Optical metasurface using sub-Vogel

Abstract

To provide a sub-hogel configuration for a high-definition light field display.SOLUTION: Optical devices and three dimensional light field display technologies are also described, and more particularly, three dimensional holographic pixels (hogels) composed of monochromatic sub-hogels and engineered metasurfaces that act as directional optical elements for light field displays. The described sub-hogel structure designs and methods are suitable for achromatic metasurfaces to provide directional pixels for multi-view light field color displays.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] (Cross-reference of related applications) This application claims priority to U.S. Patent Application No. 17 / 086,201, filed on 30 October 2020, which is incorporated herein by reference in its entirety.

[0002] This disclosure relates to three-dimensional light field display technology, and more particularly to three-dimensional holographic pixels (Hogels) composed of monochromatic sub-Hogels for light field displays. [Background technology]

[0003] An optical metasurface is an artificial surface used to manipulate wavefronts. Generally, an optical metasurface consists of a two-dimensional lattice of pillar-type structures that interact with the impacting wavefront, with lattice constants and structural size being sub-wavelengths thicker than the wavelength range of electromagnetic waves for which the structure is designed to interact. The dimensions of the pillars and the spacing between them in the metasurface are modified to obtain desired optical properties. Optical metasurfaces can shape the amplitude, phase, and polarization of electromagnetic beams. The use of metasurfaces in light-field display technology can enable the fabrication of substantially flat optical devices, improve the performance of optical elements, and manipulate light to impart new properties to optical systems. In the development of light-field display technology, metasurfaces show promising potential as lightweight, thin optical components that can combine several functions into a single device.

[0004] In one example of an optical metasurface, Lin's U.S. Patent Application Publication 20170219739 describes a randomly spatially multiplexed metasurface in which multiple optical elements are interleaved onto a single metasurface, utilizing the full aperture of the metasurface for all optical elements, although each element occupies only a portion of the total area. An achromatic metalens using this design is intended to be like having a dedicated lens woven for each color channel. Light from all color channels passes through all three lenses such that, for each lens, one-third of the light is focused at the intended achromatic focus and two-thirds of the light is focused elsewhere.

[0005] In another example of an optical metasurface, Lin's U.S. Patent Application Publication 20170146806 describes an array of spatially multiplexed metalenses that can be used in a light field display without separating color channels. Different coded apertures can be obtained by sizing the sub-elements, and Lin describes an implementation of apertures based on changing the phase of the wavefront. [Overview of the project] [Problems that the invention aims to solve]

[0006] An object of this disclosure is to provide a sub-Vogel configuration for high-definition light field displays. Another object of the present invention is to provide an optical metasurface comprising a three-dimensional light field display, more particularly a three-dimensional holographic pixel (Vogel) composed of monochromatic sub-Vogels for a light field display. [Means for solving the problem]

[0007] In one embodiment, an optical device is provided comprising: a Vogel array having a plurality of Vogels, each Vogel being divided into a plurality of monochromatic sub-Vogels having a plurality of monochromatic subpixels; and a directional optical element for guiding light from subpixels, the directional optical element being divided into a plurality of color regions, each color region being designed to guide light of a specific color, and the monochromatic sub-Vogels and the plurality of color regions being configured to match the color regions of the directional optical element, which is designed to guide light of a specific color from the plurality of monochromatic subpixels.

[0008] In one embodiment, the directional optical element is a metasurface.

[0009] In another embodiment, the metasurface comprises a nanostructure.

[0010] In another embodiment, the nanostructure contains titanium dioxide.

[0011] In another embodiment, each of the monochromatic subpixels can be addressed individually.

[0012] In another embodiment, the plurality of monochromatic subvogels comprises at least one monochromatic red subvogel, at least one monochromatic green subvogel, and at least one monochromatic blue subvogel.

[0013] In another embodiment, each monochromatic subvogel comprises fewer monochromatic subpixels than can be individually distinguished by the human eye.

[0014] In another embodiment, each monochromatic subvogel has between 2 and 144 monochromatic subpixels.

[0015] In another embodiment, each subpixel is smaller than 10 μm².

[0016] In another embodiment, the monochromatic subpixels in each monochromatic subvogel are arranged in a square, rectangular, or radial configuration.

[0017] In another embodiment, the directional optical element is a geometric metasurface, a Pancharatnam-Berry metasurface, an inversely designed metasurface, a dispersed phase-compensated metasurface, or a combination thereof.

[0018] In another embodiment, the optical device is a light field display.

[0019] In another embodiment, a method is provided for designing a segmented optical metasurface, comprising: defining a phase function for the metasurface; specifying a material for nanostructures in the metasurface; determining a fabrication configuration such that the metasurface is segmented into multiple color regions; determining nanostructure parameters for each color region; generating a transmission map for the metasurface based on the nanostructure parameters; designing each color region based on the nanostructure parameters and the transmission map to obtain a phase function, such that each color region is designed to guide light of a particular optical bandwidth; calculating a figure of merit for the designed metasurface; and generating an output metasurface design for the metasurface.

[0020] In one embodiment, the nanostructure parameters differ for each color region.

[0021] In another embodiment, the material for the nanostructure is titanium dioxide.

[0022] In another embodiment, the metasurface is divided into a red region, a green region, and a blue region.

[0023] In another embodiment, the method further includes, after calculating the index of merit for the designed metasurface, adjusting the nanostructure parameters and recalculating the index of merit.

[0024] In another embodiment, parameters for the nanostructure in each color region include the height of the nanostructure, the shape of the nanostructure, the unit cell spacing, the resonance boundary parameters, or a combination thereof.

[0025] In another embodiment, the nanostructure has a consistent height across the color region.

[0026] In another embodiment, the metasurface is a geometric metasurface, a Pancharatnamberry metasurface, an inversely designed metasurface, a dispersed phase-compensated metasurface, or a combination thereof.

[0027] In another embodiment, a method for displaying a light field is provided, comprising: subdividing an integral image into a plurality of elemental images, each elemental image representing a two-dimensional array of angle descriptors associated with a pair of directional coordinates; decomposing each elemental image into a plurality of color channel-specific elemental images; sending each elemental image to a Vogel, each Vogel having a plurality of subpixels, which is divided into monochromatic sub-Vogels having a plurality of monochromatic subpixels, and each color channel-specific elemental image is sent to a monochromatic sub-Vogel of the same color; and creating a light field for display.

[0028] In one embodiment, the monochromatic subpixels are adjacent to each other in the monochromatic sub-Vogel.

[0029] In another embodiment, each of the multiple element images is of equal size.

[0030] In another embodiment, the color channel-specific element image comprises a red channel, a green channel, and a blue channel.

[0031] In another embodiment, the method further includes addressing subpixels individually.

[0032] In another embodiment, an optical display device is provided comprising a Vogel array having a plurality of Vogels, each Vogel being divided into a plurality of monochromatic sub-Vogels, each monochromatic sub-Vogel comprising a plurality of monochromatic subpixels. [Brief explanation of the drawing]

[0033] These and other features of the present invention will become more apparent in the following detailed description with reference to the accompanying drawings.

[0034] [Figure 1] This figure shows how to design a metasurface suitable for use in light field displays.

[0035] [Figure 2] This figure shows a graph of the refractive index plot for TiO2.

[0036] [Figure 3] This figure shows a graph of the full width at half maximum of a subpixel as a function of the diffraction-limited pitch.

[0037] [Figure 4] This is a cross-sectional view of a 4x4 sub-Vogel array along the y-axis.

[0038] [Figure 5] This figure shows one embodiment of the present disclosure, illustrating a Subvogel 8x8 array.

[0039] [Figure 6] This figure shows how to reduce the number of metalenses required when eight-fold symmetry is applied to a Subvogel 8x8 array.

[0040] [Figure 7] This figure shows the conversion of a 6x6 pixel Vogel element image to a sub-element image, and then to a sub-Vogel image.

[0041] [Figure 8] This figure shows a simulated light field display with a further zoomed-in view of a set of three (RGB) Sub-Vogel displays.

[0042] [Figure 9A] This figure shows a graph comparing the intensity of the red channel in captured retinal images when nsh (subpixel per sub-Vogel) = 8 and 16 with the intensity of the ideal nsh = 1.

[0043] [Figure 9B] This figure shows a graph of the intensity of the red channel and pixel shift of captured retinal images when nsh (subpixel per sub-Vogel) = 32 and 64.

[0044] [Figure 9C] This figure shows a graph comparing the intensity of the green channel in captured retinal images with the ideal intensity of nsh=1, when nsh=8 and nsh=16.

[0045] [Figure 9D] This figure shows a graph of the intensity and pixel shift of the green channel in captured retinal images when nsh (subpixel per sub-Vogel) = 32 and 64.

[0046] [Figure 9E] This figure shows a graph comparing the intensity of the blue channel in captured retinal images with the ideal intensity of nsh=1, when nsh=8 and nsh=16.

[0047] [Figure 9F] This figure shows a graph of the intensity of the blue channel and pixel shift of captured retinal images when nsh (subpixel per sub-Vogel) = 32 and 64.

[0048] [Figure 10]This is a u vs v plot showing the intersection of the upper boundary conditions and the mode condition equations for transversely electrically symmetric (TE) modes and transversely electrically asymmetric modes.

[0049] [Figure 11] This figure shows the linear relationship between β and V in one embodiment of the present disclosure.

[0050] [Figure 12] This figure shows a comparison of the calculated effective media, calculated using approximate values ​​of the effective refractive index based on weighted indices of pillars and voids, in one embodiment of the present disclosure.

[0051] [Figure 13] This figure shows the smallest circle surrounding the top left subpixel of the R sub-vogel, G sub-vogel, and B sub-vogel in one embodiment of the present disclosure.

[0052] [Figure 14] This figure shows a graph of the minimum display diagonal versus field of view for different sub-Vogel sizes.

[0053] [Figure 15] This figure shows a monochromatic sub-Vogel triplet to form three color regions, and metasurfaces designed for each color region.

[0054] [Figure 16A] This is a plan view of a metasurface design for a 3x3 3-sub-Vogel array in one embodiment of the present disclosure.

[0055] [Figure 16B] This is an isometric view of a metasurface design for a 3x3 3-sub-Vogel array in one embodiment of the present disclosure.

[0056] [Figure 17A]This is a plan view of a metasurface design in one embodiment of the present disclosure, comprising a radial array of 32 sub-Vogel arrays, each comprising three sub-Vogel arrays.

[0057] [Figure 17B] This is an isometric view of the metasurface design according to one embodiment of the present disclosure, comprising a radial array of 32 sub-Vogel structures. [Modes for carrying out the invention]

[0058] Unless otherwise defined, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to whom this invention relates.

[0059] The use of the words "a" or "an," when used herein with the term "comprising," may mean "one," but also coincides with the meanings of "one or more," "at least one," and "one or more."

[0060] As used herein, the terms “comprising,” “having,” “including,” and “containing,” and their grammatical variations, are inclusive or open-ended and do not exclude additional unlisted elements and / or method steps. The term “consisting essentially of,” as used herein in relation to compositions, devices, articles, systems, uses, or methods, indicates that additional elements and / or method steps may exist, but these additions do not materially affect the manner in which the listed compositions, devices, articles, systems, methods, or uses function. The term “consisting of,” as used herein in relation to compositions, devices, articles, systems, uses, or methods, excludes the existence of additional elements and / or method steps. Compositions, devices, articles, systems, uses, or methods described herein as including some elements and / or steps may also consist essentially of those elements and / or steps in some embodiments, and of those elements and / or steps in other embodiments, regardless of whether the embodiments specifically refer to them.

[0061] As used herein, the term "approximately" refers to a variation of approximately + / - 10% from a given value. It should be understood that such variation is always included in any given value given herein, regardless of whether the variation is specifically mentioned.

[0062] Unless otherwise specified herein, the descriptions of ranges convey both the range and the individual values ​​that fall within that range to the values ​​in the same place as the numbers used to indicate the range.

[0063] Any use of examples or illustrative language, such as “such as,” “exemplary embodiment,” “illustrative embodiment,” and “for example,” is intended to illustrate or illustrate aspects, embodiments, variations, elements, or features relating to the present invention, and does not limit the scope of the present invention.

[0064] As used herein, the terms “connected” and “connected” refer to any direct or indirect physical association between elements or features of the present disclosure. Therefore, these terms can be understood to describe elements or features that are partially or completely included, mounted, combined, arranged, joined, communicated, or operably associated with one another, even if other elements or features are interposed between the elements or features described as connected.

[0065] As used herein, the term “pixel” refers to the light source and light-emitting mechanism used to construct a display. A pixel may consist of one or more subpixels, most commonly consisting of one red subpixel, one green subpixel, and one blue subpixel.

[0066] As used herein, the term “subpixel” refers to a structure comprising light-emitting elements housed within an optical microcavity. The optical microcavity is operably associated with a plurality of reflective surfaces to substantially collimate, manipulate, or adjust light. At least one of the reflective surfaces is a light-propagating reflective surface connected to the optical microcavity to propagate light out of the microcavity. This disclosure provides individually addressable red, green, and blue (RGB) subpixels. The subpixel sizes described herein range from nanoscale to a few microns, which is significantly smaller than pixel sizes previously known in the art.

[0067] As used herein, the term “light field” at a basic level refers to a function that describes the amount of light flowing in all directions through a point in open space. Therefore, the light field represents radiance as a function of the position and direction of light in free space. Light fields can be generated synthetically through various rendering processes, or captured from a light field camera or an array of light field cameras.

[0068] As used herein, the term “light field display” refers to a device that reconstructs a light field from a finite number of light field radiance samples input to the device. Generally, the radiance samples represent the color components red, green, and blue (RGB), but it should be understood that other combinations of colors are possible. In reconstruction in a light field display, the light field can also be understood as a mapping from a four-dimensional space to a single RGB color. The four dimensions include the vertical and horizontal dimensions of the display and two dimensions that describe the directional components of the light field. The light field is defined as a function. LF: (x,y,u,v) → (r,g,b) Here, x and y are Cartesian coordinates or position coordinates of a location in the light field, and u and v are direction descriptors or angle descriptors. Fixed x f , y f In this case, LF(x f ,y f ,u,v) represents a two-dimensional (2D) image called an "element image". The element image has a fixed x f , y f This is a directional image of the light field from a given location. When multiple elemental images are arranged and connected, the resulting image is called an "integral image." The integral image can be understood as the entire light field required for a light field display.

[0069] As used herein, the term “metasurface” refers to an artificial surface used to manipulate wavefronts. The surface consists of a two-dimensional (2D) lattice of nanostructures that interact with the impacting wavefront, with lattice constants and structure sizes being subwavelength. The properties of each subwavelength structure are selected to give a specific local phase and amplitude on the wavefront. By controlling the phase and amplitude of the wavefront at each lattice site, the shape of the wavefront can be manipulated. Metasurfaces can be designed for various types of wavefronts, including, but not limited to, electromagnetic and acoustic wavefronts. Optical metasurfaces operate on light waves and can be used to planarize existing three-dimensional (3D) components such as lenses. Optical metasurfaces can be fabricated using semiconductor techniques, thereby reducing fabrication costs.

[0070] As used herein, the term "OLED" refers to an organic light-emitting diode, which is a photoelectronic device that emits light when an external voltage is applied. OLEDs can be classified into two main classes: those made from small organic molecules and those made from organic polymers. An OLED is a light-emitting diode comprising a film of an organic compound in which an electroluminescent layer emits light in response to an electric current. Generally, an OLED is a solid-state semiconductor device comprising at least one conductive organic layer disposed between an anode and a cathode and electrically connected to them. When an electric current is applied, the anode injects holes and the cathode injects electrons into the organic layer. The injected holes and electrons move toward the oppositely charged electrodes, respectively. When electrons and holes localize on the same molecule, an exciton is formed, which is a localized electron-hole pair with an excitation energy state. When the exciton relaxes, light is emitted via a photoemission mechanism. There are various types of OLEDs, including, but not limited to, active-matrix OLEDs (AMOLEDs), top-emitting OLEDs, and bottom-emitting OLEDs. AMOLEDs have all layers: a cathode, organic molecules, and an anode. The anode layer has a thin-film transistor (TFT) plane parallel to it to form a matrix. This helps to switch each pixel on or off as needed, thereby forming an image. Pixels are switched off whenever they are not needed or when there is a black image on the display, thereby extending the battery life of the device. This is the least power-consuming type of OLED and is also suitable for video because of its faster refresh rate. Applications of AMOLEDs include computer monitors, large-screen TVs, and electronic billboards or electronic advertising boards. Top-emitting OLEDs have a substrate that is either opaque or reflective. Top-emitting OLEDs are more suitable for active-matrix applications because they can be more easily integrated with opaque transistor backplanes. Manufacturers can use top-emitting OLED displays in smart cards. An OLED is bottom-emitting if the emitted light passes through a transparent or translucent bottom electrode and substrate.

[0071] As used herein, the term "hogel" is an alternative term for a holographic pixel, which is a class of conventional pixels with direction control. An array of hogels can generate a light field. In that case, the "hogel pitch" will be defined as the distance from the center of one hogel to the center of an adjacent hogel.

[0072] As used herein, the term "sub-hogel" (or sub-hogel) is a class of conventional sub-pixels with direction control. An array of sub-hogels can comprise hogels.

[0073] As used herein, the term "monochromatic" refers to a narrow-band color channel and refers to light emission with a narrow optical bandwidth.

[0074] As used herein, the term "element image" is a fixed x f , y f , LF(x f , y f , u, v), in the case of a two-dimensional (2D) image LF(x f , y f , u, v). The element image is a directional image of the light field from a fixed x f , y f position.

[0075] As used herein, the acronym "FWHM" refers to "full width half maximum", which is a measure of the spread of a function given by the difference between two extreme values of an independent variable for which the dependent variable is equal to half of its maximum value.

[0076] As used herein, the acronym "FRED" refers to Fred optical engineering software. FRED is a commercially available 3D computer-aided design (CAD) computer program for optical engineering, used to simulate the propagation of light through an optical system. FRED can process both incoherent and coherent light using Gaussian beam propagation.

[0077] As used herein, the term "transmittance" refers to the percentage of light transmitted per unit of incident light.

[0078] As used herein, the term "wavelength" is a measure of the distance between two equivalent peaks (high points) or troughs (low points) of a wave, which is a repeating pattern of moving energy, such as light or sound.

[0079] As used herein, the term “simulation” specifically refers to the generation of a computer model of something, either for research purposes or for developing and improving manufacturing specifications. A variety of simulation methods may be used, but are not limited to: Finite-difference time-domain (FDTD) methods are used to solve problems in electromagnetism and optics, and to solve Maxwell’s equations for complex shapes. FDTD is a multi-objective finite difference method in the time domain that handles nonlinear material properties in a natural way, allowing users to measure system responses over a wide range of frequencies. An equivalent technique is rigorous coupled wave analysis (RCWA), a semi-analytical method commonly employed to solve field diffraction problems of periodic structures. RCWA decomposes the field into a set of plane waves and represents the field as a sum of spatial harmonics in Fourier space. RCWA benefits from reduced simulation complexity and shorter simulation times, but becomes inaccurate for more complex shapes. To prototype optical mechanical systems, ray tracing simulations, such as those performed by FRED, are used. Given an initial set of rays, ray tracing simulates the resulting light field by calculating the propagation of rays through space and the interaction between the rays and any surfaces they collide with.

[0080] Various embodiments of compositions, devices, articles, methods, structures, apparatus, and uses disclosed herein are intended to be implemented by those skilled in the art either as is or by manufacturing such modifications or equivalents without departing from the scope of the invention.

[0081] This specification describes sub-Vogel configurations for high-definition light field displays. Optical devices and three-dimensional light field display technologies, more specifically, three-dimensional holographic pixels (Vogels) composed of monochromatic sub-Vogels, and metasurfaces designed to act as directional optical elements for light field displays are also provided. The design and methods of the sub-Vogel structures described are suitable for achromatic metasurfaces to provide directional pixels for multi-view light field color displays. To date, efficient broadband achromatic metalenses have not been found in the metasurface research community. To simplify the design of metasurfaces for organic light-emitting diode (OLED) or projector-based displays, a Vogel comprising an array of monochromatic sub-Vogels is described, where each sub-Vogel contains a unique monochromatic metalens.

[0082] A Vogel is a directional light-emitting structure composed of multiple subpixels that emits light of different colors and intensities in different directions. While this disclosure shows Vogels with multiple RGB subpixels, it should be understood that Vogels can include different combinations of the number and colors of subpixels. A light field display consists of an array of Vogels. An observer sees a spot of light emitted from each Vogel in the array. Collecting each spot of light from the Vogel array produces an image visible to the observer. A second observer in a different location sees a spot of light from each Vogel in the array, but because they are observing the light field display from a different location and therefore from a different direction, they see a different image than the first observer. In the case of an n×m array of Vogels, both observers see the image produced by the n×m array of light spots. A Vogel consists of a 2D pixel array (or subpixel array) and a directional optical element such as a lens or metasurface. Light emitted from each pixel or subpixel travels perpendicular to the pixel array. Light from each pixel passes through a directional optical element and is directed in a predetermined direction. A Vogel with a p×q pixel array sends light in different directions of p×q. A light field display consists of an (n*p)×(m*q) pixel array and an n×m array of directional optical elements, such that there are p×q pixels per Vogel in an n×m Vogel array. A Vogel is a fabrication combining a pixel array and an array of directional optical elements. Each pixel consists of subpixels, typically three adjacent RGB subpixels forming one pixel. Thus, a pixel array is also a subpixel array. In a sub-Vogel light field display, the subpixel arrays that make up each Vogel are rearranged so that, instead of grouping RGB subpixels of the same pixel together, subpixels of similar colors are grouped into clusters, in order to adapt to a directional optical element (in this case, a metasurface).

[0083] According to this disclosure, the metasurface can be considered a regularly space-multiplexed metasurface, where the metalenses for each color channel are interleaved on a single metasurface. While the metasurface is described herein as an example of a directional optical element, other directional optical elements are intended to be used. The aperture is determined by the sub-Vogel size, and each sub-Vogel interacts with a single color channel. The metasurface described herein is segmented to adapt to a color region, and each such segment has a corresponding cluster of like-color subpixels, so that the metasurface color region segment can be aligned to the wavelength of the corresponding subpixel cluster. A sub-Vogel is a cluster of like-color subpixels coupled with the corresponding metasurface color region segment.

[0084] One major hurdle in designing directional optical elements, particularly metasurfaces for light field display technology, has been achieving nanoscale pixel sizes to provide the pixel density required for high-definition light field displays of several billion pixels. The design described here achieves sub-10 micron pixel sizes while providing appropriate sub-Vogel sizes, enabling metasurface designs that can be fabricated using known fabrication tools and methods. To tune and realize achromatic metasurfaces with directional pixel functionality, it has been proposed to cluster like-color subpixels (R subpixels, G subpixels, B subpixels) and stack these subpixels with regions of a metasurface tuned to the spectrum of light emitted by like-color (monochromatic) subpixel clusters that guide synchrotron radiation, which are referred to herein as monochromatic sub-Vogels, monochromatic sub-Vogel arrays, and / or monochromatic sub-Vogel clusters.

[0085] This disclosure provides design considerations and methods necessary for designing a monochromatic sub-Vogel array coupled with an achromatic metasurface to provide directional pixels in a high-definition multi-view light-field display. Thus, metasurfaces are a strong candidate for complementing conventional refractive or diffractive optics. The metasurface concept utilizing monochromatic sub-Vogel overcomes current limitations in achieving the high angular resolution required for attractive light-field displays.

[0086] This document describes a monochromatic sub-Vogel design in which clusters of similarly colored subpixels are combined with an optical surface, such as a geometric metasurface, to achieve the desired directional pixel functionality. The technique described throughout this disclosure offers advantages over other achromatic metasurfaces. These advantages include, but are not limited to, expected improvements in efficiency, the elimination of the need for a polarizing light source, and the fact that the subpixel size is not limited by the metasurface's ability to compensate for the entire visible spectrum. When used in displays, the reduction in pixel size improves upon previously known pixels in the art by enabling the system to output more light beams in more different directions, thereby allowing for the creation of displays with higher angular resolution and improved effective resolution of multidimensional objects. An increase in the number of light field display views allows a viewer at any viewing position to receive multiple views simultaneously. This is known as a super multiview (SMV) display. SMV displays achieve improved angular resolution, resolve accommodation-convergence contradictions, and produce displays with higher quality depth of field.

[0087] Fan et al. describe a metalens array that could be used in light field displays using a dispersed phase-compensated achromatic metasurface. (Fan, Zhi-Bin. A broadband achromatic metalens array for integral imaging in the visible. Light: Science and Applications. 2019) They achieved an average efficiency of 47% and a numerical aperture (NA) of 0.08, which is too small to achieve the large field of view required for light field display applications. Lin's U.S. Patent Application Publication 20170146806 also describes a metalens array that could be used in light field displays using a dispersed phase-compensated achromatic metasurface. They achieved an average efficiency of 39% and an NA of 0.21, which is still too small to achieve the large field of view required for light field display applications. The NA of phase-compensated achromatic metalenses is limited by the maximum lens size that the nanostructure can accommodate, while still providing sufficient phase compensation to achieve achromaticity, which is directly related to the height of the nanostructure. To achieve a high numerical aperture (NA) in phase-compensated achromatic metalenses, advancements in fabrication techniques are needed to realize higher nanostructures.

[0088] This invention utilizes Sub-Vogel's method of aligning distinct regions of a metasurface to specific color channels, thereby enabling highly efficient and simplified metasurface design. Since each region of the metasurface is monochromatic, the metasurface can be a geometric metasurface, meaning that its phase can be controlled by changing the size of the nanostructures that make up the metasurface.

[0089] Khorasaninejad et al. previously reported on a 90% efficient metalense that eliminates extra losses and components without requiring a polarization source (Khorasaninejad, Mohammadreza. Polarization-Insensitive Metalenses at Visible Wavelengths. American Chemical Society, Nano Letters. October 24, 2016). However, these devices suffer from chromatic aberration, which is not particularly relevant to the present invention as each geometric metasurface is aligned to a narrowband color channel. The present invention can also be used with Pancharatnamberry metasurfaces that control the phase of the polarization plane by changing the orientation of fixed-size birefringent nanostructures. Other possible metasurface types include, but are not limited to, combinations of geometric metasurfaces (with varying nanostructure size and orientation) and Pancharatnamberry metasurfaces, inversely designed metasurfaces, and dispersion phase-compensated metasurfaces.

[0090] Various features of the present invention will become apparent from the following detailed description, along with the illustrations in the figures. The design parameters, design methods, configurations, and uses of the microcavity OLED design process and structure disclosed herein will be described with reference to various examples representing embodiments that do not limit the scope of the invention as described herein and claimed herein. Those skilled in the art will understand that there may be other variations, examples, and embodiments of the invention not disclosed herein that can be carried out in accordance with the teachings of this disclosure without departing from the scope of the invention.

[0091] Figure 1 shows a method for designing a metasurface suitable for use in a light field display. This method first requires, in 10, the definition of the required phase function. Based on the desired function of the metasurface, a phase function is selected for the metasurface under design. In one example, if the metasurface functions as a lens, the phase function will focus the light applied to the metasurface to a designed focal length, or focal spot. Following the selection of the phase function, the material type is specified in 12, which then allows for the determination of fabrication constraints in 14. An ideal material for a metasurface for a light field display has a refractive index that ensures strong confinement to achieve a full 2π phase shift within the limits imposed by fabrication and pixel size while maintaining high transmittance. This disclosure describes the use of titanium dioxide (TiO2) for fabricating nanostructures in a metasurface, but it should be understood that other materials and combinations of materials may be used to fabricate nanostructures, optionally in combination with a surface mask. Metasurface materials may include, but are not limited to, TiO2, SiO2, Si, GaN, AlO3, and Si3N4, or other materials with suitable properties. The metasurface described comprises nanostructures, in this case nanopillars, but it should be understood that the nanostructures of the metasurface described may have a variety of shapes, but are not limited to, elliptical, square, rectangular, and square horizontal cross-sections, as well as linear, angular, curved, pyramidal, and frustoconical vertical cross-sections. Metasurfaces may also optionally be fabricated on silicon dioxide (SiO2), thereby adding further flexibility to the TiO2 deposition method. Possible deposition methods, but are not limited to, include depositing TiO2 directly on the display or coordinating it in an additional step.

[0092] After determining the fabrication constraints, the array configuration is then determined in 16, and the unit cell spacing is defined in 18. The unit cell, denoted as U, specifies the intercenter distance between adjacent pillars or nanostructures in the metasurface. The unit cell size is analogous to the lattice constant in a periodic crystal structure or the lattice period in a diffraction grating, and the duty cycle is the feature dimension divided by the lattice period. Approximations for the minimum and maximum unit cell sizes can be obtained using the formulas described below. In this case, the optimal unit cell size can be determined using FDTD simulations that compare transmission maps for different unit cell sizes. The optimal unit cell size is the size that keeps the transmittance as close to 1 as possible from the minimum and maximum diameters of the single-mode resonance. Previous reports on metasurface design have used different unit cell sizes for each wavelength. For example, Khorasaninejad et al. reported U values ​​of 180 nm, 250 nm, and 350 nm for wavelengths of 405 nm, 532 nm, and 660 nm, respectively (Khorasaninejad, Mohammadreza. Visible Wavelength Planar Metalenses Based on Titanium Dioxide. IEEE Journal of Selected Topics in Quantum Electronics. Vol. 23, No. 3, May / June 2017).

[0093] Figure 2 shows a graph of the refractive index of titanium dioxide (TiO2) relative to the wavelength (nm) of light in the visible range. For visible wavelength nanostructure-based metasurfaces for light field displays, TiO2 has been shown to have a negligibly small absorption coefficient, a refractive index in the range of 2.3 to 2.7 as shown, and to achieve anisotropic structures with minimal surface roughness and a high aspect ratio.

[0094] Returning to the method shown in Figure 1, for rectangular dielectric resonators, Aieta et al. reported using FDTD sweeps to determine the optimal unit cell parameters in silicon, taking into account the function and resonance in the rectangular dielectric (Aieta, Francesco. Multiwavelength achromatic metasurfaces by dispersive phase compensation. Science Express. February 19, 2015). Fattal et al., U.S. Patent No. 9,103,973, reports that lattice constants should be selected so that optical elements do not scatter light in an undesirable manner, which can be prevented by selecting lattice constants based on the non-scattering limit defined below. In the case of a square lattice, JPEG0007910812000001.jpg13153 In the case of a hexagonal lattice, JPEG0007910812000002.jpg13153

[0095] Khorasaninejad et al. describe a method for optimizing the height and unit cell size of nanostructures at the design wavelength, where the maximum diameter is equal to the unit cell size, and this must be small enough to satisfy the Nyquist Sampling Criterion (Khorasaninejad, Mohammadreza. Polarization-Insensitive Metalenses at Visible Wavelengths. American Chemical Society, Nano Letters. October 24, 2016). According to the Nyquist Criterion, if the sampling frequency is greater than twice the highest frequency to be sampled, the repeating waveform can be correctly reconstructed. Therefore, JPEG0007910812000003.jpg11153 Here, NA is defined as the numerical aperture of the metalens.

[0096] According to this disclosure, the minimum unit cell limit can be defined based on the shape of the nanostructure. The minimum unit cell size is the maximum distance a between nanostructures. maxIn this case, the distance between adjacent nanostructures, which is synonymous with the distance between pillars, is smaller than the gap between nanopillars, a max It is defined that, at distances smaller than a certain distance between pillars, light at the design wavelength does not resonate between the nanopillars. Resonance does not occur between the nanopillars so that the sole contribution to the output comes from the nanopillars themselves. Therefore, in the non-resonant state, the optical path length between pillars must be smaller than a quarter wavelength, i.e., JPEG0007910812000004.jpg12153 Here, n gap r is the refractive index of the material surrounding the nanopillar. The minimum radius r of single-mode resonance. min Using JPEG0007910812000005.jpg16153

[0097] In that case, the minimum unit cell size can be defined as follows: U min =a max +d min In other words, JPEG0007910812000006.jpg13153 Also, under these conditions, d for larger unit cells min This will be set. JPEG0007910812000007.jpg12153

[0098] In 18, when the unit cell spacing is defined, in 20, the resonance boundary for the nanopillars must also be defined. Calculating the resonance boundary parameters, including the diameter and shape of the nanostructures in the metasurface, involves setting lower and upper limits on the cross-sectional area of ​​each nanostructure so that the nanostructures respond well and efficiently to the wavelength of the intended light color. For the design of metasurfaces for 3D light field displays, single-mode resonance per nanostructure is desirable. Therefore, the minimum diameter d of each pillar where resonance does not occur is important. min Similarly, the maximum diameter d at which single-mode resonance becomes multi-mode resonance. max It is necessary to find out the following.

[0099] The transverse refractive index profiles of many optical fibers are radially symmetric, and the index profiles of almost all fibers exhibit only small index contrast; therefore, it can be assumed that the fiber induces only weakly. This simplifies the calculation of fiber modes so that linearly polarized (LP) modes are obtained. In the case of stronger induction, transverse electrical modes and transverse magnetic modes must be distinguished, where either the electric or magnetic field is exactly perpendicular to the fiber axis. There are also hybrid modes that have non-zero longitudinal components in both the electric and magnetic fields. As used herein, HE and EH are combinations of symbols for the electric field (E) and magnetic field (H). The dominant field along the propagation direction is represented by the first symbol. For example, HE has a relatively strong longitudinal magnetic field compared to the longitudinal electric field.

[0100] The wave equation for the complex electric field profile in cylindrical coordinates is: JPEG0007910812000008.jpg14153 Here, β is the imaginary part of the propagation constant. For discrete values ​​of β at a given wavelength, there are solutions to the radial equation representing the guided modes of the fiber. All guided modes have a β value that lies between the plane wave values ​​of the cladding and the core.

[0101] The V-number can be interpreted as a kind of normalized optical frequency and is a dimensionless parameter essential to many fiber characteristics. The V-number is defined as follows: JPEG0007910812000009.jpg13153

[0102] If the V value is less than 2.405, the fiber supports only one mode per polarization direction, known as LP01, also known as a single-mode fiber or monomode fiber. For values ​​greater than V=2.405, the number of supported modes can be estimated as follows: JPEG0007910812000010.jpg13153

[0103] Using V = 2.405 in the above equation for V, the maximum radius of a single-mode fiber can be determined using the following: JPEG0007910812000011.jpg18153

[0104] Similarly, the minimum radius at which single-mode resonance begins is V=0.9, and therefore, using the following, JPEG0007910812000012.jpg19153 The minimum radius of resonance can be determined.

[0105] Following the calculation of the diameter of the resonant boundary, in step 22, the height of the nanostructure pillars in the metasurface must be specified. The height of the nanostructures must be sufficiently high so that the 2π phase is covered over the achievable diameter. Furthermore, due to fabrication constraints, it is desirable that the pillar heights be equal or at best a single height for each design wavelength.

[0106] The collaborative methodology of the Capasso group at Harvard University relies on simulation results to ensure this range, noting h = 400 nm, 600 nm, and 600 nm for wavelengths of 405 nm, 532 nm, and 660 nm, respectively (Khorasaninejad, Mohammadreza. Visible Wavelength Planar Metalenses Based on Titanium Dioxide. IEEE Journal of Selected Topics in Quantum Electronics. Vol. 23, No. 3, May / June 2017). For a 2π phase shift, it was suggested that the height can be estimated based on phase accumulation along the slab length, such that the height is as follows (Khorasaninejad, Mohammadreza. Polarization-Insensitive Metalenses at Visible Wavelengths. American Chemical Society, Nano Letters. October 24, 2016). JPEG0007910812000013.jpg12153

[0107] However, the effective refractive index ranges from approximately 1 to the refractive index value of the material, which can lead to unreliable estimates of the required height. Fattal et al., U.S. Patent No. 9,103,973, reports that the thickness of the metasurface should be less than or equal to the following height. JPEG0007910812000014.jpg16153

[0108] To ensure a large differential phase, the above equation is used for 540 nm and H < 526 nm. This value, obtained here in simulations, is smaller than the currently known value. However, one possible cause of the inconsistency in this equation is that n pillars represent the effective refractive index of the metasurface, and not simply the refractive index of the nanostructure (pillar) material. A non-periodic metasurface is expected to have an effective refractive index that is not constant at any particular point. Furthermore, if the effective refractive index value is calculated for the entire metasurface and then simplified to the ratio of filled to unfilled regions, the resulting estimate of the effective refractive index will likely be unreliable.

[0109] Through a series of steps, an equation is derived to determine the effective refractive index based on the pillar diameter and refractive index. Next, this equation is used to determine the minimum height required to achieve a 2π phase shift within the single-mode resonance region for each wavelength. Furthermore, it is shown that the phase accumulation Δφ / H per unit length is the slope of the linear fit for the data regarding pillar height versus total phase shift.

[0110] A series of equations are used to determine the effective refractive index of the nanopillar. As theoretical background to explain the development of this calculation, we first explain that the optical modes in a dielectric slab are solutions to the eigenvalue equations derived from Maxwell's equations, according to the boundary conditions imposed by the waveguide shape. Maxwell's equations can be written as follows: JPEG0007910812000015.jpg14153 Here, n is the value of the refractive index profile.

[0111] Since the structure is uniform along the z-axis, the solution to the wave equation is as follows: JPEG0007910812000016.jpg13153 Here, β is the propagation constant (z component of the wave vector), JPEG0007910812000017.jpg8153 and JPEG0007910812000018.jpg7153 is the wavefunction of the waveguide mode.

[0112] If we remove JPEG0007910812000019.jpg7153, the wave equation becomes as follows: JPEG0007910812000020.jpg12153

[0113] For each segment of the dielectric structure, a solution to the above equation can be obtained. In the confinement mode, the field amplitude is known to decrease exponentially outside the guide structure and change sinusoidally within that structure. In the TE (transverse electric) mode, the mode function is as follows: E m If (x) = Asin hx + Bcoshx, then |x| <d / 2 Ce -qx In this case, x > d / 2 De qx In this case, x < -d / 2 Here, h and q are related to the propagation constants as follows. JPEG0007910812000021.jpg24153

[0114] Using the above boundary conditions and mode condition equations for the TE symmetric mode (A=0, C=D), JPEG0007910812000022.jpg12153

[0115] In asymmetric mode, JPEG0007910812000023.jpg13153 Therefore, the propagation constant is JPEG0007910812000024.jpg13153 and This can be obtained when the file is JPEG0007910812000025.jpg12153, in which case the above boundary conditions and mode condition equations for the TE symmetric mode are as follows. utan u=v

[0116] The boundary conditions and mode condition equations for the TE asymmetric mode are as follows: -ucot u=v

[0117] Finally, the definition of the number V can be determined as follows: JPEG0007910812000026.jpg12153

[0118] Since u and v must be positive, the propagation constant can be found by finding the intersection of the above boundary conditions and mode condition equations for TE symmetric and TE asymmetric modes, and the number of V obtained from the definition of the V formula is defined as a circle of radius V as follows. u 2 +v 2 =V 2

[0119] The u-value for the intersection of the confinement modes, and Using JPEG0007910812000027.jpg12153, the propagation constant can be calculated using the following: JPEG0007910812000028.jpg11153

[0120] Defining a normalized propagation constant is useful for defining the confinement mode. JPEG0007910812000029.jpg12153

[0121] Once the pillar height is specified in 22, a transmission map is generated in 24. Once the parameters for the nanostructure are defined, the range of accessible nanostructures is defined accordingly. The transmission map maps the complex transmission coefficient as a function of the nanostructure parameters. The magnitude of the complex transmission coefficient determines the optical efficiency of the nanostructure, and the phase of the complex transmission coefficient determines the phase imparted to the synchrotron radiation from the subpixels. These maps are generated using finite-difference time-domain (FDTD) analysis software. Due to the complexity of metasurface structures, analytical techniques often fail to yield effective solutions, and therefore numerical analysis modeling techniques are employed. FDTD is one of the most common methods for modeling electromagnetic structures because it can handle heterogeneous, anisotropic, and frequency-dispersive materials. However, modeling metamaterials with high contrast between material properties in structure and free space makes numerical simulation difficult, and the accuracy of conventional FDTD methods is usually insufficient. While very fine meshes can be used to improve simulation accuracy, this requires increased computational resources. Therefore, conventional FDTD methods must be properly developed to accurately model metamaterials.

[0122] A dataset is created using phase maps and transmission maps, allowing for the selection of high transmission parameters with a desired phase. A series of sweeps are created by continuously increasing the diameter of nanopillars at specific unit cell spacings and heights. These simulations use periodic boundary conditions to emulate the field generated by an infinite array of equivalent nanopillars, from which phase and transmission parameters are extracted. A non-periodic metasurface is designed using transition maps and phase maps, where adjacent nanopillars have different diameters and therefore have different nearest-neighbor interactions, which can alter their phase and / or transmission parameters. Ideally, the range of pillar diameters is small enough for the above design approximation to be effective. However, this leaves room for further design optimization.

[0123] Using the transmission map generated by FDTD as a lookup table for nanostructure parameters, the color regions in the metasurface can be designed in 26. The color regions in the metasurface are designed based on the nanostructure parameters and transmission map to achieve a phase specified by the phase function, and each color region is designed to guide light of a specific optical bandwidth. The parameters for the nanostructure of each color region can include, but are not limited to, the height of the nanostructure, the shape of the nanostructure, the unit cell spacing, and the resonant boundary parameters. To create the desired phase profile / wavefront with uniform transmittance across the entire metasurface, the following equation is minimized by the diameter of the pillar selected from the LUT. JPEG0007910812000030.jpg10153 Here, T m φ is the average transmittance. t φ(D) is the desired phase, T(d) is the transmission parameter from the LUT, and φ(D) is the phase parameter from the LUT.

[0124] Desired phase φ t This is determined by a function of the metasurface. For a metalens with focal length f, the desired phase is given by: JPEG0007910812000031.jpg11153 Here, x and y are position coordinates relative to the center of the metalens.

[0125] Finally, in step 28, the parameters of the nanostructure array are optimized using FDTD simulation of the metasurface to maximize the calculated Figures of Merit (FOM), and in step 30, the metasurface is placed in the design. The Figures of Merit are performance metrics of a metasurface defined by its functionality. For example, the Figures of Merit of a metalens may include, but are not limited to, its focal length, full width at half maximum (FWHM) at the focal spot, and Strehl ratio (which is a comparison with the ideal intensity curve at the focal spot). If a design is available, the Figures of Merit can be calculated through the results of a design simulation. After calculating the Figures of Merit of the designed metasurface, the nanostructure parameters can be adjusted, and then the Figures of Merit can be recalculated to verify whether the performance of the metasurface has improved as a result of the nanostructure parameter adjustments. The metasurface optimization process can be an iterative process, where nanostructure parameters can be adjusted to optimize the metasurface design, and subsequent FOM calculations can be performed many times.

[0126] Sub-Vogel metal lens pitch Δx SH It is given by the following: Δx SH =N SH Δx SP Here, N SH Δx is the number of subpixels per sub-Vogel. SP is the subpixel pitch. The required angular pitch φ for each sub-Vogel is SH It is given by the following: φ SH =Φ*(N SH -1)+PS Here, PS is the FWHM (Focus-Wide Hammer) of the point spread function, and Φ is the angular resolution of the display. It has been found that a comfortable viewing experience is achieved by having an FHWM of PS equal to twice the angular resolution.

[0127] Using the above formula, it becomes possible to determine the minimum number of subpixels per sub-Vogel to overcome the diffraction limit Δθ. In Figure 3, while graphing FWHM [degrees] versus pitch [μm] for an angular resolution of 0.6 degrees and a PS of 1.2 degrees, Δx SH against φ SH And Δθ are plotted. The diffraction limit is satisfied in sub-Vogel regions containing 4x4 or larger subpixels (based on 4μmx4μm subpixels).

[0128] As the sub-vogels increase in size, the distance between RGB subpixels that combine to form individual pixels increases; therefore, the upper limit on the number of subpixels per sub-vogel is set by the eye's ability to distinguish individual subpixels. Figure 4 shows a cross-sectional view along the y-axis of a sub-vogel array with four subpixels per sub-vogel, highlighting three subpixels in adjacent sub-vogels that contribute to a single pixel observed at a distance d perpendicular to the screen 44: a blue (B) subpixel 46, a green (G) subpixel 48, and a red (R) subpixel 50. Figure 4 shows the subtended angle that defines the extent of a single pixel as seen by observer 106, centered on the central subpixel, with respect to the subpixel pitch 100 (Δx). SP ) and sub-Vogel pitch 102 (Δx SH This is shown in relation to (Δy SP It extends in the y dimension with a pitch of ). In this example, Δy SP All RGB triplets of the subpixels that make up each pixel are in the same row of the subpixel, so that only the y-dimensional pixel size is contributed to.

[0129] The angular spread of the RGB subpixels is maximized for an observer perpendicular to the screen, and therefore this view limits the sub-Vogel size. The light forming each pixel spreads over a viewing distance of 10⁴, given by the following: JPEG0007910812000032.jpg7153

[0130] Assuming that the angular resolution of the human eye is limited to β = 0.03°, the minimum viewing distance of a pixel is: JPEG0007910812000033.jpg35153

[0131] For a given minimum viewing distance, the maximum sub-Vogel size can be set using the above formula. The minimum viewing distance can be set by the near point of the human eye or by the characteristics of the light field display. JPEG0007910812000034.jpg16153

[0132] The maximum sub-Vogel pitch can be found by solving the above quadratic equation. (2Δx SH +Δx SP ) 2 >>Δy SP In this case, the maximum sub-Vogel pitch can be approximated by the following: JPEG0007910812000035.jpg12153

[0133] Figure 5 shows one embodiment of the present disclosure, which includes a Vogel 60 comprising an array of 8 × 24 multicolor sub-Vogels 52 for a total of 192 subpixels. The Vogel shown has a full-color 64 × 64 view from arrays of blue subpixels 46, green subpixels 48, and red subpixels 50.

[0134] Figure 6 shows a Vogel 60 with multiple subpixels that reduce the number of metalenses required when 8-fold symmetry is applied to an 8x8 array of sub-Vogels. As shown in Figure 6, due to the symmetry of the view, the number of unique metalenses 58 decreases from 192 in the case of 4-fold symmetry to 48, and the number of unique metalenses 58 decreases further to 30 when 8-fold symmetry is applied. In this example, the number of unique metalenses would be one per individual RGB subpixel. On larger screens, the minimum viewing distance is greater, and the number of sub-Vogels can be reduced to 48 using 16x16 arrays of 46, 48, and 50 subpixels per sub-Vogel, and when 4-fold symmetry is applied, the number of unique metalenses decreases to 12. In that case, when 8-fold symmetry is applied, that number will decrease to 9.

[0135] Integral images for sub-Vogel displays are formed by subdividing the elemental image of the Vogel display into sub-elemental images of equal size, each having an integer number of pixels. In light field displays, a fixed x f , y f , LF(x f ,y f If ,u,v), the element image is a 2D image LF(x f ,y f Represents ,u,v). The element image has a fixed x f , y f This is a directional image of the light field from a given location. In this case, each sub-element image is decomposed into three sub-sub-element images, one for each color channel, such that each pixel in the sub-element image has a subpixel corresponding to each of the sub-sub-integral images. The sub-sub-element images are arranged adjacent to each other to create the elemental images of the sub-Vogel display.

[0136] Figure 7 shows the conversion of a 6×6 Vogel 60 to a segmented Vogel 62. As shown in the figure, the segmented Vogel 62 is divided in the x direction into two multicolor sub-Vogels 52a and 52b, but it should be understood that segmentation can be performed in various directions. The Vogel 60, which may also be called an elemental image, and the segmented Vogel 62, which may also be called a sub-elemental image, have 6×6 pixels, and each pixel comprises one red subpixel, one blue subpixel, and one green subpixel. The size of each subpixel is preferably 10 μm. 2 It is smaller than that. Figure 7 further illustrates the conversion of the 6x6 divided Vogel 62 to a sub-Vogel element image 64. Note that since the subpixels of similar colors are already adjacent to each other along the remaining axes, the division of the element image into sub-element images only needs to be done along one direction; however, even in this case, it should be understood that the division can be done in various orientations. The resulting sub-Vogel element image 64 consists of monochrome sub-Vogels 66a, 66b, and 66c. The pixels in the monochrome sub-Vogels 66a, 66b, and 66c are shown arranged in a rectangular 3x6 configuration, but it should be understood that the sub-Vogels can consist of orientations such as other rectangular orientations, square orientations, or radial orientations, along with variations in the number of subpixels in each sub-Vogel.

[0137] The initial Vogel element image data is stored in a 6x6 matrix, while the sub-Vogel element image data is stored in an 18x6 matrix. Using a MatLab (or equivalent) script, a Vogel integral image can be converted to a sub-Vogel integral image, which can then be written to a txt file. To display a light field, the entire image for display is generally called an integral image, and the integral image is divided into multiple element images, which are then sent to a light field display for displaying the image. Each element image is represented by the corresponding Vogel in the Vogel array and consists of multiple Vogels arranged in the Vogel array. Each pixel in the element image has a corresponding view or orientation such that, in the normal of the display, an observer facing the display can see the pixel at the center of each Vogel in the Vogel array.

[0138] We analyzed how displays are perceived by simulating the Sub-Vogel display architecture using ray tracing software. Note that these simulations can be performed with any suitable software tool. One example of ray tracing software is FRED. As previously described, FRED refers to Fred Optical Engineering Software, a commercially available 3D CAD computer program for optical engineering used to simulate the propagation of light through optical systems. Note that, for the sake of simplification, we simulated a limited number of views.

[0139] Figure 8 shows a simulated light field display with a further zoomed-in view of a set of three monochromatic (RGB) sub-vogels, specifically a red monochromatic sub-vogel 66a, a green monochromatic sub-vogel 66b, and a blue monochromatic sub-vogel 66c. To conserve computational resources, nine views were simulated using ray tracing software. To test color mixing, the test image is a 4x8 pixel white image. Each monochromatic (RGB) sub-vogel 66a, 66b, and 66c makes up one pixel for a 3x3 view. The space 72 between the sub-vogels is reserved for additional views. Each monochromatic sub-vogel may consist of multiple subpixels, preferably between 2 and 144 monochromatic subpixels.

[0140] In these simulations, a single wavelength acts as the light source. A mixing ratio calculator was used to determine the color mixing ratio required to mix white. The ratio obtained by the calculator is the luminance ratio, which is a photometric quantity. Therefore, the output ratio of the light source was set to the luminance ratio divided by the photopic luminosity function, which is a photopic function built into the ray tracing software tool.

[0141] To analyze the perception of the Sub-Vogel display, a model of the human eye, also known as the "Arizona eye," created by Photon Engineering, was incorporated into the model. Pupil diameter and eye accommodation can be set by the user. Accommodation can be defined as the process by which the vertebrate eye changes its refractive power to maintain a sharp image or focus on an object when the distance to the object changes. The analysis plane is placed behind the retina to capture the observed image. A visual acuity of 1 degree corresponds to a length of 288 microns on the retina, and since the eye can resolve lines that are only 0.03 degrees apart, the retinal distance sampling should be 8 microns.

[0142] result The resulting settings generate a series of images that can be qualitatively evaluated. Figures 9A–9F show the intensity of each color channel in the captured retinal images for different numbers of subpixels per subvogel. These ray tracing simulations do not consider diffraction. Therefore, the case with one subpixel per subvogel represents the case of combining an ideal metalens with a conventional subpixel array. The intensity peaks correspond to the retinal position of the image formed by the pixels, or the perceived location of the pixels, in arbitrary units. sh When =8, 16, the pixel locations in all color channels are ideal, as shown in Figure 9A for red, Figure 9C for green, and Figure 9E for blue. sh This matches the location where =1, where n sh n is defined as the number of subpixels per sub-Vogel. As shown in Figure 9B, n sh If =32 or 64, the position of the pixels in the red channel is shifted in the positive x direction, n sh =64 is n sh The shift is greater than 32. As shown in Figure 9D, the pixel positions in the green channel match the ideal case. As shown in Figure 9F, the pixel positions in the blue channel are shifted in the negative x direction, n sh =64 is n sh n has a shift greater than 32. sh As n increases, the distance between subpixels of a pixel increases along the x-axis, and therefore, in a central pixel with this subpixel shape, the red subpixel is pushed in the positive x-direction, the green subpixel remains in the center, and the blue subpixel is pushed in the negative x-direction. sh When is sufficiently large, in this example n sh At values ​​of 32 and 64, the central observer perceives white pixels as separate RGB pixels. Subpixels are x SP =3.3μm and Δy SP It has dimensions of =10μm. sh When = 16, the following equation describes the light forming each pixel: JPEG0007910812000036.jpg9153 Here Δx SHMAX This corresponds to 63 μm, which is equivalent to a maximum of 19 subpixels per sub-Vogel, which is consistent with the above result. [Examples]

[0143] This specification describes an example of determining the effective refractive index of nanopillars for a metasurface designed for light field displays. Considering a step-index guide with n1=1.5, n2=1.6, d=5μm, and λ=1.55μm, JPEG0007910812000037.jpg10153V=5.64

[0144] It is expected that there are confinement modes with m-1=4 in the waveguide. Figure 10 is a plot of u versus v showing the intersections of the upper boundary conditions and mode condition equations for TE symmetric and TE asymmetric modes. From this figure, the u values ​​at the intersections are 1.33, 2.65, 3.94, and 5.14, respectively.

[0145] To determine the propagation constant and effective refractive index, note that the propagation constant is scaled from 0 to 1 when using the following formula, and extract the values ​​for the dispersion relation in a symmetric waveguide. JPEG0007910812000038.jpg16153 can be written as follows: Next, the propagation constant can be determined using the intersection values. The obtained β values ​​are 6.46, 6.40, 6.29, and 6.15.

[0146] Note that the data is nearly linear within this range, the relationship between b and V is shown in Figure 11 and can be explained as follows. b = 0.349V - 0.314

[0147] The relationship between the diameter of the pillar and the effective refractive index can be defined as follows: JPEG0007910812000040.jpg13153

[0148] To relate these variables, the effective refractive index of each pillar can be approximated by calculating V from the pillar diameter and defining the normalized propagation constant to calculate b and β.

[0149] Generally, phase accumulation from a dielectric is defined as follows: JPEG0007910812000041.jpg11153

[0150] However, the effective refractive index value used in this formula assumes a constant effective refractive index (a periodic structure with the same diameter and unit cell width). Since the effective refractive index as a function of diameter is approximately linear within the single-mode resonance limit defined above, the effective refractive index can be replaced with the difference in effective refractive index from the maximum diameter to the minimum diameter. Δn effective = n effective (d max )-n effective (d min )

[0151] Therefore, the equation for phase accumulation can be written as follows: JPEG0007910812000042.jpg12153

[0152] The phase accumulation per unit length can be written as follows: JPEG0007910812000043.jpg12153

[0153] When Δφ = 2π, the minimum height required to achieve a 2π phase shift within the resonance limit can be determined using the following: JPEG0007910812000044.jpg11153

[0154] Table 1 below shows the calculated phase accumulation and minimum height required for each wavelength. [Table 1]

[0155] Figure 12 compares the calculated effective medium with an approximation of the effective refractive index based on weighted indices for nanopillars and voids. The plot shows that this effective medium approximation (EMA) overestimates the effective refractive index. Further calculations reveal that the total phase accumulation is lower within the defined range of diameters for each wavelength. [Examples]

[0156] As explained, an implementation of a monochromatic sub-Vogel design for use as an achromatic metasurface for high-definition light field displays is provided. To determine the appropriate sub-Vogel size for a minimum light field display with a 40° field of view (FOV) and a 3.15-inch screen size, assuming that the angular resolution of the human eye is limited to β = 0.03°, the minimum viewing distance of the display is: JPEG0007910812000046.jpg14153

[0157] The minimum viewing distance is, JPEG0007910812000047.jpg15153

[0158] The near point of the human eye is d np Since the nearest point at which the eye can focus (approximately 25 cm) is greater than the minimum viewing distance of a display, the maximum sub-Vogel pitch was previously often determined using the following relationship: JPEG0007910812000048.jpg12153

[0159] Therefore, assuming a 4 μm × 4 μm subpixel, it is determined that the observer would only be able to distinguish individual subpixels for a 16 × 16 sub-Vogel at the near point. An 8 × 8 sub-Vogel would satisfy the angular resolution of the eye at the near point and at the smaller minimum viewing distance of the described embodiment of the light field display. [Examples]

[0160] Detailed sub-Vogel size calculations for light field displays are described below. The lower limit of the sub-Vogel size is set by the diffraction limit and the Rayleigh criterion. The selection of the sub-Vogel size is not trivial. The size must be large enough to satisfy the Rayleigh criterion and the diffraction limit, but small enough that individual subpixels are indistinguishable at the minimum viewing distance, which is either the near point of the eye or the minimum viewing distance of the display. The diffraction limit is given by: JPEG0007910812000049.jpg16153 Here, Δθ is the sub-Vogel angle pitch, λ is the source wavelength, Δx is the sub-Vogel pitch, and φ out Φ is the deflection angle. PS = 2Φ pitch In this case, the formula for the angle pitch of Subvogel from

[0106] is as follows: Δθ=(n sh +2)Φ pitch Here, n sh Φ is the number of subpixels per sub-Vogel along each direction (x and y), pitch h is the angular pitch of each view. The sub-Vogel pitch should be selected as follows: JPEG0007910812000050.jpg16153

[0161] (Assuming a plane wave of light) The Rayleigh criterion for resolving two points through an aperture of diameter d is given by: JPEG0007910812000051.jpg12153 Here, φ is the minimum angle between two distinguishable points, and therefore, JPEG0007910812000052.jpg14153

[0162] By taking the ratio of the two limits, it can be seen that the Rayleigh criterion is dominant in setting the minimum sub-Vogel pitch. shThe value of indicates the number of rows and columns of the sub-pixel array within the sub-horge. For example, n sh = 8 corresponds to a sub-horge having an 8×8 sub-pixel array. In this example, FIG. 12 shows the shape of the sub-pixels for the case where n sh = 4. Regarding the shape of the sub-pixels shown in FIG. 12, Table 2 shows that the Rayleigh criterion is satisfied when n sh > 8. In the case of a 64×64 view display corresponding to 64×64 pixels per horge, it is convenient to limit the number of sub-pixels per sub-horge to a factor of 64.

Table 2

[0163] The smallest resolvable circle in the plane of the display has a diameter d pixMAX given by the following. d pixMAX = d min tanβ ≒ d min β Here, d min is the minimum viewing distance of the display, β = 0.03°, which is the angular resolution of the eye. For a human to perceive the intended pixel color rather than individual sub-pixels, the sub-pixels constituting the pixel must fit within a circle of diameter d pixMAX . At the near point of the eye (25 cm), d pixMAX = 131 μm

[0164] FIG. 13 shows the minimum diameter 78 surrounding the left uppermost sub-pixels of the R sub-horge, G sub-horge, and B sub-horge. These three sub-pixels constitute one pixel. The diameter is given by the following. JPEG000791[081[2000054.jpg11154 Here, Δx *sh (Δy *sh ) is the sub-horge pitch in the X (Y) direction of the R sub-horge, G sub-horge, or B sub-horge, and Δx *sp (Δy *sp) is the subpixel pitch in the X (Y) direction of the R subpixel, G subpixel, or B subpixel. pix =d pixMAX Set n sh By defining the value as a positive real number, we can see that the maximum number of subpixels per sub-Vogel is 16 at a minimum viewing distance of 25 cm (the near point of the human eye). However, the minimum viewing distance of many displays is greater than the near point of the human eye, and is given by the following: JPEG0007910812000055.jpg16153 Here, W disp is the display diagonal, and FOV is the field of view. Figure 14 plots the minimum display diagonal versus FOV for different sub-Vogel sizes.

[0165] Figure 15 shows a triplet of three monochromatic sub-Vogels 66a, 66b, and 66c. Each monochromatic sub-Vogel 66a, 66b, and 66c consists of 4x4 subpixels of a single color. Clustering of subpixels of similar colors allows the metasurface 82 to be designed with specific properties tailored to each color region. The advantage of this configuration is that the metasurface 82, acting as a directional optical element, can be designed to have specific properties for a particular wavelength or color of light. Forming color regions larger than a single subpixel within the metasurface 82 enables metasurface designs that can actually be manufactured. A metasurface color region 84 for red is directly aligned on top of the red sub-Vogel 66a. A metasurface color region 86 for green is directly aligned on top of the green sub-Vogel 66b, and similarly, a metasurface color region 88 for blue is directly aligned on top of the blue sub-Vogel 66c.

[0166] Figure 16A shows a plan view of a metasurface 82 design according to one embodiment of the present disclosure, designed for a 3x3 array of three monochromatic sub-Vogels using the metasurface design method disclosed in Figure 1.

[0167] Figure 16B shows an isometric view of the metasurface 82 design according to one embodiment of the present disclosure, which comprises a 3x3 array of three sub-Vogels, and was designed using the metasurface design method disclosed in Figure 1.

[0168] Figure 17A shows a plan view of a metasurface 82 design according to one embodiment of the present disclosure, designed for a radial array of 32 monochromatic sub-Vogels. The shown metasurface 82 has different color regions for each subpixel color, with color region 84 designed for red sub-Vogels, metasurface color region 86 designed for green sub-Vogels, and metasurface color region 88 designed for blue sub-Vogels. The metasurface color regions 84, 86, and 88 consist of nanopillars 90 designed using the metasurface design method disclosed in Figure 1.

[0169] Figure 17B shows an isometric view of the metasurface 82 design according to one embodiment of the present disclosure, which comprises a metasurface tuned for a radial array of 32 sub-Vogels, and further shows an isometric view of a nanostructure, in this case a nanopillar, comprising a metasurface designed using the disclosed metasurface design method.

[0170] All publications, patents, and patent applications referenced herein demonstrate the skill of a person skilled in the art to which the present invention relates and are incorporated herein by reference. Any reference to prior art herein is not, and should not be construed as, an acknowledgment or any form of suggestion that such prior art forms part of common general knowledge.

[0171] Although the present invention has been described in this manner, it will be apparent that the present invention can be modified in many ways. Such modifications should not be considered departures from the scope of the invention, and all modifications that would be obvious to those skilled in the art are included in the following claims.

Claims

1. A method for displaying a light field, This involves subdividing an integral image into multiple elemental images, wherein each elemental image represents a two-dimensional array of angle descriptors associated with a pair of directional coordinates. Decomposing each elemental image into multiple color channel-specific elemental images, Sending elemental images specific to the color channels to a Vogel, wherein each Vogel has multiple subpixels and is divided into monochromatic sub-Vogels, each having multiple monochromatic subpixels, and the multiple color channel-specific elemental images are sent to monochromatic sub-Vogels of the same color. Generating a light field and Methods that include...

2. The method according to claim 1, wherein the monochromatic subpixels are adjacent to each other in the monochromatic subvogel.

3. The method according to claim 1 or 2, wherein each of the plurality of element images is of the same size.

4. The method according to any one of claims 1 to 3, wherein the element image specific to the color channel comprises a red channel, a green channel, and a blue channel.

5. The method according to any one of claims 1 to 4, further comprising individually addressing the plurality of monochromatic subpixels.

6. The method according to claim 1, wherein each element image is decomposed into multiple color channel-specific element images along one direction.

7. The method according to claim 1, wherein the monochromatic subpixels in the monochromatic subvogel of the same color are arranged in a rectangular, square, or radial configuration.

8. The method according to claim 1, further comprising displaying the light field on an optical device.

9. The method according to claim 8, wherein the optical device is a light field display.

10. The method according to claim 9, wherein each pixel in each element image has a corresponding view or orientation such that, in the normal of the light field display, the pixel at the center of each Vogel is visible to an observer facing the display.

11. The method according to claim 10, wherein the light field display comprises a directional optical element having a color region, and each color region is designed to guide light in a specific optical bandwidth.

12. The method according to claim 11, wherein the directional optical element is configured to receive elemental images specific to the color channel in the same specific optical bandwidth for each color region.

Images