WO2019136166A1

WO2019136166A1 - Angle-dependent or polarization-dependent metasurfaces with wide field of view

Info

Publication number: WO2019136166A1
Application number: PCT/US2019/012205
Authority: WO
Inventors: Wei Ting Chen; Zhujun Shi; Federico Capasso
Original assignee: Harvard University
Current assignee: Harvard University
Priority date: 2018-01-04
Filing date: 2019-01-03
Publication date: 2019-07-11
Anticipated expiration: 2020-07-04

Abstract

An optical device including a first metasurface grating and a second metasurface grating can achieve a large field of view (FOV). The first metasurface grating includes a plurality of first nanoscale elements. The first nanoscale elements define a first polarization- dependent phase profile that transmits a first light of a first polarization state in a first direction. The second metasurface grating comprises a plurality of second nanoscale elements. The second nanoscale elements define a second polarization-dependent phase profile that transmits a second light of a second polarization state in a second direction different from the first direction.

Description

ANGLE-DEPENDENT OR POLARIZATION-DEPENDENT METASURFACES

WITH WIDE FIELD OF VIEW

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of and priority to U.S. Provisional Application No. 62/613,668, filed January 4, 2018, and U.S. Provisional Application No. 62/660,812, filed April 20, 2018, the contents of which are incorporated herein by reference in their entirety.

BACKGROUND

[0001] The terminology“field of view (FOV)” refers to an angular aperture of what a user can see using lenses, cameras and other optical systems such as augmented reality devices. In an attempt to increase FOV of optical systems, multiple lenses with entrance/exits apertures can be combined together to be cascaded along an optical axis. Such an attempt can increase design complexity, cost and device volume. Particularly, in augmented devices with a single grating scheme, the FOVs can be increased by using high refractive index substrates.

[0002] In recent years, metasurfaces, composed of sub-wavelength spaced structures, have been shown to be capable of manipulating light using different parameters such as wavelength and polarization. By specifying the phase libraries of the metasurface constituent structures, the structures respond differently based on the polarization state or wavelength of the incident beam. However, the engineering of a metasurface with a phase profile that varies as a function of the angle of incidence (referred to as angle-dependent metasurface hereinafter) has proved challenging and so far, has been limited to the infrared region.

SUMMARY

[0003] At least one aspect of the present disclosure relates to a transmissive angle-dependent metasurface that works for light in, e.g., the visible spectrum. Thus, using a metasurface with tailored angle-dependent properties, compact lenses and augmented reality devices with increased FOVs can be achieved. In some embodiments, phase spectra of nanopillars (pillars in nanoscale) are designed as a function of the angle of incidence in the visible spectrum. Thus, the nanopillars are assembled to form a metasurface capable of deflecting light to designed angles depending on the angles of the incident beam. Such a metasurface can increase the FOV up to at least 3-fold compared to comparative devices with the same or similar specifications.

[0004] At least one aspect of the present disclosure relates to a waveguide display design based on polarization-dependent metagratings (also referred to as metasurface gratings). By encoding the left and right half of FOV in orthogonal polarization channels, the FOV may be increased by, e.g., about 70%, compared to designs based on comparative diffractive gratings. Metagratings that selectively diffract out TE or TM polarized light may be provided for by the present disclosure. High polarization selectivity can thus be achieved, with minimal crosstalk between the two channels. The multiplexing information in the disclosed polarization domain can be used to achieve large FOV in, e.g., AR devices.

[0005] One aspect of the present disclosure relates to an optical device including a metasurface grating includes a plurality of nanoscale elements, wherein the nanoscale elements define an angle-dependent phase profile that imparts a wavevector that varies depending on an angle of incidence of light.

[0006] In one or more embodiments, the nanoscale elements include at least one of titanium dioxide, silicon nitride, a polymer, an oxide, a nitride, a sulfide, a pure element, and a combination thereof.

[0007] In one or more embodiments, the light of incidence has a wavelength in a visible or near-infrared region of an electromagnetic spectrum.

[0008] In one or more embodiments, a cross-section of each of the plurality of nanoscale elements has a two-fold symmetry to impart wavevectors to various polarization states of incidence.

[0009] In one or more embodiments, a cross-section of each of the plurality of nanoscale elements has radial symmetry rendering a functionality of the device insensitive to the polarization of light. [0010] In one or more embodiments, the nanoscale elements define the angle-dependent phase profile such that the wavevector is a function of the angle of incidence.

[0011] In one or more embodiments, the optical device further includes a transmissive substrate including glass or polymer, the nanoscale elements disposed on the transmissive substrate.

[0012] In one or more embodiments, the optical device further includes a transmissive substrate with curved or flexible surfaces.

[0013] In one or more embodiments, the metasurface grating provides an FOV that depends on the wavevector.

[0014] In one or more embodiments, as the metasurface grating provides an FOV that satisfies FOV = n sin(72°)— 1 , where n is refractive index of a

transmissive substrate on which the nanoscale elements are disposed.

[0015] In one or more embodiments, the angle-dependent phase profile is asymmetric with respective to the angle of incidence.

[0016] In one or more embodiments, the metasurface grating provides an FOV that depends on the spatial gradient of the angle-dependent phase profile defined by the nanoscale elements.

[0017] In one or more embodiments, the nanoscale elements comprise slanted nanopillars with a nonzero slant angle with respect to the surface normal of the metasurface grating.

[0018] In one or more embodiments, the slanted nanopillars are arranged to introduce a Bragg resonance.

[0019] In one or more embodiments, the slanted nanopillars are arranged to introduce the Bragg resonance that satisfies: 2n_effA sin (0_B) = l, where L = p cos(0_slant ) , Q_B = 9_lnc + Q si_an ^i_nc is the angle of incidence, 9_slant is the nonzero slantangle, p is the grating period of the metasurface grating, and n_ef f is an effective index that is determined by the nonzero slant angle, the angle of incidence and a filling factor.

[0020] In one or more embodiments, the angle-dependent phase profile defined by the nanoscale elements imparts an angular dispersion of light phase change that depends on a filling factor of the metasurface grating, or wherein the angle-dependent phase profile defined by the nanoscale elements imparts an angular dispersion of light transmission that depends on the filling factor of the metasurface grating.

[0021] Another aspect of the present disclosure relates to an augmented reality device that includes a waveguide for overlaying augmented reality information on a view of a real-world environment, and a metasurface grating including a plurality of nanoscale elements disposed on the waveguide, wherein the nanoscale elements define an angle-dependent phase profile that imparts a wavevector that varies depending on an angle of incidence.

[0022] In one or more embodiments, the nanoscale elements define the angle-dependent phase profile such that the wavevector is a function of the angle of incidence.

[0023] In one or more embodiments, the metasurface grating provides an FOV that depends on the wavevector.

[0024] In one or more embodiments, the metasurface grating provides an FOV that satisfies 2 sin FOV = n sin(72°)— 1 , where n is refractive index of a transmissive

substrate on which the nanoscale elements are disposed.

[0025] In one or more embodiments, the metasurface grating provides an FOV that depends a spatial gradient of the angle-dependent phase profile defined by the nanoscale elements.

[0026] In one or more embodiments, the nanoscale elements are slanted nanopillars with a nonzero slanted angle with respect to a surface normal of the metasurface grating, and the slanted nanopillars are arranged to introduce a Bragg resonance.

[0027] In one or more embodiments, the slanted nanopillars are arranged to introduce the Bragg resonance that satisfies: 2n_eff/l sin(0_B) = l, where L = p cos(0_5iant) , Q_B = 9_inc + Q s_lan_t- in_c is the angle of incidence, 9_slant is the nonzero slanted angle, p is a grating period of the metasurface grating, and n_e^ is an effective index that is determined by the nonzero slanted angle, the angle of incidence and a filling factor.

[0028] According to another aspect of the present disclosure, an omni-angle optical device includes an optical resonator or an optical filter configured to perform an optical functionality, and a metasurface grating including a plurality of nanoscale elements disposed on the optical resonator or the optical filter, wherein the nanoscale elements define an angle- dependent phase profile that imparts a wavevector that varies depending on an angle of incidence, and the angle-dependent phase profile renders the optical functionality of the optical resonator or the optical filter insensitive to the angle of incidence.

[0029] According to another aspect of the present disclosure, an optical device includes a first metasurface grating including a plurality of first nanoscale elements, wherein the first nanoscale elements define a first polarization-dependent phase profile that transmits a first light of a first polarization state in a first direction, and a second metasurface grating including a plurality of second nanoscale elements, wherein the second nanoscale elements define a second polarization-dependent phase profile that transmits a second light of a second polarization state into a second direction different from the first direction.

[0030] In one or more embodiments, the first polarization state corresponds to a transverse electric (TE) mode, and the second polarization state corresponds to a transverse magnetic (TM) mode.

[0031] In one or more embodiments, a slanted angle, a height or a refractive index of the plurality of first nanoscale elements is different from a slanted angle, a height or a refractive index of the plurality of second nanoscale elements.

[0032] In one or more embodiments, the first metasurface grating including the plurality of first nanoscale elements is non-transmissive to the second light of the second polarization state.

[0033] In one or more embodiments, the second metasurface grating including the plurality of second nanoscale elements is non-transmissive to the first light of the first polarization state.

[0034] In one or more embodiments, an optical device includes a first polarizer configured to convert light into a first light of a first polarization state, a second polarizer configured to convert light into a second light of a second polarization state, and a waveguide configured to propagate the first light of the first polarization state and the second light of the second polarization state. The optical device further includes a first metasurface grating disposed on the waveguide and including a plurality of first nanoscale elements, wherein the first nanoscale elements define a first polarization-dependent phase profile that transmits the first light of the first polarization state in a first direction, and a second metasurface grating disposed on the waveguide and including a plurality of second nanoscale elements, wherein the second nanoscale elements define a second polarization-dependent phase profile that transmits the second light of the second polarization state in a second direction different from the first direction.

[0035] In one or more embodiments, the optical device includes a collimator configured to collimate the first light of the first polarization state and the second light of the second polarization state.

[0036] In one or more embodiments, the waveguide includes an in-coupler and an out- coupler, at least a portion of the first metasurface grating is disposed on the out-coupler of the waveguide, and at least a portion of the second metasurface grating is disposed on the in coupler of the waveguide.

[0037] In one or more embodiments, the first polarization state corresponds to a transverse electric (TE) mode, and the second polarization state corresponds to a transverse magnetic (TM) mode.

[0038] In one or more embodiments, a slanted angle, a height or a refractive index of the plurality of first nanoscale elements is different from a slanted angle, a height or a refractive index of the plurality of second nanoscale elements.

[0039] In one or more embodiments, the first metasurface grating including the plurality of first nanoscale elements is non-transmissive to the second light of the second polarization state.

[0040] In one or more embodiments, the second metasurface grating including the plurality of second nanoscale elements is non-transmissive to the first light of the first polarization state.

BRIEF DESCRIPTION OF THE DRAWINGS

[0041] For a better understanding of the nature and objects of some embodiments of this disclosure, reference should be made to the following detailed description taken in conjunction with the accompanying drawings.

[0042] FIG. 1 A schematically illustrates a grating coupler for augmented reality.

[0043] FIG. 1B illustrates a metasurface that causes a wavevector to be a function of angle of incidence.

[0044] FIG. 2 illustrates a field of view depending on a way that a metasurface alters wavevector for various angles of incidence.

[0045] FIG. 3 illustrates slanted pillars as examples of phase shifters of a metasurface.

[0046] FIG. 4A illustrates light phase as a function of incidence angle for various filling factors.

[0047] FIG. 4B illustrates light transmission as a function of incidence angle for various filling factors.

[0048] FIG. 5 illustrates an omni-angle resonator or filter device based on an angle- dependent metasurface.

[0049] FIG. 6(a) illustrates a schematic of an optical combiner based on polarization- dependent metagrating.

[0050] FIG. 6(b) illustrates a schematic of an out-coupler of a waveguide of the optical combiner.

[0051] FIG. 7(a) illustrates an FOV achieved by an out-coupler of a comparative diffractive grating.

[0052] FIG. 7(b) illustrates an FOV achieved by an out-coupler based on polarization- dependent metagrating.

[0053] FIG. 8(a) illustrates a unit cell of a TM (Transverse Magnetic)-pass grating.

[0054] FIG. 8(b) illustrates a unit cell of a TE (Transverse Electric)-pass grating.

[0055] FIG. 9(a) illustrates a diffraction efficiency of TE-pass gratings as a function of incident angles.

[0056] FIG. 9(b) illustrates a diffraction efficiency of TM-pass gratings as a function of incident angles.

[0057] FIG. 9(c) illustrates an overall diffraction efficiency in the transmission as a function of the output angles.

[0058] FIG. 10 illustrates transmission efficiencies at normal incidence, including transmission spectrum of TE-pass gratings, transmission spectrum of TM-pass gratings, and overall transmission.

DETAILED DESCRIPTION [0059] Angle-Dependent Metasurfaces

[0060] At least some embodiments of the present disclosure relate to metasurface gratings (also referred to as metagratings) with angular-dependent phase profile. Devices with angular-dependent metasurface gratings can be used to significantly increase the achievable field of view (FOV) of augmented reality devices, and can be used to achieve new types of optical devices. For example, slanted pillars may achieve asymmetric angle-dependent phase with a significant tunability, and may be used to realize an angle-dependent phase profile of the metasurface. Although some embodiments of the present disclosure relate to optical device designed for the visible region, by changing material composition, the disclosed technology can be adopted to other spectral regions, such as near-infrared region.

[0061] FIG. 1 A schematically illustrates a grating coupler for augmented reality. As shown in FIG. 1A, free space incident light receives a parallel wavevector from the grating coupler 130 and then is guided by total internal reflection (TIR) in a transparent substrate 110, which can include, but is not limited to, glass. The substrate 110 can be a waveguide for an augmented reality device. For example, the waveguide overlays augmented reality information on a view of a real-world environment. The rays 115 and 120 respectively correspond to light of the same wavelength guided at the maximum and minimum angles (with respect to the direction of normal incidence). The ray 115 is coupled out through a downstream grating 130. The ray 120 is guided in the substrate by TIR. The device can also function as a grating out-coupler if the light is fed from the waveguide due to reversibility.

[0062] The momentum of an incident photon is proportional to its wavevector. The magnitude of the wavevector k is equal to 2p/l. where l is wavelength of the light wave. Gratings and metasurfaces can impart a wavevector to a light beam, which is parallel to the surface with values equal to 2p/r and|Vr/;(x. v)| . respectively, where p is the grating period and Vcf>(x,y) is the gradient of the metasurface phase profile.

[0063] In comparative augmented reality devices, the incident rays from a micro-display are guided by total internal reflection after diffraction through a grating patterned on top of a substrate. In such a configuration, some rays are guided by unfavorable large angles and are hardly coupled out by the exit grating. This is illustrated by the ray 115 in FIG 1A.

Accordingly, the largest guided angle may be specified to be smaller than a critical angle (e.g., about 72 degrees). The minimal guided angle (corresponding to line 120 in FIG. 1A) may specified to be about equal to asin( /) , where n is the refractive index of the substrate.

[0064] The FOV is thus determined based on the difference in the angles of incidence Q corresponding to the maximal and minimal guided angles in the substrate. For comparative gratings without metasurfaces, the refractive index of the substrate is increased in order to increase FOV. However, increasing the refractive index means changing the material of the substrate, which can significantly increase the cost and reduce optical performance of the device.

[0065] The reason behind the FOV limitation is that the comparative grating merely provides a constant wavevector ko for different angles of incidence. To overcome the limitation, a metasurface disclosed herein can provide a wavevector k which is designed as a linear function of angle Q, k (0) =— aq + k₀ (1) where a and k₀ are constants. Such relation of k(q) and q can be parametrized to other dependence, such as k ( 0 ) =— aq² + k₀

[0066] FIG. 1B illustrates a metasurface that causes a wavevector to be a function of angle of incidence. The horizontal wavevector k provided by metasurface coupler 150 and a grating coupler 160 is a function of the angle of incidence Q. Such an angle-dependent wavevector decreases the deflection angle of ray 115 of FIG. 1A and increases the deflection angle of ray 120 of FIG. 1A. The metasurface provides less parallel momentum to the ray 115 and more momentum to the ray 120 compared to comparative gratings. The increase of FOV is related to the parameter a in Eq. 1. According to the generalized law of refraction and reflection and the conditions of the maximal/minimal guided angles, the maximum angle and the minimum angles have relationships of:

FOV == abs(9_max ) + aris(0_min). (4)

[0067] Letting DQ = abs(9_max)— abs(6_min). and using the definition of /c(0), the equations can be written as:

[0068] Thus, by tuning a and k₀, the desired FOV can be achieved. If DQ = 0, which corresponds to a symmetric FOV, then k₀ is given by: k₀ = (n sin(72°) + 1).

A (7)

[0069] For a given substrate refractive index n, the achievable FOV is determined by la, satisfying: n sin(72°)— 1.

(8)

[0070] FIG. 2 illustrates an FOV depending on a way that a metasurface alters wavevector according to Eq. 1 for various anges of incidence. As shown in FIG. 2, a horizontal FOV is a function of la . Symmetric horizontal FOV is assumed in FIG. 2. The wavevector (proportional to momentum) imparted to the light follows k(6) =—aq + k₀ , where the incident angle Q is in degrees. For the curve shown in FIG. 2, the values of the FOV function are numerically calculated based on a substrate with a refractive index of about 1.7. As shown in FIG. 2, a situation of a = 0 (constant wavevector) corresponds to a comparative grating without metasurfaces, which can merely achieve an FOV of about 36° . By introducing a nonzero a using metasurfaces, the FOV can be increased by as much as three fold, for example.

[0071] In metasurfaces, the parallel wavevector is provided by the spatial gradient of the phase profile. Therefore, the target phase profile can be derived as a function of k(6) f(l, c, Q ) = k(6)x + C(A, Q ), (9)

[0072] Here, for ease of explanation, the metasurface phase profile can be assumed to vary merely along at least one coordinate (e.g., x-coordinate). In some embodiments, the metasurface phase profile can vary along multiple directions. The C(6) term in Eq. (9) offers an additional degree of freedom for tuning the required angular dispersion. The angular dispersion may scale linearly with the size of the metasurface x. For example, if a =

2 TT

0.0035— A the FOV is about 45 degrees (about 25% larger compared to comparative gratings without metasurfaces). The phase change is άf(c,q ) άf(c,q)

Df = (; άq max άq min) * FOV = 0.16 * 2?^ (11) which is about 32p for a device having a dimension of 100 pm. In general, f(c, Q) at a given x-coordinate can be asymmetric with respect to Q.

[0073] According to some embodiments of the present disclosure, slanted pillars can be used to introduce Bragg resonance for realizing asymmetric phase response. Bragg resonances occurs when the following condition is satisfied:

2n_eff/l sin(0_B) = A, (12) where A = p cos(6_Siant) , Q_B = 6_inc + 0_slant. and p is the grating period (as shown in FIG.

3). The effective index n_e^ can be obtained by numerically solving Maxwell’s equations and is related to the slant angle of the slanted pillars, the incidence angle and the filling factor in combination. The filling factor is defined as w/p, where w is the pillar width.

[0074] FIG. 3 illustrates slanted pillars as examples of phase shifters of a metasurface. The metasurface 300 includes slanted pillars 310 disposed on a substrate 320. The slanted pillars 310 can be, e.g., nanoscale structures (e.g., nanopillars). 0_inc is the angle of incidence with respect to the surface normal. 0_slant is the slant angle with respect to the surface normal. The pillars 310 are slanted, which means that 0_slant is nonzero p is the grating period of the slanted pillars 310. In some embodiments, the material of the slanted pillars can be resin with a refractive index of, e.g., about 1.1716 at a wavelength l = 532 nm.

[0075] By varying the filling factor and/or the incidence angle of the slanted pillars, one can control the detuning from the resonance condition, and thus the phase shift of the scattered light. FIG. 4A illustrates the light phase change as a function of incidence angle for various filling factors. As shown in FIG. 4A, by varying the filling factor, the angular dispersion can be tuned from positive to negative. Relatively large angular dispersion can be achieved at even small filling factors. FIG. 4B illustrates light transmission as a function of incidence angle for various filling factors. The resonance behavior is also manifested as a dip in the transmission spectrum as shown in FIG. 4B.

[0076] The angle-dependent metasurfaces as disclosed can have other applications. FIG. 5 illustrates an omni-angle resonator or filter device based on an angle-dependent metasurface. The metasurface can be patterned on top of one or more optical resonators and/or one or more filters to render the functionalities of these devices substantially insensitive to incidence angles.

[0077] It is to be understood that the term“design” or“designed” (e.g., as used in“design wavelength,”“design focal length” or other similar phrases disclosed herein) refers to parameters set during a design phase; which parameters after fabrication may have an associated tolerance.

[0078] In some embodiments, a metasurface grating includes a substrate and multiple nanoscale elements disposed on the substrate. The nanoscale elements define an angle- dependent phase profile that imparts a wavevector that varies depending on angles of incidence.

[0079] In some embodiments, a cross-section of at least one nanoscale element is rectangular or other polygonal shape. In some embodiments, a cross-section of at least one nanoscale element is elliptical or circular. In some embodiments, a cross-section of nanoscale elements can have a 2-fold rotational symmetry, or more generally, an n-fold rotational symmetry where n is an integer that is 2 or greater than 2.

[0080] In some embodiments, nanoscale elements are composed of a semiconductor, an oxide (e.g., a metal or non-metal oxide), a nitride (e.g., a metal or non-metal nitride), a sulfide (e.g., a metal or non-metal sulfide), a pure element, or a combination of two or more of these. [0081] In some embodiments, a substrate is transparent in the visible spectrum, such as a polymer substrate, a glass substrate or one including fused silica. Suitable substrates that are transparent in the visible spectrum can have a light transmittance of at least about 40%, at least about 50%, at least about 60%, at least about 70%, at least about 80%, at least about 85%, at least about 90%, or at least about 95%, over the visible spectrum or a design or working wavelength in the visible spectrum.

[0082] In some embodiments, a substrate is curved or flexible, which offer alternative functionalities, for example to adjust the image distance to the eye or to focus light.

[0083] In some embodiments, nanoscale elements include a dielectric material. Examples of suitable dielectric materials include metal and non-metal oxides (such as an oxide of aluminum (e.g., AI2O3), silicon (e.g., S1O2), hafnium (e.g., HfCh), zinc (e.g., ZnO), magnesium (e.g., MgO), or titanium (e.g., T1O2)), metal and non-metal nitrides (such as nitrides of silicon (e.g., S13N4), boron (e.g., BN), or tungsten (e.g., WN)), metal and non- metal sulfides, and pure elements (e.g., silicon for operation at near-infrared and mid-infrared wavelengths).

[0084] In some embodiments, nanoscale elements have aspect ratios (e.g., height/width) greater than about one, such as at least about 1.5: 1, at least about 2:1, at least about 3:1, at least about 4:1, or at least about 5: 1, and up to about 10: 1 or greater, or up to about 20: 1 or greater. In some embodiments, geometric dimensions (e.g., height/width/length or diameter/height) of nanoscale elements are sub-wavelength, such as about 800 nm or less, about 700 nm or less, or about 600 nm or less.

[0085] In some embodiments, nanoscale elements are slanted nanopillars with a nonzero slant angle with respect to a surface normal of a metasurface grating. In some embodiments, the nonzero slanted angle is about 1 degree or greater, about 2 degrees or greater, about 5 degrees or greater, or about 10 degrees or greater, and up to about 45 degrees or greater, or up to about 50 degrees or greater.

[0086] Polarization-Dependent Metasurfaces [0087] With the broad range of applications in healthcare, education, gaming, navigation and advertising, augmented reality (AR) technology has gained great attention in recent years. By bringing together the virtual images and the real world into a person’s perception, AR devices provide an immersive and enriched experience to the viewers. An AR device includes a see- through optical combiner, which combines and delivers the virtual image and real world optically in front of the eyes.

[0088] Several types of optical combiner architecture have been proposed, using either refractive, diffractive, holographic optics, or a combination of them. For diffractive grating based optical combiner architecture, a diffractive grating out-coupler can be used to progressively extract the light guided by TIR (total internal reflection) in the planar glass plate. To realize a full-color display, three layers of waveguide gratings corresponding to red, green and blue (RGB) light can be stacked together, for example. Each layer is designed to extract light at a specific spectral range.

[0089] The FOV in the diffractive grating based approaches can depend on the waveguide refractive index. For example, for a waveguide refractive index of about 1.7, the horizontal FOV is less than about 40°. In contrast, the presently disclosed technology can achieve a horizontal FOV as large as about 67 ° , for example, using polarization-dependent metagratings. Similar to polarization division multiplexing in optical fiber communications where two channels with orthogonal polarizations are used to double the information capacity, certain presently disclosed technology increases the FOV by encoding the left and right FOV into two orthogonal polarization channels, TE (Transverse Electric) and TM (Transverse Magnetic). Polarization-dependent metagratings, which include subwavelength patterned nanostructures, are designed to selectively extract TE or TM light respectively (also referred to as TE-pass grating and TM-pass grating respectively). The out-coupler includes alternate columns of TE-pass and TM-pass gratings. In some embodiments as examples, a one-dimensional (1D) eyebox expansion (e.g., horizontal FOV) can be achieved at a design wavelength. The design approach can be generalized to full-color two-dimensional 2D eyebox expansion by additional diffractive optical elements that redirect the guided light at about 90° and stacking multipole layers (e.g., three layers for RGB channels respectively) of waveguides together. [0090] At least some embodiments of the present disclosure relate to a waveguide display design based on polarization-dependent metagratings. By encoding the left and right halves of FOV in orthogonal polarization channels, an overall horizontal field of view (FOV) of about 67° can be achieved using a waveguide, which is about 70% larger than that in comparative diffractive gratings. Metagratings that selectively diffract out TE or TM polarized light are designed and simulated using, e.g., rigorous coupled wave analysis (RCWA). High polarization selectivity can be achieved, with minimal crosstalk between the two channels. The transmission spectrum at normal incidence is calculated to assess the see- through effect. Remaining challenges such as fabrication issues are disclosed. The multiplexing information in the polarization domain in waveguide displays may increase the FOV in AR devices.

[0091] FIG. 6(a) illustrates a schematic of an optical combiner based on polarization- dependent metagrating. The optical engine includes a microdisplay, two orthogonal linear polarizers (e.g., X polarizer and Y polarizer) covering the left and right halves of the display respectively, and a collimator. The waveguide includes an in-coupler and an out-coupler, which are responsible for coupling in and out the free space light to guided light respectively. The waveguide can be, e.g., a high-index glass plate.

[0092] Unlike comparative designs where the grating couplers are either polarization- insensitive or work only for a specific polarization, the disclosed in-coupler and out-coupler of the waveguide imparts different transverse momentum to TE and TM light selectively. Linear polarizers that transmit X (TM) polarization or Y (TE) polarization are placed in front of the right or left part of the microdisplay panel respectively. After passing through the collimator, light from the left (TE) or right (TM) part of the FOV interacts with the in-coupler and is guided by TIR in the waveguide. When reaching the polarization-dependent metagrating out-coupler, TE and TM light is diffracted to the right and left respectively, recovering the displayed image.

[0093] FIG. 6(b) illustrates a schematic of an out-coupler of the waveguide. TE-pass and

TM-pass gratings can be spatially multiplexed together. The zoom-in view shows that the two types of metagratings are patterned with different nanostructures and/or have different grating periods. The TE-pass grating diffracts out TE light, and reflects the TM light so that the TM light continues propagating in the waveguide. Similarly, the TM-pass grating diffracts out TM light, and reflects the TE light so that the TE light continues propagating in the waveguide.

[0094] The polarization selectivity is achieved by spatially interleaving two types of metagratings, TE-pass and TM-pass gratings as shown in FIG. 6(b). The two types of metagratings have different grating periods, therefore TE and TM light from the same incident angle is diffracted to different output angles. To avoid crosstalk, the metagratings are designed to diffract out light of a specific polarization, and reflect back the other polarization as shown in FIG. 6(b).

[0095] In comparative waveguide gratings, there is a one-on-one correspondence between the guided angle in the waveguide and output diffraction angle. In disclosed technology, however, a specific guided angle can be mapped to two different output angles.

[0096] FIG. 7(a) illustrates an FOV achieved by an out-coupler of a comparative diffractive grating. As shown in FIG. 7(a), TE light and TM light share the same FOV. The light guided in the waveguide is constrained within a cone 9_{inc min} ~ 9_{inc max} . To satisfy the TIR condition, 9_{inc min} is not smaller than 9_Tm = asin - , where n is the refractive index of the glass plate (e.g., n =1.7). The maximum allowable angle 9_{inc max} is determined by the actual device geometry to avoid ghost images. In some embodiments, it is assumed 9_{inc max}=l 5°. For a given grating period P, the output angle is given by the grating equation: l

n sin 9_inc = sin 9,

p out (13)

[0097] If 9_{0Ut min} =— 9_{0Ut max} , then the maximum FOV and the corresponding grating period P are given by: n sm

FOV_max 9_{0Ut max} - 9, out, min = 2asin(-

37.5°

(14) 2l

P = 0.76 l (15)

n sin 75°+l

[0098] For general cases where 9_{0Ut min} ¹— 9_{0Ut max}, the maximum achievable FOV can be less than about 40° as long as the center of the FOV, which equals (9_{0Ut min} + 9_{0Ut max})/2, is less than about 15° away from the normal direction.

[0099] FIG. 7(b) illustrates an FOV achieved by an out-coupler based on polarization- dependent metagrating. As shown in FIG. 7(b), TE light and TM light are diffracted to two separate viewing zones. The overall FOV is increased. The out-coupler imparts different transverse momentums to TE light and TM light. The grating periods of the TE-pass and TM- pass grating are denoted by PTE and PTM respectively. Here P_TE is larger than P_TM so that TE and TM light is diffracted to the right and left region respectively. The grating equations become

[00100] To avoid any gap or overlap in the FOV, it is specified that aTM TE

s out, max = 9 out, min (18)

[00101] In some embodiments, as demonstrative examples, the metagratings may be designed for blue light, l = 460 nm . The grating periods may be chosen to satisfy the constraints above, P_TE = 460 nm, P_TM = 315 nm. In addition, 9™_{c rnax} = 9 ^_{c max} = 75° , fti™nc,min = asin - n = 37° > fti^Tn^Ec,min = 44°

[00102] Plugging the parameters into Eqn. (16)-(18), 9™_{t min} = -27°, fto5t,_max = 40°, e™_{t max} = 9 _{t min} = 10.4°. The achieved total FOV is

FOV = 9 TE

out, max ft ^s o™ut, in 67° which is about 70% larger than the maximum FOV achieved in comparative diffractive grating designs.

[00103] FIG. 8(a) illustrates a unit cell of a TM-pass grating. In some embodiments, the slanted ridge has a refractive index of about 2.4. H_t = about 350 nm , W = about 280 nm. The slanted angle is about a = 40°. The unit cell size (grating period) is about P_TM = 315 nm.

[00104] FIG. 8(b) illustrates a unit cell of a TE-pass grating. In some embodiments, the rectangular ridges have a refractive index of about 1.716. H₂ = about 250 nm , W₁ = about 90 nm, W₂ = about 40 nm. The center to center distance is about C = 140 nm. The unit cell size (grating period) is about P_TE = 460 nm.

[00105] The TM-pass grating is slanted at about 40° to increase the TM light out- coupling efficiency at large incident angles. The TE-pass grating includes at least two rectangular ridges within each unit cell. In some embodiments, the two metagratings have different slanted angles, heights, and/or refractive indices. In some other embodiments, advanced metagrating optimization methods (e.g. topological optimization) may be used to realize TE- and TM-pass unit cells that have the same refractive indices, heights, and/or slanted angles.

[00106] The grating diffraction efficiency for TE and TM light into each order can be calculated using, e.g., rigorous coupled wave analysis (RCWA). The transmitted lst order is the desired out-coupling order. The reflected 0th order carries the guided light to propagate down the waveguide. All other diffraction orders may be deemed undesired, in some embodiments.

[00107] FIG. 9(a) illustrates a diffraction efficiency of TE-pass gratings as a function of incident angles (e.g., guided angles inside the waveguide). FIG. 9(b) illustrates a diffraction efficiency of TM-pass gratings as a function of incident angles (e.g., guided angles inside the waveguide). As shown in FIGs. 9(a) and 9(b), the transmitted lst order of TM (TE) light is negligible in TE (TM) pass gratings, in accordance with the specified polarization selectivity. In the TE-pass grating, the diffraction power into undesired orders can be comparable or even larger than the desired out-coupling order, which may be further improved to avoid efficiency loss. Although they may be a source of loss, the undesired orders do not necessarily introduce undesirable ghost images, as the undesired orders are mostly reflected at an angle smaller than TIR and leave the waveguide at the backside (the environment side).

[00108] FIG. 9(c) illustrates an overall diffraction efficiency in the transmission (including transmissions of both TE-pass grating and TM-pass grating) as a function of the output angles. The left (right) half of the FOV contains TM (TE) light only. There is some residue undesired higher order (e.g., transmitted 2nd order), but the residue undesired higher order falls outside of the FOV and does not interfere with the virtual image.

[00109] In addition to the FOV of virtual images, see-through effect is another performance criterion for optical combiners. The real world image is desired to be minimally altered (ideally unaltered) after passing through the optical combiner. The see-through performance of the metagratings can be characterized by the transmission efficiency under normal incidence. FIG. 10 illustrates transmission efficiencies at normal incidence, including transmission spectrum of TE-pass gratings, transmission spectrum of TM-pass gratings, and overall transmission. The overall transmission, which is averaged over TE and TM light through TE and TM pass gratings, is relatively flat across the visible spectrum, with corresponds to a mean transmission efficiency of at least about 75%.

[00110] In some embodiments, the TE and TM pass gratings can be fabricated separately. In some other embodiments, the unit cell designs may be designed with the same material, height and slanted angle for both TE and TM pass gratings, so that they can be fabricated in one fabrication step.

[00111] In some embodiments, the residue undesired orders introduce loss of efficiency, and can to be suppressed. In some embodiments, there may be a variation of diffraction efficiency across the FOV. In some other embodiments, a uniform diffraction efficiency may be achieved, for a better use of the display’s dynamic range and viewing experience.

[00112] As used herein, the singular terms“a,”“an,” and“the” may include plural referents unless the context clearly dictates otherwise.

[00113] Spatial descriptions, such as“above,”“below,”“up,”“left,”“right,”“down,” “top,”“bottom,”“vertical,”“horizontal,”“side,”“higher,”“lower,”“upper,”“over,”“under,” and so forth, are indicated with respect to the orientation shown in the figures unless otherwise specified. It should be understood that the spatial descriptions used herein are for purposes of illustration only, and that practical implementations of the structures described herein can be spatially arranged in any orientation or manner, provided that the merits of embodiments of this disclosure are not deviated by such arrangement.

[00114] As used herein, the terms“approximately,”“substantially,”“substantial” and “about” are used to describe and account for small variations. When used in conjunction with an event or circumstance, the terms can refer to instances in which the event or circumstance occurs precisely as well as instances in which the event or circumstance occurs to a close approximation. For example, when used in conjunction with a numerical value, the terms can refer to a range of variation less than or equal to ±10% of that numerical value, such as less than or equal to ±5%, less than or equal to ±4%, less than or equal to ±3%, less than or equal to ±2%, less than or equal to ±1%, less than or equal to ±0.5%, less than or equal to ±0.1%, or less than or equal to ±0.05%. For example, two numerical values can be deemed to be “substantially” the same if a difference between the values is less than or equal to ±10% of an average of the values, such as less than or equal to ±5%, less than or equal to ±4%, less than or equal to ±3%, less than or equal to ±2%, less than or equal to ±1%, less than or equal to ±0.5%, less than or equal to ±0.1%, or less than or equal to ±0.05%.

[00115] Additionally, amounts, ratios, and other numerical values are sometimes presented herein in a range format. It is to be understood that such range format is used for convenience and brevity and should be understood flexibly to include numerical values explicitly specified as limits of a range, but also to include all individual numerical values or sub-ranges encompassed within that range as if each numerical value and sub-range is explicitly specified.

[00116] While the present disclosure has been described and illustrated with reference to specific embodiments thereof, these descriptions and illustrations do not limit the present disclosure. It should be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the true spirit and scope of the present disclosure as defined by the appended claims. The illustrations may not be necessarily drawn to scale. There may be distinctions between the artistic renditions in the present disclosure and the actual apparatus due to manufacturing processes and tolerances. There may be other embodiments of the present disclosure which are not specifically illustrated. The specification and drawings are to be regarded as illustrative rather than restrictive. Modifications may be made to adapt a particular situation, material, composition of matter, method, or process to the objective, spirit and scope of the present disclosure. All such modifications are intended to be within the scope of the claims appended hereto. While the methods disclosed herein have been described with reference to particular operations performed in a particular order, it will be understood that these operations may be combined, sub-divided, or re-ordered to form an equivalent method without departing from the teachings of the present disclosure. Accordingly, unless specifically indicated herein, the order and grouping of the operations are not limitations of the present disclosure.

Claims

CLAIMS What is claimed is:

1. An optical device, comprising:

a metasurface grating comprising a plurality of nanoscale elements, wherein the nanoscale elements define an angle-dependent phase profile that imparts a wavevector that varies depending on an angle of incidence of light.

2. The optical device of claim 1, wherein the nanoscale elements comprise at least one of titanium dioxide, silicon nitride, a polymer, an oxide, a nitride, a sulfide, a pure element, and a combination thereof.

3. The optical device of claim 1, wherein the light of incidence has a wavelength in a visible or near-infrared region of an electromagnetic spectrum.

4. The optical device of claim 1, wherein a cross-section of each of the plurality of nanoscale elements has a two-fold symmetry to impart wavevectors to various polarization states of incidence.

5. The optical device of claim 1, wherein a cross-section of each of the plurality of nanoscale elements has radial symmetry rendering a functionality of the device insensitive to the polarization of light.

6. The optical device of claim 1, wherein the nanoscale elements define the angle-dependent phase profile such that the wavevector is a function of the angle of incidence.

7. The optical device of claim 1, further comprising:

a transmissive substrate comprising glass or polymer, the nanoscale elements disposed on the transmissive substrate.

8. The optical device of claim 1, further comprising:

a transmissive substrate with curved or flexible surfaces.

9. The optical device of claim 1, wherein the metasurface grating provides a field of view (FOV) that depends on the wavevector.

10. The optical device of claim 1, wherein the metasurface grating provides an FOV that satisfies:

where n is refractive index of a transmissive substrate on which the nanoscale elements are disposed.

11. The optical device of claim 1, wherein the angle-dependent phase profile is asymmetric with respective to the angle of incidence.

12. The optical device of claim 1, wherein the metasurface grating provides an FOV that depends on the spatial gradient of the angle-dependent phase profile defined by the nanoscale elements.

13. The optical device of claim 1, wherein the nanoscale elements comprise slanted nanopillars with a nonzero slant angle with respect to the surface normal of the metasurface grating.

14. The optical device of claim 13, wherein the slanted nanopillars are arranged to introduce a Bragg resonance.

15. The optical device of claim 14, wherein the slanted nanopillars are arranged to introduce the Bragg resonance that satisfies: 2n_ef{A sin(0_B) = L, where A = p cos(B_slant) , Q_B =

Bi_ne + B_Siant. 6_inc is the angle of incidence, 9_slant is the nonzero slantangle, p is the grating period of the metasurface grating, and n_e^ is an effective index that is determined by the nonzero slant angle, the angle of incidence and a filling factor.

16. The optical device of claim 1, wherein the angle-dependent phase profile defined by the nanoscale elements imparts an angular dispersion of light phase change that depends on a filling factor of the metasurface grating, or wherein the angle-dependent phase profile defined by the nanoscale elements imparts an angular dispersion of light transmission that depends on the filling factor of the metasurface grating.

17. An augmented reality device, comprising:

a waveguide for overlaying augmented reality information on a view of a real-world environment; and

a metasurface grating comprising a plurality of nanoscale elements disposed on the waveguide, wherein the nanoscale elements define an angle-dependent phase profile that imparts a wavevector that varies depending on an angle of incidence.

18. The augmented reality device of claim 17, wherein the nanoscale elements define the angle-dependent phase profile such that the wavevector is a function of the angle of incidence, for example k ( Q ) =— aq + k₀, where a and k₀ are constants.

19. The augmented reality device of claim 17, wherein the metasurface grating provides a field of view (FOV) that depends on the wavevector.

20. The augmented reality device of claim 17, wherein the metasurface grating provides an FOV that satisfies:

21. The augmented reality device of claim 17, wherein the metasurface grating provides an FOV that depends a spatial gradient of the angle-dependent phase profile defined by the nanoscale elements.

22. The augmented reality device of claim 17, wherein the nanoscale elements are slanted nanopillars with a nonzero slanted angle with respect to a surface normal of the metasurface grating, and the slanted nanopillars are arranged to introduce a Bragg resonance.

23. The augmented reality device of claim 22, wherein the slanted nanopillars are arranged to introduce the Bragg resonance that satisfies: 2n_eiiA sin (0_B) = l. where L =

P cos (9_slant) , Q_B = 9_inc + 9_slant, 9_inc is the angle of incidence, 9_slant is the nonzero slanted angle, p is a grating period of the metasurface grating, and n_e^ is an effective index that is determined by the nonzero slanted angle, the angle of incidence and a filling factor.

24. An omni-angle optical device, comprising:

an optical resonator or an optical filter configured to perform an optical functionality; and

a metasurface grating comprising a plurality of nanoscale elements disposed on the optical resonator or the optical filter, wherein the nanoscale elements define an angle- dependent phase profile that imparts a wavevector that varies depending on an angle of incidence, and the angle-dependent phase profile renders the optical functionality of the optical resonator or the optical filter insensitive to the angle of incidence.

25. An optical device, comprising:

a first metasurface grating comprising a plurality of first nanoscale elements, wherein the first nanoscale elements define a first polarization-dependent phase profile that transmits a first light of a first polarization state in a first direction; and

a second metasurface grating comprising a plurality of second nanoscale elements, wherein the second nanoscale elements define a second polarization-dependent phase profile that transmits a second light of a second polarization state into a second direction different from the first direction.

26. The optical device of claim 25, wherein the first polarization state corresponds to a transverse electric (TE) mode, and the second polarization state corresponds to a transverse magnetic (TM) mode.

27. The optical device of claim 25, wherein a slanted angle, a height or a refractive index of the plurality of first nanoscale elements is different from a slanted angle, a height or a refractive index of the plurality of second nanoscale elements.

28. The optical device of claim 25, wherein the first metasurface grating comprising the plurality of first nanoscale elements is non-transmissive to the second light of the second polarization state.

29. The optical device of claim 25, wherein the second metasurface grating comprising the plurality of second nanoscale elements is non-transmissive to the first light of the first polarization state.

30. An optical device, comprising:

a first polarizer configured to convert light into a first light of a first polarization state; a second polarizer configured to convert light into a second light of a second polarization state;

a waveguide configured to propagate the first light of the first polarization state and the second light of the second polarization state;

a first metasurface grating disposed on the waveguide and comprising a plurality of first nanoscale elements, wherein the first nanoscale elements define a first polarization- dependent phase profile that transmits the first light of the first polarization state in a first direction; and

a second metasurface grating disposed on the waveguide and comprising a plurality of second nanoscale elements, wherein the second nanoscale elements define a second polarization-dependent phase profile that transmits the second light of the second polarization state in a second direction different from the first direction.

31. The optical device of claim 30, further comprising:

a collimator configured to collimate the first light of the first polarization state and the second light of the second polarization state.

32. The optical device of claim 30, wherein the waveguide includes an in-coupler and an out- coupler, at least a portion of the first metasurface grating is disposed on the out-coupler of the waveguide, and at least a portion of the second metasurface grating is disposed on the in coupler of the waveguide.

33. The optical device of claim 30, wherein the first polarization state corresponds to a transverse electric (TE) mode, and the second polarization state corresponds to a transverse magnetic (TM) mode.

34. The optical device of claim 30, wherein a slanted angle, a height or a refractive index of the plurality of first nanoscale elements is different from a slanted angle, a height or a refractive index of the plurality of second nanoscale elements.

35. The optical device of claim 30, wherein the first metasurface grating comprising the plurality of first nanoscale elements is non-transmissive to the second light of the second polarization state.

36. The optical device of claim 35, wherein the second metasurface grating comprising the plurality of second nanoscale elements is non-transmissive to the first light of the first polarization state.