DIFFRACTION GRATINGS

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present application claims the priority of European Patent Application No. 20305511.6, filed 18 May 2020, entitled “High-Uniformity High Refractive Index Material Transmissive and Reflective Diffraction Gratings.”

BACKGROUND

[0002] The present disclosure relates to the field of optics and photonics, and more specifically to optical device comprising at least one diffraction grating. It may find applications in the field of conformable and wearable optics (e.g. AR/VR glasses (Augmented Reality/Virtual Reality)), as well as in a variety of other electronic consumer products comprising displays and/or lightweight imaging systems, including head up displays (HUD), as for example in the automotive industry.

[0003] More particularly, but not exclusively, the present disclosure relates to diffraction gratings, containing near-field focusing and beam forming in the near-field zone elements, that can be used in a wide range of devices (as for example displays, including in and out coupling of light in waveguides for eyewear electronic devices and head-mounted displays for AR (Augmented Reality) and VR (Virtual Reality) glasses, optical sensors for photo/video/lightfield cameras, bio/chemical sensors, including lab-on-chip sensors, microscopy, spectroscopy and metrology systems, solar panels, etc.).

[0004] This section is intended to introduce the reader to various aspects of art, which may be related to various aspects of the present disclosure that are described and/or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the systems and methods described herein. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of prior art.

[0005] With the advent of nanotechnology, the ever-increasing interest to explore the optical world at nanoscale has led to an interest in manipulating visible light in the subwavelength scale.

[0006] The planar lens, thanks to its small thickness and excellent focusing capability, has been developed to replace its thick dielectric counterpart as a nanophotonic component. Several types of planar lenses have been studied so far, for example zone plates, nano-slit and nano-hole arrays, photonics crystals and metasurfaces. Although different terminologies are used in the aforementioned techniques, they share the same principle of focusing coherent waves, which is to generate a constructive interference at the focal point by curving the phase front of an incident plane wave. The performance of planar lenses has been optimized through sophisticated designs. However, most of the proposals do not allow for satisfactory control over the focal spot position and do not satisfactorily allow for changes to the orientation of an electromagnetic beam. The available solutions may not fully satisfy the needs of emerging nano- photonic applications due to their performance characteristics (e.g. chromatic aberrations and limited resolution) and fabrication difficulties.

[0007] An optical see-through head mounted display (HMD) is a device used for augmented/virtual reality (AR/VR) applications. To realize a compact near-eye display system for AR with a wide field of view, various technologies have been developed. Some AR-based HMDs use a waveguide structure in order to reduce the overall size and weight of the device. Some such structures include in- and out-couplers which are fabricated by diffractive optical elements or holographic volume gratings. To couple light into the waveguide and provide good color uniformity, diffracted non-zero order light should have high intensity across a wide angular range.

[0008] A photonic nano jet (NJ) is a narrow high-intensity optical radiation flux formed in the proximity to the shadow surface of an illuminated transparent dielectric particle with relatively small refractive index and a diameter that is comparable to or somewhat larger than the wavelength of the incident optical radiation. The physical origin of photonic nanojet formation arises from the interference of the radiation net fluxes diffracted and transmitted through a particle. One feature of a photonic nanojet is the high spatial localization of the light field in the transverse direction. The physics of photonic nanojet formation by spherical particles has been studied by means of the Mie theory. Studies have shown that the focusing properties of the arbitrary-shaped microstructures are affected by the edge diffraction phenomenon. The diffraction of light on the edge of a dielectric microstructure forms a tilted focused beam having a deviation angle that depends on the index ratio between the structure material and host medium.

SUMMARY

[0009] References in the specification to “one embodiment,” “an embodiment,” “an example embodiment,” and the like indicate that the embodiment described may include a particular feature, structure, or characteristic; but not every embodiment necessarily includes that particular feature, structure, or characteristic. Moreover, such phrases are not necessarily referring to the same embodiment. Further, when a particular feature, structure, or characteristic is described in connection with an embodiment, such feature, structure, or characteristic may be used in connection with other embodiments whether or not explicitly described. [0010] An optical system according to some embodiments comprises an optical substrate, a plurality of diffraction grating elements arranged periodically on the substrate, and a phase-modifying optical layer between the optical substrate and the diffraction grating elements, the phase-modifying layer having a refractive index greater than a refractive index of the optical substrate.

[0011] In some embodiments of the optical system, the diffraction grating elements have a refractive index greater than 3.0.

[0012] In some embodiments of the optical system, the diffraction grating elements comprise a semiconductor. In some such embodiments, the diffraction grating elements comprise silicon. In some other embodiments, the diffraction grating elements comprise aluminum arsenide.

[0013] In some embodiments of the optical system, each grating element comprises a single component having a substantially rectangular cross section.

[0014] In some embodiments of the optical system, each grating element comprises a pair of components having substantially rectangular cross sections.

[0015] In some embodiments of the optical system, each grating element has a substantially U-shaped cross section.

[0016] In some embodiments of the optical system, the phase-modifying optical layer has a refractive index greater than 2.0.

[0017] In some embodiments of the optical system, the phase-modifying optical layer comprises titanium dioxide.

[0018] Some embodiments of the optical system further include a stop layer between the phase- modifying optical layer and the diffraction grating elements.

[0019] In some embodiments of the optical system, the optical substrate is a waveguide in a waveguide display.

[0020] In some embodiments of the optical system, the diffraction grating elements are configured to operate as a reflective diffraction grating.

[0021] In some embodiments of the optical system, the diffraction grating elements are configured to operate as a transmissive diffraction grating.

[0022] A method according to some embodiments, includes directing light on an optical system as described herein. In some such embodiments, the method includes propagating the light through the optical substrate by total internal reflection. The light may comprise an image.

BRIEF DESCRIPTION OF THE DRAWINGS

[0023] FIG. 1 A is a cross-sectional schematic view of a waveguide display. [0024] FIG. 1 B is a schematic illustration of a binocular waveguide display with a first layout of diffractive optical components.

[0025] FIG. 1 C is a schematic illustration of a binocular waveguide display with a second layout of diffractive optical components.

[0026] FIG. 1 D is a schematic exploded view of a double-waveguide display.

[0027] FIG. 1 E is a cross-sectional schematic view of a double-waveguide display.

[0028] FIGs. 2A-2B illustrate cross-sectional views of a unit cell of a high refractive index material regular diffraction grating (FIG. 2A); and a high refractive index material U-shape diffraction grating (FIG. 2B).

[0029] FIGs. 3A-3D illustrate reflectance and transmittance vs. angle of electromagnetic wave incidence (α) at λ=625nm, n ₁ =1.0, n ₂ =3.897 +i0.021061, n ₃ =1.7663. FIGs. 3A and 3C illustrate results for a regular transmissive diffraction grating (as in FIG. 2A) with d=358 nm, W=80nm, H=105nm (FIG. 3A) and H=110nm (FIG. 3C). FIGs. 3B and 3D illustrate results for a u-shaped transmissive diffraction grating (as in FIG. 2B) with d’=2d=716nm, W=80nm, W ₁ =278nm, H ₁ =5nm, H=105nm (FIG. 3B) and H=110nm (FIG. 3D).

[0030] FIGs. 4A-4B illustrate cross-sectional views of unit cells of diffraction gratings with a layer of high refractive index material. FIG. 4A illustrates a high refractive index material regular diffraction grating with additional layers. FIG. 4B illustrates a high refractive index material twin-shape diffraction grating with additional layers.

[0031] FIGs. 5A-5B illustrate transmittance of the first diffraction order T ₁ vs. refractive index of the additional layer n _{L 1} for regular transmissive diffraction grating as in FIG. 4A at λ=625nm, n ₁ =1.0, n ₂ =3.897 +i0.021061, n ₃ =1.7663, d=358 nm, W=80nm, H=110nm; H _{L 2} =10nm, n _{L 2} =1.7663. In FIG. 5A, α =3°. In FIG. 5B, α =30°.

[0032] FIG. 6A-6B illustrate reflectance and transmittance vs. angle of electromagnetic wave incidence (α) at λ=625nm, n ₁ =1.0, n ₂ =3.897 +i0.021061, n ₃ = n _{L 2} =1.7663, n _{L 1} =2.5884, H=105nm, H _{L 1} = H _{L 2} =10nm. FIG. 6A illustrates results for a regular shape transmissive diffraction grating as in FIG. 4A with d=358 nm, W=80nm, H=110nm. FIG. 6B illustrates results for a twin-shaped transmissive diffraction grating as in FIG. 4B with d’=2d=716nm, W=80nm, W ₁ =260nm.

[0033] FIGs. 7A-7C illustrate calculated reflectance and transmittance vs. angle of electromagnetic wave incidence (α) at λ=620nm, n ₁ =1.0, n ₂ =2.105, n ₃ = 1.52, W=120nm, H=225nm. FIG. 7A illustrates results for a regular diffraction grating (as in FIG. 2A) with d=411.2nm. FIG. 7B illustrates results for a twin shape transmissive diffraction grating with d’=2d=822.4nm, W ₁ =260nm, H ₁ =0nm (as in FIG. 2B). FIG. 7C illustrates results for a U-shape transmissive diffraction grating (as in FIG. 2B) with d’=2d=822.4nm, W ₁ =260nm, H ₁ =50nm. [0034] FIGs. 8A-8D illustrate calculated reflectance and transmittance vs. angle of electromagnetic wave incidence (α) for a regular diffraction grating (as in FIG. 4A) at λ=620nm, n ₁ =1.0, n ₂ =2.105, n ₃ = 1.52, n _{L 2} =1.7663, d=411.2nm, W=120nm, H _{L 2} =10nm. In FIG. 8A, n _{L 1} =2.105, H=225nm, H _{L 1} = 10 nm. In FIG. 8B, n _{L 1} =2.105, H=180nm, H _{L 1} = 10 nm. In FIG. 8C, n _{L 1} =2.105, H=180nm, H _{L 1} = 15 nm. In FIG. 8D, n _{L 1} =2.3, H=180nm, H _{L 1} = 10 nm.

[0035] FIG. 9 illustrates reflectance and transmittance vs. angle of electromagnetic wave incidence (α) for twin-shape diffraction grating (as in FIG. 4B) at λ=620nm, n ₁ =1.0, n ₂ = n _{L 1} =2.105, n ₃ = 1.52, n _{L 2} =1.7663, d=822.4nm, W=120nm, H=180nm, H _{L 1} =15nm, H _{L 2} =10nm, W ₁ = 260 nm.

[0036] FIGs. 10A-10C illustrate cross-sectional views of a unit cell of: a regular reflective diffraction grating (FIG. 10A); high refractive index material regular reflective diffraction grating with additional layers (FIG. 10B); high refractive index material twin-shape reflective diffraction grating with additional layers (FIG. 10C).

[0037] FIG. 11 illustrates calculated reflectance and transmittance vs. angle of electromagnetic wave incidence (α) for regular reflective diffraction grating (see FIG. 10A) at λ=625nm, n ₁ =1.0, n ₂ = 3.1177, n ₃ = 1.7663, d=374 nm, W=160nm, H=380nm.

[0038] FIG. 12 illustrates reflectance of the first diffraction order R _-1 vs. refractive index of the additional layer n _{L 1} for regular reflective diffraction grating of FIG. 10A with λ=625nm, n ₁ =1.0, n ₂ =3.1177, n ₃ = n _{L 2} =1.7663, d=374 nm, W=160nm, H=380nm, H _{L 2} =10nm, α =3°.

[0039] FIG. 13A illustrates reflectance and transmittance vs. angle of electromagnetic wave incidence (α) for a regular reflective diffraction grating (as in FIG. 10B) with λ=625nm, n ₁ =1.0, n ₂ =3.1177, n ₃ = n _{L 2} =1.7663, n _{L 1} =2.5884, d=374 nm, W=160nm, H=380nm, H _{L 1} =5nm, H _{L 2} =10nm.

[0040] FIG. 13B illustrates reflectance and transmittance vs. angle of electromagnetic wave incidence (α) for a twin-shape reflective diffraction grating (as in FIG. 10C) at λ=625nm, n ₁ =1.0, n ₂ =3.1177, n ₃ = n _{L 2} =1.7663, n _{L 1} =2.5884, d’=748nm, W=160nm, H=380nm, H _{L 1} =5nm, H _{L 2} =10nm, W ₁ = 95 nm.

DETAILED DESCRIPTION

Example waveguide displays.

[0041] Described herein are optical systems and methods that can be implemented in waveguide display systems and methods. An example waveguide display device is illustrated in FIG. 1A. FIG. 1A is a schematic cross-sectional side view of a waveguide display device in operation. An image is projected by an image generator 102. The image generator 102 may use one or more of various techniques for projecting an image. For example, the image generator 102 may be a laser beam scanning (LBS) projector, a liquid crystal display (LCD), a light-emitting diode (LED) display (including an organic LED (OLED) or micro LED (μLED) display), a digital light processor (DLP), a liquid crystal on silicon (LCoS) display, or other type of image generator or light engine.

[0042] Light representing an image 112 generated by the image generator 102 is coupled into a waveguide 104 by a diffractive in-coupler 106. The in-coupler 106 diffracts the light representing the image 112 into one or more diffractive orders. For example, light ray 108, which is one of the light rays representing a portion of the bottom of the image, is diffracted by the in-coupler 106, and one of the diffracted orders 110 (e.g. the second order) is at an angle that is capable of being propagated through the waveguide 104 by total internal reflection.

[0043] At least a portion of the light 110 that has been coupled into the waveguide 104 by the diffractive in-coupler 106 is coupled out of the waveguide by a diffractive out-coupler 114. At least some of the light coupled out of the waveguide 104 replicates the incident angle of light coupled into the waveguide. For example, in the illustration, out-coupled light rays 116a, 116b, and 116c replicate the angle of the in- coupled light ray 108. Because light exiting the out-coupler replicates the directions of light that entered the in-coupler, the waveguide substantially replicates the original image 112. A user’s eye 118 can focus on the replicated image.

[0044] In the example of FIG. 1A, the out-coupler 114 out-couples only a portion of the light with each reflection allowing a single input beam (such as beam 108) to generate multiple parallel output beams (such as beams 116a, 116b, and 116c). In this way, at least some of the light originating from each portion of the image is likely to reach the user’s eye even if the eye is not perfectly aligned with the center of the out-coupler. For example, if the eye 118 were to move downward, beam 116c may enter the eye even if beams 116a and 116b do not, so the user can still perceive the bottom of the image 112 despite the shift in position. The out-coupler 114 thus operates in part as an exit pupil expander in the vertical direction. The waveguide may also include one or more additional exit pupil expanders (not shown in FIG. 1A) to expand the exit pupil in the horizontal direction.

[0045] In some embodiments, the waveguide 104 is at least partly transparent with respect to light originating outside the waveguide display. For example, at least some of the light 120 from real-world objects (such as object 122) traverses the waveguide 104, allowing the user to see the real-world objects while using the waveguide display. As light 120 from real-world objects also goes through the diffraction grating 114, there will be multiple diffraction orders and hence multiple images. To minimize the visibility of multiple images, it is desirable for the diffraction order zero (no deviation by 114) to have a great diffraction efficiency for light 120 and order zero, while higher diffraction orders are lower in energy. Thus, in addition to expanding and out-coupling the virtual image, the out-coupler 114 is preferably configured to let through the zero order of the real image. In such embodiments, images displayed by the waveguide display may appear to be superimposed on the real world. [0046] Some waveguide displays include more than one waveguide layer. Each waveguide layer may be configured to preferentially convey light with a particular range of wavelengths and/or incident angles from the image generator to the viewer.

[0047] As illustrated in FIGs. 1 B and 1C, waveguide displays having in-couplers, out-couplers, and pupil expanders may have various different configurations. An example layout of one binocular waveguide display is illustrated in FIG. 1 B. In the example of FIG. 1 B, the display includes waveguides 152a, 152b for the left and right eyes, respectively. The waveguides include in-couplers 154a,b, pupil expanders 156a,b, and components 158a,b, which operate as both out-couplers and horizontal pupil expanders. The pupil expanders 156a,b are arranged along an optical path between the in-coupler and the out-coupler. An image generator (not shown) may be provided for each eye and arranged to project light representing an image on the respective in-coupler.

[0048] An layout of another binocular waveguide display is illustrated in FIG.1C. In the display of FIG.

1 C, the display includes waveguides 160a, 160b for the left and right eyes, respectively. The waveguides include in-couplers 162a,b. Light from different portions of an image may be coupled by the in-couplers 162a,b to different directions within the waveguides. In-coupled light traveling toward the left passes through pupil expanders 164a,b and 165a,b, while in-coupled light traveling toward the right passes through pupil expanders 166a,b and 167a,b. Having passed through the pupil expanders, light is coupled out of the waveguides using out-couplers 168a,b to substantially replicate an image provided at the in- couplers 162a,b.

[0049] In different embodiments, different features of the waveguide displays may be provided on different surfaces of the waveguides. For example (as in the configuration of FIG. 1 A), the in-coupler and the out-coupler may both be arranged on the anterior surface of the waveguide (away from the user’s eye). In other embodiments, the in-coupler and/or the out-coupler may be on a posterior surface of the waveguide (toward the user’s eye). The in-coupler and out-coupler may be on opposite surfaces of the waveguide. In some embodiments, one or more of an in-coupler, an out-coupler, and a pupil expander, may be present on both surfaces of the waveguide. The image generator may be arranged toward the anterior surface or toward the posterior surface of the waveguide. The in-coupler is not necessarily on the same side of the waveguide as the image generator. Any pupil expanders in a waveguide may be arranged on the anterior surface, on the posterior surface, or on both surfaces of the waveguide. In displays with more than one waveguide layer, different layers may have different configurations of in-coupler, out- coupler, and pupil expander.

[0050] FIG. 1 D is a schematic exploded view of a double waveguide display, including an image generator 170, a first waveguide (WG ₁ ) 172, and a second waveguide (WG ₂ ) 174. FIG. 1 E is a schematic side-view of a double waveguide display, including an image generator 176, a first waveguide (WG ₁ ) 178, and a second waveguide (WG ₂ ) 180. The first waveguide includes a first transmissive diffractive in-coupler (DG1) 180 and a first diffractive out-coupler (DG6) 182. The second waveguide has a second transmissive diffractive in-coupler (DG2) 184, a reflective diffractive in-coupler (DG3) 186, a second diffractive out- coupler (DG4) 188, and a third diffractive out-coupler (DG5) 190. Different displays may use different arrangements of optical components (such as different arrangements of pupil expanders) on the first and second waveguides.

[0051] While FIGs. 1A-1 E illustrate the use of waveguides in a near-eye display, the same principles may be used in other display technologies, such as head up displays for automotive or other uses.

Example diffractive structures.

[0052] Example embodiments include transmissive and reflective diffraction gratings using high refractive index material. The described uses of high refractive index materials may increase the diffraction efficiency and diffraction uniformity of transmissive and reflective gratings with simple topologies. In some embodiments, an additional high refractive index thin layer and stop layer are provided between the substrate and elements of diffraction grating, which may further improve the diffraction uniformity of in- coupled diffraction order and simplify the fabrication process.

[0053] In example embodiments, high refractive index material diffraction gratings can be employed to efficiently steer light in the visible range with substantially uniform efficiency over a wide range of incidence angles. Use of additional layers on the top of waveguide may improve the diffraction uniformity of an in- coupled diffraction order and simplify the fabrication process.

[0054] To promote high diffraction efficiency of an in-coupled nonzero diffraction order, it is proposed in some embodiments to use high refractive index material for at least some of the components that make up the elements of the reflective/transmissive gratings. To provide high diffraction uniformity of corresponding diffraction order, example embodiments use an additional layer of high refractive index material on the top of the waveguide. In some embodiments, a stop layer is provided above this high refractive index material layer, which may simplify the fabrication process. The present disclosure further describes diffraction gratings comprising a plurality of grating unit cells.

[0055] Numerical simulations of the performance of some embodiments were performed for some embodiments via full-wave electromagnetic analysis of 1 D diffraction gratings. The simulations take into account dispersion and losses in the materials of the system. Analysis of the results shows that diffraction of a plane wave on the elements of the gratings may result in edge wave generation, refraction and interference leading to the improving of the efficiency of corresponding diffraction order. Due to the phase modification of the edge wave and refracted plane wave by an additional layer, the diffraction uniformity of the in-coupled diffraction order may be improved. [0056] FIGs. 2A-2B illustrate cross-sectional views of a unit cell of a high refractive index material regular diffraction grating (FIG. 2A); and a high refractive index material U-shape diffraction grating (FIG. 2B).

[0057] The general topology of the unit cell of an example symmetrical transmissive diffraction grating is illustrated in FIG. 2A. In the example of FIG. 2A, the grating element 202 in a unit cell 204 is a single high refractive index grating component. This cross-section view may correspond to high refractive index ( n ₂ ) component on the top of a homogeneous dielectric substrate medium 206 with a refractive index n ₃ ( n ₂ > n ₃ ). In some embodiments, n ₂ is at least 1.45 times as great as n ₃ . The full system is hosted by the homogeneous host medium with refractive index n ₁ . In some embodiments, n ₁ < n ₃ . W and H are the width and height of the high refractive index component. The materials and size of the constitutive parts may be configured to manage the position, direction, phase and amplitude of the edge waves diffracted by the vertical edges of the high refractive index component. For the sake of simplicity, the illustrations provided herein show structures with vertical edges parallel to the z-axis and top/bottom surfaces parallel to the xy- plane, which corresponds to the base angle being equal to 90°. Flowever, some embodiments use prismatic structures (with arbitrary base angles) or other shapes. Variation of the base angle value provides additional degree of freedom in the control of the edge wave radiation. To create the diffraction grating, a periodic array of the unit cells is provided.

[0058] The grating constant or the period of the grating is d. The period of diffraction grating may be selected to in-couple diffraction order M ₁ . The grating pitch may be selected based on the angular span that can be coupled into the waveguide to propagate by Total Internal Reflection (TIR). A linearly polarized plane wave may be incident on the grating from the top in a plane perpendicular to the grating. Example embodiments may be used for both TE and TM polarizations, but different embodiments may be configured to improve efficiency by taking into account the polarization of an incident wave.

[0059] FIG. 2B illustrates a u-shape diffraction grating unit cell 206. The unit cell in the grating of FIG. 2B may be described as two unit cells as in FIG. 2A with grating components 210, 212 together with an additional component 214 with the width W ₁ and height H ₁ between these unit cells. The pitch of u-shape diffraction grating will be equal to d ₁ =2d. Such diffraction grating will in-couple into the waveguide substrate the diffraction order M ₂ =2M ₁ . For the u-shaped diffraction grating, the distance between the high index components may be W ₁ ≤ d-W.

[0060] Some embodiments use a twin-shape diffraction grating, which is uses a unit cell similar to that of FIG. 2B but without the central block (the additional component with the width W ₁ and height H ₁ ). In some embodiments using twin-shape gratings, W ₁ < d-W. Such diffraction grating may also in-couple into the waveguide the diffraction order M ₂ =2M ₁ . [0061] Simulations were performed to determine the effects of the edge diffraction phenomenon in the single element of the period into the total response of the diffraction grating. The presented data were obtained using the COMSOL Multiphysics software. The presented analysis of the fields and power distributions inside the elements of the gratings may be used in selecting grating topologies for different applications. In the simulations, the system is illuminated by a linearly-polarized plane wave E={0,0, 1 }. The effect of the parameters of the single element on the functionality of the system is considered.

[0062] The beam-forming phenomenon is associated with the edge of the system, and the nanojet beam radiation angle is linked to Snell’s law, as described, for example, in A. Boriskin, V. Drazic, R. Keating, M. Damghanian, O. Shramkova, L. Blonde, “Near field focusing by edge diffraction," Opt. Lett., 2018. For the normal incidence of incident wave, the nanojet beam radiation angle for constitutive parts of the element of the unit cell can be determined as a function of the ratio between the refractive indexes of the media hosting the element: n ₁ and material of the element of diffraction grating n ₂ , and the base angle of the element. (The presented results are based on analysis of elements with the vertical edges and base angle equal to 90°.) For the main part of the element with refractive index n ₂ the nanojet beam radiation angle can be determined using the approximate formula: where is the critical angle of refraction. For an example embodiment, two opposite edges of the element on the top of substrate with the width I/I/ and height H will generate two nanojets (the nanojets are similar only in a case of normal incidence). The creation of a nanojet beam is the result of constructive interference between the edge wave diffracted by the vertical edge and refracted plane wave. Two edge waves (EW1 and EW2) will propagate inside the element with the angle of deviation equal to (see FIG. 2A). It was observed that the nanojet length and intensity depend significantly on the size of an element, as described, for example in B. Varghese, O. Shramkova, V. Drazic, V. Allie, L. Blonde , “Influence of an edge height on the diffracted EM field distribution,” ICTON 2019,

Angers, France, and on the refractive index ratio . Decreasing the index ratio (correspondingly increasing refractive index n ₂ ) may increase the edge wave intensity. The size of the elements and/or angle of electromagnetic wave incidence may be changed to obtain an internal reflection of the edge wave by the walls inside the elements. Taking into account the angle of edge wave propagation, it may be concluded that for high refractive index n ₂ there is total internal reflection by the walls, allowing for the full edge wave intensity to be concentrated inside the element. This may provide high scattering intensity in the forward direction for the high refractive index elements. [0063] In the case of inclined incidence, the angle of edge wave propagation will be different for two opposite edges:

Where α is the angle of electromagnetic wave incidence. It may be desirable to select the height of the element of the diffraction grating to substantially satisfy the following equation:

H = W _Y , (3) where , and W is the width of a single component in the grating element.

[0064] Using these elements to create the diffraction gratings, the dimensions of the element in some embodiments may be configured to increase the diffraction uniformity for inclined incidence angles of the electromagnetic wave. For the inclined incidence, the angles of deviation of EWi and EW2 will not be equal and depending on the angle of incidence there may be multiple EW reflections by the edges of the element.

[0065] In one analysis of the performance of diffraction grating based on the high refractive index material element, it is assumed that a linearly polarized plane wave is incident on the grating from the top in a plane perpendicular to the grating. The angles of the beams diffracted in the far field are not substantially influenced by the structure of the elements. They are determined by the period of the grating, wavelength of the incident plane wave and angle of wave incidence and refraction indexes, and they can be calculated according to the grating equation. But generated edge waves can make a complimentary input into the total response of the periodic array when generated edge waves have a proper phase and direction.

[0066] The performance of the grating is affected by the polarization of the incident wave and parameters (dimensions, form and material) of the elements. For a diffraction grating containing symmetrical single-material elements (regular structure of the same spacing) example embodiments demonstrate symmetrical distribution of intensity (T _j = T _-j , R _j = R _-j , ...., where j is the diffraction order). For the simulated case it may be assumed that the first diffraction order is in-coupled into the waveguide. So, maximal input for dual mode system (where the diffraction efficiency is configure for two diffraction modes) corresponds to the orders ±1.

[0067] The computed reflectance and transmittance for TE incidence are plotted in FIGs. 3A-3D.

[0068] FIGs. 3A-3D illustrate reflectance and transmittance vs. angle of electromagnetic wave incidence (α) at λ=625nm, n ₁ =1.0, n ₂ =3.897 +i0.021061, n ₃ =1.7663. FIGs. 3A and 3C illustrate results for a regular transmissive diffraction grating (as in FIG. 2A) with d=358 nm, W=80nm, H=105nm (FIG. 3A) and H=110nm (FIG. 3C). FIGs. 3B and 3D illustrate results for a u-shaped transmissive diffraction grating (as in FIG. 2B) with d’=2d=716nm, W=80nm, W ₁ =278nm, H ₁ =5nm, H=105nm (FIG. 3B) and H=110nm (FIG. 3D). FIGs. 3A-3D reflect the dependencies for different heights of the elements. The numerical analysis of diffraction uniformity and power for different configurations are presented below in Table 1.

[0069] FIG. 3A illustrates reflectance for 0-order and transmittance for 0 and ±1 orders at λ=625nm for a grating with the substrate with n ₃ =1.7663 (it can correspond to sapphire material, a form of AI ₂ O ₃ ). An alternative substrate material may be an episulfide material (such as those used in some eyeglasses) with a refractive index of around 1.716 at 532 nm. FIG. 3A uses a period d=358 nm. The system has been configured using silicon (Si) as the material of the elements of the gratings ( n ₂ =3.897 + i0.021061). The full-wave electromagnetic analysis was conducted for the 1 D periodic array of the elements. The simulations assume that the system is infinite in X- and Y-directions. It can be seen in FIG. 3A that the example high refractive index material diffraction grating has very high intensity for transmitted first order. The maximal intensity for this configuration is equal to η _max =85.224%.

[0070] In order to give a measure for the homogeneity of the diffraction efficiency for all angles of incidence in-coupled into the waveguide, a measure G of diffraction uniformity may be defined as:

[0071] To calculate the diffraction uniformity, consider the angular range from 3° to 45°. For a regular high refractive index material diffraction grating with reflectance/transmittance presented in FIG. 4A, the diffraction uniformity is about 86.93%. The diffraction power, which is the ratio of the total transmitted light to the incoming one over this angular range, of such grating is equal to 81.2%.

[0072] To increase the transmitted intensity of the first order at low angle of incidence, some embodiments use a modified topology of the elements. In a case of u-shape element (see FIG. 2B) with the central component with W ₁ =278nm, H ₁ =5nm the maximal intensity of the second order (d’=2d=716nm and twice bigger order will be in-coupled into the waveguide) in the corresponding angular range will be reduced to η _max =80.115%. At the same time, the transmitted intensity corresponding to the low angles of incidence will be increased providing higher diffraction uniformity. For an optimized case in FIG. 3B, G will be equal to 91.85%. The diffraction power of such grating is equal to 78.6%.

Example diffractive structures with additional layers.

[0073] Some embodiments operate to increase the transmittivity of in-coupled diffraction order at low angles of incidence. Some embodiments employ a high refractive index material diffraction grating with an additional thin layer ( H _{L 1} is the thickness of this layer with refractive index n _{L 1} ) placed on the top of the waveguide. In some such embodiments, to simplify the fabrication process, a stop layer is provided between this thin layer and elements of the grating. The stop layer material refractive index is n _{L 2} , and H _{L 2} is the thickness of this layer. Example topologies corresponding to regular and twin-shaped diffraction gratings are presented in FIGs. 4A and 4B, respectively. The utilization of an additional high refractive index layer between the substrate and elements of diffraction grating modifies the phase of the refracted edge wave, providing higher transmissivity of the in-coupled order.

[0074] FIGs. 4A-4B illustrate cross-sectional views of unit cells of diffraction gratings with a layer of high refractive index material. FIG. 4A illustrates a high refractive index material regular diffraction grating with additional layers. FIG. 4A illustrates a diffraction grating unit cell 400 with element 402 on substrate 404. The example of FIG. 4A includes a phase-modifying optical layer 406 with refractive index n _{L 1} . The grating as illustrated further includes an optional stop layer 408 with refractive index n _{L 2} .

[0075] FIG. 4B illustrates a high refractive index material twin-shape diffraction grating with additional layers. Unit cell 410 includes a pair of grating elements 412, 413 arranged on substrate 414. The example of FIG. 4B includes a phase-modifying optical layer 416 with refractive index nu. The grating as illustrated further includes an optional stop layer 418 with refractive index n _{L 2} .

[0076] FIGs. 5A-5B illustrate calculated results of dependencies of first diffraction order transmittivity on the refractive index of an additional layer for low angle of incidence (α =3°, FIG. 5A) and high angle of incidence (α =30°, FIG. 5B) at H _{L 2} = 10nm. The calculations assume that AI ₂ O ₃ is the material of stop layer. We can see that the diffraction uniformity of depends in part on the thickness H _{L 1} and refractive index of material of this additional layer n _{L 1} . The vertical dashed line in these figures corresponds to the case when n _{L 1} = n ₃ .

[0077] FIGs. 5A-5B illustrate transmittance of the first diffraction order T ₁ vs. refractive index of the additional layer n _{L 1} for regular transmissive diffraction grating as in FIG. 4A at λ=625nm, n ₁ =1.0, n ₂ =3.897 +i0.021061, n ₃ =1.7663, d=358 nm, W=80nm, H=110nm; H _L2 =10nm, n _{L 2} =1.7663. In FIG. 5A, α =3°. In FIG. 5B, α =30°.

[0078] The computed reflectance and transmittance for TE incidence for regular and twin-shape diffraction gratings with additional high refractive index and stop layers are plotted in FIGs. 6A-6B. FIG. 6A illustrates reflectance for 0-order and transmittance for 0 and ±1 orders for a grating with the same parameters as in FIG. 4A, but in this example there are two additional layers with 1x2 =1.7663, n _{L 1} =2.5884,H _L1 = H _L2 =10nm. The high refractive index layer may be titanium dioxide (TiO ₂ ). It can be seen that such a high refractive index material diffraction grating also has very high intensity for transmitted first order with maximal intensity equal to η _max =82.76%. But such a system has better intensity at low angles of incidence. So, the diffraction uniformity is increased, and it is equal to 94.83%. The diffraction power of such grating is equal to 81.75%. Example embodiments thus may provide better uniformity and diffraction power compared with a u-shaped diffraction grating. FIG. 6B illustrates the reflectivity and transmittivity for a twin-shaped diffraction grating with additional layers. [0079] FIG. 6A-6B illustrate reflectance and transmittance vs. angle of electromagnetic wave incidence (α) at λ=625nm, n ₁ =1.0, n ₂ =3.897 +i0.021061, n ₃ = n _{L 2} =1.7663, n _{L 1} =2.5884, H=105nm, H _L1 = H _L2 =10nm. FIG. 6A illustrates results for a regular shape transmissive diffraction grating as in FIG. 4A with d=358 nm, W=80nm, H=110nm. FIG. 6B illustrates results for a twin-shaped transmissive diffraction grating as in FIG. 4B with d’=2d=716nm, W=80nm, W ₁ =260nm.

[0080] A comparison between characteristics of proposed topologies for two different heights of the elements (H=105nm and H=110nm) is presented in Table 1. These characteristics correspond to λ=625nm using the following parameters: n ₁ =1.0, n ₂ =3.897 +i0.021061 , n ₃ = n _{L 2} =1.7663, d=358 nm (for regular grating with (FIG. 4A) and without (FIG. 2A) additional layers), d’=2d=716nm (for a u-shape grating (FIG. 2B) and twin-shape grating with additional layer (FIG 4B)), W=80nm, H _L1 = H _L2 =10nm, n _{L 1} =2.5884; for u- shape grating W ₁ =278nm, for twin-shape grating W ₁ =260nm. Among these examples, the regular grating with additional layers has the highest diffraction uniformity.

Topology and performance characteristics, low refractive index material transmissive diffraction grating with additional layers.

[0081] In some embodiments, the utilization of an additional high refractive index layer together with the stop layer may also increase the diffraction uniformity of the in-coupled diffraction order in the case of a low refractive index material diffraction grating. FIGs. 7A-7C illustrate calculated reflectance and transmittance vs. angle of electromagnetic wave incidence for several types of low refractive index diffraction gratings ( n ₂ =2.105) without additional layers on the top of the substrate. The utilization of the additional phase- modifying layer can provide better uniformity and utilization of the stop layer can simplify the fabrication process. To estimate the input of an additional layer into the transmittivity and reflectivity of such system we present a set of dependencies for regular diffraction grating with additional layers in FIGs. 8A-8D and for twin-shape diffraction grating with additional layers in FIG. 9. The numerical comparison for several gratings presented in Table 2 also demonstrates that example embodiments can almost double the diffraction uniformity of transmitted light.

[0082] FIGs. 7A-7C illustrate calculated reflectance and transmittance vs. angle of electromagnetic wave incidence (α) at λ=620nm, n ₁ =1.0, n ₂ =2.105, n ₃ = 1.52, W=120nm, H=225nm. FIG. 7A illustrates results for a regular diffraction grating (as in FIG. 2A) with d=411.2nm. FIG. 7B illustrates results for a twin shape transmissive diffraction grating with d’=2d=822.4nm, W ₁ =260nm, H ₁ =0nm (as in FIG. 2B). FIG. 7C illustrates results for a U-shape transmissive diffraction grating (as in FIG. 2B) with d’=2d=822.4nm, W ₁ =260nm, H ₁ =50nm.

[0083] FIGs. 8A-8D illustrate calculated reflectance and transmittance vs. angle of electromagnetic wave incidence (α) for a regular diffraction grating (as in FIG. 4A) at λ=620nm, n ₁ =1.0, n ₂ =2.105, n ₃ = 1.52, n _{L 2} =1.7663, d=411.2nm, W=120nm, H _L2 =10nm. In FIG. 8A, n _{L 1} =2.105, H=225nm, H _L1 = 10 nm. In FIG. 8B, nu =2.105, H=180nm, H _L1 = 10 nm. In FIG. 8C, n _{L 1} =2.105, H=180nm, H _L1 = 15 nm. In FIG. 8D, n _{L 1} =2.3, H=180nm, H _L1 = 10 nm.

[0084] FIG. 9 illustrates reflectance and transmittance vs. angle of electromagnetic wave incidence (α) for twin-shape diffraction grating (as in FIG. 4B) at A=620nm, n ₁ =1.0, n ₂ = n _{L 1} =2.105, n ₃ = 1.52, n _{L 2} =1.7663, d=822.4nm, W=120nm, H=180nm, H _L1 =15nm, H _L2 =10nm, W ₁ = 260 nm. [0085] As indicated by the above calculations, the utilization of an additional high refractive index layer together with the stop layer may increase (e.g. nearly double) the diffraction uniformity of the in-coupled diffraction order in the case of low refractive index material diffraction grating.

Topology and performance characteristics, high refractive index material reflective diffraction grating with additional layers.

[0086] In some embodiments, high refractive index material elements are used for fabrication of reflective diffraction gratings with high diffraction uniformity and efficiency for incoupled diffraction orders. The constructive interference between the edge waves diffracted by the vertical edges and reflected by the top and walls of the high refractive index element and refracted plane wave will provide high intensity of reflected orders. In FIG. 10A shows positions and directions of edge waves generated by the single element of a regular reflective diffraction grating.

[0087] FIGs. 10A-10C illustrate cross-sectional views of a unit cell of: a regular reflective diffraction grating (FIG. 10A); high refractive index material regular reflective diffraction grating with additional layers (FIG. 10B); high refractive index material twin-shape reflective diffraction grating with additional layers (FIG. 10C).

[0088] The computed reflectance and transmittance for TE incidence are plotted in FIG. 11. FIG. 11 illustrates transmittance for 0-order and reflectance for 0 and ±1 orders at λ=625nm for a grating with the substrate with n ₃ =1.7663 (which may correspond to sapphire material (AI ₂ O ₃ )) and with the period d=374nm. This example embodiment uses aluminium arsenide (AIAs) as the material of the elemets of the gratings ( n ₂ =3.1177). A full-wave electromagnetic analysis was performed for a 1 D array of the elements. The analysis assumes that the system is infinite in X- and Y-directions. It can be seen that such a high refractive index material diffraction grating has a high intensity for reflected first order.

[0089] FIG. 11 illustrates calculated reflectance and transmittance vs. angle of electromagnetic wave incidence (α) for regular reflective diffraction grating (see FIG. 10A) at λ=625nm, n ₁ =1.0, n ₂ = 3.1177, n ₃ = 1.7663, d=374 nm, W=160nm, H=380nm.

[0090] In some embodiments, two additional layers are provided between the waveguide and elements of the diffraction grating to modify the reflectivity of the in-coupled order. The dependencies of reflectivity R _-1 for regular reflective diffraction grating on the refractive index nu and thickness Hu of first additional layer at α =3° are presented in FIG. 12.

[0091] FIG. 12 illustrates reflectance of the first diffraction order Ru vs. refractive index of the additional layer nu for regular reflective diffraction grating of FIG. 10A with λ=625nm, n ₁ =1.0, n ₂ =3.1177, n ₂ = n _{L 2} =1.7663, d=374 nm, W=160nm, H=380nm, H _L2 =10nm, α =3°. [0092] Reflectances and transmittances for two different reflective grating topologies presented in FIGs. 10B and 10C vs. angle of electromagnetic wave incidence are depicted in FIGs. 13A-13B. It may be observed that utilization of additional layers can also increase the diffraction uniformity in a case of reflective diffraction gratings.

[0093] FIG. 13A illustrates reflectance and transmittance vs. angle of electromagnetic wave incidence (α) for a regular reflective diffraction grating (as in FIG. 10B) with λ=625nm, n ₁ =1.0, n ₂ =3.1177, n ₃ = n _{L 2} =1.7663, n _{L 1} =2.5884, d=374 nm, W=160nm, H=380nm, H _L1 =5nm, H _L2 =10nm.

[0094] FIG. 13B illustrates reflectance and transmittance vs. angle of electromagnetic wave incidence (α) for a twin-shape reflective diffraction grating (as in FIG. 10C) at λ=625nm, n ₁ =1.0, n ₂ =3.1177, n ₃ = n _{L 2} =1.7663, n _{L 1} =2.5884, d’=748nm, W=160nm, H=380nm, H _L1 =5nm, H _L2 =10nm, W ₁ = 95 nm.

[0095] Example embodiments provide diffraction grating devices with high efficiency and uniformity.

[0096] Some embodiments use high refractive index material for the elements of transmissive and reflective diffraction gratings. The diffraction gratings in some embodiments contain symmetrical single- material elements using a regular structure of the same spacing, resulting in a symmetrical distribution of an intensity. Use of high refractive index material provides high diffraction efficiency and diffraction uniformity of corresponding orders for gratings with a relatively simple topology. Parameters of the grating may be selected using, for example, Equation (3).

[0097] Some embodiments operate to increase the transmitted intensity of in-coupled diffraction order at low angles of incidence. In some such embodiments, the pitch of the grating for the proposed u- and twin- shape topologies is increased to allow for in-coupling of the second diffraction order (instead of first diffraction order in the case of regular diffraction grating) into the waveguide. To increase the diffraction uniformity of the diffraction order in-coupled by the waveguide, example embodiments use an additional high refractive index thin layer and stop layer between the substrate and elements of diffraction grating.

The utilization of an additional high refractive index layer between the substrate and elements of diffraction grating modifies the phase of refracted edge wave providing higher transmissivity of the in-coupled order. The thickness of this additional layers is much less than the wavelength of an incident electromagnetic wave (H _L1,L2 << λ/n _L1,L2 ).

[0098] Some embodiments are amenable to fabrication using relatively straightforward techniques.

[0099] Example embodiments may be used in any optical system that operates to deviate an image or light with a micro-structure, potential advantages including simplicity of fabrication and robustness.

Example application domains are head-up displays, solar cell panels for maximizing light collection, OLED display light extraction, among many others. [0100] While the above examples refer primarily to the use of devices configured for visible light, other embodiments are configured for use with longer or shorter wavelengths, such as infrared or ultraviolet light, or for use with waves in other parts of the electromagnetic spectrum. Such embodiments may employ materials that are transparent to the wavelengths for which they are designed.

Additional embodiments.

[0101] In some embodiments, an optical system includes an optical substrate; and a plurality of diffraction grating elements arranged periodically on the substrate, wherein the diffraction grating unit cells comprise at least one high refractive index component.

[0102] In some embodiments, the high refractive index component has a refractive index greater than 2.5. In some embodiments, the high refractive index component has a refractive index greater than 3.0.

[0103] In some embodiments, the high refractive index component comprises a semiconductor, such as silicon or aluminum arsenide, among others.

[0104] In some embodiments, the high refractive index component comprises a high refractive index dielectric metasurface.

[0105] In some embodiments, the respective grating elements comprise a single grating component having a substantially rectangular cross section.

[0106] In some embodiments, the respective grating elements comprise a pair of grating components having a substantially rectangular cross section.

[0107] In some embodiments, the respective grating elements have a substantially u-shaped cross section.

[0108] In some embodiments, the optical substrate is a waveguide, such as a waveguide in a waveguide display.

[0109] In some embodiments, the diffraction grating unit cells are configured to operate as a reflective diffraction grating. In some embodiments, the diffraction grating unit cells are configured to operate as a transmissive diffraction grating.

[0110] In some embodiments, the optical system further includes a phase-modifying optical layer between the optical substrate and the diffraction grating unit cells. The phase-modifying optical layer may be a substantially continuous layer. The phase-modifying layer may have a refractive index greater than a refractive index of the optical substrate. The phase-modifying optical layer may have a refractive index greater than 2.0.

[0111] Some embodiments further comprise a stop layer between the phase-modifying optical layer and the diffraction grating elements. [0112] In some embodiments, an optical system includes an optical substrate, a plurality of diffraction grating elements arranged periodically on the substrate; and a phase-modifying optical layer between the optical substrate and the diffraction grating elements, where the phase-modifying layer has a refractive index greater than a refractive index of the optical substrate. The phase-modifying optical layer may be a substantially continuous layer with a refractive index greater than 2.0. The phase-modifying optical layer may have a refractive index greater than 2.5. Some embodiments further include a stop layer between the phase-modifying optical layer and the diffraction grating elements.

[0113] Some embodiments include a method in which light is directed on an optical system as described herein. The light may be light representing an image, for example in a waveguide display system. Where the substrate is a waveguide, the method may include coupling the light into the waveguide.

[0114] An optical system according to some embodiments includes: an optical substrate; a plurality of diffraction grating elements arranged periodically on the substrate; and a phase-modifying optical layer between the optical substrate and the diffraction grating elements, the phase-modifying layer having a refractive index greater than a refractive index of the optical substrate.

[0115] In some embodiments, the phase-modifying optical layer is a substantially continuous.

[0116] In some embodiments, the phase-modifying optical layer has a refractive index greater than 2.0. In some embodiments, the phase-modifying optical layer has a refractive index greater than 2.5.

[0117] Some embodiments further include a stop layer between the phase-modifying optical layer and the diffraction grating elements.

[0118] In some embodiments, a method is performed that includes directing light on the optical system. The light may comprise an image.

[0119] In some embodiments, the refractive index of the high refractive index component is at least 1.45 times as great as a refractive index of the substrate.

[0120] In some embodiments, a diffractive system includes: a substrate that is transparent to at least a first wavelength of electromagnetic radiation; and a plurality of diffraction grating elements arranged periodically on the substrate; wherein the diffraction grating elements comprise at least one component having a refractive index at the first wavelength that is at least 1.45 times as great as a refractive index of the substrate at the first wavelength.

[0121] Although features and elements are described above in particular combinations, one of ordinary skill in the art will appreciate that each feature or element can be used alone or in any combination with the other features and elements.