Optical metasurface with sub-hogels

Abstract

A sub-hogel configuration for high definition light field displays. An optical device and three-dimensional light field display technology are also described, and more specifically, a three-dimensional holographic pixel (hogel) composed of a single color sub-hogel and a designed metasurface is described for use as a directional optical element for a light field display. The described sub-hogel structure design and method are applicable to achromatic metasurfaces to provide directional pixels for multi-view light field color displays.

Description

[0001] This invention is a divisional application of the patent with application number 2021800733566, application date March 31, 2021, and invention title "Optical Metasurface with Sub-HOGEL".

[0002] Cross-references to related applications

[0003] This application claims priority to U.S. Patent Application US17 / 086201, filed October 30, 2020, the contents of which are incorporated herein by reference in their entirety. Technical Field

[0004] This disclosure relates to three-dimensional light field display technology, and more specifically, to three-dimensional holographic pixels (hogels) composed of monochromatic hogels for light field displays. Background Technology

[0005] Optical metasurfaces are engineered surfaces used to manipulate wavefronts. They typically consist of a two-dimensional lattice with a cylindrical structure that interacts with the incident wavefront, where the lattice constant and structure dimensions have a subwavelength thickness relative to the electromagnetic wavelength range to which the structure is designed to interact. The column dimensions and spacing within the subsurface are designed differently to achieve the desired optical performance. Optical metasurfaces can shape the amplitude, phase, and polarization of electromagnetic beams. Using subsurfaces in light field display technology allows for the creation of nearly flat optical devices, improving the performance of optical elements and manipulating light to provide optical systems with novel properties. In the development of light field display technology, metasurfaces have shown promising potential as lightweight and thin optical components that can combine multiple functions into a single device.

[0006] In one example of an optical metasurface, Lin's U.S. Patent Application Publication No. 20170219739 describes a metasurface with random spatial multiplexing, in which multiple optical elements are interleaved on a single metasurface to individually utilize the full aperture of the metasurface of all optical elements, since they occupy only a small fraction of the total area. The purpose of using an achromatic metallic lens with this design is to provide a dedicated lens for each interleaved 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 focal point, and two-thirds of the light is focused elsewhere.

[0007] In another example of optical metasurfaces, Lin's U.S. Patent Application Publication No. 20170146806 describes a spatially multiplexed metallic lens array that can be used in light field displays without separating color channels. The sub-elements can have different coded apertures, and Lin describes an implementation based on modifying the wavefront phase. Summary of the Invention

[0008] The purpose of this disclosure is to provide a sub-hogel configuration for a high-definition light field display. Another object of the invention is to provide a three-dimensional light field display, and more specifically, to provide an optical element surface comprising three-dimensional holographic pixels (hogels) composed of monochromatic sub-hogels for the light field display.

[0009] In one aspect, an optical device is provided, comprising: a hogel array including a plurality of hogels; a hogel array including a plurality of hogels, each hogel being partitioned into a plurality of monochromatic sub-hogels, each monochromatic sub-hogel including a plurality of monochromatic subpixels; and a directional optical element for guiding light from the subpixels, the directional optical element being partitioned into a plurality of color regions, each color region being designed to guide light of a specific color, the monochromatic subpixels and the plurality of color regions being configured such that the plurality of monochromatic subpixels are aligned with the color regions of the directional optical element designed to guide light of a specific color from the monochromatic subpixels.

[0010] In the implementation scheme, the directional optical element is a metasurface.

[0011] In another embodiment, the meta-surface includes a nanostructure.

[0012] In another embodiment, the nanostructure comprises titanium dioxide.

[0013] In another embodiment, each of the monochrome sub-pixels is individually addressable.

[0014] In another embodiment, the plurality of monochromatic hogel includes at least one monochromatic red hogel, at least one monochromatic green hogel, and at least one monochromatic blue hogel.

[0015] In another implementation, each monochromatic hogel comprises fewer monochromatic subpixels than the human eye can distinguish individually.

[0016] In another implementation, each monochromatic sub-hogel has 2 to 144 monochromatic subpixels.

[0017] In another implementation, each subpixel is less than 10 pm2.

[0018] In another implementation, the monochrome subpixels in each monochrome subhogel are arranged in a square, rectangular, or radial configuration.

[0019] In another embodiment, the directional optical element is a geometric element surface, a Pancharatnam-Berry element surface, a reverse-designed element surface, a dispersion phase-compensating element surface, or a combination thereof.

[0020] In another embodiment, the optical device is a light field display.

[0021] In another aspect, a method for designing a partitioned optical metasurface is provided, comprising: defining a phase function of the metasurface; specifying a material for nanostructures in the metasurface; determining a fabrication configuration such that the metasurface is partitioned into multiple color regions; determining nanostructure parameters for each color region; generating a transmission map of the metasurface based on the nanostructure parameters; designing each color region to achieve the phase function based on the nanostructure parameters and the transmission map, each color region being designed to guide light with a specific optical bandwidth; calculating a quality factor for the designed metasurface; and generating an output metasurface design for the metasurface.

[0022] In the implementation scheme, the nanostructure parameters are different for each color region.

[0023] In another embodiment, the material of the nanostructure is titanium dioxide.

[0024] In another embodiment, the metasurface is divided into red, green, and blue regions.

[0025] In another embodiment, the method further includes adjusting the nanostructure parameters and recalculating the quality factor after calculating the quality factor of the designed metasurface.

[0026] In another embodiment, the parameters for the nanostructure of each color region include nanostructure height, nanostructure shape, cell spacing, resonant boundary parameters, or combinations thereof.

[0027] In another embodiment, the nanostructure has a uniform height over the color region.

[0028] In another embodiment, the meta-surface is a geometric meta-surface, a Pancharatnam-Berry meta-surface, a reverse-designed meta-surface, a dispersion phase-compensated meta-surface, or a combination thereof.

[0029] In another aspect, a method for displaying a light field is provided, comprising: subdividing an integral image into a plurality of element images, each element image representing a two-dimensional array of angle descriptors associated with a pair of orientation coordinates; decomposing each element image into a plurality of color channel-specific element images; sending each element image to a hogel, each hogel comprising a plurality of sub-pixels and partitioned into monochromatic subhogels comprising a plurality of sub-monochromatic pixels, wherein the color channel-specific element images are sent to monochromatic subhogels of the same color; and thereby creating a light field for display.

[0030] In the implementation, the monochrome subpixels are adjacent to each other in the monochrome subhogel.

[0031] In another embodiment, each of the plurality of element images is of equal size.

[0032] In another embodiment, the color channel-specific element image includes a red channel, a green channel, and a blue channel.

[0033] In another embodiment, the method further includes individually addressing the sub-pixels.

[0034] In another aspect, an optical display device is provided, including a hogel array comprising a plurality of hogels, each hogel being partitioned into a plurality of monochrome sub-hogels, each monochrome sub-hogle comprising a plurality of monochrome sub-pixels. Attached Figure Description

[0035] These and other features of the invention will become more apparent in the following detailed description, with reference to the accompanying drawings.

[0036] Figure 1 This describes a method for designing metasurfaces suitable for light field displays.

[0037] Figure 2 This shows a graphical representation of the TiO2 refractive index.

[0038] Figure 3 This shows a graphical representation of the full-width half-maximum of a subpixel as a function of the diffraction-limited spacing.

[0039] Figure 4 The image shows a cross-sectional view of a 4x4 sub-hogel array along the y-axis.

[0040] Figure 5 The following illustrates one embodiment of the present disclosure, which depicts an 8x8 sub-hogel array.

[0041] Figure 6This shows that if 8x8 symmetry is applied to an 8x8 sub-hogel array, the number of superlenses required is reduced.

[0042] Figure 7 This describes how to convert a 6x6 pixel hogel element image into a partial element image, and then into a subhogel image.

[0043] Figure 8 This displays a simulated light field display that is further magnified on a set of three (RGB) sub-hogels.

[0044] Figure 9A : Shows the relationship with ideal n sh =1 compared to when n sh Graphical representation of the red channel intensity of the captured retinal image when (subpixel / subhogel) = 8, 16.

[0045] Figure 9B : Shows when n sh Graphical representation of the intensity of the red channel and pixel offset of the captured retinal image when (subpixel / subhogel) = 32,64.

[0046] Figure 9C : Shows the relationship with ideal n sh Compared to =1, n sh Graphical representation of the intensity of the green channel in retinal images captured at =8,16.

[0047] Figure 9D : Shows when n sh Graphical representation of the intensity of the green channel and pixel offset of the captured retinal image when (subpixel / subhogel) = 32,64.

[0048] Figure 9E : Shows the relationship with ideal n sh Compared to =1, n sh Graphical representation of the intensity of the blue channel in retinal images captured at =8,16.

[0049] Figure 9F : Shows when n sh Graphical representation of the intensity of the blue channel and pixel offset of the captured retinal image when (subpixel / subhogel) = 32,64.

[0050] Figure 10 :yes right The figure shows the intersection of the boundary conditions and mode condition equations for the aforementioned transverse electric (TE) symmetric and asymmetric modes.

[0051] Figure 11The diagram illustrates the linear relationship between β and V in an embodiment of this disclosure.

[0052] Figure 12 The illustration shows a comparison between the effective medium calculated based on the weighted index of the strut and the air gap and the effective index approximation, in one embodiment of this disclosure.

[0053] Figure 13 The diagram illustrates the smallest circle of the top left sub-pixel of the R, G, and B sub-hogels in one embodiment of this disclosure.

[0054] Figure 14 The graph shows the minimum display diagonal and field of view for different subhogel sizes.

[0055] Figure 15 This shows three monochromatic sub-hogels, forming three color regions and a meta-surface designed for each color region.

[0056] Figure 16A The diagram shows a plan view of the metasurface design of a 3x3 sub-hogel array arrangement in an embodiment of this disclosure.

[0057] Figure 16B An isometric view of the meta-surface design for a 3x3 sub-hogel array arrangement is shown in one embodiment of this disclosure.

[0058] Figure 17A The diagram shows a plan view of a meta-surface design in an embodiment of the present disclosure, which includes a radial array of 32 sub-hogels, each sub-hogel array.

[0059] Figure 17B An isometric view of the meta-surface design according to an embodiment of the present disclosure is shown, comprising a radial array of 32 sub-hogels. Detailed Implementation

[0060] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0061] In this article, the word “one” or “the” may mean “one” when used with the term “includes”, but it is also consistent with the meanings of “one or more,” “at least one,” and “more than one.”

[0062] As used herein, the terms “comprising,” “having,” “including,” and “comprise,” and their grammatical variations, are inclusive or open-ended and do not exclude additional, unreferenced elements and / or method steps. When used herein in conjunction with a composition, apparatus, article, system, use, or method, the term “substantially constitutes” indicates that additional elements and / or method steps may be present, but these additions do not materially affect the manner in which the composition, apparatus, article, system, method, or use functions. When used herein in conjunction with a composition, apparatus, article, system, use, or method, the term “consisting of” excludes the presence of additional elements and / or method steps. Compositions, apparatuses, articles, systems, uses, or methods described herein as including certain elements and / or steps may also be substantially constituted by such elements and / or steps in some embodiments, and by such elements or steps in other embodiments, whether or not such embodiments are specifically mentioned.

[0063] As used herein, the term “approximately” refers to a change of approximately + / - 10% from a given value. It should be understood that such change is always included in any given value provided herein, whether specifically mentioned or not.

[0064] Unless otherwise stated herein, the description of ranges in this document is intended to convey the range and the individual values ​​falling within the range to the same positional values ​​as the numbers used to represent the range.

[0065] The use of any example or exemplary language, such as “for example,” “exemplary embodiment,” “illustrative embodiment,” and “for example,” is intended to illustrate or represent aspects, embodiments, variations, elements, or features relating to the invention, and is not intended to limit the scope of the invention.

[0066] As used herein, the terms “connection” and “linked” refer to any direct or indirect physical association between elements or features of this disclosure. Thus, these terms may be understood to mean elements or features that are partially or wholly contained within, attached to, coupled to, arranged together, connected together, communicate with, or operatively associated with each other, even if there are other elements or features between the elements or features described as being connected.

[0067] As used in this article, the term "pixel" refers to the light source and emission mechanism used to create a display. A pixel may include one or more subpixels, and most commonly includes a red subpixel, a green subpixel, and a blue subpixel.

[0068] As used herein, the term "subpixel" refers to a structure comprising light-emitting devices housed within an optical microcavity. The optical microcavity is operatively associated with a plurality of reflective surfaces to substantially collimate, manipulate, or tune 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. As described herein, subpixel sizes range from nanometers to several micrometers, which is significantly smaller than pixel sizes previously known in the art.

[0069] As used in this article, the term "light field" at a basic level refers to a function that describes the amount of light flowing through a point in space in each direction without occlusion. Therefore, a light field represents radiation as a function of the position and direction of light in free space. Light fields can be synthesized through various rendering processes or captured from a light field camera or an array of light field cameras.

[0070] As used herein, the term "light field display" is a device that reconstructs a light field from a finite number of light field radiation samples input to the device. Generally, the radiation samples represent the red, green, and blue (RGB) color components, although other color combinations are understandable. For the reconstruction in a light field display, the light field can also be understood as a mapping from four-dimensional space to a single RGB color. The four dimensions include the vertical and horizontal dimensions of the display, and two dimensions describing the directional components of the light field. The light field is defined as the following function:

[0071]

[0072] in These are the Cartesian coordinates or position coordinates of the position within the light field. It is a direction or angle descriptor. For fixed... , , This represents a two-dimensional (2D) image, often referred to as an "elemental image." An elemental image is derived from a fixed... , An oriented image of the light field captured at a specific location. When multiple element images are joined side-by-side, the resulting image is called an "integral image." An integral image can be understood as the entire light field required for a light field display.

[0073] As used herein, the term "meta-surface" refers to an engineered surface used to manipulate wavefronts. This surface consists of a two-dimensional (2D) lattice of nanostructures that interacts with the incident wavefront, where the lattice constant and structural dimensions are subwavelength. The properties of each subwavelength structure are selected to impart specific local phase and amplitude to the wavefront. By controlling the phase and amplitude of the wavefront at each lattice location, the shape of the wavefront can be manipulated. Meta-surfaces can be designed for a wide variety of wavefront types, including but not limited to electromagnetic and acoustic wavefronts. Optical meta-surfaces manipulate light waves and can be used to flatten existing three-dimensional (3D) components, such as lenses. Optical metasurfaces can be fabricated using semiconductor technology, thereby reducing manufacturing costs.

[0074] As used herein, the term "OLED" refers to an organic light-emitting diode, a photoelectric device that emits light when an external voltage is applied. OLEDs can be divided into two main categories: those made of small organic molecules and those made of organic polymers. An OLED is a light-emitting diode in which the emitting electroluminescent layer comprises an organic compound film that emits light in response to an electric current. Typically, an OLED is a solid-state semiconductor device comprising at least one conductive organic layer disposed between and electrically connected to an anode and a cathode. When a current is applied, holes are injected into the anode, and electrons are injected into the organic layer from the cathode. The injected holes and electrons migrate toward their respective oppositely charged electrodes. When electrons and holes are localized on the same molecule, excitons are formed, which are localized electron-hole pairs with excited energy states. When the excitons relax through a photoemission mechanism, light is emitted. Various types of OLEDs exist, including but not limited to active matrix OLEDs (AMOLEDs), top-emitting OLEDs, and bottom-emitting OLEDs. AMOLEDs have a complete cathode, organic molecule, and anode layer. The anode layer has a thin-film transistor (TFT) plane parallel to it, thus forming a matrix. This allows each pixel to be switched on or off as needed to form an image. Pixels are turned off whenever they are not needed, or when a black image appears on the display, thus extending the device's battery life. This is the lowest power consumption type of OLED and has a faster refresh rate, making them suitable for video as well. AMOLED applications include computer monitors, large-screen TVs, electronic signs, or billboards. Top-emitting OLEDs have an opaque or reflective substrate. Top-emitting OLEDs are better suited 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. OLEDs are bottom-emitting if the emitted light passes through a transparent or translucent bottom electrode and substrate.

[0075] As used herein, the term "hogel" is an alternative term for a holographic pixel, which is a traditional cluster of pixels with directional control. A group of hogels can generate a light field. Therefore, "hogel spacing" is defined as the distance from the center of one hogel to the center of the adjacent hogel.

[0076] As used herein, the term "subhogel" (or subhogel) is a cluster of traditional subpixels with orientation control. A group of subhogels may comprise a single hogel.

[0077] As used in this article, the term "monochrome" refers to a narrow bandwidth color channel and describes light emission with a narrow optical bandwidth.

[0078] As used in this article, the term "elemental image" refers to a fixed image. , , Two-dimensional (2D) images The element image is fixed. , Orientation image of the light field at the location.

[0079] As used in this article, the acronym "FWHM" stands for "Full Width Half Maximum," which is an expression for the range of a function given by the difference between the two extreme values ​​of the independent variable, at which the dependent variable is equal to half of its maximum value.

[0080] As used in this article, the abbreviation "FRED" refers to FRED optical engineering software. FRED is a commercial 3D computer-aided design (CAD) computer program for optical engineering, used to simulate the propagation of light in optical systems. FRED can handle both incoherent and coherent light using Gaussian beam propagation.

[0081] As used in this article, the term "transmittance" refers to the percentage of light transmitted per unit of incident light.

[0082] As used in this article, the term “wavelength” is a measurement of the distance between two identical peaks (high points) or troughs (low points) in a wave, which is a repeating pattern of propagating energy, such as light or sound.

[0083] As used herein, the term "simulation" refers to a computer model that produces something, particularly for researching or developing and refining manufacturing specifications. Various simulation methods can be used, including but not limited to the following: Finite-Difference Time-Domain (FDTD) methods are used to solve problems in electromagnetics and photonics, addressing Maxwell's equations in complex geometries. FDTD is a general-purpose finite-difference time-domain method that handles the properties of nonlinear materials in a natural way and allows users to measure the system response over a wide frequency range. A similar technique is Rigorous Coupled-Wave Analysis (RCWA), a semi-analytical method commonly used to solve field diffraction problems of periodic structures. RCWA decomposes the field into a set of plane waves, represented by the sum of spatial harmonics in Fourier space. RCWA benefits from reduced simulation complexity and time, but inaccuracies can occur in more complex geometries. Ray tracing simulations, such as those performed by FRED, are used for prototyping optomechanical systems. Given an initial set of rays, ray tracing simulates the resulting light field by propagating rays through space and calculating the interactions of the rays with any surfaces they strike.

[0084] It is conceivable that various embodiments of the compositions, apparatuses, articles, methods, structures, devices, and uses disclosed herein can be implemented by those skilled in the art as is, or by making such changes or equivalents without departing from the scope of the invention.

[0085] This paper describes a sub-hogel configuration for high-definition light field displays. An optics device and a three-dimensional light field display technology are also provided; more specifically, three-dimensional holographic pixels (hogels) composed of monochromatic subpixels and a designed metasurface are provided, which serves as the directional optics element for the light field display. The described sub-hogel structure design and method are applicable to achromatic metasurfaces, providing directional pixels for multi-view light field color displays. To date, the metasurface research community has not found an effective broadband achromatic metallic lens. To simplify the design of metasurfaces for organic light-emitting diode (OLED) or projector-based displays, a grating comprising an array of monochromatic sub-hogels is described, where each sub-hogel includes a unique monochromatic metallic lens.

[0086] Hogels are directional light-emitting structures that emit light of different colors and intensities in different directions, composed of multiple subpixels. In this disclosure, a hogel is shown as having multiple RGB subpixels; however, it should be understood that hogels can include different combinations of the number and color of subpixels. A light field display consists of a set of gratings. An observer will see a point of light emitted by each hogel in the array. The accumulation of each point of light from the hogel array will produce the image seen by the observer. A second observer at another location will see a point of light from each hogel in the array, but because they are observing the light field display from a different location, they are observing from a different direction, so the image they observe is different from that of the first observer. For an n×m hogel array, both observers will see an image produced by the n×m light spot array. A hogel consists of a 2D pixel array (or subpixel array) and directional optical elements (such as lenses or metasurfaces). Light emitted by each pixel or subpixel propagates perpendicular to the pixel array. The light from each pixel passes through the directional optical elements and is guided to a predetermined direction. A hogel with a pxq pixel array will send light in different directions of pxq. A light field display consists of an (n*p) x (m*q) pixel array and an n x m array of directional optics, such that each hogel in the n x m-hogel array has pxq pixels. Hogels are the product of combining a pixel array with an array of directional optics. Each pixel is composed of subpixels, typically three adjacent RGB subpixels forming one pixel. Therefore, a pixel array is also a subpixel array. In a subhogel light field display, the subpixel array that makes up each hogel is reorganized such that instead of grouping RGB subpixels of the same pixel together, similar color subpixels are grouped into clusters to accommodate the directional optics (in this case, the meta-surface).

[0087] According to this disclosure, a meta-surface can be considered as an ordered spatially multiplexed meta-surface in which metallic lenses for each color channel are interwoven onto a single meta-surface. The meta-surface is described herein as an example of a directional optical element; however, other directional optical elements are conceivable. The aperture is determined by the sub-hogel size, and each sub-hogel interacts with a single color channel. The currently described meta-surface is segmented to fit color regions such that each segment has a corresponding cluster of sub-pixels of the same color, thereby allowing the meta-surface color region segments to be tailored to the wavelength of the corresponding sub-pixel clusters. A sub-pixel is a cluster of sub-pixels of a similar color coupled to a corresponding meta-surface color region segment.

[0088] A significant hurdle in designing directional optical elements, particularly meta-surfaces for light field display technologies, is achieving nanometer-scale pixel sizes to provide the pixel density required for high-resolution light field displays, which typically have billions of pixels. The designs described so far achieve pixel sizes below 10 micrometers while providing sufficient sub-hogel sizes to facilitate meta-surface designs that can be fabricated using known manufacturing tools and methods. To customize and realize achromatic meta-surfaces with directional pixel capabilities, a clustering of near-color subpixels (R, G, B subpixels) is proposed, and these are hierarchically layered with a region of the meta-surface customized to the spectrum of light emitted by a cluster of near-color (monochrome) subpixels that guide the emission of light; this is referred to herein as a monochromatic subhogel, a monochromatic subhogel array, and / or a monochromatic subhogel cluster.

[0089] This disclosure provides design considerations and methods for designing a monochromatic sub-hogel array coupled to an achromatic metasurface to provide oriented pixels for a high-definition, multi-view light field display. Therefore, metasurfaces are strong candidates for enhancing conventional refractive or diffractive optics. The metasurface concept utilizing monochromatic sub-hogels overcomes current limitations in achieving the high angular resolution required for compelling light field displays.

[0090] Monochromatic subhogel designs are currently described, in which clusters of subpixels of similar colors can be combined with optical surfaces (e.g., geometrical surfaces) to achieve desired directional pixel capabilities. The techniques described throughout this disclosure are advantageous compared to other achromatic metasurfaces. These advantages include, but are not limited to: anticipated efficiency improvements, the elimination of the need for polarized light sources, and the ability of metasurfaces to compensate for the full visible spectrum without limitation on subpixel size. It should be noted that, when used in displays, the reduced pixel size allows the system to output a greater number of beams in more diverse directions, thereby improving pixels previously known in the art by allowing the generation of higher angular resolution displays with improved effective resolution of multidimensional objects. The increased number of light field display views allows a viewer at any viewing position to receive multiple views simultaneously; this is known as a Super Multi-View (SMV) display. SMV displays offer improved angular resolution, eliminate accommodation convergence conflicts, and produce displays with higher quality depth of field.

[0091] Fan et al. described a metallic lens array that can be used in light field displays using dispersion-phase-compensated achromatic elementary surfaces (Fan, Zhi Bin. Broadband achromatic metallic lens array for visible light integration imaging. 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 No. 20170146806 also describes a metallic lens array that can be used in light field displays using dispersion-phase-compensated achromatic elementary surfaces. They achieved an average efficiency of 39% and an NA of 0.21, still too small to achieve the large field of view required for light field display applications. The NA of phase-compensated achromatic metallic lenses is limited by the maximum lens size that can be accommodated in nanostructures, while still providing sufficient phase compensation to achieve achromaticity, which is directly related to the height of the nanostructure. Higher NA phase-compensated achromatic metallic lenses require advances in manufacturing to achieve larger nanostructures.

[0092] This invention utilizes sub-hogels that customize the separated regions of a metasurface into specific color channels, allowing for efficient and greatly simplified metasurface design. Since each region of the metasurface is monochromatic, the metasurface can be a geometric metasurface, meaning that the phase can be controlled by varying the size of the nanostructures constituting the metasurface.

[0093] Khorasaninejad et al. previously reported a 90% efficient metallic lens that does not require a polarization source to avoid additional losses and components (Khorasaninejad, Mohammadreza. Polarization-Insensitive Metallic Lenses for Visible Wavelengths. American Chemical Society. Nano Letters. October 24, 2016). However, these devices exhibit chromatic aberration, which is irrelevant to this invention because each geometric element surface is customized to a narrow-bandwidth color channel. This invention can also be used with Pancharatnam-Berry metasurfaces, which control the phase of the polarization wavefront by altering the orientation of a fixed-size birefringent nanostructure. Other possible element surface types include, but are not limited to, combinations of geometric and Pancharatnam-Berry element surfaces (altering the size and orientation of the nanostructure), inversely designed element surfaces, and dispersion phase-compensating element surfaces.

[0094] Various features of the invention will become apparent from the following detailed description and the illustrations in the accompanying drawings. The design parameters, methods, constructions, and uses of the microcavity OLED design processes and structures disclosed herein are described with reference to various examples of representative embodiments, which are not intended to limit the scope of the invention described and claimed herein. Those skilled in the art will recognize that other variations, examples, and embodiments of the invention can be practiced based on the teachings of this disclosure without departing from the scope of the invention, but which are not disclosed herein.

[0095] Figure 1 A method for designing metasurfaces suitable for use in light field displays is illustrated. The method first requires defining a desired phase function 10. A phase function is selected for the metasurface being designed based on the desired function of the metasurface. In one example, if the metasurface is intended to be used as a lens, the phase function will focus the light applied to the metasurface to the designed focal length or focal spot. After selecting the phase function, 12 a material type is specified, which then allows the determination of the fabrication configuration 14. The ideal material for the metasurface used in a light field display has a refractive index that ensures a strong configuration to achieve a full 2π phase shift within the range imposed by fabrication and pixel size, while maintaining high transmittance. This disclosure describes the use of titanium dioxide (TiO2) in the fabrication of nanostructures in metasurfaces; however, it is understood that other materials and combinations of materials may be used in the fabrication of 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 described metasurface includes nanostructures, in this case nanopillars; however, it should be understood that the described metasurface nanostructures can have various shapes, including but not limited to elliptical, square, rectangular, and square horizontal cross-sections, and straight, angular, curved, pyramidal, and truncated conical vertical cross-sections. The metasurface can also be selectively fabricated on silica (SiO2), which adds further flexibility to TiO2 deposition methods. Possible deposition methods include, but are not limited to, depositing TiO2 directly over the display or aligning it in an additional step.

[0096] Once the fabrication configuration is determined, a 16-array configuration is established, and an 18-cell spacing is defined. The cell, denoted as U, specifies the center-to-center distance between adjacent pillars or nanostructures in the metasurface. The cell size is analogous to the lattice constant in a periodic crystal structure, or the grating period in a diffraction grating, where the duty cycle is the characteristic size divided by the grating period. Approximate values ​​for the minimum and maximum cell sizes can be determined using the equations described below. FDTD simulations can then be used to determine the optimal cell size, comparing transmission maps with different cell sizes. The optimal cell size will be one that keeps the minimum and maximum diameters of transmission from single-mode resonance as close as possible to 1. Previous reports on metasurface design have used different cell sizes for each wavelength. In one example, Khorasaninejad et al. reported U=180 nm, 250 nm, and 350 nm, which are applicable to wavelengths of 405 nm, 532 nm, and 660 nm, respectively (Khorasaninejad, Mohammadreza. Visible wavelength planar superlenses based on titanium dioxide. IEEE Quantum Electronics Journal, Vol. 23, No. 3, May / June 2017).

[0097] Figure 2 The graph shows the refractive index of titanium dioxide (TiO2) versus wavelength (nm) in the visible light range. For metasurfaces based on visible wavelength nanostructures used in optical field displays, TiO2 has a negligible absorption coefficient, a refractive index in the range of 2.3–2.7, as shown in the figure, and has been shown to enable the realization of high aspect ratio, anisotropic structures with minimal surface roughness.

[0098] Back Figure 1 The method shown, for rectangular dielectric resonators, Aieta et al. reported using FDTD scanning to determine the optimal cell parameters in silicon, which takes into account the characteristics and resonance in the rectangular dielectric (Aieta, Francesco. Dispersion phase-compensated multiwavelength achromatic metasurfaces. Science Letters. February 19, 2015). US Patent 9,103,973 to Fattal et al. reports that the lattice constant should be chosen so that the optical element does not scatter light in an undesirable manner, which can be prevented by selecting the lattice constant based on the following defined no-scattering limit:

[0099]

[0100] For square lattices, and

[0101]

[0102] For hexagonal lattices.

[0103] Khorasaninejad et al. describe a method for optimizing the height and cell size of nanostructures at a design wavelength, where the maximum diameter equals the cell size, which must be small enough to satisfy the Nyquist sampling criterion (Khorasaninejad, Mohammadreza, "Visible Wavelength Polarization-Insensitive Metallic Lenses," ACS, Nano Letters, October 24, 2016). The Nyquist criterion states that as long as the sampling frequency is greater than twice the highest frequency to be sampled, the repetitive waveform can be correctly reconstructed; therefore:

[0104]

[0105] NA is defined as the numerical aperture of a metallic lens.

[0106] According to this disclosure, the minimum unit cell boundary can be defined based on the geometry of the nanostructure. The minimum unit cell size is defined as the maximum distance between nanostructures. At this location, and smaller than the gap between adjacent nanostructures, in this case, the distance between nanopillars is synonymous, and the distance between pillars is less than At this time, light of the designed wavelength will not resonate between the nanopillars. The lack of resonance between the nanopillars means that the sole contribution to the output comes from the nanopillars themselves. Therefore, the no-resonance condition requires the optical path length between the pillars to be less than a quarter wavelength, or:

[0107]

[0108] in It is the refractive index of the material surrounding the nanopillar. The minimum radius using single-mode resonance. :

[0109]

[0110] The minimum unit size can be defined as

[0111]

[0112] in:

[0113]

[0114] This condition also applies to larger unit cells. :

[0115]

[0116] Once the cell spacing of 18 has been defined, the boundaries of the resonant conditions for the 20 nm pillars must also be defined. The resonant boundary parameters, including the diameter and shape of the nanostructures in the metasurface, are calculated, including setting lower and upper limits for the cross-sectional area of ​​each nanostructure to ensure a favorable and efficient response of the nanostructures to light of the desired wavelength. For the design of the metasurface of a 3D light field display, single-mode resonance of each nanostructure is required. Therefore, for each pillar that does not resonate, the minimum diameter needs to be determined. Similarly, it is necessary to determine the maximum diameter at which a single-mode resonance transforms into a multi-mode resonance. .

[0117] The transverse refractive index distribution of many optical fibers is radially symmetric, and the refractive index distribution of almost all fibers exhibits only small refractive index contrast, allowing the assumption that the fiber is only weakly guided. This simplifies the calculation of fiber modes, resulting in linearly polarized (LP) modes. In the case of stronger guidance, it is necessary to distinguish between transverse electric and transverse magnetic modes, where the electric or magnetic field is exactly perpendicular to the fiber axis. Mixed modes with non-zero longitudinal components of both electric and magnetic fields also exist. As used in this paper, HE and EH are combinations of the symbols for 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 stronger longitudinal magnetic field compared to the longitudinal electric field.

[0118] The wave equation for a complex electric field profile in cylindrical coordinates is:

[0119]

[0120] in It is the imaginary part of the propagation constant. At a given wavelength, for... The discrete values ​​of the radial equation have solutions, representing the guided modes of the optical fiber. All guided modes have... Value, that The value lies between the plane wave values ​​of the cladding and the core.

[0121] The V-number is a dimensionless parameter that can be interpreted as a normalized optical frequency, crucial for many fiber optic properties. It is defined as:

[0122]

[0123] For V values ​​below 2.405, the optical fiber supports only one mode LP01 in each polarization direction, and is called single-mode or single-mode fiber. For values ​​greater than V = 2.405, the number of supported modes can be approximated as:

[0124]

[0125] Using V=2.405 in the above equation for V, the maximum radius of a single-mode fiber can be found using the following formula:

[0126]

[0127] Similarly, the minimum radius at which single-mode resonance begins is V = 0.9, therefore:

[0128]

[0129] The minimum radius of resonance can be determined.

[0130] After determining the diameter of the resonant boundary, the height 22 of the nanostructure pillars in the metasurface must be specified. The height of the nanostructures must be high enough to ensure the achievable diameter of the 2π phase coverage. Furthermore, due to manufacturing constraints, it is desirable that the pillars be of equal height, or have at most a single height per design wavelength.

[0131] The collective approach of the Harvard Capasso group relies on simulation results to ensure this range, noting that h for wavelengths of 405 nm, 532 nm, and 660 nm are 400 nm, 600 nm, and 600 nm, respectively (Khorasaninejad, Mohammadreza. Visible Wavelength Planar Lenses Based on Titanium Dioxide. IEEE Transactions on Quantum Electronics, Vol. 23, No. 3, May / June 2017). It has been suggested that the height can be estimated based on phase accumulation along the plate length, therefore for a 2π phase shift, the height (Khorasaninejad, Mohammadreza. Polarization-Insensitive Metalenses at Visible Wavelengths. ACS. Nano Letters. October 24, 2016) is:

[0132]

[0133] However, the effective refractive index can range from approximately 1 to the material's refractive index value, leading to unreliable estimates of the required height. US Patent 9103973 by Fattal et al. reports that the thickness of the metasurface should not exceed:

[0134]

[0135] To ensure a large differential phase, the above equation is used for 540 nm, where H < 526 nm. This value is smaller than the one determined in the simulation here and is currently known. However, one source of inconsistency with this equation might be... It is the effective index of the metasurface, not just the refractive index of the nanostructure (pillar) material. Aperiodic metasurfaces are expected to have an effective index that is not constant at any particular point. Furthermore, if the effective index value is calculated for the entire metasurface and further simplified to the ratio of filled area to unfilled area, the final estimate of the effective index value will be unreliable.

[0136] Through a series of steps, an equation for determining the effective refractive index based on the pillar diameter and refractive index was found. This equation was then used to determine the minimum height required to achieve a 2π phase shift within the single-mode resonant region at each wavelength. Furthermore, the phase accumulation per unit length was also determined. The slope is shown as the linear fit of the data on column height versus total phase shift.

[0137] To determine the effective refractive index of the nanopillar, a series of equations were used. The theoretical background describing this computational evolution first describes how the optical modes in the dielectric slab are solutions to the eigenvalue equations derived from Maxwell's equations, configured by the boundary conditions imposed by the waveguide geometry. Maxwell's equations can be written as:

[0138]

[0139]

[0140] in It is the value of the refractive index distribution.

[0141] Since the structure is uniform along the z-axis, the solution to the wave equation is:

[0142]

[0143]

[0144] in It is the propagation constant (the z-component of the wave vector). and It is the wave function of the guided mode.

[0145] eliminate The wave equation becomes:

[0146]

[0147] Seek solutions to the above equations in each segment of the dielectric structure. It is well known that for confined modes, the field amplitude decreases exponentially outside the guiding structure and varies sinusoidally inside. For the TE (transverse electric) mode, the mode function is:

[0148]

[0149]

[0150]

[0151] in and Related to the propagation constant, as shown below:

[0152]

[0153]

[0154] Using the boundary conditions and mode condition equations of the above TE-symmetric mode (A=0, C=D):

[0155]

[0156] For asymmetric modes:

[0157]

[0158] Therefore, the propagation constant can be determined if and Then the boundary conditions and the mode condition equations for the above TE-symmetric mode become:

[0159]

[0160] The boundary conditions and mode condition equations for the above TE asymmetric mode become:

[0161]

[0162] Finally, we can find that the definition of V is:

[0163]

[0164] because and It must be positive. The propagation constant can now be determined by finding the intersection of the boundary conditions for both TE-symmetric and asymmetric modes with the aforementioned mode condition equations. Number from The definition of a number equation is defined as having a radius of... A circle such that:

[0165]

[0166] Intersections using restricted patterns Value and The propagation constant can be calculated using the following formula:

[0167]

[0168] Defining a normalized propagation constant is useful for defining constrained modes:

[0169]

[0170] Once the pillar height 22 is specified, a transmission map 24 is generated. The range of achievable nanostructures is thus defined when the nanostructure parameters are defined. The transmission map maps the complex transmission coefficients to functions of the nanostructure parameters. The magnitude of the complex transmission coefficients determines the optical efficiency of the nanostructure, while the phase of the complex transmission coefficients determines the phase of light emitted from the sub-pixels. These mappings are generated using Finite-Difference Time-Domain (FDTD) analysis software. Due to the complexity of metasurface structures, analytical techniques often fail to provide effective solutions, thus numerical modeling techniques are employed. FDTD is one of the most popular methods for electromagnetic structure modeling due to its ability to handle non-uniform, anisotropic, and dispersive materials. However, numerical simulation becomes challenging for modeling metamaterials with high contrast between the material properties of the structure and free space, and the accuracy of traditional FDTD methods is often insufficient. Using extremely fine meshes can improve simulation accuracy but requires increased computational resources. Therefore, it is necessary to appropriately develop traditional FDTD schemes to accurately model metamaterials.

[0171] Phase and transport maps are used to create a dataset from which high transport parameters with desired phases can be selected. A series of scans are generated, with the diameters of the nanopillars increasing sequentially at specific cell spacings and heights. These simulations use periodic boundary conditions to simulate the fields generated by an infinite array of identical nanopillars, from which phase and transport parameters are extracted. Transition and phase maps are used to design aperiodic metasurfaces where adjacent nanopillars have different diameters; therefore, the pillars will have different nearest-neighbor interactions, which may alter their phase and / or transport parameters. Ideally, the range of pillar diameters is small enough that the above design approximations are valid; however, this leaves room for further design optimization.

[0172] Using the transmission map generated by FDTD as a lookup table for nanostructure parameters, color regions 26 in the metasurface can be designed. The color regions in the metasurface are designed based on nanostructure parameters and the transmission map to achieve a phase specified by a phase function, where each color region is designed to guide light with a specific optical bandwidth. The parameters of the nanostructure for each color region may include, but are not limited to, nanostructure height, nanostructure shape, cell spacing, and resonant boundary parameters. To create the desired phase profile / wavefront with uniform transmission on the metasurface, the pillar diameter selected from the LUT minimizes the following equation:

[0173]

[0174] in Is it average transmission? Expected phase These are transmission parameters from the LUT. These are phase parameters derived from the LUT.

[0175] Required phase The phase is determined by a function of the element surface. For a metallic lens with a focal length of f, the required phase is given by the following formula:

[0176]

[0177] Where x and y are the position coordinates relative to the center of the metal lens.

[0178] Finally, FDTD simulations of the metasurface are used to optimize the parameters of the nanostructure array to maximize the calculated coefficient of merit (FOM)28, and the metasurface is placed in design30. The figure of merit is a performance metric of the metasurface defined by its function. For example, the figure of merit for a metallic lens includes, but is not limited to, its focal length, full width at half maximum (FWHM) at the focal point, and Strehl ratio (a comparison to the ideal intensity curve at the focal point). Given a design, the figure of merit can be calculated using the results of design simulations. After calculating the figure of merit of the designed metasurface, the parameters of the nanostructure can be adjusted, and the figure of merit can subsequently be recalculated to see if the metasurface performance improves due to the adjustment of the nanostructure parameters. The optimization process for the metasurface can be iterative, and the nanostructure parameters can be adjusted, and subsequent FOM calculations can be performed multiple times to optimize the metasurface design.

[0179] Spacing of the sub-hogel metal lens It is given by the following formula:

[0180]

[0181] in It is the number of subpixels / subhogels, and This refers to the subpixel spacing. It represents the corner spacing required for each sub-hogel. Given by the following formula:

[0182]

[0183] in It is the FWHM of the point spread function, where Φ is the angular resolution of the display. It has been found that having twice the angular resolution... FHWM provides a comfortable viewing experience.

[0184] Using the above equations, the minimum number of subpixels / subhogels can be determined to overcome the diffraction limit. At an angular resolution of 0.6 degrees and a PS resolution of 1.2 degrees, and exist Figure 3 The graph of FWHM[deg] relative to pitch [µm] is used in the text. The plotting is performed. For a subhogel containing 4x4 or more subpixels (based on 4μm x 4μm subpixels), the diffraction limit is satisfied.

[0185] The upper limit on the number of subpixels / subhogels is set by the eye’s ability to distinguish individual subpixels, because larger subhogels increase the distance between the RGB subpixels that combine to form each individual pixel. Figure 4 The diagram shows a cross-sectional view of the sub-hogel array along the y-axis. Each sub-hogel array has four sub-pixels / sub-hogels. Three sub-pixels are highlighted: blue (B) sub-pixel 46, green (G) sub-pixel 48, and red (R) sub-pixel 50. Among adjacent sub-hogels, these sub-hogels contribute to the observation of a single pixel at a distance d perpendicular to the screen 44. Figure 4 This shows the angle of a single pixel centered on the central sub-pixel, relative to the sub-pixel spacing of 100, as observed by observer 106. and sub-pixel spacing 102 ( This relates to the subpixel extending into the y-axis with a spacing of (Δy). SP In this example, all the RGB triplet subpixels that make up each pixel are located in the same row of subpixels, so only Δy SP It contributes to the pixel size in the y-axis.

[0186] For a viewer perpendicular to the screen, the angular spread of the RGB subpixels is maximized; therefore, this viewpoint will limit the size of the subhogel. Light forming each pixel propagates at a viewing distance of 104, which is given by the following equation:

[0187]

[0188] Assuming the angular resolution of the human eye is limited to β = 0.03°, the minimum viewing distance for a pixel is:

[0189]

[0190]

[0191] For a given minimum viewing distance, the above equation can be used to set the maximum subhogel size. The minimum viewing distance can be set either by the near point of the human eye or by the characteristics of the light field display:

[0192]

[0193] By solving the above quadratic equation, the maximum sub-hogel spacing can be obtained. In this case, the maximum subhogel spacing can be approximated as:

[0194]

[0195] Figure 5 An embodiment of this disclosure is shown, depicting a pixel 60 comprising an array of 8x24 multicolor sub-hogels 52 for a total of 192 subpixels. The hogel shown has a full-color 64x64 view from an array of blue subpixels 46, green subpixels 48, and red subpixels 50.

[0196] Figure 6 The diagram illustrates a hogel 60 comprising multiple subpixels. Applying an 8x8 symmetry to the subhogel array reduces the required number of metal lenses. (See diagram for example.) Figure 6 As shown, due to the symmetry of the view, for quadruple symmetry, the number of unique meta-lenses 58 is reduced from 192 to 48, and if octet symmetry is applied, the number of unique meta-lenses is further reduced to 30. In this example, the number of unique meta-lenses would be one per individual RGB subpixel. For larger screens with a greater minimum viewing distance, a 16x16 subpixel array of 46, 48, or 50 subpixels per pixel can be used, reducing the number of subpixels to 48, and applying quadruple symmetry reduces the number of unique meta-lenses to 12. Next, applying octet symmetry reduces this number to 9.

[0197] The integral image of a Hall effect display is formed by subdividing the element image of the Hall effect display into equal-sized partial element images, each with an integer number of pixels. The element images represent a two-dimensional (2D) image. For fixed , , For light field displays, the element images are fixed. , The orientation image of the light field at the location is obtained. Then, each partial element image is decomposed into three sub-part element images, each for each color channel, such that each pixel of the partial element image has a corresponding sub-pixel in each sub-part integral image. The sub-part element images are placed adjacent to each other to create the element image of the subhogel display.

[0198] Figure 7The diagram illustrates the transformation of a 6x6 hogel 60 into a segmented hogel 62. As shown, the segmented hogel 62 is divided into two colored sub-hogels 52a and 52b in the x-direction; however, it is understood that the segmentation can be performed in various directions. In the hogel 60, also known as the element image, and the segmented hogel 62, also known as the partial element image, there are 6x6 pixels, each pixel comprising a red sub-pixel, a blue sub-pixel, and a green sub-pixel. The size of each sub-pixel is preferably less than 10µm. 2 . Figure 7 The transformation of a 6x6 segmented hogel 62 into a sub-hogel element image 64 is further illustrated. It should be noted that dividing the element image into sub-elements only needs to occur along one direction, since subpixels of the same color are already adjacent to each other along the remaining axis; however, it should be understood again that division can be performed in various directions. The resulting sub-hogel element image 64 consists of monochromatic sub-hogels 66a, 66b, and 66c. The pixels in the monochromatic sub-hogels 66a, 66b, and 66c are shown arranged in a rectangular 3x6 configuration; however, it should be understood that the sub-hogels can be arranged in different directions, such as other rectangular directions, square directions, or radial directions, with the number of sub-hogels per subpixel varying.

[0199] The initial hogel element image data is stored in a 6x6 matrix, while the sub-hogel element data is stored in an 18x6 matrix. The hogel integral image can be converted into a sub-hogel integral image using MATLAB (or an equivalent) script, and this image can be written to a .txt file. For displaying the light field, the entire image used for display is typically called the integral image, and the integral image is divided into multiple element images, which are sent to a light field display for display. Each element image is displayed by associated hogels within a hogel array and consists of multiple hogels arranged in the hogel array. Each pixel in an element image has a corresponding view or orientation, such that a viewer facing the display at the normal to the display will see the pixel at the center of each hogel in the hogel array.

[0200] The architecture of the subhogel display was simulated using ray tracing software to analyze how the display would be perceived. It should be noted that these simulations can be performed using any suitable software tool. One example of a ray tracing software tool is FRED. As mentioned earlier, FRED refers to FRED Optical Engineering Software (FRED), a commercial 3D CAD computer program for optical engineering, used to simulate the propagation of light through optical systems. It should be noted that, for simplicity, a limited number of views were simulated.

[0201] Figure 8 A simulated light field display, further magnified on a set of three monochrome (RGB) sub-hogels, is shown, specifically red monochrome sub-hogel 66a, green monochrome sub-hogel 66%, and blue monochrome sub-hogel 66.c. To conserve computational resources, nine views were simulated in ray tracing software. The test image was a 4x8 pixel white image used to test color mixing. Each monochrome (RGB) sub-hogel 66a, 66b, and 66c creates one pixel for a 3x3 view. The space between sub-hogels 72 is reserved for additional views. Each monochrome sub-hogel may include multiple subpixels, and preferably has 2 to 144 monochrome subpixels.

[0202] In these simulations, a single wavelength acts as the light source. A blending ratio calculator is used to determine the color blending ratio required to blend white. The ratio provided by the calculator is the luminance ratio, which is the light measurement; therefore, the power ratio of the light source is set as the luminance ratio divided by the photometric luminance function, which is the photometric function built into the ray tracing software tool.

[0203] To analyze the perception of the subhogel display, a human eye model, also known as the "Arizona eye," created by Photonics Engineering, was incorporated into the model. The pupil diameter and eye accommodation can be set by the user. Accommodation can be defined as the process by which a vertebrate eye changes its optical power as distance changes in order to maintain a clear image or focus on an object. The analysis surface was placed behind the retina to capture the observed image. The sampling distance to the retina was set to 8 micrometers because 1 degree of vision corresponds to a length of 288 micrometers on the retina, and the eye can distinguish lines separated by 0.03 degrees.

[0204] result

[0205] The resulting setup produced a series of images, which underwent qualitative evaluation. Figure 9A -F indicates the intensity of each color channel in the captured retinal image for different numbers of subpixels / subhogels. These ray-tracing simulations do not consider diffraction; therefore, the case of only one subhogel per subpixel represents the case of an ideal metallic lens paired with a conventional subpixel array. The intensity peaks correspond to the retinal location of the image formed by the pixels or the perceived location of the pixels, expressed in arbitrary units. For n sh =8, 16, the positions of pixels in all color channels and the ideal n sh =1 position matching, such as Figure 9A For the red text shown, Figure 9C As shown in green, and Figure 9E For the blue area shown, where nsh Defined as the number of subpixels / subhogels. For n sh =32, 64, the position of the pixel in the red channel is offset in the positive x direction, where n sh =64 has a ratio of n sh =32 larger offset, such as Figure 9B As shown; pixel position matching in the green channel is as follows Figure 9D The ideal case is shown; the position of the pixel in the blue channel is offset in the negative x direction, where n sh =64 has a ratio of n sh =32 larger offset, such as Figure 9F As shown. With n sh As n increases, the distance between subpixels of a pixel increases along the x-axis, such that for a central pixel with that subpixel geometry, red subpixels are pushed forward in the x-direction, green subpixels remain in the center, and blue subpixels are pushed backward in the x-direction. When n is sufficiently large... sh In this case, the central viewer will perceive the white pixel as a separate RGB pixel, in which n sh =32 and 64. The size of the subpixel is and For n sh =16, the following equation describes the light that forms each pixel:

[0206]

[0207] in This corresponds to a maximum of 19 sub-pixels / subhogels, which is consistent with the results above.

[0208] Example 1:

[0209] This article describes an example of determining the effective index of nanopillars for a metasurface designed for a light field display. Consider the step-by-step index guide. :

[0210]

[0211]

[0212] It is expected that there will be in the waveguide Restricted mode. Figure 10 This describes the boundary conditions and mode condition equations for the aforementioned TE symmetric and asymmetric modes. right A comparison diagram of the points. This diagram shows the intersection points... The values ​​were 1.33, 2.65, 3.94 and 5.14, respectively.

[0213] To determine the values ​​of the propagation constant and effective refractive index, the values ​​of the dispersion relation in the symmetric waveguide are extracted, noting that the propagation constant is scaled from 0 to 1 using the following equation:

[0214]

[0215] It can be written as:

[0216]

[0217] The value of the propagation constant can then be found using the value of the intersection point. The values ​​were 6.46, 6.40, 6.29 and 6.15, respectively.

[0218] Note that within this range, the data is approximately linear. Figure 11 As shown and The relationship between them can be described as follows:

[0219]

[0220] The relationship between column diameter and effective index can be defined as:

[0221]

[0222] To link these variables together, calculations are performed based on the diameter of the column. ,calculate and Define a normalized propagation constant, and then the effective exponent of each column can be approximated.

[0223] Typically, the phase accumulation from the dielectric is defined as:

[0224]

[0225] However, the effective index value used in this equation assumes that the effective index value is constant (for periodic structures with the same diameter and cell width). Since the effective refractive index as a function of diameter is approximately linear within the single-mode resonant boundary defined above, it can be replaced by the difference in effective refractive index from the maximum diameter to the minimum diameter:

[0226]

[0227] Therefore, the equation for phase accumulation can be written as:

[0228]

[0229] The phase accumulation per unit length can be written as:

[0230]

[0231] if The minimum height required to achieve a 2π phase shift within the resonant boundary can be found using the following formula:

[0232]

[0233] Table 1 below calculates the required phase accumulation and minimum height for each wavelength.

[0234] Table 1: Required phase accumulation and minimum height for each wavelength

[0235]

[0236] Figure 12 The calculated effective medium here is compared to an approximation of the effective index based on a weighted index of nanopillars and air gaps. The figure shows that this effective medium approximation (EMA) overestimates the index. Further calculations also revealed lower total phase accumulation over the diameter defined for each wavelength.

[0237] Example 2:

[0238] As described above, an implementation of a monochromatic subhogel design for use as an achromatic metasurface in a high-definition light field display is provided. To determine the appropriate subhogel size for a minimum light field display size of 3.15" and a field of view (FOV) of 40°, considering the human eye's angular resolution limitation of β = 0.03°, the minimum viewing distance for the display is:

[0239]

[0240] The minimum viewing distance is:

[0241]

[0242] Due to the near-field aspect of the human eye (The closest point the eye can focus on is ~25cm) greater than the minimum viewing distance of the monitor, which is used to determine the maximum subhogel spacing using the following relationship:

[0243]

[0244] Therefore, it can be determined that, assuming 4µm x 4µm subpixels, a viewer can only distinguish a single subpixel of a 16x16 subhogel at near distance. An 8x8 subhogel would satisfy the angular resolution of the eye at near distance and a smaller minimum viewing distance for the described embodiment of the light field display.

[0245] Example 3:

[0246] This article describes the detailed calculation of subhogel sizes for light field displays. The lower bound of the subhogel size is set by the diffraction limit and the Rayleigh criterion. The choice of subhogel size is not trivial: the size must be large enough to satisfy the Rayleigh criterion and the diffraction limit, while being small enough that individual subpixels are indistinguishable at the minimum viewing distance (i.e., the near point of the eye or the minimum viewing distance of the display). The diffraction limit is given by the following formula:

[0247]

[0248] in It is the angular spacing of the sub-hogel. It is the source wavelength. It is the hogel spacing. It's the deflection angle. In the case of

[00106] , the angular spacing equation of the sub-hogel becomes:

[0249]

[0250] in It is the number of subpixels / subhogels along each direction (x and y). h is the corner spacing for each view. Subhogel spacing should be selected so that:

[0251]

[0252] Rayleigh's criterion for resolving two points through an aperture of diameter d (assuming light is a plane wave) is given by the following equation:

[0253]

[0254] Where ϕ is the minimum angle between two distinguishable points; therefore:

[0255]

[0256] By taking the ratio of the two limits, it was found that the Rayleigh criterion dominates in setting the minimum subhogel spacing. The value represents the number of rows and columns of the sub-pixel array within the sub-hogel. For example... This corresponds to a subhogel with an 8x8 subpixel array. In this example, Figure 12 Showing The sub-pixel geometry. For Figure 12 The sub-pixel geometry shown satisfies the conditions shown in Table 2. The Rayleigh criterion applies. For a 64x64 view display, corresponding to 64x64 pixels per hogel, it is convenient to limit the number of subpixels / subhogels to 64.

[0257] Table 2: Minimum subhogel size (micrometers)

[0258]

[0259] The diameter of the smallest resolvable circle in the display plane Given by the following formula:

[0260]

[0261] in It is the minimum viewing distance for the monitor. =0.03°, this is the angular resolution of the human eye. In order for humans to perceive the expected pixel color, rather than individual subpixels, the subpixels that make up a pixel must have a diameter of... A circle. At the closest point to the eye (25 cm):

[0262]

[0263] Figure 13 The diagram shows the minimum diameter of 78 for the top-leftmost sub-pixel, including the R, G, and B sub-pixels. These three sub-pixels constitute one pixel. The diameter is given by the following formula:

[0264]

[0265] in It is the subhogel spacing of R, G, or B subhogels in the X (Y) direction. It is the subpixel spacing of R, G, or B subpixels in the X direction. This is achieved by setting... And require As positive real numbers, it was found that for a minimum viewing distance of 25cm (the near point of the human eye), the maximum number of subpixels / subhogels is 16. However, the minimum viewing distance for many displays is greater than the near point of the human eye, and is given by the following formula:

[0266]

[0267] in It displays the diagonal. It's about perspective. Figure 14 The minimum display diagonal was plotted for different subhogel sizes. .

[0268] Figure 15A triplet of three monochromatic sub-hogels 66a, 66b, and 66c is shown. Each monochromatic sub-hogel 66a, 66b, and 66c consists of 4x4 sub-pixels of the same color. Because sub-pixels of similar colors are clustered together, a subsurface 82 with specific properties can be designed for each color region. One advantage of this configuration is that the subsurface 82, as a directional optical element, can be designed to possess properties of a specific wavelength or color. Forming color regions larger than a single sub-pixel in the metasurface 82 allows for practically fabricable metasurface designs. The metasurface color region 86 for red 84 is directly aligned on top of the red sub-hogel 66a. The metasurface color region 86 for green is directly aligned on top of the green sub-hogel 66b, and similarly, the metasurface color region 88 for blue is directly aligned on top of the blue sub-hogel 66c.

[0269] Figure 16A A plan view of a metasurface 82 designed according to an embodiment of the present disclosure is shown, the metasurface 82 using... Figure 1 The publicly available meta-surface design method is used to design a 3x3 array of three monochromatic subhogels.

[0270] Figure 16B An isometric view of the design of the meta-surface 82 according to an embodiment of the present disclosure is shown, the meta-surface 82 comprising... Figure 1 The publicly disclosed meta-surface design method is used to design a 3x3 array of three sub-hogels.

[0271] Figure 17A A plan view of a meta-surface 82 designed according to an embodiment of the present disclosure is shown. The meta-surface 82 is designed as a radial array of 32 monochromatic sub-hogels. The shown meta-surface 82 has a different color region for each sub-pixel color, including a color region 84 designed for red sub-hogels, a meta-surface color region 86 designed for green sub-hogels, and a meta-surface color region 88 designed for blue sub-hogels. Meta-surface color regions 84, 86, and 88 are composed of nanopillars 90, using... Figure 1 The design is carried out using the disclosed meta-surface design method.

[0272] Figure 17B An isometric view of the meta-surface 82 design according to one embodiment of the present disclosure is shown, which includes a meta-surface customized for a radial array of 32 sub-hogels, and further shows an isometric view of a nanostructure (in this case, a nanopillar) including the meta-surface designed using the disclosed meta-surface design method.

[0273] All publications, patents, and patent applications mentioned in this specification indicate the skill level of a person skilled in the art to which this invention pertains and are incorporated herein by reference. Any reference to prior art in this specification is not, and should not be construed as, an admission or in any way implying that such prior art constitutes part of common general knowledge.

[0274] From this description, it will be apparent that the invention can be varied in many ways. Such variations should not be considered as a departure from the scope of the invention, and all such modifications that are obvious to those skilled in the art should be included within the scope of the following claims.

Claims

1. A method for displaying a light field, comprising: The integral image is subdivided into multiple element images, each element image representing a two-dimensional array of angle descriptors associated with a pair of orientation coordinates; Each element image is decomposed into multiple color channel-specific element images; Each color channel-specific element image is sent to the corresponding monochrome sub-hogel of the hogel, wherein the hogel comprises multiple sub-pixels and is partitioned into multiple monochrome sub-hogels, each comprising multiple monochrome sub-pixels of the same color, and wherein the color channel-specific element image is sent to the monochrome sub-hogel of the same color, thereby creating a light field for display.

2. The method of claim 1, wherein the plurality of monochrome subpixels of the same color are adjacent to each other in the monochrome subhogel.

3. The method according to claim 1 or 2, wherein the color channel-specific element image includes a red channel element image, a green channel element image, and a blue channel element image.

4. The method according to claim 1 or 2 further includes individually addressing the plurality of monochrome sub-pixels.

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

6. The method of claim 1 or 2, wherein each monochromatic sub-hogel comprises 2 to 144 monochromatic subpixels.

7. The method according to claim 1 or 2, wherein the element image is a directional image of the light field taken at a fixed spatial location.

8. The method of claim 1 or 2, wherein the monochrome subpixels in each monochrome subhogel are arranged in a square configuration, a rectangular configuration, or a radial configuration.

9. The method of claim 1 or 2, wherein decomposing each element image comprises subdividing the element image into partial element images, decomposing each partial element image into sub-partial element images for each color channel, and placing the sub-partial element images adjacent to each other to create a sub-hogel element image.

Images