffraction grating includes a first array of optical structures arranged on a plane and forming a two-dimensional grid, the first array including first adjacent optical structures spaced apart from one another in each of a first direction and a second direction in the plane of the output diffraction grating such that they are not in contact with one another, and a second array of optical structures arranged on the plane and forming a second two-dimensional grid, the second array including second adjacent optical structures similarly spaced apart from one another such that they are not in contact with one another; the first array is superimposed on the second array such that the first and second arrays are spatially offset from one another in the first and second directions and are not in contact, and an optical structure from the second array is disposed between one of the first adjacent optical structures; each of the optical structures in the first array includes a different shape in the plane from each of the optical structures in the second array.

Description

[0001] This application is a divisional application of patent application No. 202180052980.8, entitled "Method for designing a diffraction grating for an augmented reality or virtual reality display and a diffraction grating for an augmented reality or virtual reality display", filed on September 1, 2021, with international application number PCT / EP2021 / 074093, and entered the Chinese national phase on February 27, 2023. Technical Field

[0002] This invention relates to a diffractive waveguide combiner for augmented reality or virtual reality displays. Specifically, one aspect of the invention relates to a waveguide in which light coupled into the waveguide is extended in two dimensions by diffractive optical elements and coupled out of the waveguide toward an observer. This can allow for pupil replication, eye-tracking range extension, and relay of projected images in augmented reality or virtual reality displays. Background Technology

[0003] Augmented reality displays provide users or observers with a view of their real-world environment combined with other images, such as those artificially generated by computerized display systems. Typically, the overlaid images provide information relevant to the real-world environment. For example, in transportation applications, overlaid images can provide navigation assistance or information about hazards. In medical applications, such as those in an operating room, overlaid images can provide real-time information about the patient, such as heart rate and blood oxygen levels, or provide supplementary data such as X-ray images or other medical scans to assist surgeons. In video game applications, overlaid images can include computer-generated characters or objects that can then interact with the real world, including the observer, in response to data collected from other sensors, such as cameras.

[0004] In some augmented reality display systems, the entire image presented to the observer is in the form of a computer-generated display output on a monitor or other visual display screen. In these systems, cameras are used to capture images of the real-world environment, these images are then combined with a computer-generated image, and the resulting combination is displayed to the observer using image processing software and hardware of the computerized display system. Suitable display systems are widely available and are typically found in personal computers, smartphones, tablets, and other devices that combine computing processing, image capture, and visual displays.

[0005] In other augmented reality display systems, the observer views the real world directly through transparent or semi-transparent optical devices (often called combiners). The combiner provides a means to overlay additional images onto this real-world view. These images are typically generated by a computerized display system connected to suitable image projection hardware, such as a microdisplay-based projector.

[0006] Providing observers with direct observation of the real-world environment, rather than through image capture and re-display, offers several advantages, such as: the field of view, resolution, and dynamic range of real-world observation far exceed the capabilities of any currently available artificial display hardware; eliminating the need to place a display screen in front of the observer allows for a smaller and more socially acceptable form factor for the display system; and real-world observation includes three-dimensional data and focus guidance known to be important for long-term wear and avoiding eye strain.

[0007] Augmented reality display systems that combine direct observation of the real-world environment with additionally generated images can be fixed to larger facilities such as the cockpit of an aircraft (in which case they are often called head-up displays (or HUDs)) or fixed to part of a portable device worn by the observer (in which case they are often called head-up displays (HMDs)).

[0008] A virtual reality display is a display in which the entire image seen by the observer is artificially generated. The combiner used in AR-HMDs can also be configured for virtual reality head-mounted displays (VR-HMDs) simply by suppressing the observation of the real world (e.g., by using an opaque black screen between the combiner and the real world, rather than between the combiner and the observer's eyes).

[0009] Several different methods exist for optically combining computer-generated images with a real-world view. One simple method is to make the combiner a partially reflective pane of glass and place it at an angle so that reflections from the glass allow the observer to see an image that would otherwise be outside their field of view. This is the method used in many automated prompting systems, where the tilted glass provides the observer with a view of the written text on the display screen reflected from the glass, as well as a direct view of the real world through the glass via light from the real world. Here, the reflected light from the display screen appears to be superimposed on the view of the real-world environment.

[0010] For augmented reality head-mounted displays (AR-HMDs), it is advantageous if the display is not too large or bulky for the user, especially if it is expected to be worn for extended periods. This requirement makes the use of simple, tilted, partially reflective screens impractical for any situation other than a small field of view with superimposed images.

[0011] US 4,711,512 describes an optical device that uses a diffraction grating and waveguide transmission of light to realize a combiner for an augmented reality display. In this method, the combiner comprises a planar waveguide made of a light-transmitting material such as suitable glass or plastic. The waveguide is placed in front of one (or both) of the user's eyes, and a projector is provided to one side of the waveguide and outside the user's direct field of view. Light from the projector is coupled into the waveguide by scattering from a diffraction grating on the surface of the waveguide in the region in front of the projector or embedded in the waveguide in the region in front of the projector. The diffraction grating is designed such that the scattered projected light will be totally internally reflected within the waveguide and is generally directed to the waveguide region in front of the user's eyes. The light is then coupled out of the waveguide by scattering from another diffraction grating, making it visible to the user. The projector can provide information and / or images that enhance the user's view of the real world.

[0012] The eye-tracking range (EMR) of an AR-HMD is a measure of the spatial area of ​​the projected image output from the display that can be viewed by the observer's eye. AR-HMDs are typically expected to have an EMR significantly larger than the size of the eye pupil (typically 2 mm to 8 mm) to allow for a degree of tolerance in the wearing position of the display system. Too small an EMR can result in a vanishing image if the observer's eye is not precisely in the correct position, leading to frustration and stress. For direct viewing of the projector, the size of the EMR is determined by the size and position of the projector's exit pupil and the eye's position relative to the projector. Increasing the EMR size requires reducing the projector's F-number, which not only complicates its design but also increases the weight and size of the entire system—neither of which is desirable if a compact form factor is desired. Diffractive waveguide combiners (DWCs)—which use diffraction gratings and waveguides to operate—offer an alternative method to increase the size of the display system's EMR.

[0013] In US 4,711,512, a diffraction grating (hereinafter referred to as the output grating) for outputting light propagating in a coupled waveguide is designed to couple only a portion of the energy of the beam incident upon it. Each time the beam interacts with the output grating, it splits into at least two beams—an output coupled beam exiting the waveguide and a beam continuing to propagate within the waveguide. The light propagating in the waveguide will interact with the output grating again after traveling the distance required for reflection from the waveguide surface, and may interact with the output grating multiple times, if size permits. In this way, a single input beam can be output multiple times. If it can be configured such that the size of the waveguide pupil is greater than or equal to the distance between successive interactions with the output grating, the total output from the beam, consisting of multiple overlapping beams, will, to some extent, synthesize into a much larger output beam. Therefore, the size of the output beam no longer depends solely on the size of the projector's exit pupil. This phenomenon is called pupil replication and can be used to output projected light over an extended spatial region, thus providing a larger range of eye movement than would otherwise be possible. In US4,711,512, multiple replications of the beam are possible only in the direction of propagation of the waveguide light from the input grating. This limits the extension of the eye-tracking range to only along that direction. Furthermore, beams corresponding to different points in the output field of view will extend in slightly different directions. This limits the size of the eye-tracking range that can be observed simultaneously across the entire projection field of view of the display system.

[0014] WO 2016 / 020643 discloses an optical device as part of a combiner for an augmented reality display, characterized by pupil replication and extended eye-tracking range in two dimensions. WO 2016 / 020643 provides input diffractive optical elements to couple light from a projector into waveguide propagation within a transparent planar substrate. The optical device includes an output element consisting of two diffractive optical elements stacked one on top of the other, such that each diffractive optical element can receive light from the input diffractive optical element and couple it toward the other diffractive optical element in the pair. These diffractive elements can scatter a portion of the incident light, allowing it to maintain waveguide propagation but change direction, and scatter a portion of the incident light according to the beam direction, allowing it to couple out of the waveguide where it can be observed. By combining the redirection of the beam in different directions and the coupling out of the waveguide, the diffractive elements provide pupil replication in more than one direction, thus providing an extension of the eye-tracking range in two dimensions.

[0015] In some embodiments of WO 2016 / 020643, two diffractive optical elements are arranged one on top of the other in a photonic crystal. This can be achieved by an array of pillars arranged in a plane within the waveguide, wherein the pillars have a different refractive index compared to the surrounding waveguide medium. Alternatively, the pillars can be configured as a surface relief structure arranged on one of the outer surfaces of the waveguide. In WO 2016 / 020643, the pillars are described as having a circular cross-sectional shape when viewed in the waveguide plane. This arrangement has been found to be very effective in simultaneously extending light in two dimensions and coupling light out of the waveguide. Compared to other diffractive combiners, the embodiments of WO 2016 / 02 / 0643 also provide more efficient use of space on the waveguide, which can reduce manufacturing costs.

[0016] WO 2018 / 178626 discloses an optical device characterized by an output element with an optical structure having a rhomboid cross-sectional shape. A modified rhomboid cross-sectional shape is also disclosed, wherein the modified rhomboid feature is a cut at two opposite vertices of the rhomboid profile. Compared to a circular structure, the optical structure with this modified rhomboid shape can exhibit a more balanced brightness along the central light band of the output element relative to the rest of the output element. This can reduce undesirable "stripe" effects that might otherwise appear in the output image, and thus improve the brightness uniformity of the output from the combiner.

[0017] In the photonic crystal embodiment of WO 2016 / 020643 and in WO 2018 / 178626, diffractive optical features are arranged in a two-dimensional periodic array with hexagonal symmetry. The vector sum of the two grating vectors associated with this array and the grating vector associated with the one-dimensional input diffraction element is zero. As disclosed in WO 2018 / 178626 and WO 2016 / 020643, this arrangement can provide two-dimensional pupil replication and eye-tracking range extension, as well as coupling light out of the waveguide toward the observer.

[0018] Although the modified rhombus structure in WO 2018 / 178626 is effective, it is prone to some drawbacks.

[0019] First, it is necessary to ensure that the modified rhombus is precisely sized, including features such as the dimensions of the cuts. Small deviations in shape from the intended design can lead to undesirable scattering properties. For example, variations in the rhombus shape can modify the relative proportions of light coupled in various directions, which can produce a bright central band in the observed image. This introduces challenging tolerances to the manufacturing processes that form these structures.

[0020] Second, the shape of the modified rhombus structure, with its narrow dimensional requirements, limits the extent to which the optical element can vary relative to its position. Instead of altering the structure to achieve optimal scattering characteristics for every location, the modified rhombus structure must be designed as a compromise of the desired characteristics across the entire optical element.

[0021] Third, the strict constraints on the shape of the modified rhomboid structure also limit the extent to which the structure can be optimized by considering other factors. For example, although the diffractive waveguide combiner is specifically designed and manufactured to receive the light carrying the image from the projector's input pupil, and then propagate this single input pupil across the output region of the device to produce an eye-tracking range that allows the user to perceive the image within a certain angular range while viewing through the waveguide, the same diffractive element can also cause undesirable diffraction of external ambient light (such as sunlight or electric lighting), potentially causing rainbow artifacts in the wearer's eye-tracking range. This is because, due to the dispersive nature of light scattered from the diffraction grating, the spectrally broad external light for a typical light source is split into its component colors. These rainbow artifacts may appear as iridescent stripes or bands that can appear throughout the user's field of view and thus negatively impact the user experience by distracting the user from viewing the intended projected image and / or the real world. Therefore, an improved waveguide is needed that is less prone to rainbow artifacts, at least in the central portion of the eye-tracking range region of the waveguide where the wearer is most likely to observe the projected image. For many use cases, minimizing such artifacts is desirable. However, if the optical structure has a strictly limited shape and size, the extent to which this can be achieved with that structure is limited.

[0022] Finally, the optical elements described in both WO 2018 / 178626 and WO 2016 / 020643 require a dimensional expansion of the output element such that the two-dimensional expansion can be spread diagonally to satisfy the designed eye-tracking range in a direction orthogonal to the direction from the input grating to the output grating. This increases the size of the device compared to the minimum size required for a given eye-tracking range.

[0023] The purpose of this invention is to overcome these problems and limitations. Summary of the Invention

[0024] As part of an AR-HMD system, a properly configured diffractive waveguide combiner can provide two functions: first, relaying and outputting an image from the projector so that it can be combined with a transmissive view of the real-world environment; and second, providing an extension of the eye-tracking range via pupil replication. Typically, in performing these functions, the combiner is expected to provide a high level of optical efficiency, meaning that as much light as possible projected onto the combiner is coupled out through the designed eye-tracking range. It is also expected that the combiner provides the user with high image fidelity for both the real-world view and the superimposed projected image, meaning good uniformity of brightness and color, high contrast, low haze, and high image sharpness across all relevant viewing angles. In some applications, it is equally important that the attenuation of the real-world view is low and artifacts such as iridescent scattering from strong light are minimized.

[0025] A diffractive waveguide combiner for use in an AR-HMD system may include: a material substrate for transmitting light through the waveguide; at least one region comprising a diffraction grating for coupling light into the combiner, the diffraction grating being referred to herein as an input grating; and at least one region comprising a diffraction grating for coupling light out of the combiner and towards one or more eyes of an observer, the diffraction grating being referred to herein as an output grating. The substrate may be made of a transparent optical material, preferably a material with low absorptivity and haze at visible wavelengths, such as optical glass or optical polymers. The output grating may at least provide the function of coupling light out of the waveguide, but it may also provide additional functions, such as pupil replication for eye-tracking range extension, as disclosed in the prior art discussed above. The input and output gratings are typically spatially distinct, allowing the projector to be positioned to point towards the input grating, and the observer to position themselves to observe the light coupled from the output grating and to observe the real world without interfering with the projector.

[0026] According to one aspect of the invention, a grating is provided as an output element of a diffractive waveguide combiner for an augmented reality or virtual reality display, comprising: a first rectangular periodic array of optical structures arranged in a plane, wherein the period of the first rectangular array is defined by the spacing between adjacent optical structures of the first rectangular array; a second rectangular periodic array of optical structures arranged in a plane, wherein the period of the second rectangular array is defined by the spacing between adjacent optical structures of the second rectangular array; wherein the first rectangular array of optical structures is superimposed on the second rectangular array of optical structures in the plane such that the arrays are spatially offset from each other in the plane; wherein the first array of optical structures and the second array of optical structures differ from each other in at least one characteristic, or the first array of optical structures is offset from the second array of optical structures by a factor different from half the period of the first rectangular array or the second rectangular array, such that the first array of optical structures and the second array of optical structures are configured to receive light from an input direction and couple various orders of light in a direction angular to the input direction, and couple various orders of light out toward an observer.

[0027] This type of grating can be referred to as an interlaced rectangular grating (IRG). The grating can have an array of optical structures arranged in a repeating pattern, wherein the optical structures of a first array overlap with those of a second array. The two arrays of optical structures are arranged such that the orientations of their rectangular patterns are the same. By superimposing the optical structures, the first array of optical structures is distributed in or on a plane around the optical structures of the second array of optical structures. In some embodiments, the array of optical structures may include an array of holes in a material layer on or within a substrate. For example, the optical structure may be an air-filled hole such that there is a refractive index difference between the air within the hole and the surrounding material, which may be on the substrate or may be the substrate forming the hole. In other embodiments, the array of optical structures may include a surface relief structure extending from the substrate surface and surrounded by air or a material with a different refractive index.

[0028] In the plane, a first direction, called the x-direction of the grating, and a second direction, called the y-direction of the grating, are defined. The first direction is arranged parallel to one of the sides of the first rectangular periodic array, and the second direction is arranged orthogonal to the first direction and parallel to one of the other sides of the first rectangular array. The z-direction of the grating can be defined as a direction perpendicular to the grating plane. In this way, the x-period can be defined as the interval between the nearest pairs (i.e., adjacent optical structures) of the optical structures of the first rectangular array as measured along the x-direction. The y-period is defined as the interval between the nearest pairs (i.e., adjacent optical structures) of the optical structures of the first rectangular array as measured along the y-direction. The second rectangular array has the same x-period and y-period as the first rectangular array, which are determined by the distances between the nearest pairs of optical structures of the second rectangular array as measured along the x-direction and y-direction, respectively.

[0029] The offset can be an x-offset, defined as the interval between a fixed point on one of the optical structures of the first rectangular array and a fixed point on one of the optical structures of the second rectangular array, as measured along the x-direction. Alternatively, the offset can be a y-offset, defined as the interval between a fixed point on one of the optical structures of the first rectangular array and a fixed point on one of the optical structures of the second rectangular array, as measured along the y-direction. Factors may include a first parameter describing the offset in the x-direction between the first and second rectangular arrays and / or a second parameter describing the offset in the y-direction between the first and second rectangular arrays. In this way, an offset different from half the period can be different from half the period in the x-direction and / or half the period in the y-direction.

[0030] Preferably, the offset is measured between the optical structures of the first array and the second array, which are closest to each other. For convenience, a fixed point can be chosen, but for simple optical structures, the fixed point will typically be the center of the structure as seen when the structure is observed in the grating plane.

[0031] Preferably, the first array and the second array of the optical structure are configured to receive light from the input direction and couple the various orders of light in a direction at an angle to the input direction to provide a two-dimensional extension of light, and couple the various orders of light out toward the observer.

[0032] Preferably, the first rectangular periodic array forms a first 2D grating with rectangular symmetry, and the second rectangular periodic array forms a second 2D grating with rectangular symmetry. The grating can have a physically feasible limited range. Therefore, the first and second rectangular periodic arrays can be truncated into regions or a set of different regions within the plane associated with the grating. Each of these regions can be described by a closed contour defining the shape in which the grating will exist, and note that although the spatial extent of the first and second periodic arrays can be nearly identical, the offset between the arrays requires that they cannot be truncated into exactly the same contour within the plane, but this can be done within one period in the x and y directions, and this will have a negligible effect on the light scattering characteristics of the grating.

[0033] A grating can be used as the output element of a waveguide. This can be a DWC for an AR or VR display. An IRG configured as the output element of a DWC will scatter incident light according to the diffraction principle derived from the periodic structure. Specifically, this means that the incident monochromatic beam will be scattered in various directions, as described by the diffraction order derived from the periodicity of the IRG.

[0034] A diffraction order that changes the direction of light without coupling it out of the waveguide is called a steering order, while a diffraction order that couples light out of the waveguide is called an entrance order. As described in WO 2016 / 020642, the steering order and the entrance order together can provide pupil replication, eye movement range extension, and output coupling. For devices operating on these principles to function well, it is important that these diffraction orders are balanced in intensity relative to each other and relative to the direction, wavelength, and polarization of the incident beam.

[0035] By offsetting a first array of optical structures from a second array of optical structures by a factor different from half the period of either the first or second rectangular array, and by ensuring that the second array of structures is otherwise identical to the first array in terms of its IRG, the presence of an eye-level order can be ensured. The directional properties and magnitude of these eye-level orders will depend on the degree to which the offset differs from half the period. Specifically, the presence of an eye-level order can be ensured when the x-offset differs from half the x-period and / or the y-offset differs from half the y-period, wherein the directional properties and magnitude of the eye-level order will depend on the degree to which the x-offset differs from half the x-period and / or the y-offset differs from half the y-period. In this way, the scattering characteristics of such an IRG used as an output element can be varied as needed.

[0036] By using an optical structure with a first periodic rectangular array through an IRG with at least one characteristic different from that of the optical structure with a second periodic rectangular array, the presence of an entrance order can also be ensured.

[0037] The steering order of the IRG can also depend on the shape and material composition of the optical structures of the first and second periodic rectangular arrays, as well as the offset between these arrays.

[0038] If the optical structures of the first and second periodic rectangular arrays are identical, and the x-offset and y-offset are equal to half the x-period and y-period, respectively, this ensures that there is no entrance-eye order and only the steering order is allowed. Therefore, by utilizing how various steering and entrance-eye orders depend on the shape of the optical structures, the differences in x-offset and y-offset, and the differences in characteristics between the optical structures of the first and second arrays, the scattering characteristics of the IRG used as the output element of the DWC can be varied as needed. Specifically, the steering order can be used to distribute light in two dimensions across the cross-rectangular grating, thus providing pupil replication to extend the provided eye movement range, while the entrance-eye order is used to output coupled light towards the observer, allowing the projected image to be seen by the appropriate input coupled into the DWC.

[0039] The optical structures of the first array have a different shape in the plane than those of the optical structures in the second array, and the optical structures can differ from each other in at least one characteristic. An eye-level can be achieved by giving the optical structures of the first or second array a different shape than those of the other array. This is possible even if the x-offset and y-offset are equal to half the x-period and y-period, respectively. The shape can be a cross-sectional shape in the plane. For example, the optical structure in the first array can have a circular cross-section, while the optical structure in the second array can have a rectangular cross-section. Alternatively, the optical structure in the first array can have a circular cross-section, while the optical structure in the second array can consist of multiple elements with triangular cross-sections. Any shape and any combination of shapes can be conceived, as long as they are different between the arrays. This means that shapes such as circles, squares, rectangles, triangles, or any other conceivable shape can be used, and the number of elements constituting the optical structure in each array can be one, two, or more.

[0040] Alternatively or additionally, the optical structures of the first and second arrays may differ from each other in at least one inherent optical property, including refractive index, permittivity, permeability, absorptivity, and / or birefringence. In this way, the optical structure of the first array may be composed of materials having refractive index, permittivity, permeability, absorptivity, and / or birefringence different from those of the second array. The optical structures of the two arrays may be composed of a variety of different materials. As long as the spatial distribution of the refractive index, permittivity, permeability, absorptivity, and / or birefringence of these materials is different from that of the first array compared to the second array, an entrance-to-eye order with non-zero scattering intensity may exist.

[0041] Alternatively or additionally, the optical structures of the first array may have different dimensions in the plane than the optical structures in the second array, and the optical structures may differ from each other in at least one characteristic. When viewed in the plane, the dimensions may be the dimensions of the cross-section of the optical structure. For example, the dimensions of the optical structures in the first array may be smaller than those in the second array.

[0042] Alternatively or additionally, the optical structures of the first array may have a different orientation in the plane than the optical structures of the second array, and the optical structures may differ from each other in at least one characteristic. For example, the optical structures of the first array may be oriented at an angle in the plane relative to the optical structures of the second array. They may be oriented at an angle of 30°, 45°, or 90° relative to each other. Alternatively, they may be oriented at any other angle relative to each other. In some arrangements, the optical structures of the first array may be a mirror image of the optical structures of the second array.

[0043] In other arrangements, besides or instead of the above, the optical structures of the first array may differ from those of the optical structures in the second array in at least one characteristic because the optical structures of the first array have a different height or physical extent in a direction perpendicular to the plane. The optical structures have a three-dimensional profile. The height is perpendicular to the cross-sectional area as described above. This may be in the z-direction. For example, the optical structures of the first array may extend by a greater amount in a direction orthogonal to the plane compared to the optical structures of the second array, and vice versa.

[0044] In some arrangements, different physical extents may include optical structures in the first array having different blazes than those in the second array. For example, at least one of the optical structures in the first and / or second arrays may have a height or physical extent that varies along the plane in a direction perpendicular to the plane. In this way, a blazed grating can be formed. In some arrangements, this may apply only to the optical structures of the first array. In other arrangements, it can be applied to the optical structures of both arrays, as long as there is a difference in the height variation between the two optical structures in each array, or due to different properties as described herein. This allows for further control over directional scattering characteristics. The height variation may be along a single axis of the plane, or along multiple axes of the plane.

[0045] The aforementioned different characteristics between the first rectangular array and the second rectangular array can be selected to achieve control over the diffraction order of light scattered from the output grating of the diffraction waveguide combiner composed of such staggered rectangular gratings.

[0046] In some arrangements, the second array of the optical structure may be offset from the first array of the optical structure by a distance different from half the x-period in the x-direction, and may be offset from the first array of the optical structure by a distance equal to half the y-period in the y-direction. Alternatively, the second array of the optical structure may be offset from the first array of the optical structure by a distance different from half the y-period in the y-direction, and may be offset from the first array of the optical structure by a distance equal to half the x-period in the x-direction. In another variation, the second array of the optical structure may be offset from the first array of the optical structure by a distance different from half the x-period in the x-direction, and may be offset from the first array of the optical structure by a distance different from half the y-period in the y-direction. In this way, the offset different from half the period may be in the x-direction, the y-direction, or both directions.

[0047] It has been found that shifting by a factor different from half the period in only a single axis direction produces a symmetric steering order about a plane perpendicular to the shifted direction. If the sign of the diffraction order is flipped and the direction of the light is mirrored relative to the plane of symmetry, the symmetric steering order is a steering order with identical scattering properties. Furthermore, shifting by a factor different from half the period in both directions reveals even greater directional differences between steering orders. This provides flexibility in adjusting the output element to vary the intensity of a particular steering order.

[0048] It has been found that if the optical structures of the first and second arrays are identical, there will be no entry-level diffraction in the y-direction when the x-offset is zero and the y-offset is equal to half the period. The entry-level diffraction in the x-direction may still exist. The diffraction orders permissible only in the y-direction are the zeroth order and the diffraction order that redirects the beam back in the y-direction. If this arrangement is to be used at the edge of an IRG configured as the output element of a DWC, it can be used to capture light that would otherwise escape toward the edge of the DWC and redirect the light back toward the inner region of the IRG, where it can then be output toward the observer. This recycling of light that would otherwise be lost can be used to increase the optical efficiency of the IRG.

[0049] Similarly, it has been found that when the y-offset is zero and the x-offset is equal to half the period, there will be no entry-level order in the x-direction. The entry-level order in the y-direction may still exist. The diffraction orders permissible only in the x-direction are the zeroth order and the diffraction order that redirects the beam back in the x-direction. This redirection order can be used to redirect light back towards the inner region of the IRG, where it can then be output towards the observer. By selectively configuring the IRG at its edges with regions that provide light redirection in either the x or y directions, depending on which is advantageous according to the dominant direction of light in a particular part of the IRG, the optical efficiency of light output from the waveguide can be increased.

[0050] The period of the optical structure in the first array is constant across the plane, while the period of the optical structure in the second array is also constant across the plane. This means that the optical structures of both arrays have long-range periodicity across the waveguide in both the x and y directions.

[0051] In some arrangements, the optical structures of the first and / or second arrays can form a continuous structure. In this way, the optical structures of the first array do not have to be distinct entities, but can be combined to form a continuous structure or a series of continuous structures. The same may be true for the optical structure of the second array. Conceptually, there is no difference between a hybrid optical structure with the periodicity of a rectangular array and a rectangular array consisting of discrete structures repeated at each node of the array and having a shape such that they are adjacent to each other when repeated.

[0052] Interlaced rectangular gratings can also be created by combining a first array of optical structures and a second array of optical structures using methods other than superposition. If the first and second arrays of optical structures can each be represented as arrays of surface relief structures of the same material, and the surface relief structures have a height that varies with position, such as when measured relative to a reference plane, then the interlaced rectangular grating can be created in various ways as a surface relief structure with a certain height at a given position in the plane, the height of which depends on the height of the optical structures of the first and second arrays at that position. Possible values ​​for the resulting height at a given position on the reference plane of an interlaced rectangular grating with such a surface relief structure include, but are not limited to:

[0053] The sum of the heights of the optical structures of the first and second arrays at their positions in the reference plane;

[0054] The average height of the optical structures of the first and second arrays at positions in the reference plane;

[0055] The maximum height of the optical structures of the first and second arrays at positions in the reference plane;

[0056] The minimum height of the optical structures of the first and second arrays at a position in the reference plane;

[0057] The height of the optical structure of the first array at a position in the reference plane, unless it is zero, where the height will be the height of the optical structure of the second array;

[0058] The height of the optical structure of the second array at a position in the reference plane, unless it is zero, where the height will be the height of the optical structure of the second array; or

[0059] The difference in height between the optical structures of the first array and the optical structures of the second array at a position in the reference plane, and in the case that the difference can be the height of the first array minus the height of the second array, or the absolute value of the difference between the height of the first array and the height of the second array.

[0060] It should be noted that any x-offset and / or y-offset between the first and second arrays of the optical structure will be applied to the relevant array of the optical structure before they are combined.

[0061] Alternatively, if both the first and second arrays of the optical structure are arrays of shapes that can be represented using a three-dimensional geometric description (e.g., a mesh surface, a collection of geometric primitives such as cuboids, cylinders, ellipsoids, and tetrahedrons, or others), then an interlaced rectangular grating can be created using a representation that is the result of an application of geometric union, geometric intersection, or geometric difference operations between the first and second arrays of the optical structure. Again, it should be noted that any x-offsets and / or y-offsets between the first and second arrays of the optical structure will be applied to the relevant arrays of the optical structure before they are combined.

[0062] Alternatively, if both the first and second arrays of the optical structure are represented as arrays of three-dimensional volume functions or three-dimensional voxels describing the optical properties relative to the positional structure, then staggered rectangular gratings can be created using a representation based on a volume function or voxel description, wherein the optical properties described by a function or voxel at a given position in three-dimensional space depend on a mathematical relation relating to the optical properties of the corresponding volume functions or three-dimensional voxels representing the optical structure at that position. Using this method, possible values ​​for the optical properties of the staggered rectangular grating at a given position include, but are not limited to:

[0063] The sum of the values ​​of the corresponding optical properties of the optical structures of the first and second arrays at the location;

[0064] The average value of the corresponding optical properties of the optical structures of the first and second arrays at the location;

[0065] The maximum value of the corresponding optical properties of the optical structures of the first and second arrays at the location;

[0066] The minimum value of the corresponding optical property of the optical structure of the first and second arrays at the position;

[0067] The value of the corresponding optical property of the optical structure of the first array at the location, unless they are the values ​​of the corresponding optical properties of the vacuum, in which case the value of the corresponding optical property will be the value of the corresponding optical property of the optical structure of the second array;

[0068] The values ​​of the corresponding optical properties of the optical structure of the second array at the location, unless they are the values ​​of the corresponding optical properties of a vacuum, in which case the values ​​of the corresponding optical properties will be the values ​​of the corresponding optical properties of the optical structure of the first array; or

[0069] The difference in the value of the corresponding optical properties of the optical structure of the first array at position compared with the optical structure of the second array at position, and, where the difference can be calculated by subtracting the value of the first array from the value of the second array, or the absolute value of the difference between the values ​​of the two arrays.

[0070] Similarly, it should be noted that any x-offset and / or y-offset between the first and second arrays of the optical structure will be applied to the relevant array of the optical structure before they are combined.

[0071] Interlaced rectangular gratings, generated by combining two arrays of optical structures, can be modified by applying one or more layers of coating to the surface of the structure. Each layer of the coating can have optical properties different from the other layers in the coating and / or the optical structure on top of which the coating is applied. Interlaced rectangular gratings with multi-layer structures can also be created for multi-layer optical structures and multi-layer coatings formed on top of each other.

[0072] In some embodiments, the characteristics of the optical structure of the first array of diffraction grating optical structures can be spatially varied across a plane. Alternatively or additionally, the characteristics of the optical structure of the second array of diffraction grating optical structures can be spatially varied across a plane. Such variation of a single optical structure can be the size of the structure in the grating plane, the height of the structure perpendicular to the grating plane, the orientation of the structure, and / or any shimmering shape applied to the structure. Alternatively, the variation of the structure can be a more complex shape variation, or even involve dividing the individual structures of one or both in the array into multiple individual elements. Advantageously, this allows for variations in the scattering characteristics of the grating at different locations to suit the requirements of those locations. For example, outside the central region of the grating, increasing the diffraction efficiency of a non-zero diffraction order to increase the brightness and uniformity of light from such regions may be advantageous.

[0073] Alternatively or additionally, the diffraction grating varies spatially across the plane by measuring the characteristic differences between the first and second arrays of the optical structure, or by measuring the cross-plane variation of the offset between the first and second arrays of the optical structure by a factor different from half the period. Advantageously, this allows the output from different regions of the waveguide to vary. This means that the scattering characteristics across the output element can be varied as needed. For example, the shape, orientation, height, height variation, or any other characteristic differences or combinations of characteristic differences between the optical structures of the first and second arrays can vary across the plane. For example, the first and second arrays of the optical structure may have similar characteristics to each other in one region of the plane, while having more pronounced differences in different regions of the plane. This variation in the measurement of difference can be gradual. For example, the optical structure of the first and / or second arrays may gradually change in a transition region from having a first shape, orientation, height, or height variation in the first region of the plane to having a second shape, orientation, height, or height variation in the second region of the plane. In this way, the optical structure of the first and / or second arrays can gradually transition from having a first shape, orientation, height, or height variation in the first region of the plane to having a second shape, orientation, height, or height variation in the second region of the plane. This can be achieved through geometry morphing (also known as geometric metamorphosis or mesh morphing), which smoothly transforms the shape of one 3D object into the shape of another 3D object by applying warping and other distortion transformations. Advantageously, this prevents abrupt changes between grating regions that could affect scattering.

[0074] In other arrangements, this change across the plane may not be gradual. For example, there may be: a region in which the first and second arrays of optical structures each have a first shape, orientation, height, or height variation; and a second adjacent region in which the first and second arrays of optical structures each have a second shape, orientation, height, or height variation.

[0075] Alternatively or additionally, the factors that deviate from each other in the first and second arrays can vary across the plane, and can be in the x-direction, y-direction, or both directions of the plane. In some regions of the plane, the factors can be almost equal to or exactly equal to half of the x-period and y-period in the x-direction and y-direction, respectively, where the factors vary across the plane such that the factors deviate from half of the period.

[0076] A grating can be composed of multiple sub-regions by varying the first and second optical structures across the grating, and / or varying the differences between them. Each sub-region can have a specific arrangement of optical structures such that each sub-region has diffraction characteristics tailored to the needs of that particular location on the grating. For example, as described above, a sub-region at the edge of the grating can be arranged to capture light that would otherwise escape toward the edge of the DWC and send the light back toward the IRG closure region of the DWC, where the light can then be output toward the observer. In some arrangements, the transition between sub-regions may be abrupt. In other arrangements, the transition may be smooth, such that there is a gradual change in optical structure between the sub-regions.

[0077] In some arrangements, the grating may include a first array or a second array of optical structures providing a region where light diffraction is negligible. In such an arrangement, another of the first or second array of optical structures forms a rectangular grating. Alternatively or additionally, the grating may include a region where adjacent optical structures in the first and / or second arrays of optical structures form a continuous structure, thereby forming a one-dimensional grating in said region. This may be a one-dimensional horizontal grating for providing an entrance-to-the-eye level, a one-dimensional horizontal grating for providing a rotational level, a one-dimensional vertical grating for providing an entrance-to-the-eye level, a one-dimensional vertical grating for providing a rotational level, and / or a one-dimensional diagonal grating for providing a turning level.

[0078] In other arrangements, an interlaced rectangular grating can be provided, comprising a region where the optical structures of the first and second arrays are identical, and the positional offset between the first and second arrays is equal to half the x-period in the x-direction and zero in the y-direction. In this way, such a region of the interlaced rectangular grating will provide an entrance step for the beam propagating primarily in the y-direction within the DWC, and a turning step that will tend to turn back for the beam propagating in the x-direction. Alternatively, an interlaced rectangular grating can be provided, comprising a region where the optical structures of the first and second arrays are identical, and the positional offset between the first and second arrays is equal to half the y-period in the y-direction and zero in the x-direction. In this way, such a region of the interlaced rectangular grating will provide an entrance step for the beam propagating primarily in the x-direction within the DWC, and a turning step that will tend to turn back for the beam propagating in the y-direction.

[0079] The first and second arrays of optical structures can differ from each other in at least one characteristic, and the first array of optical structures is offset from the second array of optical structures by a factor different from half the period of either the first or second rectangular array on at least one axis in the plane. This axis can be in the x-direction or the y-direction. This factor can be a distance different from half the x-period and / or half the y-period. Further control over the scattering characteristics can be achieved by controlling both the different characteristics between the first and second arrays of optical structures and the positional offset between the first and second optical arrays.

[0080] In some spatially varying IRGs, the diffraction grating can be spatially varied across a plane by the optical structures of the first and second arrays having dimensions in a plane that gradually decreases toward the edge of the diffraction grating, or by a gradually decreasing height in a direction perpendicular to the plane. In some arrangements, the dimensions of the optical structures of the first and / or second arrays can vary across the plane. In some cases, the dimensions of the optical structures can decrease across the plane. This can be in the x-direction and / or y-direction. This can be the cross-sectional dimensions and / or height of the optical structures. In such arrangements, the dimensions of the optical structures can decrease toward the edge of the optical elements. Advantageously, this can reduce the scattering intensity of the optical structures toward the edges. This can have the effect of reducing the visibility of the edges of the grating region on the waveguide as seen by an external observer. Preferably, this reduction in dimensions is consistent between the first and second arrays. This ensures reduction of any undesirable scattering effects, such as unusually strong scattering orders. Alternatively, the optical structures can be modified such that their cross-sectional dimensions are increased, thus merging them with their nearest optical structures. By increasing the size of the cross-section to fill any gaps in the structure, the intensity of undesirable scattering effects can also be reduced, thereby reducing the visibility of the edges of the grating region to an external observer.

[0081] In some arrangements, a first array of optical structures can be arranged on a first grating, and a second array of optical structures can be arranged on a second grating. As described above, the first and second gratings can be superimposed and offset from each other. In some arrangements, both the first and second gratings can be displaced from their intended positions in some regions. This displacement can be in the x-direction, the y-direction, or both the x- and y-directions. Preferably, this displacement will be the same for both gratings. This displacement can consist of discrete steps on different regions of the grating, or it can be continuous in manner. This displacement can be described by a first position correlation function and a second position correlation function, the first position correlation function providing the position displacement value of the first and second gratings in the x-direction, and the second position correlation function providing the position offset value of the first and second gratings in the y-direction. In some arrangements—where the grating comprises multiple different sub-regions (i.e., spatially varying IRGs)—the different position displacements of the first and second gratings can be associated with each sub-region. Introducing position displacements into the first and second gratings will provide a phase shift for any beam of light with a non-zero diffraction order scattered from the grating. Here, the magnitude of the phase shift at a given position depends on the magnitude of the grating position shift in each of the x and y directions at that position, as well as the x and y periods of the grating and the diffraction order in the case of interaction. In this way, the position- and diffraction-order-related phase shifts can be incorporated into the grating.

[0082] As a result of this arrangement, the total phase of a given beam propagating through the DWC can depend on the path taken by the beam, including the phase shift caused by the interaction between the beam and the grating, as well as the distance the beam propagates. Advantageously, the use of the phase shift caused by the positional displacement of the first and second gratings can provide phase compensation for the phase variations of the individual diffraction orders of the IRG due to spatial variations in the IRG. Another possible advantage is that the additional phase shift depending on the path taken through the DWC can reduce the effects of multi-beam interference from the combination of split beams, which could otherwise negatively impact the uniformity of the output from the DWC.

[0083] Instead of shifting the position of the grating associated with the optical structure, another method to introduce a position- and diffraction-order-related phase shift is to apply distortion in the grating plane. Appropriate distortion can apply the shift to the position of the optical structure, as well as slightly perturb the shape of the structure. The shift of the grating structure position can occur in any direction within the grating plane. Generally, the distortion can vary with the position across the grating plane, such that the positional shift of the structure caused by the distortion varies over a wide range of directions. Preferably, the magnitude of the distortion can be small, such that the change in the structural positional shift between adjacent unit cells of the grating is a fraction of the period of the unperturbed grating. Preferably, for a shift along the x-direction, this change between adjacent unit cells can be less than 0.1% of the x-period, and for a shift along the y-direction, it can be less than 0.1% of the y-period. As long as the perturbation to the structure shape is small, the effect on diffraction efficiency will also be small. In this case, the main effect of the distortion will be to introduce a phase shift for any beam with a non-zero diffraction order scattered from the grating. Here, the magnitude of the phase shift at a given position depends on the magnitude of the positional shift in each of the x and y directions at that position, as well as the x and y periods of the grating and the diffraction order of their interaction. In this way, the position- and diffraction-order-related phase shifts can be incorporated into the grating. Advantageously, the use of the phase shift caused by grating distortion can be used to provide phase compensation for the individual diffraction orders of the IRG due to spatial variations in the IRG, or the phase shift can be used to mitigate multi-beam interference effects that might otherwise affect the uniformity of the output from the DWC.

[0084] Alternatively, the waveguide thickness can be varied in a direction perpendicular to the waveguide plane. This variation can be small. It can be achieved by the thickness of the waveguide substrate, the thickness of the base layer beneath the grating, or by having an additional layer with varying thicknesses. This layer can preferably be a transparent resin. Small variations in thickness can be used to introduce path-dependent phase shifts in the various beams propagating through the DWC. This additional phase difference between different beams, depending on their paths, can help reduce the impact of multi-beam interference effects on the uniformity of the output from the DWC.

[0085] According to another aspect, a diffractive waveguide combiner for an augmented reality or virtual reality display is provided, comprising a waveguide that is a substrate configured to transmit light, wherein an output grating, which is the diffractive grating described above, is arranged in or on the waveguide; and an input grating for coupling light toward the output grating into the waveguide.

[0086] The substrate can be planar. The waveguide can be a planar flat waveguide. The grating can be placed in or on the waveguide. For example, it can be placed on one of the outer surfaces of the flat plate. Alternatively, it can be placed inside the flat plate, provided that the refractive index of the grating's optical structure is different from that of the flat plate. The plane of the waveguide can be the same as the plane on which the first rectangular array and the second rectangular array are arranged.

[0087] The waveguide may include: a planar plate of transparent optical material, surrounded by a medium with a refractive index lower than that of the planar plate, such that light arranged at a sufficiently large angle of incidence will be confined within the plate in a direction perpendicular to the plane of the plate by total internal reflection. Preferably, the plane of the plate is parallel to the plane of the grating.

[0088] It is not necessary to cover the entire spatial range of the flat panel. However, in some arrangements, the grating may need to cover the entire spatial range of the flat panel, so that the flat panel has a limited spatial range of at least the grating size.

[0089] The grating is configured to receive light from an input direction and scatter diffraction patterns of light in directions at various predetermined angles relative to the input direction, including those toward one or more eyes of an observer. In this way, it serves as the output element of a waveguide combiner. Preferably, the waveguide includes an input diffraction optics element configured to couple light into the waveguide and provide light to a first and a second array of optical structures in the input direction. The input diffraction optics element may be a one-dimensional diffraction grating comprising grooves in a surface of the waveguide, wherein the orientation of the grooves matches the x-direction or y-direction of an interlaced rectangular grating. The input grating may be an input grating as described in WO 2016 / 020643.

[0090] Preferably, the input grating is highly efficient for coupling light into the waveguide. One way to achieve this is by making the structure of the diffraction grating blaze, such that light is preferentially guided to the staggered rectangular grating and has a grating vector parallel to the x or y direction of the IRG.

[0091] In some arrangements, it may be advantageous for the first or second array of an IRG to consist of zero structures that do not produce any physical geometry.

[0092] An array of optical structures within a waveguide can be referred to as a one-dimensional or two-dimensional photonic crystal. The waveguide can be housed within an optical display. This optical display can be a VR or AR device. This may include VR or AR headsets, head-mounted displays, or head-up displays.

[0093] Preferably, a projector is provided to project light toward the input diffractive optical element. The projector may be multicolored and oriented such that the optical axis of the projector is located outside the waveguide plane.

[0094] As described above, optical structures can be arranged in substantially the same plane within a waveguide. This can be achieved by placing the structure on one of the outer surfaces of the waveguide and creating a surface relief structure on the grating. Alternatively, these structures can be embedded within the waveguide as variations in refractive index, permittivity, permeability, absorptivity, and / or birefringence. Both of these are examples of one-dimensional or two-dimensional photonic crystals, depending on whether the structure is periodic in one or two dimensions.

[0095] In some arrangements, the input grating can also be an interlaced rectangular grating. In this configuration, the entrance-to-eye step is equivalent to the input coupling step, and preferably, the IRG will be designed such that these steps provide effective coupling of light to the waveguide within the combiner.

[0096] In other arrangements, the waveguide may include a single grating according to the aspects described above, which serves as both an input grating and an output grating. In other words, a single interlaced rectangular grating can be used both to receive input light from the projector and to couple light outwards towards the observer. Preferably, in this arrangement, the offset between the optical structures and / or the rectangular array will vary relative to their positions in the IRG plane to provide effective coupling of light from the projector in the input region and effective pupil replication and output of light in the output region, which refers to the area that guides light into the observer's eye movement range.

[0097] According to another aspect, a method for manufacturing a diffraction grating for an augmented reality or virtual reality display is provided, comprising the steps of: providing a plurality of optical structures; arranging the plurality of optical structures as described above.

[0098] According to another aspect of the invention, a grating is provided for use in a diffractive waveguide combiner (DWC) for augmented reality or virtual reality displays, comprising: a first rectangular periodic array of optical structures arranged in a plane, wherein the period of the first rectangular array is defined by the spacing between adjacent optical structures of the first rectangular array; a second rectangular periodic array of optical structures arranged in a plane, wherein the period of the second rectangular array is defined by the spacing between adjacent optical structures of the second rectangular array; wherein the first rectangular array of optical structures is superimposed on the second rectangular array of optical structures in the plane such that the arrays are spatially offset from each other in the plane; wherein the first array of optical structures and the second array of optical structures are identical, and the first array of optical structures is offset from the second array of optical structures by a factor equal to half the period of either the first or second rectangular array, such that the first array of optical structures and the second array of optical structures are configured to receive light from an input direction and couple different orders of light in a direction angular to the input direction. This can be considered a perfectly symmetrical staggered rectangular grating. Alternatively, the staggered rectangular grating according to the above aspect can be configured to include a region corresponding to such an arrangement.

[0099] This type of diffractive element may not preferentially couple light outwards towards the observer. Instead, it preferentially presents only the steering step, which means that the entrance-to-eye step is suppressed. This type of diffractive element can be used to provide a spatial distribution across the waveguide. This type of diffractive element can be combined with diffractive output elements as described above to achieve outward coupling. Alternatively, this type of diffractive element can be combined near or adjacent to the diffractive output elements of a single 2D rectangular array with optical structures, or near or adjacent to another IRG, which is appropriately configured to also provide an entrance-to-eye step so that light can be coupled outwards towards the observer.

[0100] In other arrangements, a waveguide comprising multiple output gratings may be provided, each of which may be an IRG according to the various arrangements described above. The multiple output gratings may at least partially overlap in the waveguide plane and be offset from each other in a direction perpendicular to the waveguide plane. In some arrangements, the periods of the first and second rectangular arrays of each of the multiple output gratings are identical. The planes of these IRGs may be parallel to each other. The individual IRGs may be located on opposite surfaces of the waveguide or embedded within the waveguide. The planes of the IRGs may be offset by a distance much longer than the wavelength of light. In some arrangements, preferably, the spacing between these different IRGs is longer than the coherence length of the light from the projector.

[0101] In some arrangements, when projected onto a plane parallel to the IRG plane, the areas covered by the IRG can overlap at least to some extent. The x-periods of the IRGs can be identical to each other. Similarly, the y-periods of the IRGs can be identical to each other. Other aspects of the IRGs, such as the shape and composition of various optical structures and the offset between the first and second arrays of the IRGs, can differ. Each IRG can vary spatially according to the methods and arrangements described above. Using multiple IRGs can provide increased control over light scattering within the waveguide. For example, one grating can be configured to preferentially provide steering order scattering, while another grating can be configured to preferentially provide eye-level scattering, or a specific eye-level scattering.

[0102] According to another aspect, an augmented reality or virtual reality display may be provided, which includes a diffractive waveguide combiner according to any of the above aspects.

[0103] According to another aspect, a diffraction grating is provided as an output element of a diffraction waveguide combiner for an augmented reality or virtual reality display, comprising: a first rectangular periodic array of optical structures arranged in a plane, wherein the period of the first rectangular array is defined by the spacing between adjacent optical structures of the first rectangular array; a second rectangular periodic array of optical structures arranged in a plane, wherein the period of the second rectangular array is defined by the spacing between adjacent optical structures of the second rectangular array; wherein the first rectangular array of optical structures is superimposed on the second rectangular array of optical structures in the plane such that the arrays are spatially offset from each other in the plane; wherein the first array of optical structures and the second array of optical structures differ from each other in at least one characteristic, or the first array of optical structures is offset from the second array of optical structures by a factor other than half the period of the first rectangular array or the second rectangular array, such that the first array of optical structures and the second array of optical structures are configured to receive light from an input direction and couple various orders of light in a direction angular to the input direction, and couple various orders of light out toward an observer.

[0104] Preferably, since the optical structure of the first array has a different shape in the plane than the optical structure in the second array, the optical structures are different from each other in at least one characteristic.

[0105] Preferably, since the optical structures of the first array have different dimensions in the plane than the optical structures in the second array, the optical structures are different from each other in at least one characteristic.

[0106] Preferably, since the optical structures of the first array have a different orientation in the plane than the optical structures in the second array, the optical structures are different from each other in at least one characteristic.

[0107] Preferably, since the optical structures of the first array have a different physical range or height in a direction perpendicular to the plane than the optical structures in the second array, the optical structures are different from each other in at least one characteristic.

[0108] Preferably, the different physical ranges include the optical structure of the first array having a different scintillation than the optical structure in the second array.

[0109] Preferably, the optical structures of the first array are different from each other in at least one of the following: refractive index, permittivity, permeability, absorptivity or birefringence, since the optical structure of the first array has a different refractive index, permittivity, permeability, absorptivity or birefringence than the optical structure of the second array.

[0110] Preferably, the first array of optical structures and the second array of optical structures are different from each other in at least one characteristic, and the first array of optical structures is offset from the second array of optical structures on at least one axis of the plane by a factor different from half the period of the first rectangular array or the second rectangular array.

[0111] Preferably, the optical characteristics of the first array of the diffraction grating's optical structure vary spatially across the plane.

[0112] Preferably, the diffraction grating varies spatially across the plane by measuring the differences in the characteristics of the cross-plane variation.

[0113] Preferably, the measure of the cross-plane variation of a factor that is different from half of the period.

[0114] Preferably, the grating varies spatially across the plane along a first axis and / or a second axis orthogonal to the first axis, such that the grating includes at least one region in which the first array of optical structures and the second array of optical structures are not different from each other in at least one characteristic, and in this region:

[0115] The first array of the optical structure is offset from the second array of the optical structure along both the first and second axes by a factor equal to half the period of the first and second rectangular arrays; and / or

[0116] The first array of the optical structure is offset from the second array of the optical structure on the first axis by a factor equal to half the period of the first rectangular array and the second rectangular array, and is not offset from the second array of the optical structure on the second axis; and / or

[0117] The first array of the optical structure is offset from the second array of the optical structure on the second axis by a factor equal to half the period of the first rectangular array and the second rectangular array, and is not offset from the second array of the optical structure on the first axis.

[0118] Preferably, the diffraction grating varies spatially across the plane to form a region of the grating, in which a first array of optical structures or a second array of optical structures provides negligible diffraction of light.

[0119] Preferably, the diffraction grating is spatially varied across a plane by the following regions having gratings, which include adjacent optical structures in a first array and / or a second array of optical structures forming a continuous structure, thereby forming a one-dimensional grating in said regions.

[0120] Preferably, the diffraction grating varies spatially across the plane by means of the optical structures of the first array and the optical structures of the second array having dimensions in a plane that gradually decreases toward the edge of the diffraction grating or heights that gradually decrease in a direction perpendicular to the plane.

[0121] Preferably, the diffraction grating varies spatially across the plane to form multiple regions, each region having a different measure of characteristic difference or a measure of a factor different from half the period.

[0122] Preferably, each of the multiple regions has a boundary between the other multiple regions that undergo spatial changes.

[0123] Preferably, the transition zone between the optical structures of multiple different regions is gentle.

[0124] Preferably, the transition zone between the first region and the second region includes the optical structure in the first region in the form of an optical structure that smoothly transitions into the second region.

[0125] Preferably, a first array of optical structures is arranged on a first grating, and a second array of optical structures is arranged on a second grating, wherein the gratings all undergo spatially correlated shifts across the plane of the grating in one or more regions, thereby providing phase changes to compensate for grating variations or reduce multi-beam interference effects.

[0126] Preferably, the diffraction grating comprises one or more layers of coating applied to the top of a surface relief structure forming the optical structure. Preferably, one or more layers of coating can be applied in an orientation such that the thickness of the coating depends on the surface normal direction of the optical structure. Preferably, the orientation of each layer in the coating does not need to be the same. Preferably, one or more layers of coating can be applied such that the coating thickness on the optical structure is uniform, regardless of the orientation of the structure.

[0127] Preferably, the diffraction grating is composed of multiple layers and / or materials forming the optical structure.

[0128] According to another aspect, a diffractive waveguide combiner for an augmented reality or virtual reality display is provided, comprising a waveguide that is a substrate configured to transmit light, wherein an output grating, which is a diffractive grating according to the foregoing aspect, is arranged in or on the waveguide; and an input grating for coupling light toward the output grating into the waveguide.

[0129] Preferably, the waveguide includes a plurality of output gratings according to the above aspects, wherein the plurality of output gratings at least partially overlap in the waveguide plane and are offset from each other in a direction perpendicular to the waveguide plane.

[0130] Preferably, the optical structures of the multiple output gratings are arranged differently from each other. By having different optical structure arrangements among the multiple output gratings (e.g., different offsets or different characteristics between the first and second arrays), each of the multiple output gratings can be customized to have different diffraction characteristics. In some arrangements, the optical structure arrangement of the first multiple output gratings can be such that the first multiple output gratings primarily provide two-dimensional expansion of light, while the optical structure arrangement of the second multiple output gratings can be such that the second multiple output gratings primarily couple out different orders of light toward the observer.

[0131] Preferably, the waveguide includes a plurality of output gratings according to the above aspects, wherein the periods of the first rectangular array and the second rectangular array of each of the plurality of output gratings are the same.

[0132] Preferably, the waveguide includes a plurality of output gratings according to the above aspects, each output grating having an associated input grating forming a grating pair, wherein each grating pair is configured to interact with light in a specific wavelength range.

[0133] Preferably, the output grating is a diffraction grating with spatial variation according to the above aspects, and wherein the input grating is formed by the region of the output grating.

[0134] Preferably, the output diffractive waveguide combiner includes multiple waveguides arranged on top of each other to form a composite stack of waveguides.

[0135] Preferably, the waveguide comprises multiple waveguides that are adjacent to each other.

[0136] Preferably, a first array of optical structures is arranged on a first grating, and a second array of optical structures is arranged on a second grating, wherein the gratings undergo spatially correlated shifts across the plane of the grating in one or more regions, thereby providing phase changes to compensate for grating variations or reduce multi-beam interference effects. Both gratings are shifted in the x-direction and / or y-direction by independent position-correlated parameters that vary spatially across the grating. In this way, beams scattered from the grating with non-zero diffraction orders will acquire a phase shift, which depends on the degree of grating shift at the interacting locations. This phase shift can be used to compensate for grating variations or reduce multi-beam interference effects. Alternatively, the grating may be distorted in the grating plane, including shifts in the position of the optical structures of the grating, thereby providing phase changes to compensate for grating variations or reduce multi-beam interference effects. Distortion in the grating plane may cause a small shift in the position of the optical structures of the grating. In this way, a beam scattered from a grating with a non-zero diffraction order will acquire a phase shift, which depends on the displacement of the position of the optical structure as a result of distortion. This phase shift can be used to compensate for grating variations or reduce multi-beam interference effects.

[0137] Preferably, the waveguide has a thickness that varies across the waveguide plane in a direction perpendicular to the waveguide plane, thereby enabling phase changes of light to compensate for grating variations or reduce multi-beam interference effects.

[0138] Preferably, the output grating is a surface relief grating including a base layer, which has a thickness varying across the waveguide plane in a direction perpendicular to the waveguide plane, thereby enabling phase changes of light to compensate for grating variations or reduce multi-beam interference effects.

[0139] Preferably, the output grating and / or the input grating are formed by a surface relief structure on the waveguide or an embedded structure in the waveguide.

[0140] Preferably, the optical structure of the output grating consists of multiple different elements located at different positions perpendicular to the waveguide plane.

[0141] Preferably, the output grating consists of a layer within the waveguide that has varying optical properties relative to the surrounding waveguide.

[0142] According to another aspect, an augmented reality or virtual reality display is provided, which includes a diffractive waveguide combiner according to the above aspects.

[0143] According to another aspect, a method for manufacturing a diffraction grating for an augmented reality or virtual reality display is provided, comprising the steps of: providing a plurality of optical structures; arranging the plurality of optical structures as described in the above aspects.

[0144] According to another aspect, an output diffraction grating of a diffraction waveguide combiner includes: a first array of optical structures arranged on a plane to form a two-dimensional grating, the first array of optical structures including first adjacent optical structures, the first adjacent optical structures being spaced apart from each other in each of a first direction and a second direction different from the first direction in the plane of the output diffraction grating, such that the first adjacent optical structures do not contact each other; and a second array of optical structures arranged on the plane to form a second two-dimensional grating, the second array of optical structures including second adjacent optical structures, the second adjacent optical structures being spaced apart from each other in each of the first direction and the second direction, such that the second adjacent optical structures do not contact each other. The first array of the optical structures is superimposed on the second array of the optical structures in the plane, such that the first array and the second array of the optical structures are spatially offset from each other in the first and second directions in the plane and do not contact each other, and the optical structures from the second array of the optical structures are disposed in the plane of the output diffraction grating between one of the first adjacent optical structures of the first array; each optical structure in the first array of the optical structures includes a first shape in the plane of the output diffraction grating, and each optical structure in the second array of the optical structures includes a second shape in the plane that is different from the first shape. Attached Figure Description

[0145] Embodiments of the invention will now be described by way of example only, with reference to the accompanying drawings, in which:

[0146] Figures 1a to 1e It is a series of diagrams illustrating the relationship between point grids, structures, and periodic structure arrays, as well as the identification of possible unit cells in a periodic structure array.

[0147] Figure 2 It is a top view of a one-dimensional diffraction grating;

[0148] Figures 3a to 3c Perspective views of portions of various one-dimensional diffraction gratings with different shapes but the same grating vector are shown;

[0149] Figures 3d to 3f It shows Figures 3a to 3c The cross-sectional view of the unit cell of the diffraction grating shown in the figure on the xz plane;

[0150] Figures 4a to 4f A series of top views of diffraction gratings are shown, demonstrating how a two-dimensional grating can be constructed from the overlap of two one-dimensional gratings, thus producing a two-dimensional grid, as well as examples of different two-dimensional gratings with the same underlying grid.

[0151] Figures 5a to 5b A simplified representation of a projector used in augmented reality or virtual reality display systems is shown;

[0152] Figure 6 A prior art head-up display system utilizing a diffractive waveguide combiner is shown;

[0153] Figure 7 It is a top view of a prior art optical device for extending an input beam in two orthogonal directions;

[0154] Figure 8a The grating vectors used to construct a two-dimensional diffraction grating with a rectangular grid are shown;

[0155] Figure 8b A top view of a portion of a two-dimensional diffraction grating with a rectangular grid is shown;

[0156] Figure 9a This is a perspective view of a diffractive waveguide combiner including an output grating according to one aspect of the present invention;

[0157] Figure 9b Is with Figure 9a Top view of the same diffractive waveguide combiner;

[0158] Figures 9c to 9f This is a perspective view of a diffractive waveguide combiner showing an example path of a beam through a waveguide;

[0159] Figure 10 This illustrates the generation of multiple output beams from a single input beam. Figure 9a Cross-sectional view of the diffractive waveguide combiner;

[0160] Figure 11 A top view of a portion of an interlaced rectangular grating according to one aspect of the invention is shown;

[0161] Figures 12a to 12b A top view of a portion of a fully symmetrical interlaced rectangular grating according to one aspect of the invention is shown;

[0162] Figures 12c to 12d The identifier for the alternative grating vector is shown in the grid of a perfectly symmetrical staggered rectangular grating;

[0163] Figures 12e to 12f A top view showing the outline of an example optical structure used in an embodiment of the present invention;

[0164] Figure 12g It shows the use of Figures 12e to 12f The structure shown is a top view of a portion of an interlaced rectangular grating according to one aspect of the invention;

[0165] Figures 12h to 12i A top view showing the outline of an example multi-element optical structure used in embodiments of the present invention is shown;

[0166] Figure 12j It shows the use of Figures 12h to 12i The structure shown is a top view of a portion of an interlaced rectangular grating according to one aspect of the invention;

[0167] Figure 13a A top view of a portion of an interlaced rectangular grating with a specific arrangement in the x-direction is shown;

[0168] Figure 13b A top view of a portion of an interlaced rectangular grating with a specific arrangement in the y-direction is shown;

[0169] Figure 14a A replica of the pupil of a diffractive waveguide combiner using a two-dimensional output grating with existing technology is shown.

[0170] Figure 14b A replica of the pupil of a diffractive waveguide combiner using a two-dimensional output grating according to an aspect of the present invention is shown;

[0171] Figure 15a A top view of a portion of an interlaced rectangular grating with various structures longer than the unit cell of the grating is shown;

[0172] Figure 15b The unit cell of a periodic structure is shown, consisting of individual structures longer than the unit cell.

[0173] Figure 15c A single structure of overlapping adjacent regions is shown, with the adjacent regions having the same size and shape as the cell element;

[0174] Figure 15d A top view of an interlaced rectangular grating is shown, which has a structure that connects to form a continuous periodic feature;

[0175] Figure 15e The unit cell is shown as a structure that will be connected to form a continuous periodic feature;

[0176] Figures 16a to 16c A perspective view showing the method of geometric construction of the grating structure;

[0177] Figure 16d A cross-sectional view of a surface relief grating structure embedded within a medium is shown;

[0178] Figure 17a A perspective view showing the structural modification with a highly correlated tilt introduced into the structure is shown;

[0179] Figure 17bThe perspective view shows structural modifications made by adding various types of slopes to the sidewalls of the structure.

[0180] Figure 17c A perspective view showing a structural modification that introduces shimmering to the top surface of the structure is shown;

[0181] Figure 17d A perspective view showing structural modifications that round off the corners and / or edges of the structure is shown;

[0182] Figure 17e A top view shows a structural modification that rounds the cross-sectional profile of the structure when viewed in the plane of the structure to which the grating is associated.

[0183] Figure 17f A perspective view showing the structural modification of introducing undercutting into the structure is shown;

[0184] Figure 17g A perspective view showing the structural modification that produces a structural reversal is shown;

[0185] Figure 17h A perspective view showing a structural modification with additional small structures placed on the structural surface is shown;

[0186] Figure 17i A top view shows an intermediate shape applied to two structures with different shape profiles;

[0187] Figures 18a to 18d Various methods for adding coatings to interlaced rectangular gratings are shown;

[0188] Figures 19a to 19b A cross-sectional view of an example of a multilayer grating structure is shown;

[0189] Figures 20a to 20j Various methods for creating differences between periodic structures are shown;

[0190] Figure 21a This is a perspective view of a diffractive waveguide assembly featuring an interlaced rectangular grating, according to one aspect of the invention;

[0191] Figure 21b Is with Figure 21a Top view of the same diffractive waveguide combiner;

[0192] Figure 22a A cross-sectional view of the configuration of the present invention using multiple diffractive waveguide combiners is shown;

[0193] Figures 22b to 22c A top view shows another configuration of the invention using multiple diffractive waveguide combiners;

[0194] Figure 23This is a top view of a unit cell of an interlaced rectangular grating according to the present invention, wherein one optical structure array may have a different shape compared to another optical structure array;

[0195] Figure 24 It shows the basis Figure 23 The diagram shows a series of unit cell configurations with general definitions, and a graph illustrating how the diffraction efficiencies of the two steering orders and the entrance order vary depending on parameters controlling the shape of one side of the structure constituting the staggered rectangular grating.

[0196] Figure 25 It shows the basis Figure 23 The diagram shows a series of unit cell configurations with general definitions, and a graph illustrating how the diffraction efficiencies of the two steering orders and the entrance order vary depending on parameters controlling the shape of one side of the structure constituting the staggered rectangular grating.

[0197] Figure 26 A series of heatmaps are shown, illustrating the variation of diffraction efficiency for various diffraction orders with respect to parameters controlling the shape of one of the structures constituting the staggered rectangular grating;

[0198] Figure 27 This is a top view of a unit cell of an interlaced rectangular grating according to the invention, showing the displacement of one optical structure array relative to another;

[0199] Figures 28a to 28c It is a series of unit cell configurations, and shows the application of a system based on... Figure 27 The graph shows how the diffraction efficiency of two steering orders varies with the incident angle for multiple staggered rectangular gratings of a generally defined unit cell.

[0200] Figures 29a to 29c It is a series of unit cell configurations, and a graph showing how the diffraction efficiency of two steering orders varies with the incident angle for multiple staggered rectangular gratings with unit cells based on the same square structure array, wherein there are different shifts between these structures.

[0201] Figure 30 It is a series of graphs corresponding to the examples of the present invention, showing how the diffraction efficiency changes with the vertical shift of one optical structure array relative to another optical structure array relative to the staggered rectangular grating;

[0202] Figure 31 It is a series of graphs corresponding to the examples of the present invention, showing how the diffraction efficiency changes with the horizontal shift of one optical structure array relative to another optical structure array relative to the staggered rectangular grating;

[0203] Figure 32 These are a series of heatmaps corresponding to examples of the present invention, showing the variation of diffraction efficiency of various diffraction orders with respect to the parameters controlling the shift of one optical structure array relative to another optical structure array.

[0204] Figures 33a to 33d It is a series of unit cell configurations and a heatmap showing the simulated brightness output from a diffractive waveguide combiner having output elements composed of staggered rectangular gratings, characterized by various shifts between the array of structures in the y-direction;

[0205] Figures 34a to 34d It is a series of unit cell configurations and a heatmap showing the simulated results of the brightness output from a diffractive waveguide combiner having output elements composed of staggered rectangular gratings, characterized by various shifts between the array of structures in the x-direction;

[0206] Figure 35a A top view of another configuration of the unit cell according to the invention is shown;

[0207] Figure 35b It shows the basis according to Figure 35a A perspective view of a portion of an interlaced rectangular grating of a periodic unit cell array;

[0208] Figure 36 The diagram illustrates the diffraction efficiency of various diffraction orders relative to control. Figure 35a A series of heatmaps showing the changes in the parameters of the shape of the optical elements in the image;

[0209] Figure 37 It shows Figure 35b The periodic structure shown and composed of Figure 35a The diagram shows a periodic structure formed by unit cells, followed by a perspective view of the structure in reverse modification.

[0210] Figure 38 The diagram illustrates the diffraction efficiency of various diffraction orders relative to control. Figure 35a A series of heatmaps showing the shape of the optical elements in the structure, followed by changes in the parameters of the structural inversion modification;

[0211] Figures 39a to 39b A diffractive waveguide combination of multiple optical elements is shown as a feature according to various aspects of the invention;

[0212] Figures 40a to 40h Examples of various types of spatial variations of optical elements according to various aspects of the present invention are shown;

[0213] Figure 41This is a top view of a diffractive waveguide combiner with spatially varying output grating elements, as described in various aspects of the present invention.

[0214] Figure 42 The top view of the diffractive waveguide combiner according to various aspects of the invention features a spatially variable grating element that allows it to be used for both input and output coupling of light.

[0215] Figure 43 An interpolation scheme applicable to this invention is shown;

[0216] Figure 44 A top view is shown of the geometric deformation method applied to the present invention;

[0217] Figure 45 This is a table showing several qualitatively different behaviors of a DWC with a suitable grating period of and , based on the 2D accumulation order and the beam associated.

[0218] Figure 46 This is a table of various diffraction orders between the cumulative order values, which may be particularly important for DWC operations; and

[0219] Figure 47 This is a table summarizing the key characteristics of an ideal diffractive waveguide combiner. Detailed Implementation

[0220] It is generally accepted that spatial periodic structure arrays (objects with translational symmetry) can be decomposed into discrete point arrays, called grids, with the same structure placed at each point of the discrete point array. Figure 1a A portion of a two-dimensional infinite grid 101 with points having rectangular symmetry is shown. Figure 1b A single square structure 102 is shown. Figure 1c The diagram shows the result of applying the same copy of structure 102 at each point in grid 101 to create a periodic rectangular structure array 103. The unit cell is part of the periodic array, and the complete periodic structure is reconstructed by repeating it by placing copies of themselves adjacent to each other with translational symmetry of the grid. The simple unit cell is the smallest part of the periodic structure array required to reconstruct the array. The simple unit cell is not unique and can be chosen for convenience. Figure 1d A grid 103 is shown with one possible unit cell 104 and another possible unit cell 105. The unit cell 104 is defined with an angle coinciding with the center of a 2×2 optical structure array, and the unit cell 105 is defined with a center coinciding with the center of one of the optical structures. When repeated at each grid point, both 103 and 104 will produce the same rectangular periodic array. For clarity, in Figure 1e These unit cells are shown again in the image.

[0221] It is well known that systems with optical properties that vary in a spatially periodic manner, such as an array of periodic surface relief structures created between media with different refractive indices, or an array of periodic structures with one refractive index encapsulated in media with different refractive indices, will scatter incident light in directions determined by the direction and wavelength of the light, as well as the periodicity and orientation of the grating associated with the periodic structure array. The scattering intensity in different directions depends on the composition and shape of the varying optical properties, as well as the wavelength, direction, and polarization of the incident light.

[0222] When a periodic structure is arranged in a plane and used to scatter waves such as electromagnetic waves, it is usually called a diffraction grating. A structure that is periodic only in one direction is usually called a one-dimensional diffraction grating or 1D grating, while a structure that is periodic in two dimensions is usually called a two-dimensional grating or 2D grating. Other terms are also used for periodic light-scattering structures, such as photonic crystals of various dimensions. Layered periodic structures are also possible, and when used to scatter electromagnetic waves, they are named after the physicist Sir Lawrence Bragg and, depending on the dimension of the periodicity, are usually called 1D Bragg gratings, 2D Bragg gratings, or 3D Bragg gratings.

[0223] A diffractive waveguide combiner (DWC) is an optical device that uses diffraction gratings to perform functions that can facilitate augmented reality (AR) or virtual reality (VR) display systems. When used as part of such a display system, the DWC receives light from an artificial source, such as a computer-controlled image-based display system like a microprojector, and then outputs that light again from different locations within the combiner, allowing the light to be received by an observer or other detection system. In augmented reality display systems, the DWC can also provide a transmissive view of the surrounding physical world. The intended result is that the image from the artificial source will be perceived by the viewer as superimposed on the field of view of the surrounding physical world, thus providing an augmented reality display experience. This specification will use the term "real-world light" to refer to light from the surrounding physical world as seen through transmissive viewing via the DWC, and the term "projected light" to refer to light from the artificial source received by the DWC and superimposed on the field of view of the surrounding physical world.

[0224] The present invention relates to a novel configuration of a two-dimensional grating having characteristics and features suitable for use as an output element in a diffractive waveguide combiner (DWC).

[0225] Electromagnetic waves and k-space

[0226] In principle, any electromagnetic radiation field can be decomposed into a superposition of monochromatic plane waves. In a linear isotropic homogeneous medium with refractive index n, the electric field of a given plane wave can be expressed as a function of position r and time t, such as...

[0227] (1)

[0228] in, It is a constant vector describing the amplitude and polarization of a plane wave. It is the wave vector. It is the angular frequency of the wave. = ,as well as This refers to the complex conjugate of the first part of the expression, such that... These are only real values ​​(this term is usually omitted for simplicity). The wave vector and angular frequency are related to the speed of light via the dispersion relation. Related

[0229] (2)

[0230] wave vector length = By the following comparison with the wavelength of light in a vacuum The refractive index of the material in which the wave vector propagates. Related

[0231] , (3)

[0232] in

[0233] (4)

[0234] It should be noted that for most materials, the refractive index It depends on the wavelength in a vacuum, but for clarity this is not explicitly shown throughout the instruction manual.

[0235] Using Descartes for position A coordinate system allows us to express positional components as row vectors.

[0236] (5)

[0237] A Cartesian coordinate system can also be defined for wave vectors, whose basis vectors are parallel to the Cartesian coordinates of physical space. The basis vectors of the coordinate system are parallel. This vector space is called the k-space, and the components of the wave vector can be written as row vectors.

[0238] (6)

[0239] If we define spherical angle and To describe wave vectors The direction, among which, describe The angle between the z-direction and the Cartesian coordinate system, and Describe the projection onto the xy plane The polar angle can then be used to write the wave vector as...

[0240] (7)

[0241] Without loss of generality, but for considerable convenience, a plane of spatial periodic structure can be defined as being considered a three-dimensional Cartesian structure. The xy-plane of the coordinate system. Unless otherwise stated elsewhere in this specification, it will be assumed that the planes of any spatially periodic structures arranged in a plane are parallel to such an xy-plane, which may be a globally applied coordinate system or a locally defined coordinate system for such convenience. Also... Defined as a two-dimensional subspace of k-space parallel to the xy-plane. subvectors (and therefore) (plane), which gives

[0242] (8)

[0243] The wave vector subvector in this two-dimensional subspace is called the xy wave vector, and the associated subspace of the k-space is called the kxy space. In many cases, the interaction of light with a grating will occur in a medium such as a glass waveguide, and the light will undergo refraction to couple into that medium. Such refraction can be calculated using Snell's law. Alternatively, it can be noted that, due to the boundary conditions at the smooth interface between different media and the absence of any features such as a diffraction grating, the components of the wave vector in the local plane tangent to the interface remain unchanged during refraction. Therefore, if the interface between the media is in Cartesian... In the xy plane of the coordinate system, as is the case in most of this paper, the xy wave vector will remain unchanged during refraction, which can help clarify the analysis and make it easier to present optical phenomena in the work.

[0244] Any structure realized in the physical world is not truly infinite in extent, meaning that translational symmetry does not extend beyond the edges of a finite periodic array. This invention relates to spatial periodic arrays, which, while not infinite in extent, consist of a large number of unit cells, numbering at least in the millions. The invention also relates to the propagation of beams within a spatial extent smaller than a grating. Thus, by considering an infinite periodic array, and where appropriate, taking into account deviations due to finite size effects, the treatment of beam scattering as it leaves the grating is well approximated.

[0245] Waveguide coupling via a one-dimensional diffraction grating

[0246] The accepted principle of optics is that light will scatter from a periodic structure in space along directions characterized by vector equations, which involve the wave vector components of the light and vectors derived from the grating associated with the periodic structure. These vectors are called grating vectors. If the grating is arranged in a plane, then this equation will only involve sub-vectors within the plane of the grating.

[0247] Figure 2 A top view of a one-dimensional diffraction grating 201 arranged in the xy plane is shown. The grating consists of rows with the same characteristics, also referred to as grooves, spaced apart by a distance... Separate, the distance is the period of the grating. In Figure 2 In the diagram, the grating grooves are represented by a series of lines. These grooves are oriented such that a line drawn orthogonal to the grooves and also in the xy-plane forms an angle with the x-axis. This can be achieved by using a series of Dirac delta functions. To mathematically describe the lines of a grating.

[0248] , (9)

[0249] Among them, Called with Figure 2 The diagram shows the grating function associated with the 1D diffraction grating. Such a function can be used in the mathematical processing of the interaction between light and the grating structure, for example, through recognized methods and principles of Fourier optics. The grating vector associated with grating 201 is also shown. Defined as a vector within the grating plane, its direction is orthogonal to the grooves of the grating and is given by the following formula:

[0250] (10)

[0251] It is noted that It is a two-dimensional vector in kxy space, which is the result of arranging the grating plane parallel to the xy plane of the coordinate system.

[0252] The diffraction of a monochromatic plane wave from such a grating will produce a diffracted plane wave beam with an xy wave vector given by the 1D grating equation.

[0253] , (11)

[0254] Or, in terms of the row vectors of the scalar components,

[0255] , (12)

[0256] in, This is a parameter describing the diffraction order of the interaction and can be zero, a positive integer, or a negative integer. Here, It has different components. and The xy wave vector of the incident plane wave, given the x-direction component and the y-direction component; Is and by The diffraction order is characterized by the xy wave vectors of the scattered wave corresponding to it, and has respectively been determined by... and The x-direction components and y-direction components are given; and It is associated with 1D diffraction gratings. A two-dimensional grating vector in a plane. The interaction of light with a grating characterized by a non-zero diffraction order can be called diffraction interaction. A beam of light generated by the interaction with a grating whose diffraction order is non-zero can be called a beam that has undergone diffraction interaction.

[0257] If a plane-wave beam (also called a collimated beam) undergoes successive interactions with a given 1D diffraction grating, then each interaction will obey the 1D grating equations. In such a case, after any number of interactions with the same grating, the xy-wave vector of the beam will... The following relationship must exist:

[0258] , (13)

[0259] in, It is the xy wave vector of the original beam before it first interacts with the grating, and It is an integer formed by the sum of all diffraction orders of the previous interactions, and the sum of all diffraction orders is here called the beam with grating vector. The cumulative order of grating interactions. For example, if the beam undergoes N interactions with the same diffraction grating, and If is the diffraction order of the i-th interaction, then It is given by the following formula:

[0260] (14)

[0261] generally, The value can be zero, positive, or negative. (and) The beam corresponding to a specific value must obey the same dispersion relation as the incident light, and therefore the amplitude of the full three-dimensional wave vector of the scattered light will be given by the following equation:

[0262] , (15)

[0263] in, It is the refractive index of the medium in which the beam propagates. Here, It is the wavelength of a wave in a vacuum. It is the frequency of the wave, and These are the speeds of light in a vacuum, and they remain constant for a given monochromatic beam of light. By paying attention to the definition of the scalar components of the diffracted wave vector, it can be correlated with the Cartesian components of the wave vector.

[0264] , (16)

[0265] And extend the expression for the amplitude of the wave vector.

[0266] , (17)

[0267] The above expression can be rearranged to solve the problem and provide the solution.

[0268] , (18)

[0269] And therefore

[0270] (19)

[0271] The z-component of the incident beam has the same sign. The values ​​of are called the transmission diffraction order, while those values ​​where the sign of the z-component of the wave vector changes are called the reflection diffraction order. The zero or complex value of corresponds to the following solution, where

[0272] (20)

[0273] It also describes beams that do not propagate freely away from the grating. Such beams are called evanescent orders to indicate the corresponding evanescent electromagnetic waves. Without additional structures interacting with them, such as another layer of optical structure, these orders will not transmit energy. For a grating placed at the interface between two media with different refractive indices, the transmission order... The value can differ from the reflection order. Therefore, for both transmission and reflection diffraction orders, different ranges of orders can be non-evanescent.

[0274] For incident on and with refractive index At the interface of the medium parallel to the xy plane, the refractive index is... For light propagating in a medium, the beam will undergo total internal reflection (TIR), requiring a refractive index of [insert value here]. The beam in the medium is evanescent. This is given by the following equation:

[0275] . (twenty one)

[0276] Therefore, for a refractive index of [missing information] arranged on a surface parallel to the xy plane, Systems composed of planar waveguides and systems with a refractive index of A collimated beam propagating in the surrounding medium can be used to identify three regions in k-space based on the beam's xy wave vector:

[0277] 1. Free propagation region in k-space—The wave vector in this region of k-space represents a beam that can propagate freely in both the planar waveguide and the surrounding medium. The wave vector in the free propagation region of k-space satisfies the inequality...

[0278] . (twenty two)

[0279] 2. Waveguide Propagation Region in k-Space—The wave vector in this region of k-space represents a beam of light that can propagate freely within the planar waveguide but not freely within the surrounding medium, and therefore such a beam in the waveguide will undergo total internal reflection from the interface with the surrounding medium, which is parallel to the xy plane and in which the xy wave vector remains unchanged. The wave vector in the waveguide region of k-space satisfies the inequality...

[0280] . (twenty three)

[0281] 3. The evanescent region in k-space—The wave vector in this region of k-space represents a beam that is evanescent in both the waveguide and the surrounding medium. Without certain modifications to the system, it is impossible for such a beam to propagate or transmit energy. The wave vector in the evanescent region of k-space satisfies the inequality...

[0282] . (twenty four)

[0283] The ability to switch the beam between the free propagation region and the waveguide propagation region in k-space using a diffraction grating while taking into account the constraints imposed by the evanescent region is key to the DWC function.

[0284] By using a refractive index with parallel planar sides A material plate can confine a light beam in a direction orthogonal to the planar surface of the waveguide, while allowing the light to propagate within the waveguide. This confinement can be used to allow the light beam to be transmitted (i.e., relayed) from one location to another within a thin device: light leaving the projector will satisfy the conditions of the free propagation region and thus propagate freely through the medium between the projector and the waveguide, typically air; a diffraction grating with appropriate period and orientation on the planar waveguide can be used to diffract the light from the projector, such that it satisfies the waveguide propagation conditions and is confined within the planar plate by TIR; at a separate location from the first diffraction grating, a second diffraction grating with the same period and orientation as the first diffraction grating can be used to diffract some or all of the light beam out of the waveguide region and into the free propagation region of k-space, where the beam can then leave the waveguide, for example, towards the observer's eye.

[0285] The second grating can have a different period and orientation than the first grating. In this case, the same inequality applies to the region controlling the k-space. In this scenario, the xy-wave vectors, based on the initial wave vector and the grating vector interacting with the beam, will acquire additional terms due to the different grating vectors of the second grating, thus producing…

[0286] (25)

[0287] Here, It is the grating vector of the second grating, and It is the cumulative order of interaction with the grating.

[0288] The spatial repeating features of a 1D diffraction grating are often referred to as grooves. These grooves can be complex in shape and can even be made of multiple materials. Figure 3a , Figure 3b and Figure 3c A perspective view of a portion of three different 1D diffraction gratings is shown, all of which lie in the xy plane and have a direction pointing to the x-axis. The same grating vector and the same grating period (=0) However, they have different surface relief structures in the z-direction. In order to form a complete three-dimensional relief structure, each of these sections is extruded in the y-direction to form a one-dimensional array of grooves.

[0289] Figure 3a A perspective view of a grating 301 with a two-tiered surface relief structure is shown. A cross-sectional view of the unit cell 304 of this grating is shown in... Figure 3d It is shown separately and consists of a single protrusion from the surface.

[0290] Figure 3b A perspective view of a cross-section of a grating 302 with a serrated surface relief structure is shown, wherein the grating relief is composed of inclined ramps along the grating vector direction. Such a grating structure is also called a blazed structure. A cross-sectional view of the unit cell 305 of this grating is shown in... Figure 3e It is shown separately and consists of a single peak with a different tilted surface on each side.

[0291] Figure 3c A perspective view of a grating 303 with a multi-element, multi-level relief structure is shown. A cross-sectional view of the unit grating 306 is also shown. Figure 3f As shown, it consists of two separate elements. Although different elements exist within a unit cell, grating 303 still has the same grating vector as gratings 301 and 302 because this is due to the periodicity of the array.

[0292] Since gratings 301, 302, and 303 have the same grating vector, any non-evanescent order of the incident beam will diffract in the same direction. However, the different shapes of the structures will mean that, for a given incident beam direction, wavelength, and polarization, the ratio of light coupled into the non-evanescent transmission diffraction order and the reflection diffraction order will generally be different for each structure in the structure.

[0293] Interaction between waveguide light and two-dimensional diffraction grating

[0294] A method to provide a mathematical representation of a two-dimensional grating in the xy plane can be generalized by taking the product of the grating functions of two different one-dimensional gratings (9). Figure 4a A schematic diagram of two one-dimensional gratings 401 and 402 in the xy plane is shown, each having a grating vector. and In row vector form, these raster vectors are given by the following equation:

[0295] (26)

[0296] as well as

[0297] , (27)

[0298] in, and These are the periods of gratings 401 and 402, respectively, and and These are the angles describing the orientation of the grating vectors of gratings 401 and 402 (note that, as...). Figure 4a The plotted raster 401 has a negative angle. The 2D raster function is generated by the overlap of these gratings. It can be written as a product of a series of Dirac delta functions.

[0299] (28)

[0300] Figure 4b The overlapping 1D grating modes are shown to generate a cross grating structure 403. The product of the δ functions in equation (28) will be non-zero only at the points where the gratings cross, thus obtaining... Figure 4c It has a cross grating structure and Figure 4d The dot array 404 shown does not have a cross structure. This is due to the raster function. The description refers to the grating of a two-dimensional grating. This can be derived from the grating function. The analysis finds the location of each grid point, thus providing...

[0301] , (29)

[0302] as well as

[0303] , (30)

[0304] in, Give the raster points described by index values ​​i and j Coordinates. These indices can be positive integers, negative integers, or zero.

[0305] Diffraction gratings for light scattering can be generated based on a grating by associating each point with the same structure or set of structures. Such a structure should exhibit at least some variations in optical properties, such as refractive index, permittivity, permeability, birefringence, and / or absorptivity, within or relative to the medium surrounding the structure. Figure 4e and Figure 4f A top view representation of a periodic array of cylindrical structures based on grid 404 arranged periodically in the xy plane is shown. Figure 4e A top view of the rectangular column structure array 405 is shown, and Figure 4f A top view of the triangular prism structure array 406 is shown. Similar to the case of a one-dimensional grating, the direction of the monochromatic plane wave diffracted by these or other structures based on grating 404 will depend on the periodicity and orientation of the grating, not on the shape of the individual structures. Such scattering is governed by 2D grating equations, which can be expressed in vector form as:

[0306] , (31)

[0307] Or, in terms of the row vectors of the scalar components,

[0308] (32)

[0309] Here, A two-dimensional diffraction order describing the interaction, where each component can be zero, a positive integer, or a negative integer; and It has an x-component and y component , and by The xy wave vectors of the scattered wave corresponding to the two-dimensional diffraction order of the index. Similar to a one-dimensional grating, a beam that has interacted successively with the same 2D diffraction grating will have wave vectors that satisfy the following equation. :

[0310] (33)

[0311] Here, It is the xy wave vector of the original beam before it first interacts with the 2D grating, and and It is an integer formed by the sum of all diffraction orders of the previous interactions. Here, the set of values ​​is... This is called the 2D cumulative order of a 2D grating. If we consider using a 2D grating to subject the beam to multiple diffraction events, and the diffraction order at the i-th interaction is... If only a single diffraction beam is selected after each diffraction event, then the cumulative order before and after the i-th interaction are respectively... and Its value is related to the following:

[0312] , (34)

[0313] as well as

[0314] (35)

[0315] if It is the cumulative order after the beam undergoes N interactions with the same diffraction grating, and If the value is the two-dimensional diffraction order of the i-th interaction with the grating, then... and It is given by the following formula:

[0316] , (36)

[0317] as well as

[0318] (37)

[0319] From these equations, it is clear that, due to and If it is a positive integer, a negative integer, or zero, then and It must also be a positive integer, a negative integer, or zero.

[0320] The z-component of a three-dimensional wave vector can be derived from the wavelength of the beam in vacuum (which remains unchanged) and the refractive index of the medium in which the beam propagates. And found in the diffraction xy components of the wave vector,

[0321] (38)

[0322] Similar to the case of a one-dimensional grating, the z-component of the incident beam has the same sign. The values ​​of are called the transmission diffraction order, while those values ​​where the sign of the z-component of the wave vector changes are called the reflection diffraction order. The zero or complex value corresponds to the solution, where

[0323] (39)

[0324] It is an evanescent order and does not couple energy or produce a free-propagating beam. It is quite possible that for some orders, only the transmitted or reflected beam will be non-evanescent.

[0325] Similar to 1D gratings, three regions in k-space can be identified, where the refractive index is determined by the surface arranged parallel to the xy plane. A system composed of planar waveguides and a refractive index of Different propagation modes are possible within the surrounding medium. Multiple interactions with the 2D grating have led to... The xy-wave vector of the cumulative order beam can be written as

[0326] , (40)

[0327] in, This is the xy wave vector of the beam before it interacts with the 2D grating. Then, the three regions of k-space can be defined as follows:

[0328] 1. Free propagation region in k-space:

[0329] (41)

[0330] 2. Waveguide propagation region in k-space:

[0331] (42)

[0332] 3. The vanishing region of k-space:

[0333] (43)

[0334] Similar to 1D gratings, a beam can undergo a transition between a free propagation region and a waveguide region when interacting with a properly configured 2D grating. However, in the case of a 2D grating, as long as... and Non-collinear, the xy wave vectors can deflect in more than one direction. This additional degree of freedom provides the grating with a greater capacity for spatially distributing light within the waveguide. This can be advantageously used to support functions such as two-dimensional exit pupil expansion in DWC.

[0335] In a planar waveguide with a properly configured 2D diffraction grating, a beam can propagate through the waveguide and interact with the 2D grating at certain regions of the waveguide. At each interaction, the beam can be split into multiple separate beams corresponding to different diffraction orders of the grating. Some of these beams can continue to be confined within the waveguide by TIR and thus can interact with the grating again, potentially splitting into multiple beams again. This process continues until the various beams are absorbed, escape from the grating region due to propagation from the waveguide medium (which is permissible for the xy wave vector in the free propagation region of k-space), escape from the grating region due to propagation from the region of the waveguide covered by the grating, and / or absorbed or otherwise escape from the waveguide, for example, by impacting a side of the planar waveguide other than the surface parallel to the xy plane.

[0336] Following the interaction of two-dimensional gratings, the beam's orientation will depend on the 2D cumulative order of the beam, determined up to the most recent grating interaction. Therefore, the beam will undergo an evolution of its cumulative order, and in doing so, branch paths will be traced through the waveguide. Multiple beams with different cumulative order evolutions but derived from the same incident collimated monochromatic beam coupled into the waveguide will trace different paths. Thus, the accumulation of these beams can provide a spatially distributed distribution of the input light across a properly configured portion of the waveguide. Such paths can be analyzed analytically or through computational methods such as ray tracing.

[0337] Having correlated the layout of two-dimensional periodic structures with the 2D grating equations, it is now possible to design 2D gratings with scattering characteristics in a specified direction. Similar to the case of 1D gratings, the proportion of light coupled into a particular grating order will depend on the actual structure associated with the grating, as well as the wavelength, direction, and polarization of the incident light.

[0338] Diffraction efficiency of a diffraction grating

[0339] The term diffraction efficiency will be used to describe the radiated power of a specific diffraction order relative to the incident beam. Here, the transmission and reflection orders of the diffraction grating will be distinguished because they correspond to different beams, although they have the same xy wave vector. In mathematical representation, exponential values ​​can be used. This indicates whether the beam is the transmission or reflection order of the associated grating. Here... It is called the transmission index and is defined for a transmitted beam. =1 and for the reflected beam =-1, therefore it can be declared

[0340] , (44)

[0341] in, , These are the z-components of the wave vectors of the incident and scattered beams, respectively. It is a function with a sign, either positive or negative. If defined...

[0342] (45)

[0343] As having diffraction order and transmittance index The diffraction efficiency of the beam is then used as the incident wave vector. and normalized electric vector The diffraction efficiency, a function of the given information, will be given by the following formula:

[0344] , (46)

[0345] in

[0346] (47)

[0347] It is the intensity of the incident beam, and

[0348] (48)

[0349] It is for the diffraction order. and transmittance index The intensity of the scattered beam. Since intensity is the radiated power per unit area measured in a plane perpendicular to the propagation direction, the possible changes in beam size during diffraction must be taken into account, therefore this item is included.

[0350] , (49)

[0351] in, It is a unit vector in the direction perpendicular to the grating surface. It is the incident wave vector, and It is the diffraction wave vector. The intensity of a monochromatic plane wave electromagnetic radiation beam can be calculated from the Poynting vector associated with the electromagnetic wave. Typically, the calculation of the scattering characteristics of a grating, and therefore its diffraction efficiency, takes into account the vector nature of the electromagnetic field, and thus includes the polarization effects of both the incident and outgoing beams.

[0352] Various methods can be used for mathematical or computational analysis of grating design to calculate the scattering of light to various diffraction orders. For simple cases and under certain approximations, analytical calculations can be performed. The use of mathematical convolution here allows for the description of periodic arrays of finite structures. Such methods are well-established in Fourier optics and are particularly effective for gratings that introduce only small perturbations to the incident wave.

[0353] Typically, it is not possible to solve for the optical scattering properties of diffraction gratings using purely analytical methods. Instead, numerical techniques such as the finite-difference time-domain (FDTD) method with periodic boundary conditions or semi-analytical methods such as strictly coupled-wave analysis (RCWA) must be employed. These methods are well-established, and a large body of literature in the public domain describes their use for the analysis of diffraction gratings. Furthermore, several sophisticated software packages are available commercially (e.g., the Lumerical DEVICE kit from Lumerical Ltd.) and freely (e.g., the Meep package, originally from MIT), making these techniques readily accessible to those skilled in the art.

[0354] Projectors for augmented reality displays using diffractive waveguide combiners

[0355] To understand the operation of a DWC, it's helpful to understand the principles by which the projected light can be configured for use with the DWC. The eye-tracking range (OLR) is the entire spatial area of ​​the field of view from which the projected light output by the DWC can be observed. Such an area is needed to ensure that the output from the DWC can be observed for changes in the position of the fixation center and the wearing position of the display system relative to the DWC's range of eye movements, such as eye rotation. The size, shape, and position of the OLR within a specified distance or range are often design requirements for the DWC. In many cases, the size and shape of the OLR are designed as minimum requirements, not precise ones.

[0356] Many digital light calibrators (DWCs) output waveguide beams multiple times to expand the size of the eye-tracking range. For such DWCs, it may be advantageous to collimate each projected beam so that the wavefront of the beam is planar. Assuming the beam has a medium size and a relatively short propagation distance (e.g., beam diameter > 0.25 mm, propagation distance < 100 mm), the wavefronts of the various beams output from the DWC will also be planar, even if the propagation distances of each beam within the beam may differ. This means that different outputs derived from the same initial beam will appear to originate from the same location, as long as they have the same orientation. If the beam is not collimated, different outputs derived from the same initial beam may appear to originate from slightly different locations due to the evolution of the wavefront between different output events. This can cause undesirable artifacts for the viewer, such as a loss of image sharpness or a small shift in the visual position of the image portion depending on the position of the observing eye within the eye-tracking range. To avoid such artifacts, it may be advantageous to ensure that the projection light supplied to the DWC is collimated.

[0357] Figure 5a A simplified perspective view is shown of a projector system 501 that can be used to provide projection light for a DWC-based augmented reality or virtual reality display. Figure 5bA cross-sectional view of the same projector 501 is shown. In this system, source image output light, consisting of a computer-controlled pixel-based image display 502, is collimated by a lens system 503 and guided toward the input coupling element of the DWC to provide projection light to an AR or VR display system.

[0358] Suitable technologies for display 502 include emissive displays such as pixel displays based on organic light-emitting devices (OLED displays), pixel displays based on micro-light-emitting devices (μLED displays), or micro cathode ray tubes (CRT displays), and reflective displays such as those based on digital micromirror devices (DMD displays) or liquid crystal on silicon (LCOS displays). For projectors based on reflective displays, it is necessary to... Figure 5a Additional optical elements, not shown, are used to provide incident illumination on display 502 and to filter or redirect the light based on polarization or using total internal reflection. The operating principles of various display technologies suitable for providing projected light are well-known and widely disseminated; the purpose of this description is to outline some of the requirements that may be preferred for DWC-based AR or VR display systems and to provide a mathematical description that helps to illustrate the invention.

[0359] During operation, each point on display 502 emits or reflects light toward lens system 503, thereby generating a collimated beam with a unique direction determined by the point on the display. For example, points 504 and 505 generate collimated beams 506 and 507, respectively, each of which... Figure 5a The image is schematically illustrated by three rays of light. In this way, the projector converts the pixel position at display 502 into the direction of a plane wave behind lens 503. Therefore, the projected light from the entire display 502 can be decomposed into a set of plane waves, each of which is associated with a unique point on the display. Typically, the light from the display will not be monochromatic, so each collimated beam can be further decomposed within a certain wavelength range.

[0360] To write the expression for the electromagnetic waves generated by the projector, the following definition is useful:

[0361] f The focal length of the imaging system 503 of the projector 501;

[0362] W Half-width of image display 502 (total length of the display in the x direction is 2W).

[0363] H Half height of image display 502 (total length of the display in the y direction is 2H);

[0364] The horizontal position on monitor 502 ( ) and vertical ( Cartesian coordinates, such as those measured relative to the center of the display and within the plane of the display;

[0365] The function describing the exit pupil of projector 501 is typically a function with a unit value within a region and zero everywhere else. The pupil is usually circular in shape, but this is not required; note that it can also be... The function is defined, but for simplicity, it will be kept as zero here;

[0366] Description at wavelength Due to the image display position And the function of the electric field amplitude generated at the output; and

[0367] From image display 502 at position And has wavelength The wave vector of the collimated beam, such as that collimated by the imaging system 503 and output by the projector 501.

[0368] As an example, suppose the projector is in Descartes In the coordinate system, the z-axis is perpendicular to the plane of the display 502, the optical axis of the imaging system 503 coincides with the normal projected from the center of the display, and the u and v directions of the display 502 are parallel to the plane of the display. The x and y directions of the coordinate system. For a projector with a high-quality imaging system exhibiting negligible aberrations and distortions, the wave vector... It can be written in row vector form as

[0369] (50)

[0370] The field of view of the projector 503's output can then be found by considering the range of the display and using equation (50). Referring to the horizontal and vertical angles of view of the projection beam is sometimes advantageous. Horizontal angle It refers to the angle between the beam and the z-axis when projected onto the xz plane, and the vertical projection angle. It is the angle between the beam and the z-axis when projected onto the yz plane. Using this definition, the wave vector of the beam is given by the following equation:

[0371] (51)

[0372] Therefore, it can be seen

[0373] , and (52)

[0374] .

[0375] Horizontal field of view Defined as the angle to which the range of the output wave vector is directed when projected onto the xz plane, and given by the following equation:

[0376] (53)

[0377] Similarly, vertical field of view Defined as the angle to which the range of the output wave vector is directed when projected onto the yz plane, and given by the following formula:

[0378] (54)

[0379] The electromagnetic field output by projector 501 observed at the exit pupil. It can be written as a set of plane waves truncated by the spatial range of the exit pupil.

[0380] (55)

[0381] .

[0382] This decomposition means that instead of dealing with complex, arbitrary electromagnetic fields, the output from the projector can be viewed as a collection of separate, spatially truncated monochromatic plane wave components, each of which is easier to analyze. A complete description is then given by the superposition of these components. Furthermore, for many projector systems, these components are incoherent relative to each other, so this superposition can be performed in the intensity domain of the detected image. By analyzing the propagation of the various plane wave components, it becomes clear how DWC can be used to map the output from the projector onto an observation device such as the wearer's eye.

[0383] This form has been established, and a collimated beam can now be defined as an electromagnetic plane wave with a non-zero wavefront amplitude over a finite region, typically determined by the exit pupil of the projector. In this scheme, the projection light of an AR or VR display system is a collection of collimated beams, where each beam corresponds to a point in the projected image transmitted by the display system.

[0384] Converting a spatially distributed source object into a set of collimated beams—where the direction of a given beam depends on the location on the source object in a manner similar to equation (50)—generally refers to placing the object at infinity, similarly having a much larger object at a very large distance, such that when interacting with a system at hand, the wavefront from any point source on the object becomes planar. An imaging system such as a camera or the observer's eye, focused at infinity and configured to receive collimated beams, will produce a sharp point at the location determined by the direction of the incident plane wave. Thus, an imaging system focused at infinity and trained to observe a set of collimated beams generated by optically placing the object at infinity will produce an image of the original object.

[0385] Strictly speaking, since these plane waves will be finite in extent, diffraction will cause the waves to spread as they propagate due to the introduction of the pupil function. However, for the purposes of this invention, the pupil size and propagation distance of interest ensure that any spread has a negligible effect beyond the usual diffraction limitation on image resolution. Furthermore, for the analysis based on decomposing the projected light into a set of collimated beams to be valid before the moment of detection by the eye or image sensor, any effect that is nonlinear with respect to the amplitude of the electromagnetic wave must remain negligible. This condition is well satisfied for the wavelength range and light intensity commonly used in AR and VR display systems.

[0386] Other image generation devices are also possible when used with augmented or virtual reality displays that utilize DWC, such as those based on scanning laser beams or using holographic principles. These can also be decomposed along the routes outlined above, although coherent interference effects between different parts of the image and other parts may be more important for these systems.

[0387] It is generally advantageous for a projector system configured to be used with a DWC if the projector's imaging system's exit pupil is located externally so that it can be placed close to or coincide with the DWC's input coupling element.

[0388] Existing technology examples of diffractive waveguide combiners

[0389] Figure 6A schematic diagram of a DWC-based head-up display system as described in US 4,711,512 is shown. Here, an image is formed by a CRT display 601 and collimated by a lens 602, thereby converting the image into a set of collimated beams. The collimated beams are incident on a waveguide 603, in which a 1D diffraction grating 604, referred to as the input grating, is located. The input grating has a specific spacing and orientation to couple incident light within a target range of the incident angle into total internal reflection (TIR) ​​within the waveguide 603 and guide the light upward toward another 1D diffraction grating 605, referred to as the output grating. The light remains confined within the waveguide 603 by total internal reflection until it is incident on the output grating 605, at which point some of the light is diffracted to an angle below the TIR threshold and exits the waveguide toward an observer 606.

[0390] Figure 7 This is a top view of a known waveguide 701 (as described in WO 2016 / 020643) that can be used as a diffraction combiner in an augmented reality display system. The described system has an input diffraction grating 702 disposed on the surface of the planar waveguide 701 for coupling light from a projector (not shown) into the waveguide. The input grating 702 consists of a 1D grating having a grating vector pointing along the X-axis. The light coupled into the waveguide travels towards an output element 703 comprising a two-dimensional photonic crystal 704 via total internal reflection. In this example, the photonic crystal 704 comprises pillars (not shown) having a circular cross-sectional shape as viewed from these top views. These pillars have a refractive index different from the refractive index of the surrounding waveguide medium, and they are arranged in an array with hexagonal symmetry. The hexagonal grating from which this array is derived has a grating vector at a 60° angle to the grating vector associated with the input grating. In some arrangements, the grating vector of the input grating has the same length as the grating vector of the output grating. Figure 7 In the coordinate system shown, the grating vector of the input grating It is given by the following formula:

[0391] , (56)

[0392] in, It is the period of the input grating, and the grating vector of the output grating. , It is given by the following formula:

[0393] , (57)

[0394] as well as

[0395] (58)

[0396] Note that, according to this definition, the sum of the grating vector of the input grating and the grating vector of the output grating is zero.

[0397] (59)

[0398] When used as a DWC for augmented reality displays with non-monochromatic light, the result of equation (59) is important for the waveguide's functionality. Essentially, this result indicates that in the grating vector... , and The cumulative change of the xy wave vector after the first-order diffraction is zero. Note that this relationship does not state anything about the z-direction of the beam. Therefore, the beam after such a series of diffraction orders will travel in the xy plane in the same direction as the initial beam before being scattered by any of these diffraction orders, and the beam's propagation direction in three dimensions will be the same as the initial beam or reflected about the xy plane.

[0399] Two-dimensional grating with rectangular grid

[0400] Figure 8a Two one-dimensional gratings are shown. Grating 801 is a one-dimensional grating arranged in the xy-plane with its grating vector parallel to and aligned with the x-axis, and grating 802 is a one-dimensional grating arranged in the xy-plane with its grating vector parallel to the y-axis of the Cartesian coordinate system. The grating vectors of 801 and 802 are given by the following equation: For grating 801,

[0401] , (60)

[0402] And for grating 802,

[0403] , (61)

[0404] in, It is the period of grating 801, and It is the period of grating 802.

[0405] Figure 8b A top view of a two-dimensional grating 803 with a rectangular orthogonal grid is shown. The grating 803 is arranged in the xy plane and has a grid obtained from overlapping gratings 801 and 802. Figure 8b The dashed lines above indicate the original gratings 801 and 802 and are not intended to suggest any physical structure. At each point of the grating obtained from the overlapping gratings 801 and 802, pillars 804 are placed using a material with a different refractive index than the medium surrounding the grating. In this way, a two-dimensional diffraction grating capable of scattering light is realized. For diffraction order { }, the xy wave vectors before and after scattering from the grating (represented as...). and The relationship between them is given by the following formula:

[0406] , (62)

[0407] It can be extended to row vector form to be given as follows:

[0408] , (63)

[0409] in, and A diffraction grating constructed using orthogonal grating vectors is called a rectangular grating.

[0410] Figure 9a A perspective view of a diffractive waveguide assembly 903 is shown, which comprises an optically transmitting substrate 905 configured as a planar waveguide, arranged in accordance with Cartesian principles. The principal optical surface is parallel to the xy-plane of the coordinate system and has a region with an input grating 901 and a region with an output grating 902. The input grating 901 and the output grating 902 can each be on the front or rear surface of the waveguide, or embedded in a planar surface within the waveguide. The gratings do not need to be on the same surface. The output grating 902 is arranged such that it is positioned separately from the input grating 901. The output grating 902 can be adjacent to the input grating 901, or there can be a region between the two gratings that does not contain gratings or other optical structures. The output grating 902 can be positioned such that the direction of the line drawn from the center of the input grating 901 to the center of the output grating 902 is along the y-direction of the Cartesian coordinate system associated with the waveguide. Figure 9b A top view of the DWC 903 is shown, illustrating the surface of the waveguide substrate 905, the input grating 901, and the output grating 902, all of which are parallel to the xy plane of the associated Cartesian coordinate system.

[0411] The microprojector 904 is arranged to output an image that is optically converted into a set of collimated beams of finite size in the manner described above, and said beams are guided to be incident on the input grating 901. Typically, the output from the microprojector 904 is part of a computer-controlled display system (not shown). As described above, for a given wavelength in a vacuum... Each point in the image will be associated with a unique wave vector, which is represented here as ,in These are the coordinates of a point in the projected image from the microprojector 904. (And...) The associated xy wave vector is Representation. Coordinates The precise parameterization is not unique and does not need to be specified, but it is sufficient to note that each coordinate pair should uniquely describe a point in the image, and therefore the direction of the collimated beam from the microprojector. For convenience, the definition will be derived from... The resulting associated coordinate pairs, where and yes For each function of , the wave vector at a point is given by the following equation:

[0412] (64)

[0413] It is possible The aspect is rewritten with more compact notation as

[0414] (65)

[0415] The input grating 901 is arranged to have a grating vector , The direction pointing from the center of the input grating 901 to the center of the output grating 902 is given by the following formula:

[0416] (66)

[0417] Here, The period of the input grating is chosen such that the range of the collimated output beam from the microprojector 904, after first-order diffraction by the input grating 901, will be coupled into the waveguide range of the waveguide substrate 905. This requires that for all xy wave vectors associated with the beam from the microprojector 904, Satisfying the inequality

[0418] , (67)

[0419] in, It is the refractive index of the medium surrounding the waveguide, and This is the refractive index of the 905 waveguide substrate. Note the refractive index of... The definition can be written as

[0420] , (68)

[0421] The inequalities of the waveguide region in k-space can be expressed in... Aspect written as

[0422] (69)

[0423] generally, and Both depend on the wavelength; however, for clarity, this is not explicitly shown here.

[0424] The output grating 902 has the same characteristics as... Figure 8b The grating 803 shown is a similar rectangular orthogonal grating and is defined as having a grating vector given by the following formula. and :

[0425] , (70)

[0426] as well as

[0427] (71)

[0428] Note the period of the grating and They don't have to be equal. For the purposes of DWC, these periods can have similar amplitudes, making...

[0429] (72)

[0430] When interacting with the output grating 902, the xy wave vector It will depend on the order of the interaction. and grating vector , and , making

[0431] , (73)

[0432] Or in terms of quantity

[0433] , (74)

[0434] (75)

[0435] Typically, for a waveguide beam, multiple interactions with the output grating 902 are possible, in which case the beam's xy wave vectors will be derived from a 2D cumulative order. Characterization, giving

[0436] , (76)

[0437] Or in terms of quantity

[0438] , (77)

[0439] (78)

[0440] It can be seen from this that the x-component of the xy wave vector depends only on the x-component of the wave vector of the collimated monochromatic beam coupled to the waveguide and the grating vector. and cumulative order Similarly, note that the y-component of the xy wave vector depends only on the y-component of the wave vector of the collimated monochromatic beam coupled to the waveguide, and the grating vector. , and cumulative order .

[0441] If set In this case, a special situation related to DWC will occur. The expression becomes

[0442] (79)

[0443] Then, by choosing a choice that satisfies the following inequality Value to represent when , Conditions of the time-wave vector in the waveguide region of k-space

[0444] (80)

[0445] For a suitable grating period and DWC can be based on 2D cumulative order. To describe several qualitatively different behaviors associated with beamforming. These are in Figure 45 This is described in Table 1. Figure 45 In Table 1, the term "approximately oriented" is intended to refer to the direction of the light beam projected onto the xy plane, and therefore the z-direction of the wave vector is not considered. Furthermore, Figure 45 The approximate directions described in Table 1 are intended to refer to the principal components of the xy wave vector. For example, the approximate +y direction refers to the xy wave vector where the y component has the largest amplitude and is positive in sign. In this case, these directions are accurate. Whenever the beam is reflected from the surface of the waveguide, the beam that propagates through the waveguide in the z-direction of the wave vector will necessarily flip in sign.

[0446] exist Figure 45 In all cases shown in Table 1, the z-component of the beam will satisfy the following relationship:

[0447] , (81)

[0448] in, or This depends on whether the beam described by the wave vector is inside the waveguide substrate 905 or in the medium surrounding the waveguide.

[0449] in The free propagation condition corresponds to the xy wave vector recovering to its initial value. This condition describes a collimated beam that can be emitted from the waveguide, and therefore, if the incident collimated beam corresponds to a portion of the image, so does the emitted beam. The existence of this condition demonstrates the potential of the DWC to provide a relay function for the beam from the microprojector 904; if the set of collimated beams generated from the microprojector 904 is coupled into the waveguide both through the input grating 901 and then through the cumulative order of the output grating 902... The waveguide is coupled out again, and if the beam set is ensured to be observed by a suitable imaging detector (e.g., an observer's eye or a camera), the observer can see an image from the microprojector 904, thus successfully completing the relay.

[0450] Having cumulative order The z-component of the wave vector of the beam will have the same value or the same amplitude but opposite sign as the initial beam from the microprojector 904 when emitted from the waveguide. The first case is referred to here as transmission mode output because it has the following direction: just as the wave vector has passed through the waveguide by conventional optical transmission, except that, of course, the position of the beam will be moved due to the waveguide confinement and propagation of the beam between the input grating 901 and the output grating 902. The case where the sign of the output beam is opposite to that of the initial beam from the microprojector 904 is referred to here as the reflection mode output, in which case the expected direction of the wave vector that causes it to be reflected from a conventional mirror surface parallel to the xy plane is used as a reference. Again, note that the beam position will be shifted due to waveguide confinement and propagation between the input grating 901 and the output grating 902. As with other diffraction orders, the diffraction intensity entering the transmission or reflection output mode will depend on the structure and composition of the gratings, as well as the wavelength, direction, and polarization of the incident beam.

[0451] Other values ​​are possible in principle, depending on... , , and However, in many practical situations, beam

[0452] or , (82)

[0453] It will fade away gradually. For all but... In addition to the above-mentioned other situations, , and Some combinations can also lead to evanescent waves. When this occurs, it means that for... , and Such values ​​must be prevented from propagating along paths that require the use of 2D cumulative order. , and Some values ​​may also lead to the free propagation of waves, especially for or In such cases, this provides an additional mechanism for the output from the DWC, but this is generally undesirable as it often leads to image artifacts. These problems can be suppressed by selecting a grating period that ensures any beams generated by these propagation modes will be very weak and / or located outside the eye-tracking range of the DWC.

[0454] In addition to Figure 45 In addition to the 2D cumulative order shown in Table 1, it is helpful to note the various diffraction orders between the cumulative order values, which may be particularly important for the operation of DWC. These orders are in Figure 46 Listed in Table 2. With Figure 45 As in Table 1, the direction refers to the direction of the beam in the xy plane, and the z component of the wave vector is ignored.

[0455] As mentioned above, the diffraction efficiency of coupling between non-evanescent steps typically depends on the structure and composition of the grating, as well as the wavelength, direction, and polarization of the incident beam.

[0456] Figure 46 The diffraction orders recorded in Table 2 can be roughly grouped into entrance-eye orders (STE, TEAT+X, TEAT-X, TEAT-Y) or turning orders (T+X, TX, BT-Y, BT-X, BT+X, TTB+X, TTB-X). It is worth noting that for the entrance-eye orders, the order value... and The sum is given by the following formula:

[0457] +1 or -1, (83)

[0458] For the turning order, the sum of the order values ​​is:

[0459] +2, 0, or -2. (84)

[0460] Another important diffraction order is the zeroth-order interaction. {0,0}. This order corresponds to the case where the xy wave vector remains unchanged; therefore, a beam confined within the waveguide by the TIR will remain confined, and a beam propagating freely through the waveguide will remain free (although it may reflect from the waveguide surface). This is important for both the projected beam transmitted within the DWC and the real-world beam. Typically, in augmented reality applications, it is preferred that real-world light be directed toward the observer through the waveguide. It is primarily the zero-order interaction with the grating that allows for such transmissive viewing. In many AR applications, it is desirable to view the surrounding physical world as brightly as possible, meaning that the transmission efficiency of real-world light should be as high as possible. This requires the zero-order diffraction efficiency to be as close as possible to 1 for the angle of incidence of the beam corresponding to the free propagation region in k-space. Note that the beam direction of real-world light is necessarily different from the waveguide direction of the projected light. Therefore, in some systems, it may be advantageous to employ a diffraction structure that provides scattering characteristics specifically dependent on whether the beam falls within the directional range associated with the waveguide projected light or the freely propagating real-world light.

[0461] Various cumulative orders coupled between these orders and diffraction order This provides a wide-range path for the TIR-confined beam to interact with the output grating 902 once or more. Typically, because multiple diffraction orders will occur simultaneously, several new beams will emerge with each interaction with the output grating 902, each of which will result in a different cumulative order. The new beam travels in different directions. The number of beam paths that the beam can pass through the waveguide tends to increase exponentially with the number of interactions with the output grating 902.

[0462] Figures 9c to 9f A perspective view of several exemplary paths of the beam through the DWC 903 is shown. Here, the paths are represented by rays (light rays) pointing in the wave vector direction of the corresponding collimated beam. All paths begin with the same light ray 906 from the microprojector 904, which strikes the input grating 901 and couples in the approximately +y direction into the waveguide propagation ray 907. Ray 907 thus corresponds to the cumulative order {0,0}. For clarity, the bounces of the light between the surfaces of the DWC due to waveguide propagation, which would result in the zigzag path shown in the figure, are not shown. Typically, many bounces occur between the waveguide surfaces as the beam propagates through the waveguide; those bounces that do not change the beam direction correspond to zero-order diffraction with the output grating 902 and mean that the xy wave vector remains unchanged.

[0463] Figure 9cThe path of beam 907 through the waveguide is shown until it reaches point 909, where the beam couples out of the waveguide along path 908 via the STE-order reflection mode toward observer 919.

[0464] Figure 9d The path of beam 907 through waveguide propagation is shown until it reaches point 911, where the beam is redirected in the approximately +x direction at order T+X. The beam then propagates through waveguide until it reaches point 912, where it is then coupled out of the waveguide along path 910 via a reflection mode of order TEAT+X toward observer 919.

[0465] Figure 9e It shows the relationship with Figure 9d The path is similar to the one in the diagram, except that at point 911, the beam is redirected in the approximately -x direction at the TX order. After propagating through the waveguide to point 914, the beam is then coupled out of the waveguide along path 913 via a TEAT-X order reflection mode toward the observer 919.

[0466] Figure 9f The path of beam 907 through the waveguide until it reaches point 916 is shown, where the beam is redirected in the approximately -x direction at the TX order. The beam then propagates through the waveguide until it reaches point 917, where it is redirected in the approximately -y direction at the TTB-X order. The beam then propagates through the waveguide until it reaches point 918, where it is then coupled out of the waveguide along path 915 via a TEAT-Y order reflection mode toward observer 919.

[0467] DWC's relay function is provided by Figures 9a to 9f The example shown is provided by means of the spatial separation of the input grating 901 and the output grating 902. The requirement that the beam must travel between different regions of the waveguide 903 necessarily requires that when the beam is coupled out of the waveguide 903 through the output grating 902, it must be in a spatially different position from the input grating 901.

[0468] DWC's pupil expansion function is... Figures 9a to 9f The example shown is provided by means of multiple paths that allow the same input beam to exit from the waveguide at different locations, but with the same direction and the same xy wave vector as the input beam. For such pupil expansion to be effectively achieved, it is important that the distance between the interaction with the output grating 902 remains sufficiently short, such that the separated output beams are close to or overlap each other. This will ensure that the pupil of the observer 919 overlaps with at least a portion of one of the output beams, a necessary condition for possible observation.

[0469] The distance between the surface of waveguide 903 and the interaction with the output grating 902 Depends on the given cumulative order wave vector and waveguide thickness :

[0470] (85)

[0471] Based on the initial wave vector direction parameters Equation (85) can be written as:

[0472] (86)

[0473] The size of each output beam will depend on the overlap between the input grating 901 and the beam from the microprojector 904. Typically, the size and shape of the input grating 901 are sufficient to accommodate all the beams from the microprojector 904 within the grating. In this case, the size of the output beam will be determined by the beam from the microprojector 904.

[0474] Assuming good overlap with the input grating 901 is achieved, then to achieve good pupil expansion, it is generally desirable to ensure... > ,in It is from the microprojector 904 corresponding to the wavelength. and direction The beamwidth, which is projected onto the xy plane of the input grating 901 and measured in the direction of the xy wave vector, corresponds to... , , , and For many projector designs, the value... It will be the diameter of the circular exit pupil.

[0475] Figure 10 A cross-sectional view of the diffractive waveguide combiner 903 is shown. Figure 10A collimated beam from a microprojector (not shown), represented by ray 1001, is incident on the input grating 901 of the DWC 903 and coupled into the waveguide for propagation. This beam propagates in a generally +y direction toward the output grating 902, where it is split into multiple branch paths. Some of these paths lead to the output beam, as illustrated by rays 1002, 1003, 1004, 1005, and 1006. The output beam is oriented toward a detector 1007, which can be a camera, an observer's eye, or some other optical detection system. The detector 1007 has a limiting aperture 1008 (also called an entrance pupil) that blocks part or all of some of the output beams 1002, 1003, 1004, 1005, and 1006. For clarity, aperture 1008 is shown as separate from detector 1007; however, in reality, this aperture is typically inside the detector, such as the pupil of a human eye or the aperture stop of a camera lens. The portion of the beam transmitted through aperture 1008 constitutes a portion of the new beam 1009, referred to herein as the detected beam. Typically, each input beam to the DWC is associated with its corresponding detected beam, which is derived from the overlapping set of output beams and the intersection of the detector aperture used to observe the output from the DWC.

[0476] Characteristics of an ideal diffractive waveguide combiner

[0477] Generally, diffractive waveguide combiners function by: coupling light into the waveguide using a diffraction grating, spatially distributing the light across a portion of the waveguide via multiple branch paths, and recoupling at least some of the light toward an observer or other detector. These key functions have been described in detail and are referred to as input coupling (describing the conversion of incident light into waveguide propagation), output coupling (describing the conversion of waveguide light into freely propagating light traveling outside the waveguide), relaying (describing the transmission of light from one spatial region to another), and eye-tracking range extension (describing the generation of multiple overlapping beams from a single input beam, thereby extending the size of the spatial region that can be viewed over it compared to the input).

[0478] It is helpful to clarify some of the characteristics required for effective DWC execution. Figure 47 Table 3 summarizes some key characteristics of an ideal diffractive waveguide combiner.

[0479] In practice, it is impossible to simultaneously meet the ideal requirements of DWC, and any practical implementation will be a balanced compromise, depending on the relative importance of various characteristics of the current task, which is constrained by the limitations of both design and manufacturing.

[0480] As previously mentioned, the beam can appear with relative intensity through many different paths through the DWC, the relative intensity depending on both the structure and composition of the grating and the wavelength, direction, and polarization of the beam. It has been found that achieving good uniformity across the entire eye-tracking range is difficult for output gratings based on rectangular orthogonal gratings. Specifically, for some portions of the eye-tracking range, the beam output may occur primarily via the STE step, while for others, a beam that has already undergone at least a T+X or TX steering step is required to reach the desired position within the waveguide. These beams are then followed by the TEAT entry-eye step to output the beam. The significant difference in the combined efficiency of the steering and TEAT entry-eye steps compared to the STE step can lead to non-uniformity in the observed image's position relative to the viewer's eye within the eye-tracking range and / or the angle of view relative to the image.

[0481] Definition of Interlaced Rectangular Grating (IRG)

[0482] The interlaced rectangular grating (IRG), introduced as the subject of this invention, provides a new method for designing and controlling the diffraction efficiency of different diffraction orders of rectangular gratings. This additional control can help provide excellent performance for diffractive optical elements in applications such as output gratings used as diffractive waveguide combiners.

[0483] An interlaced rectangular grating can be defined as follows:

[0484] i) Two periodic rectangular structure arrays (periodic structure PS1 and periodic structure PS2) are each defined as having rectangular orthogonal grids arranged in the same plane; for convenience, without loss of generality, and unless otherwise stated, this plane is defined as Cartesian. The xy plane of the coordinate system; this coordinate system can be a locally defined coordinate system created purely to describe the grating itself, or it can be a global coordinate reference for a larger system;

[0485] ii) The gratings (grating L1) of periodic structure PS1 and the gratings (grating L2) of periodic structure PS2 are both formed by grating vectors located in the planes of periodic structures PS1 and PS2. and structure; and They are orthogonal to each other;

[0486] iii) The IRG unit cell has a rectangular shape located in the plane of the periodic structures PS1 and PS2; a pair of sides of the IRG unit cell are parallel to the grating vector. And has an equal value to the grating vector The length of the associated period; the other pair of sides of the IRG unit cell are parallel to the grating vector. And has an equal value to the grating vector The length of the associated period; the position of the IRG unit cell is not uniquely defined in the xy plane and can be chosen for convenience;

[0487] iv) In the plane of periodic structures PS1 and PS2, grid L2 is offset from grid L1 by the following vector: this vector lies in the plane of the periodic structure and is referred to as the grid offset vector. The grid offset vector provides the offset of grid L2 in both the x and y directions.

[0488] v) Associate the same structure S1 at each point of grid L1. The structure is limited in scope and can be composed of multiple materials. Thus, a periodic structure PS1 is created by placing the same copy of structure S1 at each point of grid L1.

[0489] vi) Associate the same structure S2 at each point of grid L2. The structure is limited in scope and can be composed of multiple materials. Therefore, a periodic structure PS2 is created by placing the same copy of structure S2 at each point of grid L2.

[0490] vii) An interlaced rectangular grating is created by combining periodic structures PS1 and PS2 on essentially the same plane, which can then be placed on the surface of a substrate or embedded within the substrate.

[0491] For convenience, and unless otherwise stated, any implementation of the interlaced rectangular grating described herein is based on the definitions detailed in i) to vii) above, and is associated with a set of structures S1 and S2, gratings L1 and L2, and grating vectors. and Grid offset vector The periodic structure PS1 formed by grid L1 and structure S1, the periodic structure PS2 formed by grid L2 and structure S2, and the IRG unit cell are associated. Further modifications and changes to the IRG are possible, and any such changes will be explicitly detailed in the following description.

[0492] It should be noted that the term "structure" is intended to imply any kind of variation in physical properties relative to position. For example, the term can refer to the geometry of materials with different refractive indices, or it can refer to variations in optical properties within a single material, such as variations in the orientation of liquid crystal molecules that cause spatial variations in birefringence. Furthermore, the term "structure" can refer to more than one type of material or variant, and thus structures S1 and S2 can be constructed as a complex of multiple substructures, which can be separate or interconnected, and each of them can be composed of different materials.

[0493] In some arrangements, structures S1 and / or S2 are made of materials with different optical properties than the medium surrounding the combined structure. Such differences in optical properties include, but are not limited to, refractive index, permittivity, permeability, birefringence, and / or absorptivity. Typically, structures characterized by such variations in optical properties can be used as two-dimensional diffraction gratings for light scattering, including diffraction grating elements used in diffraction waveguide combiners.

[0494] If the periodic structures PS1 and PS2 are spatially separate and therefore do not overlap, they can be directly superimposed in a plane to form an IRG. However, if the structures overlap, some combination principle should be applied. For example, a geometric union can be envisioned, where the overlapping regions between PS1 and PS2 are spatially merged. If the optical properties of the overlapping PS1 and PS2 are different, rules can be used to specify the combination result. For example, if the variation is a change in refractive index, the rule could be to make the refractive index of one structure superior to that of the other, take the average, or take the maximum / minimum value, or take a third value. In some cases, the combination can be determined by the manufacturing method.

[0495] Any structure realized in the real world must have a certain thickness in a direction orthogonal to the plane of the IRG, even if it is a single atomic layer. IRGs used for light scattering in DWC typically have a thickness in the range of 1 nm to 10,000 nm, or 10 nm to 2,000 nm, or 20 nm to 500 nm.

[0496] Figure 11 A top view of a portion of an exemplary interlaced rectangular grating (IRG) 1101 according to the present invention is shown. IRG 1101 comprises a superposition of periodic structures PS1 and PS2. Figure 11 In the diagram, the points of grid L1 constituting the periodic structure PS1 are represented by circles 1102, and the points of grid L2 constituting the periodic structure PS2 are represented by intersections 1103. From... Figure 11 As can be seen, the grid L1 of periodic structure PS1 and the grid L2 of periodic structure PS2 overlap each other on the plane. The dots 1102 or intersections 1103 are not intended to convey the physical structure. The grating vectors used to construct grids L1 and L2 are as required by the general definition of an IRG. and For two grids to be identical, they must be the same. For convenience, and without loss of generality, a local Cartesian expression can be defined. A new coordinate system is established, aligning these raster vectors with the x and y axes of the new coordinate system, and thus arranging the raster in the xy plane of the new coordinate system. Therefore, the raster vectors can be written as:

[0497] , (87)

[0498] as well as

[0499] (88)

[0500] Grid L2 lies in the same plane as grid L1, but with a position offset. This positional offset can be represented by a vector called the grid offset vector when grids are arranged in a plane. It is specified by a two-dimensional vector, where the components describe the positional offset in the x and y directions.

[0501] (89)

[0502] Here, It is the offset between grids L1 and L2 in the x-direction, and This is the offset in the y-direction between L1 and L2. The points of grids L1 and L2. The coordinates can be found from equations (29) and (30), and the positions of the points for the raster L1 indexed by i and j can be given using the expressions for the raster vectors given in (87) and (88). :

[0503] , (90)

[0504] The grid and the position of points in grid L2, which is also indexed by i and j. :

[0505] , (91)

[0506] Raster indices i and j are used to count raster positions and can be positive integers, negative integers, or zero. Coordinates Define the origin of the grid. Since the origin of the Cartesian coordinate system can be redefined for convenience and for clarity, this coordinate is set to (0,0), and these terms, including those used in the remainder of this specification, are ignored unless otherwise stated.

[0507] In this example, structure S1 is a column with a circular cross section 1104, while structure S2 is a column with a triangular cross section 1105.

[0508] Since each grating in the periodic structure constituting the IRG has the same periodicity as the IRG, the diffraction order of the IRG is expected to conform to the diffraction order of the rectangular grating given by equation (62). If IRG 1101 is used as Figure 9a The output grating 902 in the diffraction waveguide combiner 901 shown can be employed... Figure 46The nomenclature of diffraction orders is given in Table 2, and note that... Figure 45 The specific cumulative orders are given in Table 1. As with other diffraction gratings, the efficiency of various diffraction orders for a given incident beam will depend on the shape and composition of the structure, the layout of the grating, and the wavelength, direction, and polarization of the incident beam.

[0509] Diffraction and scattering characteristics of staggered rectangular gratings

[0510] A specific type of IRG, referred to herein as a fully symmetric interlaced rectangular grating (FSIRG), is defined as an interlaced rectangular grating that satisfies the following additional constraints:

[0511] i) FSIRG structures S1 and S2 are identical in shape, composition, and optical properties; and

[0512] ii) The grid offset vector is selected such that a point in grid L2 is located at the midpoint between points in grid L1 in both the x and y directions.

[0513] (92)

[0514] Figure 12a FSIRG 1201 is shown, where structures S1 and S2 are pillars 1204 with circular cross sections. Points of grid L1 in FSIRG 1201 are represented by dots 1202, and points of grid L2 are represented by intersections 1203 (again, dots and points do not represent physical differences for clarity). The grids are arranged such that the grating vectors are given by equations (87) and (88). Points of grid L1 indexed by i and j... The coordinates are:

[0515] , (93)

[0516] and the points of grid L2 indexed by i and j The coordinates are:

[0517] (94)

[0518] Figure 12b It shows the relationship with Figure 12a The same perfectly symmetrical staggered rectangular grating 1201. Because structures S1 and S2 are set to be identical and the offset vector is set to... Therefore, alternative original gratings from which periodic structures can be generated can be identified. Instead of interleaving the two gratings, the same overall structure can be derived from the new grating L3, where structure S1 is repeated at each point of the grating. Glue L3 is composed of... Figure 12b The dot 1205 and the dashed line shown above indicate that neither the dot nor the dashed line is intended to convey the physical structure.

[0519] grating vector of L3 grid and It can be derived by considering the geometry derived from the diagonal rows drawn through the grid points. Figure 12c The diagram shows the grating vectors used to construct the grating L3. The grating has two adjacent rows, 1207 and 1208. Based on this geometry, the angle of the grating rows relative to the x-axis can be determined. It is given by the following formula:

[0520] , (95)

[0521] And therefore, the grating vector Angle opposite to the x-axis The sine and cosine of the sine and cosine are given by the following formula:

[0522] , (96)

[0523] , (97)

[0524] (98)

[0525] With grating vector The distance between adjacent rows of the raster It can also be found from geometric constructions and is given by the following formula:

[0526] (99)

[0527] In row vector form, raster vector It has a form similar to equation (26) and is given by the following:

[0528] , (100)

[0529] At once , In other words, it can be written as

[0530] (101)

[0531] Figure 12d The diagram shows the grating vectors used to construct the grating L3. The grating consists of two adjacent rows, 1209 and 1210. The grating vector... Angle opposite to the x-axis The sine and cosine of the sine and cosine are given by the following formula:

[0532] , (102)

[0533] , (103)

[0534] (104)

[0535] With grating vector The distance between adjacent rows of the raster It can also be found from geometric constructions and is given by the following formula:

[0536] , (105)

[0537] This is The same. In row vector form, the raster vector... It has a form similar to equation (27) and is given by the following:

[0538] , (106)

[0539] At once , In other words, it can be written as

[0540] (107)

[0541] The expressions given in equations (29) and (30) can be used to determine the raster period. and Based on grating vector and The parameterization determines the coordinates of the points in grid L3. Substituting the parameterization into expressions of the form (29) and (30) gives...

[0542] , (108)

[0543] as well as

[0544] , (109)

[0545] in, These are the x and y coordinates of a point in raster L3, indexed by values ​​a and b, where a and b are positive integers, negative integers, or zero.

[0546] Since a and b in equations (108) and (109) are integers or zero, the quantities a + b and a - b must also be integers or zero. Furthermore, if a + b is even, then a - b must also be even, because the evenness of a + b implies that a and b are either both odd or both even. Similarly, if a + b is odd, then a - b must also be odd.

[0547] If we assume that a + b is even, then it can be written as

[0548] a + b = 2c, (110)

[0549] as well as

[0550] a – b = 2d, (111)

[0551] Where c and d are positive integers, negative integers, or zero. Therefore, for an even value of a + b, the coordinates of a point on the grid are given by the following formula.

[0552] , (112)

[0553] Note that if i = c and j = d, then it has the same coordinates as the grid L1 given by equation (93). If we instead assume that a + b is odd, it can be written as

[0554] a + b = 2e + 1, (113)

[0555] as well as

[0556] a – b = 2f + 1, (114)

[0557] Where e and f are positive integers, negative integers, or zero. Therefore, for odd values ​​of a + b, the coordinates of a point on the grid are given by the following formula:

[0558] , (115)

[0559] Note that if i = e and j = f, then it is the same as the coordinates of grid L2 given by equation (94). Equations (112) and (115) prove that the points of grid L3 are the same as the combinations of points of grids L1 and L2 as given by equations (93) and (94), thus proving the equivalence of the two methods described for the construction of FSIRG. It has been found that the construction of FSIRG based on grid L3 allows for the inference of far-reaching results on the diffraction order of FSIRG.

[0560] Proof of suppression of certain diffraction orders of FSIRG

[0561] By considering FSIRG 1201 constructed from grating L3, the grating vector can be given according to equations (101) and (107). , Write the equation of the grating for the scattering of the light beam.

[0562] , (116)

[0563] in It is the xy-wave vector of the incident beam on the grating, and It has xy wave vectors The diffraction order of the scattered beam. Based on the properties of wave scattering from a diffraction grating, the order value... and It must be a positive integer, a negative integer, or zero. As mentioned earlier, it is also expected that the scattering from the grating satisfies the grating equation:

[0564] , (117)

[0565] in and The grating vector is given by equations (87) and (88), and It has xy wave vectors The diffraction order of the scattered beam.

[0566] Note that equations (116) and (117) describe scattering from the same grating. Therefore, the possible wave vector in equation (116) Possible wave vectors of equation (117) There must be a correspondence between them, allowing them to be identical. Therefore, it should be possible to derive the raster vector. and Related diffraction order and grating vector and Related levels A certain relationship between them. Based on the equations (87), (88), (101), and (107) respectively. , , and The definition can determine

[0567] , (118)

[0568] as well as

[0569] , (119)

[0570] Substituting these results into equation (116) gives

[0571] (120)

[0572] If you set it to equal The expression, in Description and In the case of the same vector, the expression must be true, given...

[0573] , (121)

[0574] as well as

[0575] (122)

[0576] Pick and The sum of the given

[0577] (123)

[0578] because It can be a positive integer, a negative integer, or zero; therefore, equation (123) indicates the diffraction order value. and The sum must be even or zero. However, based on the grating equation (117) for rectangular gratings, the sum can be chosen to be odd. and The value pairs. This presents a clear contradiction, because such value pairs cannot correspond to the diffraction order of equation (116). The solution to this obvious contradiction is + odd-numbered diffraction order The diffraction efficiency must be zero. In essence, although the grating equation (117) for a rectangular grating shows that these orders exist mathematically, the fact that they must have zero intensity means that they do not exist physically, and therefore there is no contradiction in terms of any physically measurable result. In this case, the two descriptions of the FSIRG produce consistent predictions of the direction of the diffracted beam in the physical world. Since these conclusions are derived from the grating of the FSIRG rather than its actual structure, they will apply to any FSIRG capable of scattering the incident light of any diffraction order.

[0579] This result regarding the scattering characteristics of FSIRG can be examined using methods familiar to those skilled in the art. For example, analytical calculations are possible by applying the Floquet-Bloch theorem, using the symmetry of the grating L3 imposed on the solution of a plane wave scattered by an interlaced rectangular grating as defined herein. Alternatively, computational methods such as the finite-difference time-domain (FDTD) method with periodic boundary conditions, or semi-analytical methods such as strictly coupled-wave analysis (RCWA), can be used.

[0580] Therefore, if a perfectly symmetrical staggered rectangular grating is appropriately configured as the output grating element of a DWC, such that... Figure 46 The order naming convention in Table 2 is appropriate and can be declared. Figure 46 All entrance orders listed in Table 2 must have zero diffraction efficiency, and only the turning order and the zeroth order can have non-zero efficiency. In other words, the output grating configured as an FSIRG cannot actually pass through... Figure 46 The eye-level in Table 2 couples light out of the waveguide.

[0581] Used to correct symmetry breaking in diffraction order

[0582] Figure 12e A cross-sectional view of a cylindrical structure 1211 with a circular cross-section is shown, and Figure 12f A cross-sectional view of a columnar structure 1212 with a square cross-section is shown. Figure 12g An interlaced rectangular grating 1213 with the same period as FSIRG 1201 is shown. In IRG 1213, structure S1 is a circular cross-section cylinder 1211, and structure S2 is a square cross-section cylinder 1212. Due to the difference between structures S1 and S2, it is no longer possible to use the vectors given in equations (101) and (107). and The grating is constructed by repeating a single structure at each point of a single grid. Therefore, it is no longer possible to conclude that: if + If the number is odd, then the diffraction order of the rectangular grating used to construct the IRG is... It must have zero efficiency. On the contrary, the diffraction efficiency must depend on the shapes of S1 and S2, as well as the difference between the shapes of the structures S1 and S2.

[0583] As will be proven, with + Compared to diffraction efficiencies of zero or even orders, + The diffraction efficiency of odd-order diffraction is particularly sensitive to the difference in shape between structures S1 and S2.

[0584] It is important to note that structures S1 or S2 do not need to include a single element to apply these conclusions. As an example, Figure 12j An interlaced rectangular grating 1216 is shown, wherein structure S1 includes, as shown in the figure Figure 12h The three circular pillars 1214 shown, and the structure S2 including as follows Figure 12i The two rectangular pillars 1215 are shown. For this IRG, a non-evanescent entrance-to-eye efficiency is expected to be non-zero. If the IRG is formed by structures S1 and S2, each comprising three circular pillars 1214, the resulting grating will be an FSIRG with an entrance-to-eye efficiency that is necessarily zero.

[0585] The IRG unit cell described herein is a rectangle with sides aligned to the x and y directions, the length in the x direction being equal to the x-period of grid L1 (or equivalently grid L2), and the length in the y direction being equal to the y-period of grid L1 (or equivalently grid L2). As mentioned above, the position of the unit cell relative to the periodic structure can be arbitrarily chosen within the grating plane. Figure 12g The IRG 1213 shown illustrates several possible unit cells, as indicated by the dashed lines: a unit cell 1217 having structure S2 at its center; another possible simple unit cell 1218 having structure S1 at its center; and another simple unit cell 1219 constructed to horizontally bisect two vertically adjacent copies of structure S1 and vertically bisect two horizontally adjacent copies of structure S2.

[0586] Symmetry breaking through changes in composition

[0587] Another way to introduce differences between structures S1 and S2 is to alter the composition of the structures in ways that differentiate their optical properties. For example, if the permittivity of the structures is made different from each other, they will scatter light differently, resulting in an IRG that is no longer perfectly symmetrical, and therefore... + An odd-numbered non-evanescent order does not necessarily have zero diffraction efficiency.

[0588] Symmetry breaking through changes in raster offset

[0589] Now consider modifying FSIRG so that the grid offset vector between grids L1 and L2 is no longer equal to... ,in and These are the periods of L1 and L2 in the x and y directions, respectively. With this change, the vectors shown in equations (101) and (107) can be removed. and The grating is constructed by repeating a single structure at each point of the grid. Therefore, it results in... + The argument that odd-numbered diffraction orders must have zero diffraction efficiency is also no longer applicable.

[0590] If we now consider the raster offset vector and Very small deviations can be expected despite + Odd-numbered non-evanescent diffraction orders will not be exactly canceled out, but the deviation from zero efficiency can be expected to be very small, and depends on the grid offset vector and The degree of deviation. Therefore, it can be expected that when compared with... + Compared to diffraction orders that are even or zero, + The diffraction efficiency of odd order will affect the grid offset vector and Small deviations exhibit much greater sensitivity.

[0591] Methods for controlling the efficiency of diffraction order

[0592] By allowing the differences between control structures S1 and S2, and controlling the positional offsets between rectangular gratings L1 and L2 used to construct the staggered rectangular grating, additional methods can be provided to control the diffraction efficiency of certain diffraction orders. In such a scheme, a fully symmetric staggered rectangular grating and a rectangular grating can be viewed as two extreme cases of a general staggered rectangular grating, providing, on the one hand, the case where certain diffraction orders must be zero, and on the other hand, the case where, for similar structures, the magnitudes of these orders will generally be much larger, provided they are not evanescent.

[0593] For convenience, the following terms will be used to refer to the degree to which an IRG may deviate from an FSIRG: the degree to which structures S1 and S2 differ in shape from each other is called the degree of broken shape symmetry of the IRG; the degree to which S1 and S2 differ in composition is called the degree of broken composition symmetry of the IRG; the overall difference between structures S1 and S2, whether in shape, composition, optical properties, or a combination thereof, is called the degree of broken structure symmetry of the IRG; the positional offset between grids L1 and L2 and... The deviation is referred to as the degree of symmetry of the broken position of the IRG; and the difference between structures S1 and S2 and / or the offset of grids L1 and L2 is related to... The degree of deviation is called the degree of IRG symmetry breaking.

[0594] Reference Figure 47The criteria listed in Table 3 have shown that, when rectangular gratings are used as output gratings in diffractive waveguide combiners, achieving good performance from rectangular gratings requires a degree of control over the relative diffraction efficiencies of various steering and entrance orders. As will be demonstrated by examples of the present invention, the ability to further control the diffraction efficiencies of the entrance diffraction order through the use of staggered rectangular gratings with a controlled degree of broken symmetry can provide favorable performance for applications using such gratings as output elements of diffractive waveguide combiners.

[0595] Alternate arrangement of highly symmetrical staggered rectangular gratings

[0596] Figure 13a A top view shows an example of a specific case of an interlaced rectangular grating 1301, referred to as a horizontally symmetric interlaced rectangular grating (HSIRG) and defined as an IRG with the following specific characteristics:

[0597] i) The periods of grids L1 and L2 in the x-direction are And in the y direction is ;

[0598] ii) The raster offset vector is derived from Give;

[0599] iii) Structures S1 and S2 are identical, and in the diagram shown here, they are assumed to be columns with circular cross-sections.

[0600] The diffraction order of this grating will follow equation (117). However, it should be noted that the grating can also be constructed with a period of in the x-direction. A rectangular grating. Similar to the case of FSIRG, in order for the two methods of constructing HSIRG to be compatible, certain diffraction orders of equation (117) must have zero diffraction efficiency. For HSIRG, this requirement is that if... If the order is odd, then the order will have zero efficiency. (See reference...) Figure 46 The diffraction orders listed in Table 2 indicate that the only entry-eye orders with non-zero efficiency are STE and TEAT-Y, while the only steer orders with non-zero efficiency are the gyratory orders BT-X, BT+X, BT-Y, and BRT+Y. This arrangement completely suppresses other steer orders and entry-eye orders.

[0601] Figure 13b A top view of an example of an interlaced grating 1302 is shown. This interlaced grating is referred to as a vertically symmetric interlaced rectangular grating (VSIRG) and is defined as an IRG with the following specific characteristics:

[0602] i) The periods of grids L1 and L2 in the x-direction are and in the y direction ;

[0603] ii) The raster offset vector is derived from Give;

[0604] iii) Structures S1 and S2 are identical, and in the diagram shown here, they are assumed to be columns with circular cross-sections.

[0605] The diffraction order of this grating will follow equation (117). However, it should be noted that the grating can also be constructed with a period of in the y-direction. A rectangular grating. Similar to the FSIRG case, in order for the two methods of constructing a VSIRG to be compatible, certain diffraction orders of equation (117) must have zero diffraction efficiency. For a VSIRG, this requirement is that if... If the order is odd, then the order will have zero efficiency. (See reference...) Figure 46 The diffraction orders listed in Table 2 indicate that the only entry-eye orders with non-zero efficiency are TEAT+X and TEAT-X, while the only steer orders with non-zero efficiency are the gyratory orders BT-X, BT+X, BT-Y, and BRT+Y. This arrangement completely suppresses other steer orders and entry-eye orders.

[0606] Similar to FSIRG, introducing a degree of broken symmetry by deviating from the precise conditions of HSIRG or VSIRG will result in a non-evanescent diffraction order with zero efficiency receiving some energy from the incident beam. For small deviations, it can be expected that the diffraction efficiency of the suppressed diffraction order for a given incident beam in a given direction, wavelength, and polarization will depend on the size, shape, and optical properties of structures S1 and S2, as well as the degree of broken symmetry. For HSIRG, the degree of broken positional symmetry will be the deviation of the grid offset vector from... The degree of symmetry at the broken position. Similarly, for HSIRG, the degree of symmetry at the broken position will be the degree of deviation of the raster offset vector. The degree of.

[0607] Therefore, by utilizing the concepts of FSIRG, HSIRG, and VSIRG, and in conjunction with the use of broken symmetry, this invention provides a series of methods for providing considerable control over eye-orders, or certain combinations of eye-orders and turning orders.

[0608] Advantages of using interlaced rectangular gratings as diffraction waveguide combiners in display systems

[0609] WO 2018 / 178626 describes a method for designing two-dimensional gratings based on a modified rhombic structure. This method has been shown to possess certain scattering properties, which are advantageous for use as output gratings in DWCs. However, it has been found that in order to control the relative intensity of certain entrance-to-eye diffraction orders, the parameters describing the modified rhombic shape must be within a certain range. This limits the extent to which the scattering properties of the grating can be optimized to improve performance, for example, by changing the shape of the rhombus relative to the position on the grating, as this may result in a loss of control over the efficiency of certain entrance-to-eye diffraction orders, leading to a loss of wearer uniformity. The staggered rectangular gratings described in this invention, in addition to the shape and optical properties of the grating structure, can utilize the degree of broken symmetry to provide an additional degree of control over grating scattering. This, in turn, can provide more control over the optimization of scattering properties to suit applications such as using IRGs as output elements in DWCs.

[0610] An additional advantage of this invention is that it makes it easier to obtain the diffraction order that directs light towards the input direction of the IRG. (See also...) Figure 45 Table 1 in the table refers to tables with cumulative order. The beam. Due to the reduced number of waveguide diffraction orders, the grating provided by this invention can provide more efficient coupling into the cumulative order than methods such as those described in WO 2018 / 1786262. This allows for designs that provide... The diffraction efficiency of the cumulative diffraction order is increased without excessive loss due to beam scattering into undesirable diffraction orders. The structural symmetry of many designs achieved by this invention also provides more favorable coupling. Cumulative order. Used for beam coupling. Possible pathways for the order include through BT-Y diffraction order pairs. Diffraction of cumulative order beams and diffraction order pairs through TTB+X and TTB-X Diffraction of cumulative-order beams. Such as... The increased availability of accumulator order directions can improve the uniformity of output from the DWC by providing more paths for the beam through the waveguide and thus a greater degree of uniformity in the output resulting from the combination of these beams. Using reflected light can also provide an increase in the overall efficiency of the DWC, as such beam paths offer more opportunities for the beam to couple out of the waveguide toward the observer.

[0611] Another advantage of this invention compared to existing technologies is that the size of the output grating can be smaller for a given eye-tracking range. This can be seen by using a pupil replication map. A pupil replication map is a diagram showing the location of beam outputs that may occur due to repeated interactions with diffractive elements such as IRGs or other two-dimensional diffraction gratings through various branch paths of the DWC. Essentially, at each output location, a replication of the input beam is considered the output. The result of the entire beam set is the previously described extended exit pupil, which in turn provides an extended eye-tracking range. Therefore, the extent and coverage of the pupil replication map are among the main factors in determining the eye-tracking range of the system. It should be noted that for a given DWC, each input beam direction and wavelength will produce its own corresponding pupil replication map.

[0612] The projected eye-tracking range (which is typically spatially separated from the DWC) is found by placing the system's eye-tracking range (ETR) at its defined position relative to the DWC and projecting it backward along the angle of view onto the DWC's output grating. The area of ​​the output grating covered by this projected eye-tracking range is the portion of the output grating that should output light at a given angle of view to cover the eye-tracking range at that angle of view. For an image to be seen at all locations within the DWC's eye-tracking range, the pupil replication event at a point in the field of view must cover the corresponding projected eye-tracking range at that point in the field of view. Since light can only be output from the DWC at points where a diffraction grating exists, the limiting position of the projected eye-tracking range calculated across the entire field of view and projected onto the DWC will set the minimum size for the output grating.

[0613] Figure 14a A pupil replication diagram 1401 of a DWC with a 2D diffraction grating configuration as described in WO 2018 / 178626 is shown. Here, only the major turning order of the grating design is included when considering the allowed paths. Pupil replication diagram 1401 shows the location of the input grating 1402 of the DWC, which is a 1D diffraction grating with its grating vector parallel to the y-axis of the diagram. The output grating 1403 is a 2D diffraction grating according to WO 2018 / 178626, whose grating vector is ±60° to the y-axis of the diagram. Each pupil replication event is shown as a circle 1404. A pupil replication diagram of the upper right field is shown here. The projected eye-motion range 1405 of this field is calculated by projecting the eye-motion range backward from the expected position of the observer's eye onto the waveguide surface.

[0614] For this grating, the pupil replication pattern indicates that the xy-wave vectors point in a substantially diagonal direction after one of the major turning orders. To ensure that the projected eye-tracking range 1405 is covered by the pupil replication event, the pupil must begin to rotate at a distance significantly closer to the input grating than the eye-tracking range 1405. This requires the output grating to have an additional region above the most extreme eye-tracking range position 1405, which increases the minimum size of the grating. Figure 14a As shown in the example, in order to achieve an eye-tracking range of 11×12 mm with a field of view of 35°×20°, the output grating must have a minimum size of 38×30 mm.

[0615] Figure 14b A pupil replication diagram 1406 with an output grating for a DWC according to the present invention is shown. The input grating 1407 is the same as the input grating 1402, but the output grating 1408 is an IRG with x-periods and y-periods equal to the periods of the input grating 1402. The field of view of the projection display used with the display is the same. Compared to grating 1403, the pupil replication position after the turning step from grating 1408 travels in a more horizontal direction. As a result, the additional space required above the projected eye-tracking range 1409 to ensure coverage of the pupil replication event can be much smaller, and the size of the output grating can be significantly reduced. Figure 14b In the example shown, to achieve an eye-tracking range of 11×12 mm with a field of view of 35°×20°, the output grating must have a minimum size of 27×30 mm. Figure 14a Compared to the example in the example, this reduces the size by 11 mm in the y-direction. A smaller grating will impose fewer constraints on the overall size and shape of the DWC, potentially reducing manufacturing costs and providing greater freedom in the shape factor of designs that incorporate such gratings.

[0616] Simulation method of staggered rectangular gratings in diffractive waveguide combiners

[0617] It is important to emphasize that while symmetry-based independent variables can be used to determine that the efficiency of certain diffraction orders of FSIRG, HSIRG, or VSIRG must be zero, for any IRG, computational techniques are typically required to determine the diffraction efficiency or the associated polarization correlation coefficient. As previously mentioned, suitable methods include numerical techniques such as the finite-difference time-domain method (FDTD) with periodic boundary conditions, or semi-analytical methods such as strictly coupled-wave analysis (RCWA).

[0618] Typically, numerical simulation methods are needed to calculate the performance of an IRG in practical applications, such as if it were used as a grating element in a DWC. For cases where the coherence length of the light source used is shorter than the distance between successive grating interactions, a reasonable approximation is to consider each interaction independently and use numerical ray tracing to calculate the various beam paths resulting from the successive interactions with the waveguide surface. The contribution of each of these paths to the total output can be calculated by considering the required grating interactions for a given path. Given the wavelength, direction, and polarization of the incident beam represented by one or more rays, the diffraction efficiency of each order can be calculated using the methods described above for each interaction. The subsequent radiant flux, direction, and polarization of the various diffracted beams are then determined from the calculated diffraction efficiency and the grating equations acting on the xy-wave vectors described by the rays. By aggregating the contributions from a large number of paths and determining those contributions that will be detected by the observer's representation, the output from the DWC can be simulated.

[0619] Ray tracing methods have been widely used in optical simulations, including systems characterized by waveguides and / or diffraction gratings. Such methods can be easily implemented using custom simulation code or commercial software such as Zemax OpticStudio® (Zemax LLC). In ray tracing simulations, various practical characteristics of the physical world realization of the DWC can be considered. For example, the finite extent of the grating can be considered by using the hit coordinates of the light's interaction with the surface and performing tests on whether such coordinates lie within a region defined as having a grating, which can be described by polygons or other methods. Ray tracing can also be used to simulate the edges of the DWC itself, for example, by describing the edges using polygons, surfaces, or other geometric primitives and performing tests to determine which surface a given ray will next illuminate on its path through the DWC. Processes such as absorption or scattering can then be applied to the light based on the surface it illuminates. In this way, complex simulation models of the DWC's behavior can be developed and used to predict its performance.

[0620] Methods for the design and representation of interlaced rectangular gratings

[0621] For a diffraction grating to scatter light, there must be some variation in at least one optical property in and around the grating, including but not limited to refractive index, permittivity, permeability, birefringence, and / or absorptivity. In many cases, this variation can be achieved by using an embedded structure with at least one different optical property in the surrounding matrix of the material, or as a surface relief structure comprising at least one material on a substrate of the same or different materials, and protruding into the surrounding medium of a different material than the surface relief structure. For diffraction, at least one optical property of the medium surrounding the surface relief structure must be different from at least a portion of the surface relief structure. The surrounding medium for gratings arranged as surface relief structures on the surface of a DWC is typically air, but this is not always the case. In a sense, any surface relief structure can be considered an embedded structure in the matrix of the surrounding medium. Therefore, similar methods can be used to design and represent surface relief structures and embedded structures.

[0622] Any design of a grating will require some representation or description of the shape and composition of the IRG so that it can be designed, simulated, and manufactured in the physical world. Various representations suitable for describing a range of surface relief structures are developed herein to elucidate aspects of the invention and illustrate how these aspects can be implemented in practical applications such as simulation and manufacturing. Those skilled in the art will understand that, in addition to the methods outlined herein, a wide range of feasible methods exist for the representation of IRGs.

[0623] A method for designing and representing the geometry of interlaced rectangular gratings based on mathematical construction.

[0624] In some methods, gratings can be created from three-dimensional structures made of one or more materials. For a grating constructed according to such a principle, a representation can be used to describe the geometry of each interface between the various materials used. In some methods, we can include extensions to the geometry in our representation, such as adding layers of new geometries derived from existing geometries to represent the results of processes such as coating. In other methods, we can consider modifications to the geometry of the grating, such as the rounding of sharp features, as a tool to change design performance or as a method to represent manufacturing constraints. We can consider various combinations and multiple applications of these methods to potentially produce fairly complex geometries that include many different regions of different materials.

[0625] In systems that describe materials through surface geometry, each material must be associated with its own surface geometry description. A method for generating surface geometry descriptions of interlaced rectangular gratings includes the following steps:

[0626] 1. We assume the bottom of the grating is in the xy plane (i.e., z = 0). We define the grating vectors for the gratings L1 and L2 used to construct the IRG as:

[0627] , (124)

[0628] as well as

[0629] (125)

[0630] 2. We define the clipping function. To describe the limited scope of IRG. The value is 1 in the area where the raster exists, and 0 elsewhere. If no cropping is needed, then... =1, and with Coordinates are irrelevant.

[0631] 3. We use the raster function given by the following formula. To represent grid L1:

[0632] , (126)

[0633] And we use the raster function given by the following formula. To represent grid L2:

[0634] (127)

[0635] in, It is the raster offset vector.

[0636] 4. We will use surface geometry functions The structure S1 is defined as an IRG, and it is described as the distance of the structure protruding from the grating plane in the z-direction. A function of coordinates. Similarly, we will use functions... The representation of structure S2 defined as IRG. Function and It can be a mathematical function, the output of a computational algorithm, a grid or mesh of discrete values ​​combined with an interpolation scheme, or a set of parametric surfaces such as a non-uniform rational B-spline surface. Importantly, for the definition here, the function... and Only each should be returned A single value for coordinate input. and Both are defined as having non-zero values ​​only within a rectangular region in the xy plane that has the same size and orientation as the IRG unit cell, wherein the IRG unit cell has a length of [missing information] in the x-direction. And the length in the y direction is The region is a rectangle. Typically, this region is centered at the origin (0,0), but this is not mandatory.

[0637] 5. Based on the representation of grid L1 and structure S1, we can use periodic surface geometric functions To represent the periodic structure PS1, the periodic surface geometry function is defined as a grid function. With structure function convolution,

[0638] (128)

[0639] Here, the symbol Representation function and exist Two-dimensional convolution in space. The distance in the z-direction from which the periodic structure protrudes from the grating plane is described as... Functions of coordinates. Similarly, the periodic structure PS2 can be represented by periodic surface geometric functions:

[0640] (129)

[0641] Performing convolutions in equations (128) and (129) provides:

[0642] , (130)

[0643] as well as

[0644] (131)

[0645] Note that these definitions ensure that the IRG always includes a complete copy of structures S1 and S2.

[0646] 6. IRG is constructed by combining PS1 and PS2, and is derived from the IRG surface function. This represents the distance in the z-direction from which the combined periodic structure protrudes from the grating plane as... Functions of coordinates. Periodic structure functions. and Combinations can be performed in various ways. The simplest method is to add the structures together, thus giving:

[0647] (132)

[0648] However, overlapping regions where both structure functions are non-zero will result in structures stacking on top of each other. This may neither reflect the design intent nor meet manufacturing constraints. A more general approach to composition can be defined using a masking function as follows:

[0649] (133)

[0650] By calculating in the given The product of masking functions evaluated for each periodic structure in coordinate system We can mathematically identify the overlapping grating portions of two structures. To determine the IRG surface function at the overlapping region, we can define a combiner function. The combiner function can be constructed from various expressions according to the requirements and intent of the representation. Valid definitions of combiner functions include, but are not limited to, the following examples:

[0651] Combiner: (134)

[0652] Differential combiner, variant 1: (135)

[0653] Differential combiner, variant 2: (136)

[0654] Absolute difference combiner: (137)

[0655] Average combiner: (138)

[0656] Minimal combiner: (139)

[0657] Maximum combiner: (140)

[0658] First element preference combiner: (141)

[0659] Second element preference combiner: (142)

[0660] Then the IRG surface function can be defined as

[0661] (143)

[0662] For some representations, allowing the periodic structure function to have a certain range of values ​​is helpful, making it difficult to use z = 0 as a criterion for determining whether two structures exist and therefore whether they overlap. Instead, one can base it on specifically specified values. The masking function is defined by the detection, and the value is... Selected as easily as required to represent the desired structure and Distinguish between values ​​within a certain range. In this case, the masking function can now be defined as...

[0663] (144)

[0664] If the IRG surface function is defined as having [a certain property] in a region where neither of the two periodic structure functions is defined... If the value is , then the IRG function can now be defined as

[0665] (145)

[0666] This completes the description of the layers of the IRG geometry. Multiple layers can be computed by following the same process. These layers can be offset relative to each other in position by applying a position offset to the IRG surface function, where such offset can be in the x, y, and / or z directions.

[0667] In the above representation scheme, and It is defined as having non-zero values ​​only within a rectangular region of the same size as the IRG unit cell. Typically, this region is centered at the origin (0,0), but this is not mandatory. Outside this rectangular region, according to the definition, and All are zero. This can be achieved by using a rectangle function. To achieve, Defined as

[0668] (146)

[0669] if If a function does not conform to the rule regarding zero values ​​outside the IRG unit cell, then a suitable truncated version of the function centered at the origin (0,0) is given by the following equation:

[0670] (147)

[0671] Equation (147) itself is constrained by and The definition of any structure is limited. However, for some systems, it may be desirable to represent structures that extend beyond the limits of the IRG unit cell, as this can bring advantageous properties to the IRG's performance. Based on our definition of periodic structures, we know that everything regarding the shape of the structure can be represented within the unit cell of the IRG. Therefore, to represent long structures, we need a method to contain them within a single unit cell.

[0672] Figure 15a A top view of a portion of IRG 1501 is shown, where structures S1 and S2 each comprise pillars 1502 and 1503, the lengths of pillars 1502 and 1503 in the y-direction being greater than the y-dimension of the IRG unit cell. A rectangular region 1504 with dimensions equal to the IRG unit cell can be drawn around one of the copies of structure S1; similarly, a rectangular region 1505 can be drawn around one of the copies of structure S2. A suitable structure function is then fully defined within the unit cell rectangle 1504. It can be defined by finding the portion of the periodic structure array PS1 located within rectangle 1504.

[0673] Figure 15b The periodic structure PS1 of IRG 1501, located within rectangle 1504, is shown. A copy of structure S1 1506 is located at the center of the rectangle and extends beyond the top and bottom edges of the structure. This is to form the structural function. We first trim structure S1, which extends through the top edge 1507 and the bottom edge 1509. The unit cells are completed by adding portions of vertically adjacent copies of structure S1, where they overlap with rectangle 1504, thus achieving the desired effect in the structure function. Additional features are generated at the bottom 1508 and top 1510. The structure function within rectangle 1505 can be applied. The equivalent process applies to structures that extend beyond the x-direction limit of the unit cell length, or structures that extend beyond both the x-direction and y-direction limits of the unit cell rectangle.

[0674] The mathematical representation of this process can be constructed by taking the sum of shifted versions of the structure functions describing the entire structure, but clipping each of these into a unit cell rectangle. Figure 15c A single structure S1 1513 is shown placed at the center of the unit cell rectangle 1504. As shown, additional rectangles 1511 and 1512, having the same dimensions as 1504, are placed at the top and bottom of 1504, respectively. Within each of these rectangles, a portion of S1 that must be enclosed within rectangle 1504 can be seen. Mathematically, if If a function describes a structure that extends beyond the unit cell rectangle, then it is correctly limited to a structure function within a single unit cell. It is given by the following formula:

[0675] (148)

[0676] Here, assuming It has a zero value outside the required part of the structure. If used instead... The value of indicates the lack of structure, and a masking function can be used to obtain the expression.

[0677] (149)

[0678] Equations (148) and (149) can be generalized to the necessary number of adjacent rectangles to ensure that the structure is correctly represented by a structure function confined within a single unit cell. For example, if it is necessary to extend this to eight rectangles surrounding the unit cell rectangle (horizontal and vertical edges plus diagonals), and if... If the function describes the extended structure, then the structure function enclosed in a rectangle the size of a unit cell is given by the following equation:

[0679] (150)

[0680] Here, it is assumed that the part outside the structure is composed of Similarly, if alternative values ​​are used to indicate the lack of structure, a masking function can be used, as shown in equation (149).

[0681] If structures S1 or S2 overlap each other within their own periodic structures when repeated on their respective grids, the resulting structures, as outlined in this paper, will have the sum of the heights of the overlapping components. This does not preclude the use of this process, but it should be kept in mind when designing structures and considering their applicability as repeated periodic structures.

[0682] In addition to extending beyond the IRG unit cell, the periodic structures PS1 and PS2 can also include continuous structures. In this case, the appropriate structure function will be a structure function that is fully defined within a rectangle of size equal to the IRG unit cell, where the structure function is defined such that opposite edges are aligned with each other to connect and form a continuous structure. Figure 15d IRG 1514 is shown, which includes structures 1515 and 1516. For periodic structures PS1 and PS2, structures 1515 and 1516 are continuous in the y direction, respectively. Figure 15eA suitable structure S1 for generating the periodic structure PS1 is shown, defined within a rectangle equal in size to the unit cell 1517. The edges of structures 1518 and 1519 form a single continuous structure when the unit cells are placed adjacent to each other. Essentially, we note that a continuous structure is merely an isolating structure of size and shape within the unit cell, which, when repeated on a periodic array, is adjacent to a copy of itself, thus forming a continuous structure. Therefore, the definition of an interlaced rectangular grating can include both continuous and isolating structures.

[0683] A common type of structure consists of one or more shape profiles that are extruded in the z-direction to form columns. If a structure is formed by columns all extruded to the same height, the resulting structure is often called a binary structure. This is further defined if the column profiles can be described in the xy-plane as polar functions of angles. Then a suitable structure function A suitable definition is given by the following formula:

[0684] , (151)

[0685] in It is the height of the column, and we use Here, It is from Descartes Coordinates to polar coordinates Find the polar angle when using coordinates The quadrant-sensitive arctangent function. In another way of describing the geometry of extruded surfaces, we can use... Edge polygon Defined as a polygon vertices A list of coordinates, where It is a polygon of A list of coordinate pairs. Then, we can define a function with the following properties. :

[0686] (152)

[0687] Therefore, for a single structure, the corresponding structure function It will be

[0688] (153)

[0689] The height of the i-th structure is determined by The x and y coordinates of the polygon of the i-th structure are given by... The given structures can be represented by the following structure functions:

[0690] , (154)

[0691] Where M is the number of elements in the structure. In this way, complex multi-element structures can be created. It should be noted that this method can also be applied to create multi-level structures. By defining polygons that lie on top of each other, equation (154) can be used to represent multi-level structures.

[0692] After constructing a surface representation using mathematical formulas, it is usually necessary to convert that representation into a format suitable for other purposes such as simulation or manufacturing. The necessary format is specified by the requirements of the process, but many methods are available to those skilled in the art and can be applied directly.

[0693] For example, some applications might require representing a raster as a mesh of triangular polygons. This mathematical representation can be converted into a mesh format by first constructing a triangular mesh in the xy-plane and evaluating a mathematical function at each vertex of that mesh to obtain the mesh's z-value. The result would be a contour mesh of triangles that approximates the mathematical function. Such a representation is necessarily an approximation of the true geometry; for example, an infinitely steep wall in a structure caused by a sudden step in the z-value would be limited by the choice of mesh resolution around such a transformation. However, the mesh resolution can be adjusted such that the difference between the approximate and true representations is essentially negligible for practical purposes.

[0694] Some applications may require a voxel-based representation of the grating. A voxel-based description is provided as a three-dimensional grid of coordinates, where one or more values ​​of interest are described at each coordinate. Such values ​​are typically material properties related to electromagnetic radiation interactions, such as permittivity.

[0695] Voxel representation can be constructed by first creating a 3D mesh of the required size and resolution. The mesh is considered to describe the corner vertices of a set of continuous 3D cuboids as the voxels. Each voxel has: a Cartesian coordinate system at the center of its associated cuboid. Coordinates, the Cartesian Coordinates are typically calculated as the arithmetic mean of the coordinates of the corner vertices; and a set of properties related to the requirements of the use for representation. Values ​​and / or indexes that describe the inherent optical properties of the material at that voxel. Note that the index i is used to indicate the i-th voxel represented.

[0696] Then, based on the material specification of the geometry of the surface representation, the mathematical representation can be transformed into voxel space by iterating through all voxels and comparing the z-value of the voxel center with the function value at that point for each voxel.

[0697] For example, assuming that the refractive index is included The material IRG is placed in a material with a refractive index of On the substrate of the material, and with a refractive index of The dielectric surrounds it. If the substrate surface is located... And the IRG function The definition is to make So we know that, in In this case, the system material is the substrate material, while In this case, the material will be the material of the surrounding environment. Between these constraints, the material will be the material of the IRG. Therefore, for coordinates... For the i-th voxel, we can determine the refractive index using the following equation. :

[0698] (155)

[0699] This process can be applied to the entire property set by replacing the refractive index value with the value of the relevant property. Alternatively, in some systems, equation (155) can be used, but with the refractive index replaced by an index value corresponding to the chosen material. A separate lookup table of material property values ​​can then be associated with each material index value. As with the mesh representation, the voxel-based representation is generally an approximation of the original representation, but by adjusting the resolution of the voxel mesh, the difference can be negligible from a practical point of view.

[0700] Ultimately, the accuracy of any numerical representation will be dictated by limitations on computational resources such as memory and computing power. Fortunately, it has been found that the computing power of modern personal computers is sufficient to handle a wide range of designs and representations with adequate accuracy.

[0701] A method for designing and representing interlaced rectangular grating geometry based on 3D geometric modeling technology

[0702] The process of generating the IRG surface function given in equation (143) requires that the resulting surface geometry be in each The coordinates have a single z-value. This excludes descriptions of certain geometries, such as those characterized by a structure in which the geometry has certain... The coordinates have more than one z-value, such as undercut geometry or highly inclined surfaces. Instead of seeking mathematical descriptions of structures S1 and S2, we can construct these structures using methods developed for the design of three-dimensional geometry, such as those used in three-dimensional computer-aided design systems (3D CAD) or three-dimensional computer graphics systems.

[0703] These systems typically offer a wide range of geometry modeling processes for constructing and manipulating 3D geometries. These include tools for extruding, lofting, and sweeping 2D contours; 3D geometric primitives such as cuboids, cylinders, ellipsoids, and tetrahedrons; tools for generating and manipulating polygonal meshes; and tools for creating and manipulating surfaces, including those based on non-uniform rational B-splines (NURBS), which can be used to represent a broad range of geometries. Typical computer modeling systems also provide extensive tools for trimming, stitching, blending, twisting, and otherwise manipulating geometry, as well as tools for combining geometry through operations such as geometric union (also known as Boolean union, Boolean merge, and addition in various modeling systems), geometric intersection, and geometric subtraction. By continuously applying such geometry modeling and creation tools and by combining multiple elements, a wide range of geometrically complex 3D structures can be created.

[0704] The commercial software described herein, demonstrating methods for geometry creation and modification, is widely available and includes SolidWorks® (Dassault Systèmes SolidWorks Corporation), Catia (Dassault Systèmes SE), and Autodesk Maya (Autodesk, Inc.). Examples of open-source software include the Blender project and FreeCAD (both licensed under GPLv2+).

[0705] Generally, the geometry modeled in a given system can be exported in a variety of vendor-independent file formats. Suitable formats capable of describing various types of geometry include the Initial Graphics Exchange Specification (IGES) file format and the Product Model Data Exchange Standard (STEP) file format. This allows data to be converted into polygon mesh files such as the Stereolithography (STL) file format from 3D Systems and the Polygonal File Format (PLY) developed by Stanford University. Such files can then be imported for use in simulation and manufacturing software. The specifications for these file formats are publicly available, so if a given system does not support the required format, software modules can be written to import the data and parse it into an appropriate format for future purposes, such as simulating the scattering characteristics of a grating design based on the described geometry or producing manufacturing tools to create a physical-world implementation of the design. Such import routines can also perform tagging of the material types of the different entities described by the file, allowing material properties and labels to be assigned as needed.

[0706] It is important to recognize that while these systems are designed to create larger structures, incorporating scaling functions into simulation tools that use geometries created by such systems is straightforward. For example, 1 mm in a CAD system can be scaled to correspond to 1 nm in a simulation system. It is equally important to recognize that in a CAD system, only a single unit cell of the IRG needs to be modeled and exported to simulation or other design tools. The structure can then be replicated across the entire array as needed, although for certain purposes such as simulations of electromagnetic wave scattering from periodic structures, typically only a single unit cell is required due to the invocation of periodic boundary conditions as part of the simulation process.

[0707] As an example, Figure 16a A cylindrical structure 1601, a spherical structure 1602, and a cuboid structure 1603 are shown. A composite structure 1604 can be created by placing the sphere 1602 at the end of the cylinder 1601 and performing a geometric union operation, then placing the result on the cuboid 1603 and performing another geometric union operation. Such a structure can be used as structure S1 or S2 of an IRG.

[0708] Structures S1 and S2 must be constructed such that, in the x and y directions, they are each completely confined within a rectangular region in the xy plane whose size and orientation are equal to the IRG unit cell. This may require using copy and trim operations to obtain the portions of the structure that overlap with the edges of the IRG unit cell, in order to create a version of the structure located within the IRG unit cell. For example, forming Figure 15a The extended structure 1502 of a portion of the IRG 1501 shown can be derived from... Figure 15b The modified multi-element structure shown is replaced by one that is entirely confined within a single unit cell 1504. This modified structure is formed by taking three consecutive copies of structure 1501 from vertically adjacent unit cells and trimming the structure so that only the portion located within the single unit cell is retained. Such a geometric editing process is straightforward with modern 3D modeling tools such as those mentioned above.

[0709] In this method, periodic structures PS1 and PS2 are created through a simple pattern copying operation, where a copy of structure S1 is placed at each point of grid L1 of the IRG, and a copy of structure S2 is placed at each point of grid L2 of the IRG. This is similar to the convolution operation shown in equations (128) and (129). A geometric union operation of adjacent copies of structures S1 and S2 can be used to connect the structures together to form periodic structures PS1 and PS2, respectively.

[0710] An IRG is formed by a combination of periodic structures PS1 and PS2. In this approach, how to handle the overlapping regions of PS1 and PS2 when constructing the IRG must be considered. Typically, this combination will be a geometric union of the structures. If PS1 and PS2 consist of closed geometries, tests can be conducted to see if the geometry of one part lies within the other, thus determining the appropriate trimming and stitching operations required to create the geometric union. If open surfaces are used for PS1 and PS2, it is generally advantageous to add additional geometry to the representation to create one or more closed volumes, i.e., volumes where all surfaces are connected to enclose a finite volume, allowing operations such as geometric union to be correctly applied in three dimensions. One approach is to use an extrusion operation from a plane parallel to the xy-plane. Figure 16b A portion of an unclosed surface 1605 is shown, representing a periodic structure protruding in the z-direction. The profile of surface 1605 in a plane parallel to the xy-plane can be used to define a planar surface 1606. Extrusion from surface 1606 upwards into surface 1605 in the z-direction forms a closed geometry 1607 suitable for geometric union operations.

[0711] In some implementations, the IRG will be a surface relief structure on the substrate. Such a combination can be achieved through the geometric union of the IRG and a cuboid with its face parallel to the xy plane of the IRG. If the substrate has different optical properties than the IRG, for example due to the inclusion of different materials, the boundary between the substrate and the IRG must be maintained in the geometric representation, and a method must be chosen to determine whether the optical properties of the overlapping geometry between the substrate and the IRG are related to the optical properties of the substrate, the IRG, or some combination of the two. For such an IRG to be physically feasible, all parts of the surface relief structure need to be connected to the substrate in some way.

[0712] In other embodiments, the IRG will be embedded in a medium M, such as the substrate itself, wherein the optical properties of the medium and the IRG are different in at least one respect. Figure 16c A surface relief structure 1608 to be embedded within a medium M is shown. The geometric representation of the medium M can be constructed by extruding a 2D profile in the xy plane along the z-direction. The resulting plate 1609 should extend at least within the range of the IRG in the x, y, and z directions. A representation combining the medium M and the IRG can be achieved by first performing a geometric subtraction of the plate 1609 from a copy of the surface relief structure 1608, resulting in a plate 1610 with the geometry of the IRG cut from it. The geometric union of this cut plate 1610 and the surface relief structure 1608 (where the inner surface between the IRG and the plate SL is preserved) completes the representation of the composite embedding structure 1611. Figure 16dA cross-sectional view of the composite embedded structure 1611 is shown, illustrating the areas of the cutting medium 1610 and the surface relief structure 1608.

[0713] Representations of IRGs constructed from various 3D geometries may also need to be converted into other representations for other purposes, such as simulation and manufacturing. Mesh-based representations can be achieved using various recognized tessellation methods to convert various geometries into approximations constructed from triangles and polygons. Voxel-based representations can be constructed by considering whether the center coordinates of each voxel lie within the geometry of the IRG. Based on such a test, the properties associated with the voxels can be correspondingly set as properties of the IRG material or the surrounding material.

[0714] Methods for modifying the geometry of interlaced rectangular gratings

[0715] In some cases, it is useful to apply modifications to the geometric representation. Such modifications can be appropriate to have a geometry that better matches the constraints of a manufacturing process, or they can be analogous to steps in the manufacturing process. Modifications can be mathematical transformations of surfaces described by mathematical formulas, 2D and 3D geometric primitives, or derived geometric meshes. Alternatively, modifications can be algorithms that perform an analysis of the input geometry and compute results based on that analysis. Some modifications can be selectively applied to only a portion of the geometry of the IRG. Furthermore, many modifications can be applied sequentially, where the input to one modification takes the geometric output from another modification. If the modifications represent a manufacturing process, then in this way, complex geometric features that are practically achievable with current manufacturing methods can be created. Modifications do not need to be applied to the entire IRG; instead, they can be applied to structures S1 and S2 or periodic structures PS1 and PS2 before the IRG is constructed. Some examples of geometric modifications are provided below:

[0716] i) Linear coordinate transformation: The transformation range of the system can be derived based on linear coordinate transformation. Essentially, the new... The set of coordinates can be derived from the input according to the following relationship: From the set of coordinates, we can derive:

[0717] (156)

[0718] in, It is a 3×3 transformation matrix that fully describes the transformation, and Represents a vector or matrix The transpose of the expression. Such transformations can be applied to the result of a mathematical function representation or to coordinates associated with a mesh representation. Transformations of particular note include:

[0719] a. Scaling transformation—the geometry is scaled according to the x, y, and z directions respectively. , and The scaling of the coefficients is achieved through the following transformation matrix:

[0720] (157)

[0721] b. Rotation around the z-axis – the geometry rotates by an angle. Counterclockwise rotation around the z-axis is achieved using the following transformation matrix:

[0722] (158)

[0723] Rotation around the x and y axes is also feasible and may be relevant to isolated structures, but due to the constraint that the grating grid is parallel to the xy plane, rotation around the x and y axes is not suitable for application to the entire IRG. However, such rotation may be applicable to structures S1 and S2.

[0724] c. Slant modification — Figure 17a A perspective view of a single-surface relief structure 1701, an example of a single element of an IRG, is shown. A tilted structure 1702 can be obtained by applying a shift to the position of this structure according to its height above the xy-plane. This tilt is achieved through the following transformation matrix:

[0725] , (159)

[0726] Where α and β are the angles of inclination projected onto the xz and yz planes, respectively. Figure 17a In the example shown, β = 0. Skew operations within the xy-plane or between all three coordinate axes are also possible, but they will affect the IRG's raster vectors or cause the raster's grid to no longer be parallel to the xy-plane. However, such skew operations may be applicable to structures S1 and S2.

[0727] A series of linear transformations M1, M2, ..., M N The combined effect can be calculated by multiplying the transformation matrices together:

[0728] , (160)

[0729] in, It is a composite transformation. Typically, any transformation affecting the x and y coordinates, in addition to translation (which may depend on the z-coordinate), will also transform the IRG's raster vectors when applied to the entire raster, and will usually change its operation.

[0730] ii) Draft modification — Figure 17b A perspective view of a single-surface relief structure 1703, an example of a single element of an IRG, is shown. Draft modifications involve adding controlled tapers to the faces of the model to make the walls less steep, thus allowing the size of the structure to vary with height. Positive draft means that the vertical walls are gradually tapered so that the structure becomes smaller with increasing height, and negative draft means that the vertical walls are gradually tapered so that the structure becomes larger with increasing height. Structure 1704 shows a cross-sectional view of the result of applying positive draft to structure 1703 while maintaining the shape of the top of the structure. Similarly, structure 1705 shows the result of applying positive draft while maintaining the shape of the bottom of structure 1703, and structure 1706 shows the result of applying positive draft while maintaining the shape of structure 1703 at a midpoint between the top and bottom of the structure. Structure 1707 shows the result of applying negative draft while maintaining the shape of the top of structure 1703. Draft modifications can be selectively applied to a structure based on location or criteria such as the slope of the surface before applying draft (i.e., modifications can be restricted to be applied only to steep walls). To better represent the limitations of the manufacturing process (e.g., chemical etching following electron beam lithography), or to ensure the structure is more suitable for mass production, such draft application may be appropriate. For example, applying positive draft to the sidewalls of the structure can facilitate demolding during molding processes such as injection molding or nanoimprint lithography.

[0731] iii) Shining Modification - Figure 17c A perspective view of a single-surface relief structure 1708, an example of a single element of an IRG, is shown. Structure 1709 shows a cross-sectional view of the result of a blazing modification of structure 1708, in which the slope of the top of the structure is modified at a specified and controlled angle. The application of blazing can affect the direction dependence of the diffraction efficiency of the grating, and therefore the application of blazing may be advantageous for optimizing the design to preferentially change the light distribution in various directions allowed by the grating equations.

[0732] iv) Rounding modification — Figure 17d A perspective view of a single-surface relief structure 1710, an example of a single element of an IRG, is shown. In the rounding modification, the sharp corners of the structure are replaced by rounded surfaces, the radius of which can be controlled. Structure 1711 shows a cross-sectional view of the result of applying rounding to the outer corners of structure 1710. Structure 1712 shows a cross-sectional view of the result of applying rounding to the inner corners of structure 1710. Structure 1713 shows the result of applying rounding to both the inner and outer corners of structure 1710. Depending on the process used to create the rounding, it may be appropriate to selectively apply rounding only to the part or structure, or to apply rounding to two two-dimensional projections instead of all three-dimensional projections. Figure 17e A top view of a columnar structure 1714 with a square outline is shown. Rounding in the xy-plane results in a modified structure 1715; however, when viewed in a projection including the z-axis, the modified structure 1715 may still exhibit a cross-section showing abrupt transitions. Rounding is relevant because any manufacturing process has limitations on the degree to which it can reproduce sharp corners. For example, nanoscale manufacturing techniques have limitations on the resolution of features they can create, meaning that at scales smaller than 100 nm, corners are often significantly rounded as a natural consequence of the process's resolution. Modification processes can also introduce controlled rounding, for example, by configuring plasma processes that preferentially erode sharp features, thereby introducing a certain degree of rounding. The shape of the rounding itself can be described using a variety of curved geometries, including arcuate portions, spherical portions, cylindrical portions, or generally curved surfaces (e.g., patches of a properly configured NURBS surface). Rounding is sometimes also called filleting and is a feature widely available in many 3D modeling systems.

[0733] v) Undercut Modification – Undercut modification involves removing material from a portion of the structure to create an undercut, meaning that for all (x, y) coordinates, the structure is no longer single-valued at the z-position. Figure 17f A perspective view of a single-surface relief structure 1716, an example of a single element of an IRG, is shown. By removing material from one side of the substrate of 1716, an undercut structure 1717 is created, which may result in favorable properties regarding the direction, wavelength, and polarization dependence of the light scattering characteristics of the diffraction grating.

[0734] vi) Reverse modification — Figure 17g A perspective view of a single surface relief structure 1718, an example of a single element of an IRG, is shown. Here, reverse modification is defined as exchanging the material grade of the structure within a certain height range with the material grade of the surrounding material—typically air. Structure 1719 shows the result of applying reverse modification to structure 1718, meaning that the cylinder of structure 1718 is now a cavity 1720 within structure 1719. Many nanoscale manufacturing processes include a replication step, in which a surface relief imprint is made by the structure. Such an imprint is a practical example of reverse modification, so it is important to understand the role this modification can play and the methods for describing it. For example, if mass production is carried out by replicating a master surface through a molding process, that master surface must be a reverse-modified version of the final surface. Although the periodic structures PS1 and PS2 constituting the IRG will be characterized by the absence of material rather than the presence of material after reverse modification, the same symmetry rules governing whether the eye-to-eye diffraction order of the IRG has non-zero efficiency will apply.

[0735] vii) Moth-eye modification— Figure 17h A cross-sectional view of a single-surface relief structure 1721, an example of a single element of an IRG, is shown. Moth-eye modifications involve adding small structures to the surface of an existing structure, which then alters the optical properties of the entire structure. Typically, the added structures are similar in shape. Structure 1722 shows a cross-sectional view of the result of adding sharp, needle-like protrusions 1723 to structure 1721 as an example of moth-eye modification. Other modifications may involve additional high aspect ratio protrusions or transforming a smooth outer surface into a nanoscale porous surface. Such structures can be created as part of a primary manufacturing process or through auxiliary processes such as plasma etching.

[0736] viii) Geometry modification — Figure 17i Top views of columnar structure 1724 with a circular outline and columnar structure 1725 with a rectangular outline are shown. Three-dimensional geometric deformation (also known as geometric deformation or mesh deformation) is the smooth transformation of the shape of a 3D object into another shape by applying warping and other distortion transformations. Shapes 1726, 1727, and 1728 illustrate a range of intermediate shapes that can be created using deformation methods. For simple shapes, such methods can be performed within the parameters of, for example, the 3D geometric modeling system described above. For example, although the outline of structure 1724 is most easily described as a circle with a diameter of D, the outline of structure 1724 can also be constructed as a square with a side length of D, followed by a corner rounding operation (also known as a fillet operation) applied to all four corners, where sharp corners are replaced by 90° arc segments with a radius of D / 2. The outline of structure 1725 is a rectangle with a length of W in the x-direction and a length of H in the y-direction. Intermediate shapes can be created by first constructing a rectangle whose dimensions fall between the square used to construct the outline of structure 1724 and the rectangular outline of structure 1725. Then, a corner rounding operation can be applied to the four corners of the rectangle using a radius between D / 2—as used to modify outline 1724 from a square to a circle—and zero—as applied to the sharp corners of outline 1725. Finally, an extrusion operation will be used to create the 3D cylinder. Such an extrusion will extend to the height between the two structures. The dimensions required for this process can be represented parametrically. For example, suppose we will... Defined as a deformation transformation parameter that controls the degree to which one shape transforms into another, such that... =0 corresponds to structure 1724. =1 corresponds to structure 1725, and 0 < <1 corresponds to an intermediate shape that smoothly transitions between contours. Then, we can use... Interpolation is performed between the dimensions required for the above geometric construction operations: First, we construct a rectangle whose length in the x-direction is given by the following function:

[0737] , (161)

[0738] The length of the rectangle in the y-direction is given by the following function:

[0739] (162)

[0740] Then, we apply a corner rounding operation, where the corners of the rectangle are replaced with 90° arc segments with radii given by the following function:

[0741] (163)

[0742] Finally, to create the column shape, a geometry extrusion operation should be applied to the shape up to the desired height. If the height of structure 1724 is... And the height of structure 1725 is The height of the extrusion operation is then given by the following formula:

[0743] (164)

[0744] Structures 1726, 1727, and 1728 respectively illustrate the methods for targeting values The results of this method, using parameters 0.25, 0.5, and 0.75 to transform between structures 1724 and 1725, are shown. It should be noted that this parameterization is merely an example, and many other parameterizations can be used, including those that transform different dimensions of features at different rates (e.g., height relative to the deformation transformation parameter can transform from one form to another faster than relative to the corner radius). A range of algorithms for calculating the geometry of deformations between more complex shapes are presented in the computational literature, particularly because these methods have attracted considerable interest in the filmmaking and video game industries over the years. B. Mocanu's (Pierre and Marie Curie University, 2012) doctoral dissertation, "3D Mesh Morphing," provides a review of various methods. Many algorithms rely on mesh geometry, so converting the shape of the deformable endpoints to a geometrically equivalent mesh representation may be necessary. Some algorithms rely on user interaction to identify features or regions typically associated with deformation, while others attempt to automatically identify such features or regions. For practical applications, care needs to be taken to ensure that intermediate shapes are feasible for the intended manufacturing method. To ensure this, modifications to the geometry resulting from complex deformations may be necessary. Furthermore, deformation methods can be used iteratively and continuously. For example, an intermediate shape can be created between a first shape and a second shape, which can then be manipulated, and new deformations can be calculated between the first or second shape and the manipulated intermediate shape.

[0745] In many cases, to create representations of these modifications, it is necessary to convert to a mesh representation rather than a mathematical function. This is especially true for transformations that make the surface no longer single-valued in the z-direction. Furthermore, those skilled in the art will understand that these modifications are merely examples of the numerous techniques for manipulating and modifying geometry demonstrated by modeling tools available in academic literature and by 3D computer-aided design and 3D computer graphics systems.

[0746] Methods of modifying interlaced rectangular gratings by applying one or more coatings

[0747] Another form of modification to the IRG, which is composed of surface-relief structures, both in terms of geometric representation and as a practical step in fabricating devices in the physical world, involves applying one or more coatings on top of the grating surface. It has been found that applying thin films of different materials on top of the surface-relief structure can yield advantageous performance benefits. One advantage of this approach is the ability to use materials with high refractive indices, which are otherwise unsuitable for fabricating surface-relief geometries of nanostructures. The use of higher refractive index materials can provide favorable benefits for the magnitude of diffraction efficiencies across various non-zero diffraction orders and offers additional degrees of freedom for the design and optimization of the IRG.

[0748] Depending on the requirements, various coating processes can be used, and these processes can produce different results for the resulting structures.

[0749] In one approach, material can be added to the top of the surface relief structure in the z-direction. Figure 18a A cross-sectional view of the IRG is shown, with a surface relief structure 1801 comprising a portion of the IRG. A coating 1802 is introduced onto the top of the structure by adding material in the z-direction, thereby forming a composite structure 1803. A practical method for achieving such directional coating is to use physical vapor deposition (PVD), which is configured with a well-collimated beam, wherein the xy plane of the grating is arranged normal to the direction of the coating vapor.

[0750] Alternatively, directional coating can be applied in a direction away from the normal slope of the surface. Figure 18b A cross-sectional view of an IRG with a surface relief structure 1804 is shown, wherein deposited vapor 1805 is applied in a direction tilted away from the normal of the grating, resulting in directional deposition of the coating material 1806, including a masking effect. Such coating can also be achieved by means of methods such as PVD, by tilting the plane of the grating so that the direction of coating matches the design intent.

[0751] In another approach, a coating can be applied to the IRG that is conformal in all directions, meaning that the coating thickness is as equal as possible. Figure 18c A cross-sectional view of an IRG with a surface relief structure 1807 is shown, on which a conformal coating 1808 is applied. As measured in a direction normal to the surface, the coating has the same thickness at all points on the surface, except for the inner corners. Such a coating can be applied using methods such as atomic layer deposition or, depending on the geometry of the coating and the possibility of masking effects, by rotating the coating relative to the PVD source within a large tilt angle range.

[0752] By changing the tilt of the grating relative to the directional coating source, or otherwise, it is possible to create coatings that serve as intermediate states between these different situations. For example, one might not want extreme directional variations in the thickness of the coating 1806. Instead, the tilt of the grating surface is dynamically changed during the coating deposition process, and it is noted that the time spent at a given tilt angle will affect the coating build-up on the surface at that angle, which ensures that a specified thickness of material accumulates on each side of the structure 1804.

[0753] To further alter the scattering characteristics of IRG, coatings can be applied continuously with various materials. Figure 18d A cross-sectional view of an IRG with a surface relief structure 1809 is shown, on which a first coating 1810 is applied, and on top of the first coating 1810 a second coating 1811 is applied. The second coating 1811 then has a third coating 1812 applied on top. In principle, the coating process for each layer can be different, meaning that successive coatings can have different orientations, be conformal, or somewhere in between, and can have different thicknesses and materials. In this way, complex modifications to the base surface relief structure are possible, providing additional degrees of freedom for the design and optimization of the IRG's scattering properties.

[0754] The geometry representation of a coating can be generated through various methods. Typically, these will result in a surface geometry representation for each layer of material. For mathematically based descriptions, the resulting coating geometry can be generated using a function calculated based on an existing surface function. First, let's assume we define the IRG coating surface function as... , where i is the index of a coating in a system with more than one coating. For a coating applied in the z-direction, where the thickness of the i-th layer is . The corresponding IRG coating surface function is given by the following equation:

[0755] , (165)

[0756] For coatings applied in other directions, it is difficult to write a general expression because the offset surface may become self-intersecting or intersect with the underlying geometry. However, such geometries can be found using numerical algorithms based on mesh-based surface representations. Furthermore, for IRG surface functions that can evaluate gradients in both the x and y directions, the surface function for oriented coating of the i-th layer can be approximated by the projection of the coating offset onto the z-direction at given (x, y) coordinates, leading to the definition of the IRG coating surface function:

[0757] , (166)

[0758] Here, we define the zeroth coating as the surface function of the underlying IRG. ,as well as Defined as the coating direction function and is the normalized surface normal vector. and normalized coating direction vector Scalar functions. Here, the normalized surface normal vector is given by the following equation:

[0759] (167)

[0760] For the convention that surface relief structures protrude in the +z direction and the coating direction points from +z towards the surface, ensure that coating can only occur relative to the coating direction vector. A simplified definition of the coating direction function within ±90° angles is given by the following equation:

[0761] , (168)

[0762] in, It is a vector and The dot product.

[0763] Typically, the methods embodied in equations (166) through (168) will be limited for all coatings except for very thin coatings. For thicker coatings, suitable representations can be derived based on 2D and 3D geometric primitives or mesh-based geometry, where each coating—including the underlying structure—will be represented by its own mesh or a synthesis of 2D and 3D geometric primitives. For such representations, well-established methods can be used to create the derived geometry with offsets specified according to the coating rules. These derived geometries can then be examined for self-intersection features or interference with the underlying geometry using these methods, and appropriate cutting and stitching methods can be employed to create an effective geometric representation of the coated surface.

[0764] The actual implementation of coating often exhibits more complex effects in terms of coating thickness on the surface, as well as variations in the composition and properties of the coating. Such effects can be achieved through representation by using appropriate modifications to the geometry, such as using rounded corners to represent fill that may occur at interior corners, or using ray tracing and shadow casting methods to represent visual variations in coating thickness.

[0765] Method for constructing interlaced rectangular gratings using multilayer structures and coatings

[0766] Applying a coating is one method for introducing a range of new materials into a grating. Another method is to apply a new structural layer. Figure 19a A cross-sectional view is shown of a grating having a surface relief structure 1901 containing a first material M1, a cross-sectional view of a grating having a surface relief structure 1902 containing a second material M2, and a cross-sectional view of a material layer 1903 of uniform thickness containing a third material M3. By applying structure 1903 to a substrate, followed by applying structures 1901 and 1902, a new multilayer grating—which may be an IRG—is created with a surface relief structure 1904 containing the materials of structures 1901, 1902, and 1903.

[0767] In this method, a representation of this geometry can be created simply by adding surface functions. For example, if It is the IRG surface function of structure 1901. It is the IRG surface function of structure 1902, and Given the thickness of the base layer, we can define the following surface geometry functions for each layer of a multilayer IRG:

[0768] The first layer containing material M3: , (169)

[0769] The second layer containing material M1: ,

[0770] The third layer containing material M2: .

[0771] Alternatively, the representation of the mesh-based geometry can include multiple meshes, where each layer except the first is generated by summing the z-positions of the meshes from the previous layers. If the meshes have the same (x, y) coordinates for the vertices of the polygons that make up the respective meshes, then calculating the sum of the z-positions of the meshes from these layers is sufficient to calculate the mesh of the resulting layer. Typically, such overlap of the (x, y) coordinates of the vertices of different meshes is not guaranteed, and alternatively, it may be necessary to subdivide the polygons of each mesh layer until this condition is met.

[0772] When combining layers of surface geometries such as meshes—where at least a portion of the geometry is unidirectional in the z-direction—care must be taken into account to handle intersections between mesh layers, if any occur. Various methods can be used to address such intersections. One approach is to use a trimming operation to remove portions of a geometry, based on some method of prioritizing the geometries (e.g., selecting which materials have priority). Material prioritization can be achieved by considering the manufacturing process, where materials have priority according to the order in which they are deposited; thus, the first material deposited on the substrate takes precedence over the second, and so on.

[0773] Methods based on describing 3D geometry of a closed volume can be performed by overlapping different geometries on top of each other and employing rules to manage the overlapping regions. Similar to surface geometry, a rule can be used to assign a priority order among different materials, and the material assigned to any overlapping region can be set as the higher-priority material.

[0774] Another approach to multilayer gratings is to encapsulate the structure within different, distinct layers of surrounding material, for each material layer, employing the various methods described above for representing and modifying the geometry. This allows for the creation of complex multilayer geometries that can be used as IRGs. For example, Figure 19b A cross-sectional view of a portion of a multilayer IRG 1905 is shown. The multilayer IRG 1905 includes: a planar base layer 1906 of a first material M1; a first periodic IRG structure 1907 containing a second material M2, which is placed on the base layer 1906; a medium 1908 containing a third material M3, which surrounds the structure 1907 and forms a new planar layer 1909 above the top of the structure 1907; a second periodic IRG structure 1910 containing a fourth material M4, which is placed on the planar layer 1909; a medium 1911 containing a fifth material M5, which surrounds the structure 1910 and forms a new planar layer 1912 above the top of the structure 1910; and a medium 1913, which may be a medium surrounding the grating—typically air—and may be the same medium as the planar base layer 1906 or a sixth material M6. Those skilled in the art will understand that additional layers can be added to provide further design freedom.

[0775] It should be noted that in a multilayer IRG, each layer of the periodic structure must be an IRG, a rectangular grating, or a 1D grating. For all layers with 2D gratings, each layer must have the same grating vector as the others. A layer with a 1D grating must have a grating vector equal to one of the following: the grating vector of the 2D grating layer, the sum of the grating vectors of the 2D grating layers, or the difference between the grating vectors of the 2D grating layers. If this is not the case, new grating vectors may be introduced, resulting in alternative scattering directions for each beam and disrupting the image relay function of the IRG. For some layers, the structure S1 or S2 of the IRG may be empty, which is equivalent to a rectangular grating. It is also possible that the position of the grating in each layer can be shifted relative to other layers. It should also be noted that coherent scattering effects may only be possible for multilayer systems where the optical path length through the system is shorter than the coherence length of the light source used with the system. Grating layers with a spacing greater than the coherence length can be considered independent of each other and are treated separately for the purpose of calculating scattering properties (e.g., diffraction efficiency).

[0776] The allocation of materials and material properties in a multilayer representation—where systems with coatings are included in the definition of a multilayer system—can be performed in a manner similar to, but with some modifications to, the approach used for a single-layer structure. In one approach, a material index and a priority index are assigned to each surface. The priority index can be based on considerations of the intended manufacturing method, and in which surface geometries are prioritized according to the order in which they are manufactured. The material assignment at coordinates (x, y, z) is then determined by finding the highest priority surface in which that point resides (or, for the package geometry, within it). In this way, descriptions such as voxel-based representations can be achieved from the representation of the geometry of a multilayer IRG containing multiple materials.

[0777] Design and Representation Method of Interlaced Rectangular Gratings Based on Mathematical Description of Volume Properties

[0778] The use of surface geometry-based representations is well-suited for IRGs based on different materials and having varying shapes. In other embodiments of the invention, IRGs can be constructed based on variations in one or more optical properties within the material region. For example, periodic variations in the orientation pattern of a birefringent material such as a liquid crystal can be created, providing a grating structure that is particularly sensitive to the polarization of the incident beam.

[0779] Instead of representing gratings based on the geometry of structures containing different materials, an alternative approach is to directly describe the optical properties of the volume containing the IRG based on its position coordinates. One possible method for such a volumetric description of the IRG includes the following steps:

[0780] 1. We assume that the plane of the grating is the xy plane and located at z = 0. We define the grating vectors of gratings L1 and L2 used to construct the IRG as:

[0781] , (170)

[0782] as well as

[0783] (171)

[0784] 2. We define the clipping function. To describe the limited scope of IRG. The value is 1 in the area where the raster exists, and zero elsewhere. If no clipping is needed, then... =1, independent of (x, y) coordinates.

[0785] 3. We use raster functions. To represent raster L1, the raster function It is given by the following formula:

[0786] , (172)

[0787] And we use raster functions To represent raster L2, this raster function It is given by the following formula:

[0788] , (173)

[0789] in, It is the raster offset vector.

[0790] 4. We defined the volume characteristic function. This volume characteristic function represents the optical properties of the structure S1 of the IRG. Essentially, this describes how S1 introduces some modifications to the surrounding medium. Similarly, we define the volumetric property function. This represents the optical properties of the structure S2 of the IRG. The properties described by the volume characteristic function can be any physical quantity related to the representation of the grating, including but not limited to refractive index, permittivity, permeability, birefringence, absorptivity, or index values ​​indicating material composition. Function and Each of these can be a mathematical function, the output of a computational algorithm, a three-dimensional value grid combined with an interpolation scheme, or any other method that can generate unique characteristic values ​​based on (x, y, z) coordinate inputs. The finite range of any characteristics of structures S1 and S2 can be defined by defining corresponding volumetric characteristic functions. and The value is represented by a special value, which can be a null value or a number with special meaning whose value can be sufficiently different from the range of values ​​required to describe the corresponding range of optical properties. In the x and y directions, and Both are defined entirely within a rectangular area of ​​the same size as the IRG unit cell. Therefore, and The volumetric property function is defined to have non-zero values ​​only within a rectangular region in the xy-plane that has the same size and orientation as the IRG unit cell. Typically, this region is centered at the origin (0, 0), but this is not mandatory. The volumetric property function can include regions within the unit cell where no volumetric property function is defined. This can be useful when considering how structures might overlap when constructing an IRG. One way to indicate a lack of definition is to use specifically specified values. Then, this value should be taken into account when combining structures.

[0791] 5. The periodic structure PS1 of IRG is characterized by a periodic volume characteristic function. This indicates that the periodic volume characteristic function is defined as a raster function. With volume characteristic function The 3D convolution is given by the following equation:

[0792] (174)

[0793] Similarly, the periodic structure PS2 can be represented by the following periodic volume characteristic function:

[0794] (175)

[0795] The convolutions in equations (174) and (175) can be expanded as follows:

[0796] , (176)

[0797] as well as

[0798] (177)

[0799] 6. IRG is constructed by combining PS1 and PS2 together, and is determined by the IRG volume function. This function describes what is meant by "as". The change in given optical properties as a function of coordinates. Periodic structure function. and The process of combining these functions should consider possible regions where the function is considered nonexistent, and note that the structure can be embedded in the surrounding medium. Periodic structure functions. and The volume characteristic function can be defined in the following way, which makes it possible to... The absence of a feature at coordinates is determined by a specially specified value. To indicate. Then, in this case, we can define the following masking function for the periodic structure PS1:

[0800] , (178)

[0801] And for the periodic structure PS2, the following masking function is defined:

[0802] , (179)

[0803] in

[0804] (180)

[0805] Periodic structure function and Overlapping regions require a method to combine the properties described by each periodic structure. One way to control such overlap is by defining a combiner function. The combiner function can be constructed from various expressions according to the requirements and intent of the representation. The definitions of the possible functions given in equations (134) to (142) also apply to volume representations. By using the masking function and the selected combiner function, and noting that the medium surrounding the IRG is defined as having characteristic values Then the IRG volume function for the desired properties can be written as:

[0806] (181)

[0807] This completes the representation of IRG using volume functions.

[0808] It should be noted that, for clarity, single-valued scalar functions are defined here for the characteristics of the IRG and the corresponding contributions from S1 and S2. Those skilled in the art will appreciate that this definition can be generalized to many separate functions that follow the same general scheme but each describe different characteristics of the volume. In doing so, the full range of characteristics of the volume can be described. This can include tensor characteristics (e.g., permittivity tensors) required for anisotropic media such as liquid crystals, since any tensor can be composed of a sufficient number of scalar values. Alternatively, a volume description can be achieved by providing index values ​​corresponding to the choice of material, by finding a given... The material index at the coordinates is used, and then a table providing the optical properties of the material is consulted to determine the optical properties at a given point.

[0809] The use of volumetric representations is advantageous in design and simulation by facilitating a direct representation of the three-dimensional variations of the properties required to understand the response of an IRG to electromagnetic radiation. The conversion to voxel-based representations or data associated with three-dimensional meshes, as required by many simulation methods such as RCWA or FDTD, can be easily accomplished by evaluating the IRG volume function at the center coordinates of each voxel or mesh node. Volumetric methods are also well-suited for representing IRG systems in which the optical properties of the material may vary with position. Examples of such systems include those dependent on the arrangement variations of liquid crystal molecules or phase-change polymers—including certain photopolymers—and certain metamaterials.

[0810] For some practical applications, the conversion between volume representation and surface geometry representation can be advantageous. The conversion from surface geometry representation to volume representation can be accomplished using methods similar to those used to construct voxel-based representations. A given space can be determined using surface geometry data. The material at the coordinates is used, and then the desired optical properties are referenced from a lookup table associated with that material to evaluate the IRG volume function at that point. The conversion from volume representation to surface geometry representation requires that the optical properties described by the volume description match the available material. Surface geometry calculations can be performed by finding the edges of 3D regions with the same properties (potentially within a tolerance threshold). This is an example of isosurface calculation; various well-established methods exist for isosurface calculations, and various software packages support this, such as isosurface functions provided as part of the Matlab® language (MathWorks). Constructing surface geometry from volume data is particularly important for the fabrication of surface relief IRGs, where a 3D geometry is required for tooling such as master tools.

[0811] Methods for creating differences in interlaced rectangular gratings

[0812] As mentioned above, in order for the IRG to have a to-eye order with a non-zero diffraction order, and thus be able to output coupled waveguide light for observation, some methods for breaking symmetry should be employed. Figures 20a to 20jExamples of a series of methods for differentiating the periodic structures PS1 and PS2 used in designing IRGs are shown. In all cases, these structures are shown as surface relief structures in perspective views or as outlines in top views; however, the described methods are equally applicable to embedded structures, structures composed of multiple materials or multiple layers, and structures created as volumetric variations of material properties. Furthermore, in all cases, it is assumed that the structure comprises a material having at least one optical property that differs from its surrounding environment, such that the structure will scatter light. Figures 20a to 20j The methods shown are labeled as follows:

[0813] a) Proportional differences — Figure 20a A top view of a portion of IRG 2001 is shown. Here, structures S1 2002 and S2 2003 are identical, and the grid offset vector is... This means that IRG 2001 is an FSIRG. A modified IRG 2006 was created by increasing the dimensions of structure S1 2002, as observed in the xy-plane, to form a new structure S1 2004, and decreasing the dimensions of structure S2 2003, as observed in the xy-plane, to form a new structure S2 2005. Due to the breaking of shape symmetry caused by the scaling change, this new IRG 2006 may have an entrance order with non-zero diffraction efficiency, the size of which we expect depends on the scaling difference between structures S1 and S2. Alternatively, this scaling may be applied to only one structure along a single direction in the xy-plane, or to only one structure along two directions in the xy-plane by different amounts.

[0814] b) Relative grid shift — Figure 20b A top view of a portion of IRG 2007 is shown. Here, structures S12008 and S2 2009 are identical and the grid offset vector is... This means that IRG 2007 is an FSIRG. By changing the raster offset vector to shift grates L1 and L2 relative to each other, a copy of structure S2 2010 can be moved closer to some of the nearest neighboring copies of structure S1 2008. In the example shown, this shift is in the y-direction. Due to the breaking of positional symmetry, the new IRG 2011 will have a non-zero entrance order, the magnitude of which will depend on the magnitude and direction of the relative raster shift.

[0815] c) Rotational differences — Figure 20c A top view of a portion of IRG 2012 is shown. Here, structures S1 2013 and S2 2014 are identical and the grid offset vector is... This means that IRG 2012 is an FSIRG. A modified IRG 2017 is created by rotating structure S12013 clockwise around the z-axis to form a new structure S1 2015, and by rotating structure S2 2014 counterclockwise around the z-axis to form a new structure S2 2016. Due to the breaking of shape symmetry caused by the rotation, this new IRG 2017 may have an entrance order with non-zero diffraction efficiency, the magnitude of which will generally depend on the rotation angles applied to structures S1 and S2. Alternatively, the rotation may be applied to only structures S1 or S2.

[0816] d) Mirror image differences — Figure 20d A top view of a portion of IRG 2018 is shown. Here, structures S1 2019 and S2 2020 are identical and the grid offset vector is... This means that IRG 2018 is an FSIRG. A modified IRG 2022 was created by mirroring structure S2 2019 relative to the yz plane to form a new structure S2 2021. Due to the breaking of shape symmetry caused by mirroring, this new IRG 2022 may have an entrance-eye order with non-zero diffraction efficiency. Unlike other operations, mirroring cannot be applied gradually; the only choice is through the plane on which the structure is mirrored and which structures are selected for mirroring.

[0817] e) High degree of difference — Figure 20e A perspective view of a portion of IRG 2023 is shown. Here, structures S1 2024 and S2 2025 are identical and the grid offset vector is... This means that IRG 2023 is an FSIRG. A modified IRG 2028 was created by increasing the height of structure S1 2024 to form a new structure S1 2026 and decreasing the height of structure S2 2025 to form a new structure S2 2027. Due to the breaking of shape symmetry caused by the height variation, this new IRG 2028 may have an entrance-eye order with non-zero diffraction efficiency, the magnitude of which we expect depends on the height difference introduced between structures S1 and S2. Alternatively, the height variation can also be applied to only one set of structures.

[0818] f) Shining Differences — Figure 20f A perspective view of a portion of IRG 2029 is shown. Here, structures S1 2030 and S2 2031 are identical and the grid offset vector is... This means that IRG 2029 is an FSIRG. The structure exhibits a tilted top due to scintillation modification. A modified IRG 2034 is created by increasing the scintillation angle of structure S1 2030 to form a new structure S1 2032, and decreasing the scintillation angle of structure S2 2031 to form a new structure S2 2033. Due to the shape symmetry breaking caused by the scintillation variation, this new IRG 2034 may have an entrance order with non-zero diffraction efficiency, the magnitude of which we expect depends on the variation in the scintillation angles applied to structures S1 and S2. Alternatively, the scintillation variation may be applied to only one of the structures, or may include a variation in the orientation of the ramp.

[0819] g) Shape differences — Figure 20g A top view of a portion of IRG 2035 is shown. Here, structures S1 2036 and S2 2037 are identical and the grid offset vector is... This means that IRG 2035 is an FSIRG. A modified IRG 2039 was created by changing the shape of structure S22037 from having a circular profile to having a square profile 2038. Due to the breaking of shape symmetry resulting from this change, the new IRG 2039 may have an entrance order with non-zero diffraction efficiency, the size of which we expect depends on the similarity of the shapes of structures S1 and S2. Geometric deformation methods can be used to create a range of shapes with controlled differences. For example, two shapes can be used to represent two extreme possibilities of shape, and based on these shapes, deformation is used to calculate an intermediate shape, which can then be used in the IRG. As long as the deformation is smooth and continuous, it is theoretically possible to produce shapes with continuous degrees of difference from each other, thus providing a wide range of geometric shape variations. All the methods listed above, except for relative grid shifts, can be considered examples of shape differences limited to specific aspects such as height or rotation.

[0820] h) Differences in optical properties — Figure 20h A top view of a portion of IRG 2040 is shown. Here, structures S12041 and S22042 are identical and the grid offset vector is... This implies that IRG 2040 is an FSIRG. A modified IRG 2044 was created by altering the composition of structure S2 2042 to form a new structure S2 2043, such that at least one intrinsic optical property differs from S1 2040. Due to broken compositional symmetry, this new IRG 2044 may have an entrance-eye order with non-zero diffraction efficiency, the magnitude of which we expect depends on the degree of difference in the optical properties of structures S1 and S2.

[0821] i) Splitting or merging structures — Figure 20iA top view of a portion of IRG 2045 is shown. Here, structures S12046 and S22047 are identical and the grid offset vector is... This means that IRG 2045 is an FSIRG. A modified IRG 2049 was created by replacing structure S2 2047 with a new structure 2048 containing multiple elements. Due to shape symmetry breaking, the new IRG 2049 may have an entrance-eye order with non-zero diffraction efficiency. Besides splitting the structure into multiple elements, the structures can also be merged together. In fact, both of these changes can be viewed as forms of geometric deformation, and based on this, a series of intermediate structures can be created to provide a range of degrees of shape symmetry breaking. For example, Figure 20j A top view of a single structure 2050 is shown. This structure can be elongated to form a new structure 2051. By narrowing the center of structure 2051, a shape 2052 that appears to be two elements fused together can be created. By narrowing the waist between the structures to the extent that the elements are separated, a new structure 2053 containing two elements 2054 and 2055 can be formed. Therefore, structures 2051 and 2052 can be considered as intermediate structures in a series of structures between structures 2050 and 2053.

[0822] It should be noted that in applications where the IRG is part of the DWC, it is preferable that any differences created in the IRG using the methods described above or otherwise should not alter the periodicity or orientation of the IRG's grids L1 and L2. Doing so would change the orientation of various diffraction orders and could disrupt the function of the IRG in the DWC. The methods described above can be applied individually or in combination, and can even be repeated multiple times. In principle, any of the previously identified shape modification methods can be used to create symmetry breaking, including draft modifications, tilt transformations, rounding, and single-layer and multi-layer coating methods. Therefore, the modifications described in detail above should be considered as examples of various modifications. For example, any modification to the geometry can, in principle, be applied only to structure S1 and / or periodic structure PS1, or only to structure S2 and / or periodic structure PS2. Alternatively, geometric modifications can be applied to both sets of structures, but to different degrees. For example, both the periodic structures PS1 and PS2 of an IRG can undergo tilt modification, where symmetry breaking is achieved by changing the magnitude and / or direction of the tilt applied to the periodic structure PS1 relative to the magnitude and / or direction of the tilt applied to the periodic structure PS2.

[0823] It should be understood that these modifications do not require the use of FSIRG as a starting point and can be used to enhance the IRG when differences already exist between the underlying periodic structures. It is also important to note that the methods outlined above for inducing differences between periodic structures PS1 and PS2 are merely examples of different possible modifications that achieve the advantages described for controlling the diffraction efficiency of the diffraction order in the IRG.

[0824] Application of staggered rectangular gratings and diffraction waveguides

[0825] Figure 21a , Figure 21b Perspective and top views of the layout of an augmented reality display system including a diffractive waveguide assembler implemented using an interlaced rectangular grating are shown. The diffractive waveguide assembler 2101 includes: a transparent substrate 2103 configured as a planar flat waveguide; an input grating 2104; and an output element 2105 configured as an interlaced rectangular grating. The medium M surrounding the DWC 2101 has a refractive index lower than that of the substrate 2103. Typically, this medium would be air, but this is not necessary. Typically, the medium M is the same on all sides of the waveguide, but this is not necessary. Typically, the thickness of the substrate 2103 can be between 0.1 mm and 4.0 mm, and preferably, the thickness can be between 0.25 mm and 1.0 mm. The outer contour of the substrate 2103 in the xy plane is... Figure 21a The inner part is shown as a rectangle, but the outer contour can be of various shapes, as long as the input grating 2104 and IRG 2105 can be adapted to the size required to receive the output from the projector 2102 and the eye movement range of the system design.

[0826] The waveguide surfaces of substrate 2103 have very low roughness, as well as high flatness and high parallelism between each other. The non-waveguide surfaces of substrate 2103 may be coated with black or otherwise treated with light-absorbing materials, and may have rough or smooth surface treatments to reduce the scattering of light incident on the non-waveguide surfaces back to the waveguide. This scattering can degrade the performance of DWC 2101 by introducing artifacts such as haze.

[0827] Due to the light-transmitting properties of substrate 2103 and the presence of the zeroth diffraction order of the IRG (Infrared Reflection Group) with non-zero diffraction efficiency for real-world light incident from the surrounding medium M onto DWC 2101, it becomes possible to view real-world light through the waveguide surface of DWC 2101. In other configurations where viewing real-world light is not required, a light-blocking device can be used on the side of DWC 2101 opposite to the side used for viewing, wherein the blocking device is configured to prevent light from the real world from interfering with the viewing of the projected image.

[0828] Projector 2102 is configured to generate a set of collimated beams, which are guided onto input grating 2104. The output from projector 2102 can be monochromatic or cover a certain wavelength range to provide a panchromatic image. The combined beams, through the transmission of light from the real world via DWC 2101, collectively form an image focused at infinity that will be displayed by DWC 2101. Using the method described herein, the beam from projector 2102 is coupled into DWC 2101 via input grating 2104, and the beam undergoes waveguide propagation toward IRG 2105, where, due to the diffraction and scattering properties of the grating, both pupil replication for eye-tracking range extension and output coupling for observation occur through repeated interactions of the beam with IRG 2105.

[0829] Typically, the output beam from projector 2102 has a circular shape and a diameter between 0.25 mm and 10 mm, preferably between 1.0 mm and 6.0 mm. The set of beams output from projector 2102 will have a certain xy wave vector range. For projectors based on rectangular microdisplays such as LCOS, DMD, or microLED display panels, the xy wave vector range for each wavelength from projector 2102 will generally encompass an approximately rectangular region in k-space. Other optical projection techniques may produce other shapes, but any display system that produces an image with a non-zero field of view from projector 2102 will produce an xy wave vector range corresponding to at least one region in k-space.

[0830] In some applications, an observer (not shown) will observe the light coupled outward from the IRG 2105. In some arrangements, the observer will be located on the same side of the DWC 2101 as the projector 2102; in other arrangements, the observer will be located on the opposite side of the DWC 2101.

[0831] The planes of the input grating 2104 and IRG 2105 are configured to be parallel to the waveguide surface of the substrate 2103. The Cartesian definition is used. The coordinates, where the xy plane is parallel to the waveguide surface and diffraction grating of DWC 2101. Both input grating 2104 and IRG 2105 can be located on either surface of the outer waveguide surface of substrate 2103 or embedded within the substrate. Input grating 2104 and IRG 2105 do not need to be in the same plane, but the planes of the gratings should be parallel to each other. Input grating 2104 and IRG 2105 can be configured with grating vectors, whi...

Claims

1. An output diffraction grating for a diffraction waveguide combiner, comprising: A first array of optical structures arranged on a plane to form a two-dimensional grating, the first array of optical structures including first adjacent optical structures, the first adjacent optical structures being spaced apart from each other in each of a first direction and a second direction different from the first direction in the plane of the output diffraction grating, such that the first adjacent optical structures do not contact each other; as well as A second array of optical structures arranged on the plane and forming a second two-dimensional grid, the second array of optical structures including second adjacent optical structures, the second adjacent optical structures being spaced apart from each other in each of the first direction and the second direction, such that the second adjacent optical structures do not contact each other; The first array of the optical structure is superimposed on the second array of the optical structure in the plane, such that the first array of the optical structure and the second array of the optical structure are spatially offset from each other in the first direction and the second direction in the plane and do not contact each other, and the optical structure from the second array of the optical structure is disposed in the plane of the output diffraction grating between one of the first adjacent optical structures of the first array; Each optical structure in the first array of the optical structures includes a first shape in the plane of the output diffraction grating, and each optical structure in the second array of the optical structures includes a second shape in the plane that is different from the first shape.

2. The output diffraction grating according to claim 1, wherein, The optical structures of the first array and the second array are also different from each other in at least one characteristic by one or more of the following: The optical structure of the first array has a first size, and the optical structure in the second array has a second size different from the first size; The optical structure of the first array has a first orientation in the plane, and the optical structure of the second array has a second orientation in the plane that is different from the first orientation; The optical structure of the first array has a first height in a direction perpendicular to the plane, and the optical structure of the second array has a second height in a direction perpendicular to the plane, which is different from the first height; as well as The optical structure of the first array has a first blaze, and the optical structure of the second array has a second blaze that is different from the first blaze.

3. The output diffraction grating according to claim 1, wherein, The optical structures of the first array and the second array have at least one of the following: different refractive indices, different permittivity, different permeability, different absorptivity, or different birefringence.

4. The output diffraction grating according to claim 1, wherein: The optical structure of the first array is arranged periodically according to the period in the first direction and the period in the second direction. The first array of the optical structure is offset relative to the second array of the optical structure in the first direction by a factor different from half the period of the first array in the first direction, and The first array of the optical structure is offset relative to the second array of the optical structure in the second direction by a factor different from half the period of the first array in the second direction.

5. The output diffraction grating according to claim 1, wherein, The output diffraction grating is spatially varied across the plane by at least one of the characteristics of the optical structure of the first array of the optical structure or the characteristics of the optical structure of the second array of the optical structure.

6. The output diffraction grating according to claim 1, wherein, The output diffraction grating varies spatially across the plane as follows: the optical structures of the first array and the second array have dimensions that gradually decrease in the plane toward the edge of the output diffraction grating, or a height that decreases in a direction perpendicular to the plane.

7. The output diffraction grating according to claim 1, wherein, The output diffraction grating varies spatially across the plane along at least one of a first direction or a second direction orthogonal to the first direction, such that the output diffraction grating includes at least one region in which the first array and the second array of the optical structure are not different from each other in at least one characteristic, and in the at least one region, the first array of the optical structure is offset relative to the second array of the optical structure in both the first and second directions by a factor of half the period of the first and second arrays.

8. The output diffraction grating according to claim 1, wherein, The output diffraction grating varies spatially across the plane to form the region of the output diffraction grating, in which the first array of the optical structure or the second array of the optical structure provides negligible diffraction of light.

9. The output diffraction grating according to claim 1, wherein, The output diffraction grating varies spatially across the plane to form multiple regions, each of the multiple regions including the boundary between other regions in the multiple regions where the spatial variation occurs.

10. The output diffraction grating according to claim 1, wherein, The first array of the optical structure is arranged on the first grating, and the second array of the optical structure is arranged on the second grating, wherein the first grating and the second grating are spatially displaced relative to each other in one or more regions across the plane of the output diffraction grating.

11. The output diffraction grating according to claim 1, wherein, The first array and the second array of the optical structure are shifted relative to each other in at least one of the first or second directions.

12. The output diffraction grating according to claim 1, wherein, The first shape is a circle, and the second shape is a triangle.

13. The output diffraction grating according to claim 1, wherein, The first shape is circular, and the second shape is rectangular.

14. A diffractive waveguide combiner for an augmented reality or virtual reality display, comprising the output diffraction grating according to claim 1.

15. An augmented reality or virtual reality display, comprising: A diffractive waveguide combiner, the diffractive waveguide combiner comprising: Waveguide, the waveguide being used to transmit light, and having arranged in or on the waveguide: The output diffraction grating according to claim 1; as well as An input grating is used to couple light into the waveguide in the direction of the output diffraction grating.

Images