Optical Metalens

Abstract

Various embodiments of optical metalenses and electronic displays employing metalenses are described herein. In some embodiments, a metalens includes an array of passive deflector elements having varying diameters extending from a substrate, with the array having a repeating pattern of deflector element diameters. Center-to-center element spacings of the passive deflector elements may be selected as a function of the operating wavelength of the optical metalens. Each passive deflector element has a height less than a minimum wavelength within an operating bandwidth and a width less than the minimum wavelength within the operating bandwidth. The electronic display may include a multi-pixel light-emitting diode (LED) display, such as an RGB LED display. A metalens including multiple metalens subpixels may deflect light emission from each corresponding LED subpixel to a target deflection angle. Each metalens subpixel may include a two-dimensional array of passive deflector elements in a repeating pattern of deflector element diameters.

Description

Detailed Description of the Invention

[0001] Related Applications This application claims the benefit of and priority to U.S. Patent Application No. 17 / 352,911, entitled "Optical Metalenses," filed June 21, 2021, which in turn claims priority to U.S. Provisional Patent Application No. 63 / 120,546, entitled "Metalenses for Optical Displays," filed December 2, 2020, and U.S. Provisional Patent Application No. 63 / 046,094, also entitled "Metalenses for Optical Displays," filed June 30, 2020, each of which is incorporated herein by reference in its entirety.

[0002] [Technical field] The present disclosure relates to metamaterial lenses that control polarization in transmissive and reflective configurations. Additionally, the present disclosure relates to electronic displays, including red, green, and blue (RGB) electronic displays.

[0003] BRIEF DESCRIPTION OF THE DRAWINGS 1A-1C show examples of light paths through a concave optical lens, a convex optical lens, and a flat optical lens, according to various embodiments.

[0004] FIG. 2A shows a top view of an exemplary representation of a pattern of deflector elements for a metalens structure, according to one embodiment.

[0005] FIG. 2B shows an expanded perspective view of an exemplary representation of a pattern of deflector elements in the metalens of FIG. 2A, according to one embodiment.

[0006] FIG. 3A shows an exemplary diagram of a side view of a metalens having a plurality of nanopillar deflectors disposed on a substrate, according to one embodiment.

[0007] FIG. 3B shows an exemplary diagram of the metalens of FIG. 3A operative to reflect incident optical radiation, according to one embodiment.

[0008] FIG. 3C shows an exemplary diagram of the metalens of FIG. 3A for transmitting and directing incident optical radiation, according to one embodiment.

[0009] 4A-4B show a metalens for use in conjunction with a laser scanning subsystem, according to various embodiments.

[0010] FIG. 5A shows an exemplary system having a metalens and a waveguide for use in conjunction with a laser scanning subsystem, according to one embodiment.

[0011] FIG. 5B shows an exemplary display system that utilizes input and output metalens in conjunction with a waveguide, according to one embodiment.

[0012] FIG. 6A shows an example of a unit cell of a metalens having a cylindrical polarizer element for use with a red laser, according to one embodiment.

[0013] FIG. 6B shows phase shift values ​​for various diameters of the cylindrical polarizer element in a unit cell of a metalens illuminated by a red laser, according to one embodiment.

[0014] FIG. 6C shows another example of a metalens unit cell in which a cylindrical cavity is formed in a cylindrical deflector element, according to one embodiment.

[0015] FIG. 6D illustrates a side cross-sectional view of the exemplary unit cell of FIG. 6C, according to one embodiment.

[0016] FIG. 7A shows an example of a display system for forming a light field that includes a metalens with multiple rectangular polarizer elements, an array of light emitting diodes (LED array), and a polarizer, according to one embodiment.

[0017] FIG. 7B shows an example of a display system that includes a metalens with multiple rectangular polarizer elements, an LED array, and a polarizer to split the light emission from each pixel of the LED array into two different directions for pupil replication, according to one embodiment.

[0018] FIG. 8A shows an example of a display system that includes a metalens with multiple polarizer elements operating in a waveguide mode and an LED array, without a polarizer, according to one embodiment.

[0019] FIG. 8B shows another example of a display system that includes a metalens having multiple polarizer elements operating in a waveguide mode and an LED array, without a polarizer, according to one embodiment.

[0020] FIG. 9 shows a portion of an exemplary LED display and various levels of detail of a tuned metalens having multiple RGB (red, green, blue) sub-pixels, according to one embodiment.

[0021] FIG. 10A shows an exemplary unit cell of a red metalens subpixel, according to one embodiment.

[0022] FIG. 10B shows transmittance values ​​for various diameters of the cylindrical deflector element in a unit cell for the exemplary red metalens subpixel of FIG. 10A, in accordance with one embodiment.

[0023] FIG. 10C shows phase shift values ​​for various diameters of the cylindrical deflector element in a unit cell for the exemplary red metalens subpixel of FIG. 10A, in accordance with one embodiment.

[0024] FIG. 11A shows an exemplary unit cell for a green metalens subpixel, according to one embodiment.

[0025] FIG. 11B shows transmittance values ​​for various diameters of the cylindrical deflector element in a unit cell for the exemplary green metalens subpixel of FIG. 11A, in accordance with one embodiment.

[0026] FIG. 11C shows phase shift values ​​for various diameters of the cylindrical deflector element in a unit cell for the exemplary green metalens subpixel of FIG. 11A, in accordance with one embodiment.

[0027] FIG. 12A shows an exemplary unit cell for a blue metalens subpixel, according to one embodiment.

[0028] FIG. 12B shows transmittance values ​​for various diameters of the cylindrical deflector element in a unit cell for the exemplary blue metalens subpixel of FIG. 12A, in accordance with one embodiment.

[0029] FIG. 12C shows phase shift values ​​for various diameters of the cylindrical deflector element in a unit cell for the exemplary blue metalens subpixel of FIG. 12A, in accordance with one embodiment.

[0030] FIG. 13A illustrates an example of a sub-unit cell deflector element having a dual frequency response, according to one embodiment.

[0031] FIG. 13B illustrates an exemplary multi-cell deflector unit cell having dual frequency response, according to one embodiment.

[0032] FIG. 14A illustrates an example of a sub-unit cell deflector element for an RGB display, according to one embodiment.

[0033] FIG. 14B illustrates an exemplary multi-cell deflector unit cell for R, G and B frequency responses, according to one embodiment.

[0034] FIG. 15A shows an example of a transmissive metalens filter that focuses narrow band optical radiation, according to one embodiment.

[0035] FIG. 15B shows a graph of normalized power of filtered and focused optical radiation versus wavelength, according to one embodiment.

[0036] FIG. 16A shows a reflective metalens filter that focuses narrow band optical radiation, according to one embodiment.

[0037] FIG. 16B shows a graph of normalized power of filtered and focused optical radiation versus wavelength, according to one embodiment.

[0038] FIG. 17A illustrates a unit cell of an exemplary narrowband frequency selective filter, according to one embodiment.

[0039] FIG. 17B shows a graph of magnitude versus radius selection for an array of multiple passive deflector elements, according to one embodiment.

[0040] FIG. 17C shows a graph of phase shift for various radius selections of an array of multiple passive deflector elements, according to one embodiment.

[0041] FIG. 17D illustrates an example block diagram of an array of passive deflector elements for use in a unit cell of a frequency selective filter, according to one embodiment.

[0042] 18A-18F show an exemplary method for fabricating a metalens having an array of passive deflector elements having various diameters extending from a substrate, according to one embodiment.

[0043] 19A-19D show another exemplary method for fabricating a metalens having an array of passive deflector elements having various diameters extending from a substrate, according to one embodiment.

[0044] FIG. 20A illustrates a subpixel of a complementary metal-oxide semiconductor (CMOS) digital imaging sensor with a microlens and a color filter according to one embodiment.

[0045] FIG. 20B shows a sub-pixel of a digital imaging sensor that uses a metalens to filter and refract optical radiation, according to one embodiment.

[0046] Detailed Description Various embodiments, systems, devices, and methods relating to the controlled deflection of incident optical radiation are described herein. Examples are described herein for reflective optics that reflect incident optical radiation. Examples are also described herein for optically transmissive optics that refract, deflect, or otherwise modify optical radiation passing through the optically transmissive optics. In some examples, electronic displays, such as RGB LED displays, include variations of the metalenses described herein. Additionally, the metalenses described herein may be used in combination with waveguides for optical transmission and / or near eye displays (NEDs), such as head mounted displays (HMDs) and wearable displays. An input coupler may be formed using variations of the metalenses described herein such that an image source is coupled to the waveguide. The waveguide may convey the optical radiation that forms the image to an output coupler that includes another metalens according to one of the embodiments described herein.

[0047] The output coupling metalens may deflect and focus the optical radiation (e.g., based on frequency and / or using a frequency selective filter) to form an image that is visible to one eye of a user. In some embodiments, the output coupling metalens may be used to deflect and focus the optical radiation into both eyes of a user, or into the eyes of multiple users, as a stereoscopic or duplicated image.

[0048] According to various embodiments, an electronic display may include a multi-pixel light emitting diode (LED) display layer such that at least three different color LED subpixels (e.g., a red subpixel, a green subpixel, and a blue subpixel in the case of an RGB display) are used to generate light emission of different wavelengths (e.g., visible light of different colors). The metalens layer may include multiple metalens subpixels. Each metalens subpixel may correspond to one LED subpixel of the multiple LED subpixels. In some embodiments, the multi-frequency metalens subpixel may be responsive to multiple frequencies such that a single multi-frequency metalens subpixel may be used for each pixel of an RGB display.

[0049] The metalens subpixels deflect the light emission from each corresponding LED subpixel to a target deflection angle for focusing, image replication, color separation, and / or other deflection purposes. Each metalens subpixel includes an array of passive deflector elements having various diameters (e.g., a two-dimensional array for a two-dimensional LED subpixel). The passive deflector elements extend from the substrate (e.g., perpendicular to the substrate, substantially perpendicular to the substrate, or at an angle to the substrate). The passive deflector elements are arranged in a repeating pattern of deflector element diameters with a constant center-to-center element spacing and / or a frequency-dependent center-to-center element spacing.

[0050] Various embodiments of the metalenses described herein may be used in combination with imaging sensors, such as, for example, charge-coupled device (CCD) sensor arrays or complementary metal oxide semiconductor (CMOS) sensor arrays. For example, various embodiments of the metalenses described herein may be utilized in place of frequency masks, filters, microlenses, and other optical elements in CCD and CMOS digital image sensors. Frequency selective metalens can be tuned (i.e., configured with particular deflector element dimensions and deflector element patterns) to filter and / or deflect (e.g., refract or reflect) optical radiation received by each pixel or subpixel in a digital imaging sensor.

[0051] The repeating pattern of deflector element diameters may include passive deflector elements having any number of different diameters. Some of the illustrated embodiments include passive deflector elements having six different diameters. The passive deflector elements are arranged in a repeating pattern with a constant center-to-center spacing. In other embodiments, the number of passive deflector elements having different diameters may be less than six or more than six (e.g., eight different diameters, ten different diameters, or tens of different diameters). In some embodiments, the height that each passive deflector element extends from the substrate at a given metalens subpixel is constant. In fact, in some embodiments, the height that each passive deflector element extends from the substrate may be constant for all metalens subpixels, regardless of their operating frequency. Thus, the repeating pattern of the diameters of the deflector elements may vary based on the operating frequency, but the heights of the deflector elements may all be the same.

[0052] As described herein, the passive deflector elements may be polarization independent or polarization dependent. For a given frequency, the polarization dependent passive deflector elements may extend to a shorter height from the substrate than the polarization independent passive deflector elements, but the pattern of deflector element diameters may remain substantially the same.

[0053] The polarization-independent passive deflector elements may have a height-to-diameter (height:diameter) aspect ratio greater than 1. That is, the height of each polarization-independent passive deflector element is generally greater than its diameter. In contrast, the polarization-dependent passive deflector elements may have a height:diameter aspect ratio less than 1. That is, the height of each polarization-dependent passive deflector element is generally less than its diameter.

[0054] Embodiments of metalens utilizing polarization-dependent passive polarizer elements may include a polarizing filter that polarizes the optical radiation before it is deflected by the polarizer elements. For example, a polarizing layer may be disposed on the substrate between the substrate and the polarization-dependent passive polarizer elements. In such embodiments, the polarization-dependent passive polarizer elements may extend from the substrate through the polarizing layer or from the polarizing layer on the substrate. In some embodiments, the substrate and polarizing layer may be combined as, or may be described in combination as, a polarizing substrate.

[0055] The exact shape and size of the deflector elements may depend on the fabrication process and target operating characteristics utilized. In many embodiments, including the illustrated examples, the deflector elements are substantially cylindrical in shape and extend perpendicular to (e.g., extend perpendicular to) the plane of the underlying substrate. Cylindrical deflector elements can be described as having a diameter (D), a height (H), and an on-center nearest neighbor interelement spacing (P). A metalens subpixel may include many unit cells, each unit cell including a cylindrical deflector element extending from the substrate. A metalens subpixel may be formed by combining many unit cells in a two-dimensional array with cylindrical deflector elements of various diameters (e.g., in a repeating pattern of multiple deflector element diameters).

[0056] In some embodiments, the cylindrical deflector element may have a cavity or recess formed therein. The cavity may be cylindrical and may extend only partially into the cylindrical deflector element. For example, the depth of the cavity may be half the height of the cylindrical deflector element, less than half the height of the cylindrical deflector element, or more than half the height of the cylindrical deflector element. In some embodiments, the cavity may be filled with air or other material having a different electromagnetic permittivity than the deflector element.

[0057] Although many of the metalenses described herein are described in the context of electronic displays, the metalenses may be used for other purposes and applications. In various embodiments, a metalens includes an array of passive deflector elements having various diameters extending from a substrate having a repeating pattern of deflector element diameters. The center-to-center element spacing of the passive deflector elements may be selected as a function of the operating wavelength of the optical metalens. Each passive deflector element has a height that is less than a minimum wavelength in an operating bandwidth and a width that is less than the minimum wavelength in the operating bandwidth.

[0058] The repeating pattern of polarizer element diameters in the optical metalens includes a plurality of passive polarizer elements having at least six different diameters. Again, in some embodiments, the passive polarizer elements may be polarization independent. When used in combination with a polarizer or polarizing layer, the passive polarizer elements may be polarization dependent.

[0059] In one particular embodiment, an optical metalens configured to deflect red wavelengths of light includes a repeating pattern of deflector element diameters ranging from 80 nanometers to 220 nanometers. The exact height and spacing may vary based on the wavelength, the target deflection response, and the manufacturing process. However, in one particular embodiment, the deflector element height is 280 nanometers and the nearest neighbor element spacing is about 230 nanometers. In another particular embodiment, the deflector element height is 220 nanometers and the nearest neighbor element spacing is about 250 nanometers.

[0060] Again, the specific dimensional and spacing features may vary based on the wavelength, target deflection response, and / or manufacturing process, but specific examples are provided herein to facilitate a complete understanding of the systems, methods, and apparatus described herein. In one embodiment, the optical metalens is configured to deflect light of green wavelengths and has a repeating pattern of a plurality of polarization-independent passive deflector elements having diameters in the range of 80 nanometers to 150 nanometers. In one embodiment, the optical metalens is configured to deflect light of blue wavelengths and has a repeating pattern of a plurality of polarization-independent passive deflector elements having diameters in the range of 40 nanometers to 140 nanometers, or in some embodiments a narrower range (e.g., 80 to 140 nanometers). In one particular embodiment, the optical metalens for blue wavelengths of light has a repeating pattern of a plurality of deflector elements having diameters in the range of 80 nanometers to 140 nanometers.

[0061] In some embodiments, each metalens or each metalens subpixel includes a number of unit cells arranged in a one-dimensional or two-dimensional array. In some embodiments, each unit cell may include a single deflector element, and the array of deflector elements may be configured for a single frequency response (or a narrowband frequency response). In other embodiments, each unit cell may include a number of deflector elements, such that a multi-frequency response is provided by the array of deflector elements.

[0062] In another embodiment, the metalens is used within a transmissive medium to form a frequency-selective optical filter. For example, a frequency-selective optical filter may be conceptualized as a two-dimensional array of subwavelength unit cells, each unit cell including an optically transmissive medium and an array of passive deflector elements having various diameters disposed within the optically transmissive medium. Center-to-center element spacing of the passive deflector elements may be selected to reflect optical radiation within a target bandwidth to a focal point. Optical radiation outside the target bandwidth (e.g., optical radiation in a narrow bandwidth between 10 and 100 nanometers) is deflected by or passes through the optically transmissive medium.

[0063] An understanding of conventional optical lenses may be helpful in understanding the possible uses and functions of the various embodiments and applications of the metalenses described herein. Conventional optical lenses and mirrors (e.g., glass or acrylic lenses) are formed with a curvature to change the optical path of incident optical radiation. Multiple lenses and / or multiple mirrors having different refractive indices, curvatures, coatings, and other characteristics may be combined such that a particular optical goal is achieved.

[0064] 1A-1C show example optical paths through a concave optical lens 110, a convex optical lens 120, and a planar optical lens 130. Specifically, Fig. 1A shows an example of a concave lens 110 that receives incident optical radiation 115 and diverges it as diverging optical radiation 117. Fig. 1B shows incident optical radiation 125 converging as converging optical radiation 127 when passing through a convex lens 120.

[0065] 1C shows incident optical radiation 135 incident at an angle to the flat surface of plate optical lens 130. Output optical radiation 137 is shifted as it passes through plate optical lens 130. The degree or amount of phase shift is based on the difference between the refractive index of the surrounding medium (e.g., air, water, waveguide, etc.) and the refractive index of plate optical lens 130. Convex, concave, and other shaped mirrors can also be used to achieve other manipulations of the incident optical radiation.

[0066] Metamaterial-based lenses and mirrors may be formed as relatively thin (e.g., <1 mm) elements that provide controlled deflection without curvature. As described herein, the substrate surface may be configured as a transmissive surface that passes optical radiation or as a reflective surface that reflects optical radiation. Subwavelength-scale features may be patterned on the surface of the substrate to controllably deflect incident optical radiation to obtain a target optical radiation at any angle between 0° and 180°. Such devices are referred to herein as metalenses. Various embodiments and variations of metalenses are described herein. Metalenses is broadly defined herein to include both transmissive and reflective devices.

[0067] In some embodiments, subwavelength-scale features may be formed on more than one surface of a substrate. For example, subwavelength-scale features may be formed on a light-receiving surface of a transmissive substrate and on an output surface of the transmissive substrate. Metalens may be used to deflect optical radiation in free space (e.g., air) or to couple optical radiation between free space and another transmissive medium (e.g., a waveguide, a conventional optical lens, a fiber optic transmission line, etc.).

[0068] In various embodiments, a surface of the substrate (or surfaces of the substrate) is patterned with an array of deflector elements that may be uniformly spaced, periodically spaced, non-periodically spaced, and / or arranged in a repeating pattern, according to various embodiments calculated, estimated, modeled, or optimized to achieve a particular target deflection pattern.

[0069] Each deflector element in the array of deflector elements may have sub-wavelength dimensions such that the deflector element array collectively exhibits metamaterial behavior over a relatively narrow band of optical radiation (e.g., a target operating bandwidth). In some embodiments, the deflector elements may extend substantially orthogonal to a planar surface of the substrate. In applications where the metalens is used in conjunction with an RGB LED display, the fall off frequency or cutoff frequency of the narrowband response may not be as important because the frequencies of red, green, and blue light are relatively far apart on the frequency spectrum.

[0070] The contact surface of the deflector element that contacts the substrate may be circular, elliptical, square, rectangular, n-sided polygonal, or another shape. The deflector element may extend from a flat surface to a height greater than the length or width dimension of the deflector element. For example, each of the multiple deflector elements may have a circular contact surface with a diameter smaller than the smallest wavelength in the operating bandwidth and may extend as a pillar from the substrate to a height H. In various embodiments, the height H may also be smaller than the smallest wavelength in the operating bandwidth. The deflector elements may be described as being sub-wavelength, having sub-wavelength features, having sub-wavelength dimensions, and / or having sub-wavelength element spacing.

[0071] In some examples, each deflector element may be a non-circular pillar extending from the substrate or disposed within the substrate (e.g., as illustrated and described herein in the context of a frequency selective filter). For example, each deflector element may have a square, rectangular, elliptical, hexagonal, or other shaped profile and extend a predetermined height from the substrate. In some embodiments, each of the multiple deflector elements in a deflector element array may extend to the same height. In other embodiments, the heights of the various deflector elements may vary randomly, form a slope with respect to the flat surface of the substrate, and / or conform to a repeating pattern.

[0072] In some examples, each deflector element may be a pillar or nanopillar (e.g., circular or noncircular pillar) formed from titanium dioxide, polycrystalline silicon (poly-Si) and / or silicon nitride, for example, extending from a silicon dioxide or magnesium fluoride substrate. Such pillars, including both circular and noncircular variations, may be referred to as nanopillars due to their subwavelength characteristics and nanometer dimensions. In some embodiments, the substrate may include multiple layers of substrates with various refractive indices and / or may include a combination of various materials. For example, in some embodiments, the substrate may include a Bragg reflector formed as a series of layers of two or more different optical materials with different refractive indices. In various embodiments, the deflector element is a polarization-independent subwavelength passive deflector.

[0073] The deflection pattern produced by a metalens may be influenced or controlled by carefully selecting the height, diameter, spacing, and pattern arrangement of the pillars on the substrate. A metalens may have an array of deflector elements configured to produce a converging deflection pattern, a diverging deflection pattern, or another targeted deflection pattern such that a particular deflection goal is achieved.

[0074] In some embodiments, the metalens includes an array of polarization independent passive deflector elements extending from a transmissive substrate. The metalens may be incorporated as part of a laser-based scanning illumination engine such that collimated optical radiation along one dimension of an output face of the metalens is output in response to received optical radiation incident at a corresponding dimension of the receiving face of the metalens (e.g., the "receiving surface" of the metalens) at various angles of incidence.

[0075] In another embodiment, the angle of the output light emission may vary based on position on the output surface of the metalens. The spatially varying output angle of the deflected light emission may be configured to create multiple depth planes, replicate the pupil, or expand the viewing "eyebox."

[0076] In some embodiments, a single metalens may be responsive to multiple colors of optical radiation, sufficient for combination in a full-color optical display. Different functionalities may be combined within a single lens to respond to various polarization states (e.g., for spatial or temporal multiplexing). In other embodiments, multiple metalenses may be stacked, spatially multiplexed, temporally multiplexed, or otherwise configured for use in a full-color optical display. For example, three different metalenses may be stacked for use in an RGB optical display.

[0077] The stacked metalens may include a first metalens comprised of an array of deflector elements having a dimension to deflect red light emission, a second metalens comprised of an array of deflector elements having a dimension to deflect green light emission, and a third metalens comprised of an array of deflector elements having a dimension to deflect blue light emission. In some embodiments, the metalens may be used in place of injection optics for LED microdisplays or laser-based scanning lighting engines coupled to a waveguide. The metalens may be used to efficiently deflect incident optical radiation from a laser source into the waveguide for total internal reflection.

[0078] Variations of the systems and methods described herein may be used or adapted for use in near-to-eye (NTE) displays (e.g., NTE displays used in wearable technology, smart glasses, augmented reality headsets, virtual reality headsets, head-up displays, etc.). For example, a metalens may be used as part of an NTE display such that optical radiation is collimated into parallel rays that reach a user's eye at "infinite focus." Similarly, a metalens may be used as part of an NTE display such that optical radiation is delivered to a user's eye at target angles that vary spatially along the surface of the metalens, such that an image appears to arise from a target focal depth plane.

[0079] In other embodiments, a metalens may be used as part of an NTE display to duplicate a source image so that the duplicated source image appears to originate from a different location within the field of view (e.g., to facilitate enlarging the effective "eyebox" or pupil replication of the NTE display). Metalens with a wider range of divergence angles (e.g., acting as a diffuser) may be used to magnify the source image in an NTE display so that a wider effective field of view is provided.

[0080] Variations of the systems and methods described herein may be used or adapted for use in light field displays. As used herein, the term "light-field display" is used to describe any of a wide variety of displays that use a variety of techniques to render a three-dimensional image field to one or more users without the use of polarized or active shutter glasses. A light-field display delivers an image to each of the user's eyes at a slightly different perspective, providing binocular parallax for depth perception. Different images are sent to the user's eyes, so that the user perceives the image as a three-dimensional image. As an example, a lenticular lens overlaid on a digital display may be used to deliver a different image to each of the user's eyes. Three-dimensional displays that use lenticular lens technology essentially have a limited field of view.

[0081] The systems and methods associated with the metalenses described herein can be used to create advanced light field displays that can be viewed by multiple users simultaneously and from different perspectives. Similarly, metalenses can be used to create advanced light field displays that deliver imagery from various perspectives to a single user as he moves through the visual field. Multiple variations of the image may be delivered by the metalenses to different spatial locations within the visual field such that the user is provided with a natural-looking three-dimensional imagery that takes into account motion, parallax, occlusion, and / or accommodation.

[0082] Some three-dimensional displays use a two-dimensional array of microlenses (e.g., a microlens array or "MLA"), where the lenslets span the pixels of an underlying electronic display. In such embodiments, the microlenses cause a user to perceive only one of the underlying pixels based on the position of the user's eye relative to each respective lenslet. The metalens-based approach described herein avoids the undesirable fields of view, reduced fill factor, and other optical defects inherent to microlens solutions. In particular, three-dimensional displays that utilize metalenses to deliver different images (e.g., different perspectives of an image) to different locations within the field of view can provide improved optical performance, finer pitch, and a lower profile compared to comparable microlens-based solutions.

[0083] According to various embodiments, the metalenses described herein may be fabricated using any of a wide variety of suitable fabrication techniques, including, but not limited to, nanoimprinting manufacturing techniques, CMOS fabrication techniques, and / or ultraviolet lithography techniques. The relatively low aspect ratio (e.g., the ratio of height to width of each nanopillar deflector element) allows for faster, cheaper, and higher fidelity fabrication compared to competing techniques. For example, an array of nanopillar deflector elements and an underlying substrate may use electromagnetically coupled resonant modes to form an ultra-thin (e.g., less than one wavelength) metalens. In some of the specific embodiments described herein, metalenses using devices having thicknesses less than one-half (½) of the operating wavelength have been demonstrated to have transmission efficiencies of greater than 85%.

[0084] In various embodiments, an array of multiple polarization-independent passive deflector elements patterned on a transmissive or reflective substrate may be adapted to deflect a relatively narrowband of coherent optical radiation (e.g., from a laser light source) in a predetermined direction (optionally based on the origin of the optical radiation (e.g., pixel-by-pixel variation) and / or collimated to provide an effective "infinity focus").

[0085] In other embodiments, an array of polarization-dependent passive deflector elements may be patterned on a transmissive or reflective substrate for use in directing relatively broadband, incoherent light emission (e.g., from an LED light source) in a predetermined direction (optionally based on the origin of the light emission (e.g., pixel-by-pixel variation) and / or collimated to provide an effective "infinity focus").

[0086] As described herein, an array of nanopillar deflector elements may have a repeating pattern of pillars with various diameters, element spacing, and / or heights. The repeating pattern of nanopillar deflector elements may be repeated multiple times, for example, to provide a metasurface lens in which the metalens subpixels have target surface areas corresponding to the surface areas of the LED subpixels of an RGB pixel of an RGB LED display. The diameters, element spacing, and / or heights of the pillars in each array of nanopillar deflector elements may vary based on the frequency / wavelength / color of the corresponding LED subpixel. Thus, a metalens for a single pixel of an RGB display may include three different single-frequency arrays of nanopillar deflector elements "stitched" together or otherwise positioned adjacent to one another to form a multi-frequency metalens with multiple metalens subpixels for each LED pixel. The stitched multi-frequency metalens may be repeated for each pixel of the RGB display. In some cases, the stitched multi-frequency metalens may exhibit some crosstalk between the different single-frequency arrays of nanopillar deflector elements.

[0087] In other embodiments, the entire RGB display may be covered with three different metalens layers. A first metalens layer may be provided having a first pattern of nanopillars to deflect optical radiation having a first frequency. A second metalens layer may be provided having a second pattern of nanopillars to deflect optical radiation having a second frequency. A third metalens layer may be provided having a third pattern of nanopillars to deflect optical radiation having a third frequency. In some cases, vertical stacking of three metalens layers may reduce the overall efficiency of light transmission due to multilayer reflections and other losses.

[0088] In another embodiment, a multi-frequency metalens for a multicolor display (e.g., an RGB display, a two-color display, or other display) may be embodied as an in-plane spatially multiplexed array of interwoven frequency-specific nanopillars. The spatially multiplexed array of frequency-specific nanopillars may include sub-unit cells having a number of pillars equal to or greater than the number of independent frequencies to be deflected. The periodicity of the sub-unit cells is sub-wavelength and selected for zero-order diffraction. Thus, the periodicity of the sub-unit cells may be selected to be smaller than the smallest wavelength of the frequency to be deflected. For example, if the smallest wavelength to be deflected is 550 nanometers, the maximum periodicity for zero-order diffraction is about 360 nanometers and the maximum periodicity of the sub-unit cells is about 180 nanometers (e.g., Nyquist limit). For blue light having a wavelength less than 500 nanometers, the maximum periodicity for zero-order diffraction will be smaller and the maximum periodicity of the sub-unit cells will be smaller accordingly.

[0089] In some embodiments, the height of the individual pillars may be slightly higher than in other embodiments to accommodate the relatively close spacing determined by the calculated maximum possible periodicity of the sub-unit cells for the zeroth diffraction order to achieve an acceptable phase shift (e.g., in the range of 0 to 2π) for each of the independent frequencies to be deflected. For example, pillar heights of about 200 nanometers to about 400 nanometers may be appropriate, depending on the specific frequencies to be deflected. In one example, the individual pillars have a height of about 300 nanometers.

[0090] For a selected height and periodicity, the simulator or computational module may simulate or calculate the transmission and transmission phase shift for each of the multiple frequencies to be deflected for a range of pillar diameters in each sub-unit cell. Appropriate pillar diameters may be selected to achieve a target performance index and / or controllability. For example, pillar diameters may be selected to provide a transmission of at least 0.7 (e.g., 70%) and a phase shift within the range of 0-2π such that full control of deflection is provided. In some embodiments and applications, lower or higher transmission thresholds may be acceptable and / or partial deflection control (e.g., phase shifts less than 2π) may be sufficient.

[0091] The difference between the target field and the simulated field provides a figure of merit that can be calculated as follows:

number

[0092] In one simulation of a design for a dual frequency response metalens for 650 nanometers and 550 nanometers, a pillar height of 300 nanometers was selected with a sub-unit cell periodicity of 180. The simulated first-order diffraction efficiencies were 0.93 and 0.92 for wavelengths of 550 nanometers and 650 nanometers, respectively. Each repeating unit cell of the simulated metalens achieved a phase shift range of greater than 2π through six unique sub-unit cells with two pillars of various diameters in each sub-unit cell.

[0093] The generalized description of the systems and methods herein may be used and / or adapted for use in a wide variety of industrial, commercial and personal applications. Similarly, the systems and methods described herein may be used with or utilize existing computing devices and infrastructure. Some of the infrastructure that may be used with the embodiments disclosed herein is already available, such as, for example, general purpose computers, computer programming tools and techniques, digital storage media, and communication links. A computing device or controller may include a processor, such as, for example, a microprocessor, a microcontroller, logic circuits, and the like.

[0094] A processor may include one or more special purpose processing devices, such as, for example, an application-specific integrated circuit (ASIC), a programmable array logic (PAL), a programmable logic array (PLA), a programmable logic device (PLD), a field-programmable gate array (FPGA), or other customizable and / or programmable devices. A computing device may also include machine-readable storage devices, such as, for example, non-volatile memory, static RAM, dynamic RAM, ROM, CD-ROM, disks, tapes, magnetic memory, optical memory, flash memory, or other machine-readable storage media. Various aspects of certain embodiments may be implemented using hardware, software, firmware, or a combination thereof.

[0095] The components of the disclosed embodiments, as generally described and illustrated in the figures herein, may be arranged and designed in a wide variety of different configurations. Furthermore, features, structures, and operations associated with one embodiment may be applied to or combined with features, structures, or operations described with another embodiment. In many cases, well-known structures, materials, or operations have not been shown or described in detail to avoid obscuring aspects of the disclosure. The system and method embodiments provided within this disclosure are not intended to limit the scope of the disclosure, but are merely representative of possible embodiments. In addition, the steps of the method need not necessarily be performed in any particular order or sequence, nor need the steps be performed only once.

[0096] 2A shows a top view of an exemplary representation of a pattern of deflector elements 210 for a metalens structure, according to one embodiment. As shown, the deflector elements 210 may be patterned with a uniform square grid of deflector elements 210 with uniform spacing between adjacent or nearest neighboring deflector elements. Additionally, the deflector elements 210 may be configured with a uniform height. In the illustrated example, the deflector elements 210 include circular pillars arranged in a repeating pattern of multiple pillar diameters.

[0097] 2B shows a close-up perspective view of an exemplary representation of a pattern of deflector elements in the metalens of FIG. 2A , according to one embodiment. As shown, the array of deflector elements 220 includes a uniformly spaced arrangement of circular pillars extending from a substrate. The deflector elements 220 have a variety of pillar diameters that increase along one dimension (left to right) and are constant along the other dimension (top to bottom). Alternative patterns of pillar diameters may be used such that a target deflection pattern is achieved.

[0098] 3A shows an example schematic diagram of a side view of a metalens 300 with multiple nanopillar deflector elements 330 disposed on a substrate 350, according to one embodiment. As shown, the nanopillar deflector elements 330 may have a uniform height H and varying diameter D. In the illustrated example, the nanopillar deflector elements 330 are evenly spaced apart with a nearest neighbor center-to-center spacing distance P. The spacing between the centers of adjacent or nearest neighbor nanopillars may be constant, regardless of the pillars' varying diameters. As described herein, the nanopillar dimensions, pattern, and spacing are selected to achieve a target deflection pattern (e.g., deflection angle, dispersion, collimation, focusing, etc.) and a target frequency response (e.g., a target operating bandwidth of the optical radiation).

[0099] FIG. 3B shows an exemplary diagram of the metalens 300 of FIG. 3A operative to reflect incident optical radiation 370 as polarized optical radiation 375 at a target deflection angle, according to one embodiment.

[0100] FIG. 3C shows an exemplary diagram of the metalens 300 of FIG. 3A that transmits and directs incident optical radiation 371 as optical radiation 376 deflected at a target deflection angle, according to one embodiment.

[0101] 4A-4B show a metalens for use with a laser scanning subsystem, according to various embodiments. As shown and labeled, a laser source 450 may send coherent optical radiation to a scanning mirror 440. The scanning mirror 440 mechanically moves between a first position and a second position to scan the laser along a dimension (from left to right on the page). In FIG. 4A, optical radiation 410 from the laser source 450 is incident on the left side of the metalens at a first angle of incidence when the scanning mirror 440 rotates counterclockwise (shown in solid lines). Optical radiation 410 from the laser source is incident on the right side of the metalens at a second angle of incidence when the scanning mirror rotates clockwise (shown in dashed lines).

[0102] As shown, metalens 400 may be configured to transmit and deflect incident optical radiation as collimated polarized optical radiation 420 that propagates in a uniform direction along the length of the metalens 400. In such an embodiment, an array of deflector elements may be patterned on a substrate with dimensions, spacing and heights that compensate for the different angles of incidence of the optical radiation 410 as the scanning mirror rotates.

[0103] 4B, a metalens may include an array of deflector elements patterned on a substrate to have dimensions, spacing and heights that direct output optical radiation at different exit angles 420 and 421 depending on the location where the optical radiation is received. The effective deflection pattern of the metalens may be selected to achieve a targeted optical objective, such as, for example, creating multiple depth planes, replicating the pupil, or enlarging the viewing eyebox.

[0104] 5A shows an exemplary system having a metalens 500 and a waveguide 560 for use with a laser scanning subsystem including a laser source 550 and a scanning mirror 540, according to one embodiment. According to the illustrated embodiment, the metalens 500 may provide functionality equivalent to injection optics in a laser scanning illumination engine. In some embodiments, the metalens (or just an array of deflector elements) may be fabricated directly on the waveguide substrate. Given the sub-wavelength thickness of the metalens 500, this system may be much more compact and / or efficient than a similar system using traditional injection optics. The metalens 500 may deflect the received optical radiation 510 into the waveguide 560 for total internal reflection and / or transmission at 520 along the length of the waveguide 560.

[0105] 5B shows an exemplary display system utilizing input metalens coupler 565 and output metalens coupler 566 in conjunction with a waveguide 560, according to one embodiment. The display engine 570 may generate light radiation as part of an RGB display (e.g., via an LED array of multiple RGB pixels). The input metalens coupler 565 may combine the generated RGB light radiation for transmission along the length of the waveguide 560. The output metalens coupler 566 may receive the transmitted light radiation and separate it from the waveguide 560 for visualization by a user (e.g., via frequency-selective focusing onto a target plane).

[0106] 6A shows an example of a metalens unit cell 600 having a cylindrical polarizer element or "nanopillar" 620 for use with a red laser, according to one embodiment. The nanopillar 620 extends from a substrate 610 into another medium, such as, for example, air 630, other gas, or vacuum. The air 630, other gas, or vacuum may be enclosed in an enclosure, as shown, or the nanopillar 620 may extend into free space, which may be filled with air during normal use in some usage scenarios.

[0107] In the illustrated example, the center-to-center spacing P of adjacent nanopillars 620 is 456 nanometers. The height H of each nanopillar 620 may be 150 nanometers. The diameter D of the nanopillars 620 in the array of nanopillars may vary from about 160 nanometers to about 340 nanometers. The particular pattern of diameters, spacing, and heights of the nanopillars may be selected to achieve a target deflection pattern (e.g., deflection angle, dispersion, collimation, focusing, etc.).

[0108] In the illustrated example, the substrate 610 may be SiO2, which has a refractive index of about 1.45. The deflector elements, shown as cylindrical nanopillars 620, may be poly-Si, which has a refractive index of about 3.8. Air 630 or other surrounding fluids (gases, oils, liquids, etc.) or other materials may have a relatively low refractive index. For example, air 630 may have a refractive index of about 1.0.

[0109] 6B shows a graph 650 of phase shift values ​​for various diameters of cylindrical polarizer elements (i.e., nanopillars) in a unit cell of a metalens illuminated by a red laser having a wavelength of 635 nanometers, according to one embodiment. As shown, for diameters between 160 nanometers and 340 nanometers, the incident red laser light exhibits a phase shift of between about 100 degrees and about 360 degrees.

[0110] In the case of a coherent illumination source, such as a laser illumination source, each of the deflector elements in the array of deflector elements may be cylindrically shaped (e.g., a nanopillar) and may operate in a resonance mode having a height H that is less than or equal to a minimum diameter D in the array of deflector elements. Such deflector elements may be described as having an aspect ratio of less than 1 (e.g., H / D<1). Thus, the deflector elements of a metalens illuminated with laser light may be cylindrical nanopillars and may operate in a resonance mode having an aspect ratio of less than about 1.

[0111] 6C shows another example of a metalens unit cell 601 with a cylindrical cavity 622 formed in the cylindrical deflector element 621, according to one embodiment. The cylindrical deflector element 621 may extend perpendicular (i.e., at a right angle) to the plane of the substrate 611. The element spacing P of the exemplary unit cell 601 in the metalens may be 385 nanometers, and the cylindrical deflector element 621 may extend to a height of about 120 nanometers from the substrate 611. The cylindrical cavity 622 is formed in the cylindrical deflector element 621. The cylindrical cavity 622 has a radius R that is smaller than the radius R0 of the cylindrical deflector element 621. i (e.g., a percentage or ratio of radius R0).

[0112] The cylindrical deflector element 621 may extend into a region 631 of free space filled with air or another fluid. The diameter of the cylindrical deflector element 621 and the diameter of the cylindrical cavity 622 may each be selected based on a target frequency response. The metalens may be formed as a two-dimensional array of unit cells of cylindrical deflector elements 621 having various diameters within a range of diameters selected for a target deflection pattern within the operating frequency range.

[0113] 6D illustrates a side cross-sectional view of the exemplary unit cell of FIG. 6C, according to one embodiment. As shown, the cylindrical deflector element 621 extends from the substrate 611 to have a height H of 120 nanometers. In the illustrated example, the cylindrical cavity 622 has a depth of 60 nanometers. Alternative cavity depths and ratios of cavity depth to deflector element height may be used based on the target deflection pattern and target frequency response.

[0114] 7A illustrates an example of a display system 700 that includes a metalens 730, an array of light emitting diodes (LED array) 720, and a polarizer or polarizing filter 710. According to one embodiment, the display system 700 may be specifically configured to redirect light emission to form a light field. As shown, light emission from different pixels is directed in different directions such that different images are provided to a user depending on the user's position relative to the field of view of the display system 700.

[0115] According to various embodiments, any of a wide variety of illumination sources may be utilized, including LEDs, micro LEDs, OLEDs, etc. Compared to laser sources, LED illumination sources have a relatively broad frequency band that is not spatially coherent. The incoherent light from the LED array 720 is polarized by the polarizing filter 710. The polarized light from the polarizing filter 710 is deflected by the metalens 730. The metalens 730 may include pillars having a polarization-dependent rectangular or cylindrical shape to receive and deflect the polarized optical radiation after passing through the polarizing filter 710. In some embodiments, the metalens 730 and polarizing filter 710 may be stacked over a two-dimensional array of LEDs, for example.

[0116] 7B shows an example of a display system 701 having a metalens 731, an LED array 720, and a polarizer or polarizing filter 710 for splitting light emission from each pixel or subpixel of the LED array 720 into two different directions for pixel pupil replication or subpixel pupil replication, according to one embodiment. The polarizer elements of the metalens 731 are illuminated by incoherent light from the LED array 720 after passing through the polarizing filter 710. As previously mentioned, the polarizer elements may be polarization-dependent rectangular or cylindrical pillars operating in a resonant mode having a height:diameter aspect ratio of less than about 1. That is, the height of each polarizer element may be less than the respective polarizer element diameter. In some cases, the heights of the polarizer elements in a metalens are all the same (i.e., constant), and this constant height of the polarizer elements is less than the minimum diameter used in the array of polarizer elements forming the metalens.

[0117] In alternative embodiments, the metalens may include multiple polarization-dependent rectangular pillars, but omit the polarizer 710 shown in FIG. 7B. In such embodiments, the metalens is responsive to polarize optical radiation of one or more specific polarization states. In one exemplary embodiment, the metalens may include multiple rectangular pillars responsive to one polarization state intermixed (e.g., periodically or randomly) with multiple rectangular pillars responsive to a second polarization state. A metalens having intermixed rectangular pillars and responsive to two or more different polarization states may perform different lens functions based on the different polarization states of the incident optical radiation. For example, a metalens may be configured to deflect right-handed circularly polarized light to a first angle (e.g., to a user's right eye) and deflect left-handed circularly polarized light to a second angle (e.g., to a user's left eye).

[0118] 8A shows an example of a display system 800 having a metalens 830 working with an LED array 820 but without a polarizer or polarizing layer, according to one embodiment. If the polarizing filter 710 of FIG. 7A is omitted, the multiple polarizer elements of the modified metalens 830 may have a circular profile (e.g., cylindrical polarizer elements) and may be polarization independent. As previously discussed, the light emission from the LED array 820 exhibits polarization incoherence, spectral incoherence, and spatial incoherence. In such an embodiment, the polarizer elements may be designed and configured to accommodate the incoherent and unpolarized light from the LED array 820, as described herein.

[0119] In contrast, the deflector elements of a metalens that is illuminated with laser light according to various embodiments described herein may be cylindrically shaped (e.g., nanopillars) and may operate in a resonant mode with a height:diameter aspect ratio of less than about 1. In contrast, the deflector elements of a metalens that is illuminated with incoherent light (e.g., from an array of LEDs) that has been passed through a polarizing filter may be rectangular shaped (having polarization dependence) and may operate in a resonant mode with a height:diameter aspect ratio of less than about 1.

[0120] In contrast to the previously described embodiments, as shown in FIG. 8A, the deflector elements of metalens 830 illuminated with incoherent light without a polarizing filter may be cylindrical in shape, may be polarization independent, and may operate in a waveguide mode with a height greater than the diameter of the largest deflector element used in the array of deflector elements. Thus, the height:diameter aspect ratio is greater than 1. For example, the height of each nanopillar of metalens 830 may be from about 1.1 to about 8.0 times the diameter of the largest nanopillar used in the array of nanopillars, depending on the particular wavelength of light and the targeted phase shift. The illustrated display system 800 utilizes feature sizes of tens or hundreds of nanometers, and is therefore compatible with the highest pixel density displays currently available, including microLED displays.

[0121] 8B shows an example of a display system 801 having a metalens 831 and an LED array 820, but no polarizer, according to one embodiment. In the illustrated embodiment, the metalens 831 may be composed of circular or cylindrical nanopillars having an aspect ratio greater than 1 to operate in a waveguide mode. According to one embodiment, the specific diameter and spacing of the nanopillars of metalens 831 may be selected to split the light emission from each pixel of the LED array 820 into two different directions for sub-pixel pupil replication.

[0122] FIG. 9 illustrates a portion of an exemplary LED display 920 and various levels of detail of a tuned metalens 931 having a plurality of RGB pixels, according to one embodiment. As shown, the LED display 920 includes a red subpixel, a green subpixel, and a blue subpixel. The red subpixel, the green subpixel, and the blue subpixel together form an RGB pixel. The tuned metalens 931 includes a two-dimensional array of deflector elements having a pattern of element spacings and diameters selected to produce a target deflection pattern (e.g., a reflective transmission angle or a refractive transmission angle) for each LED subpixel. For example, the two-dimensional arrangement of the deflector elements for a blue subpixel is different from the two-dimensional arrangement of the deflector elements for a red subpixel and the two-dimensional arrangement of the deflector elements for a green subpixel within the same RGB pixel. The metalens 931 can be described as having tuned metalens subpixels corresponding to the plurality of LED subpixels of the LED display 920.

[0123] In some embodiments, as described herein in the context of pixel or sub-pixel duplication, light field generation and / or 3D image generation, etc., the light from each LED sub-pixel in a given RGB pixel may be directed in the same direction, in different directions, or split to deliver to two different locations.

[0124] A simplified pattern 940 of deflector elements is shown for each of a green subpixel metalens 941, a blue subpixel metalens 942, and a red subpixel metalens 943. Each subpixel metalens 941, 942, and 943 includes a plurality of deflector elements having a repeating pattern of element spacing and diameters selected to provide a target deflection angle. Also shown is an example of a repeating pattern 950 of nanopillars on a substrate. The number of pillars in each repeating pattern, the pattern of diameters, diameter range, and other characteristics of the individual pillars may vary according to the particular operating frequency and target deflection angle or pattern.

[0125] With respect to the pattern 940 of deflector elements and the exemplary repeating pattern 950 of nanopillars on a substrate, the following specific examples of center-to-center spacing P, height H, and diameter D are provided. According to one particular embodiment, the deflector elements of the green subpixel metalens 941 may have a height H of about 210 to about 280 nanometers and a center-to-center spacing P of about 160 to about 2000 nanometers, for example for green light having a wavelength of about 550 nanometers. The height H and center-to-center spacing P may be adjusted or specified based on a particular frequency or frequency range of the green light.

[0126] In the illustrated embodiment, the height H of the deflector elements of the green subpixel metalens 941 is about 260 nanometers and the center-to-center spacing P is about 180 nanometers. In a different embodiment, the deflector elements of the green subpixel metalens 941 may be configured to have a height H of about 220 nanometers and a center-to-center spacing P of about 190 nanometers. The repeating pattern of deflector elements may include deflector elements having diameters between 80 nanometers and 150 nanometers, for example. The overall size (length and width) of the green subpixel metalens 941 may be selected to correspond to the dimensions of the green subpixels 921 of the LED display 920. In applications in which the metalens 931 is used for imaging, the overall size (length and width) of the green subpixel metalens 941 may be selected to correspond to the dimensions of the green photosensors of an imaging sensor array.

[0127] In the illustrated example, the diameters D of the nanopillars in each repeating row of nanopillars in the green subpixel metalens 941 range from about 80 nanometers to about 140 nanometers to achieve a phase shift approaching or exceeding the 2π range. As discussed above, in some embodiments, a wider range of diameters (e.g., 80 nanometers to 150 nanometers) may be used to achieve a range of achievable phase shifts suitable for a particular application. A target pattern of phase shifts across the two-dimensional arrangement of the repeating rows of nanopillars in the green subpixel metalens 941 may be selected to achieve a target deflection pattern. Additionally, the number of nanopillars in each row of repeating nanopillars of varying diameters may be determined based on the target deflection pattern and the particular frequency or frequency range of green light. The total number of rows and columns of the repeating pattern of nanopillars of varying diameters may depend on the overall length and width of the green subpixel metalens 941.

[0128] The deflector elements of the blue subpixel metalens 942 may have a height H of about 210 to about 260 nanometers and a center-to-center spacing P of about 160 to about 200 nanometers, for example, for blue light having a wavelength of about 490 nanometers. Again, the height H and center-to-center spacing P may be adjusted or specified based on the particular frequency or frequency range of the blue light. In the illustrated embodiment, the height H of the deflector elements of the blue subpixel metalens 942 is about 260 nanometers and the center-to-center spacing P is about 180 nanometers. The diameter D of the nanopillars within each repeating row of nanopillars in the blue subpixel metalens 942 may be about 40 nanometers to about 140 nanometers, such that a phase shift greater than a 2π range is achieved.

[0129] A target pattern of phase shifts across the two-dimensional arrangement of repeating rows of nanopillars in blue subpixel metalens 942 may be selected to achieve a target deflection pattern (e.g., reflection or refraction angle). Further, the number of nanopillars in each row of repeating nanopillars of varying diameters may be determined based on the target deflection pattern and / or a particular frequency or frequency range of blue light. The total number of rows and columns of the repeating pattern of nanopillars of varying dimensions may depend on the overall length and width of blue subpixel metalens 942.

[0130] In one particular embodiment, the plurality of deflector elements of blue subpixel metalens 942 may be configured to have a repeating pattern with a height H of about 220 nanometers, a center-to-center spacing P of about 180 nanometers, and a deflector element diameter of 80 nanometers to 140 nanometers. As in other embodiments, the overall size (length and width) of blue subpixel metalens 942 may be selected to correspond to the dimensions of the blue subpixels 922 of the LED display 920. In applications in which metalens 931 is used for imaging, the overall size (length and width) of blue subpixel metalens 942 may be selected to correspond to the dimensions of the blue light sensors of an imaging sensor array.

[0131] The multiple deflector elements of red subpixel metalens 943 may have a height H of about 210 to about 280 nanometers and a center-to-center spacing P of 210 to 280 nanometers, for example, for red light having a wavelength of about 635 nanometers. In this particular illustration, red subpixel metalens 943 has a height H of 260 nanometers and a center-to-center spacing P of 230 nanometers. Again, the height H and center-to-center spacing P may be adjusted or specified based on the particular frequency or frequency range of the red light. Additionally, the overall size (length and width) of red subpixel metalens 943 may be selected to correspond to the dimensions of the red subpixels 923 of the LED display 920. In applications in which metalens 931 is used for imaging, the overall size (length and width) of red subpixel metalens 943 may be selected to correspond to the dimensions of the red light sensors of an imaging sensor array.

[0132] In the illustrated embodiment, the height H of the deflector elements of the red subpixel metalens 943 is about 260 nanometers and the center-to-center spacing P is about 230 nanometers. In a different embodiment, the deflector elements of the red subpixel metalens 943 may be configured to have a height H of about 220 nanometers and a center-to-center spacing P of about 250 nanometers. The repeating pattern of deflector elements may include, for example, deflector elements having diameters between 80 nanometers and 220 nanometers.

[0133] In the illustrated example, the diameters D of the nanopillars in each repeating row of nanopillars in the red subpixel metalens 943 range from about 100 nanometers to about 210 nanometers such that a phase shift over a 2π range is achieved. In a different embodiment, the diameters of the nanopillars used in the red subpixel metalens 943 range from about 80 nanometers to about 220 nanometers such that a wider range of achievable phase shifts is provided. A target pattern of phase shifts across the two-dimensional arrangement of the repeating rows of nanopillars in the red subpixel metalens 943 may be selected such that a target deflection pattern (e.g., reflection angle or refraction angle) is achieved. Additionally, the number of nanopillars in each row of repeating nanopillars of varying diameters may be determined based on the target deflection pattern and / or a particular frequency or frequency range of red light. The total number of rows and columns of the repeating pattern of nanopillars of varying dimensions may depend on the overall length and width of the red subpixel metalens 943.

[0134] In the illustrated example, the height of the nanopillars is the same for each of the red subpixel metalens 943, green subpixel metalens 941, and blue subpixel metalens 942, as described above. In alternative embodiments, the height of the nanopillars of each different colored subpixel metalens may be different. In addition, the exemplary LED display 920 includes a green pixel 921, a blue pixel 922, and a red pixel 923. However, it is understood that alternative display color schemes are possible, such as LED displays that include four or more subpixels per pixel (e.g., multiprimary displays, such as those using RGBY subpixels, RGBW subpixels, or RGBYC subpixels). In such embodiments, the tailored metalens may include any number of “subpixel metalens” or “metalens subpixels” that match the number and / or colors of subpixels used in the multiprimary LED display.

[0135] A row of nanopillars of various widths repeated along the length and / or width of a given subpixel metalens may be referred to as a nanopillar row. As described herein, the center-to-center spacing P of adjacent nanopillars in a nanopillar row may be constant. In some embodiments, the center-to-center spacing P of adjacent nanopillars in a nanopillar row may be a function of the frequency of light to be deflected (e.g., refracted or reflected). Thus, the center-to-center spacing P of adjacent nanopillars in a nanopillar row for a subpixel metalens for a blue subpixel may be different from the center-to-center spacing P of adjacent nanopillars in a nanopillar row for a subpixel metalens for a red subpixel or the center-to-center spacing P of adjacent nanopillars in a nanopillar row for a subpixel metalens for a green subpixel.

[0136] The spacing between nanopillars in adjacent nanopillar rows (e.g., across the width or along the length of the subpixel metalens) may be the same as the center-to-center spacing P of adjacent nanopillars in the individual nanopillar rows of the subpixel metalens. Alternatively, the spacing between nanopillars in adjacent nanopillar rows (e.g., across the width or along the length of the subpixel metalens) may be different from the center-to-center spacing P of adjacent nanopillars in the individual nanopillar rows of the subpixel metalens.

[0137] 10A shows an exemplary unit cell 1000 for a red metalens subpixel, according to one embodiment. As shown, a poly-Si cylindrical deflector element 1005 extends from a SiO2 substrate 1003 to have a height of 280 nanometers. The center-to-center element spacing of an array of unit cells forming the red metalens subpixel may be 270 nanometers. The red metalens subpixel may include a unit cell having a deflector element 1005 with a diameter in the range of 80 nanometers to 180 nanometers such that a phase shift over a 2π range is achieved.

[0138] 10B shows a graph 1010 of transmittance values ​​(Y-axis) for various diameters of cylindrical polarizer elements (X-axis) in a metalens unit cell for a red subpixel of an LED display having a wavelength of about 635 nanometers, according to one embodiment. As shown, the minimum transmittance value is greater than 0.85 for all diameters within the range of diameters that allow a phase shift of 0 to 2π.

[0139] 10C shows a graph 1020 of various phase shift values ​​(Y-axis) for various diameters (X-axis) of a cylindrical deflector element for a red subpixel, according to one embodiment. As shown, various possible ranges of deflector element diameters could be used to achieve a phase shift range of 2π. A diameter range of about 80 nanometers to about 180 nanometers provides a phase shift range of 2π.

[0140] FIG. 11A shows an exemplary unit cell 1100 of a green metalens subpixel, according to one embodiment. In the illustrated example, a poly-Si cylindrical deflector element 1105 extends from a SiO2 substrate 1103 to have a height of 280 nanometers. The center-to-center element spacing of an array of unit cells forming a green metalens subpixel may be 270 nanometers. Thus, the element spacing and deflector element height of the red deflector element (1003 in FIG. 10A ) and the element spacing and deflector element height of the green deflector element (1103 in FIG. 11A ) may be the same. However, a green metalens subpixel may include unit cells having deflector elements 1105 with diameters in the range of 80 nanometers to 140 nanometers, such that a phase shift approaching the 2π range is achieved. In applications where a phase shift range of less than 2π is sufficient, a narrower range of diameters may be utilized.

[0141] 11B shows a graph 1112 of transmittance values ​​(Y-axis) versus various diameters of cylindrical polarizer elements (X-axis) in a metalens unit cell for a green subpixel of an LED display having a wavelength of about 550 nanometers, according to one embodiment. As shown, by using a diameter range of 120 nanometers to 190 nanometers, the higher transmission efficiency achievable using smaller diameters may be maintained.

[0142] Figure 11C shows a graph 1122 of various phase shift values ​​(Y-axis) versus various diameters (X-axis) of a cylindrical polarizer element for a green subpixel, according to one embodiment. By comparing Figures 11B and 11C, it can be seen that the design decision of the range of diameters to use in the green metalens subpixel must balance the transmission efficiency and the available phase shift range. Narrowing the range of available phase shift may increase the transmission efficiency, while widening the range of available phase shift may decrease the transmission efficiency.

[0143] 12A shows an exemplary unit cell 1200 for a blue metalens subpixel, according to one embodiment. In the illustrated example, a poly-Si cylindrical deflector element 1205 extends from a SiO2 substrate 1203 to have a height of 280 nanometers. The center-to-center element spacing of an array of unit cells forming the blue metalens subpixel may be 230 nanometers. The blue metalens subpixel may include a unit cell having a deflector element 1205 with a diameter in the range of 40 nanometers to 140 nanometers, such that a phase shift approaching the 2π range is achieved.

[0144] FIG. 12B shows a graph 1214 of transmittance values ​​(Y-axis) for various diameters of a cylindrical polarizer element (X-axis) in a unit cell of a metalens for a blue subpixel of an LED display having a wavelength of approximately 490 nanometers, in accordance with one embodiment.

[0145] FIG. 12C shows a graph 1224 of different phase shift values ​​(Y-axis) versus different diameters (X-axis) of a cylindrical deflector element for a blue subpixel, according to one embodiment.

[0146] 13A shows an example of a unit cell 1300 having two polarizer elements 1305 and 1307 for dual frequency response, according to one embodiment. The sub-unit cell 1300 is configured for zero order diffraction of optical radiation at 550 nanometers and 650 nanometers. As shown, the maximum periodicity for the zero order diffraction is about 360 nanometers, and the maximum periodicity of the unit cell 1300 is 180 nanometers. Each of the two pillars 1305 and 1307 in the unit cell 1300 has a height of about 300 nanometers. The pillars 1305 and 1307 extend from a substrate 1303, such as a SiO2 substrate.

[0147] The difference between the target field and the simulated field provides a figure of merit that can be calculated as follows:

number

[0148] Figure 13B shows a simplified exemplary multicell metalens 1350 having a number of unit cells 1300. As described in connection with Figure 13A, according to one embodiment, the multicell metalens 1350 provides a dual frequency response. The multicell metalens 1350 is formed using a repeating pattern of a number of unit cells 1300 depicted in Figure 13A, but with a variety of diameters for the pillars 1305 and pillars 1307. Multiple multicell metalenses 1350 can be combined in a one or two dimensional array to form a larger one dimensional metalens, a larger two dimensional metalens, a metalens pixel with a targeted dimension, or a metalens subpixel with a targeted dimension.

[0149] 14A shows an example of a unit cell 1400 having three deflector elements 1405, 1407, and 1409 for an RGB display, according to one embodiment. Again, the specific diameters of each of pillars 1405, 1407, and 1409 may be calculated via simulated phase lag for the particular frequencies used in the RGB display.

[0150] FIG. 14B shows an exemplary multicell metalens 1450 having multiple unit cells 1400 for R, G, and B frequency responses, according to one embodiment. The unit cells 1400 of the metalens 1450 are formed via a repeating pattern of multiple unit cells 1400 depicted in FIG. 14A , but with varying diameters of pillars 1405, pillars 1407, and pillars 1409. Multiple multicell metalenses 1450 can be combined in a one- or two-dimensional array to form a larger one-dimensional metalens, a larger two-dimensional metalens, a metalens pixel with targeted dimensions, or a metalens subpixel with targeted dimensions. The illustrated multicell metalens 1450 includes multiple rows of seven pillars with varying diameters, where each row may be responsive to deflect a particular frequency or range of frequencies of optical radiation.

[0151] Figure 15A shows an example of a transmissive metalens filter 1525 that focuses optical radiation in a narrow band to a focal point 1535, according to one embodiment. Optical radiation outside of that narrow band passes through the transmissive metalens filter 1525 without being focused.

[0152] Figure 15B shows a graph 1550 of normalized power of filtered and focused optical radiation versus wavelength, according to one embodiment. In the illustrated embodiment, a 60 nanometer band centered at about 650 nanometers is focused by the transmissive metalens filter 1525 of Figure 5A. Other frequencies are not deflected to the focal point 1535 of Figure 5A. In this manner, the transmissive metalens filter 1525 can be described as a frequency selective metalens, or narrow band filter, and can be used in a variety of applications to control the deflection of a narrow band of optical radiation.

[0153] 16A shows a reflective metalens filter 1625 that reflects and focuses optical radiation in a narrow band to a focal point 1635, according to one embodiment. Optical radiation outside of the narrow band passes through the reflective metalens filter 1625 without being reflected.

[0154] Figure 16B shows a graph 1650 of normalized power of filtered and focused optical radiation versus wavelength, according to one embodiment. Again, a band of optical radiation around 60 nanometers, centered at 650 nanometers, is reflected and focused by the metalens filter 1625 of Figure 6A. Other frequencies are not reflected. Instead, frequencies outside of that narrow band pass through or are slightly deflected to locations other than the focal point 1635 of Figure 6B.

[0155] 17A illustrates an exemplary narrowband frequency selective filter unit cell 1700, according to one embodiment. As shown, a disk-shaped array 1750 of deflector elements is disposed within a substrate 1725. In some embodiments, the unit cell 1700 may be repeated as part of a one-dimensional or two-dimensional array with an element spacing of about 370 nanometers. The substrate 1725 may be formed, for example, from SiO2. In some embodiments, the disk 1750 of deflector elements may include deflector elements having a height of about 100 nanometers.

[0156] FIG. 17B illustrates a magnitude graph 1760 versus radius selection of an array of passive deflector elements in the disk-shaped array of deflector elements 1750 of FIG. 17A, according to one embodiment.

[0157] 17C shows a graph 1775 of phase shift values ​​for various radius selections of the disc-shaped array of passive deflector elements 1750 of FIG. 17A, according to one embodiment. As with the previous embodiment, the radius of the disc-shaped array of passive deflector elements 1750 may be selected such that a target functionality of transparency and tunability is achieved.

[0158] FIG. 17D illustrates an example block diagram of a disk-shaped array 1750 of passive deflector elements for use in the example frequency-selective filter unit cell 1700 described in connection with FIGS. 17A-17C, according to one embodiment.

[0159] 18A-18F show an exemplary method for fabricating a metalens having an array of passive deflector elements having various diameters extending from a substrate, according to one embodiment.

[0160] In Fig. 18A, a fused silica substrate is cleaned. In Fig. 18B, a poly-Si layer is deposited on the fused silica substrate. For example, the poly-Si film may be deposited using a low pressure chemical vapor deposition (LPCVD) process. In other embodiments, a plasma enhanced chemical vapor deposition (PECVD) process, a high-density plasma chemical vapor deposition (HDPCVD) process, and / or any of a wide variety of alternative chemical vapor deposition (CVD) processes may be utilized to deposit the poly-Si layer (or another suitable material) on the fused silica substrate (or another suitable substrate material).

[0161] A photoresist or other resist for lithography may be applied over the deposited poly-Si layer, as shown in Figure 18C. In Figure 18D, a lithographic method, such as E-beam lithography (EBL) or another nanolithography technique, is used to define a pattern of deflector element diameters included in the metalens. As described herein, the pattern of deflector element diameters may be repeated one or more times, and the pattern of deflector element diameters may be selected to provide a target deflection pattern for optical radiation within a target operating bandwidth.

[0162] As shown in FIG. 18E, a reactive ion etch may be used to etch away the undeveloped poly-Si of the resist. In FIG. 18F, the resist may be removed to reveal the poly-Si pillars (or other shaped deflector elements) extending from the fused silica substrate. Although the side views in FIGS. 18A-18E show a one-dimensional row of pillars, it will be understood that the same method can be used to fabricate a two-dimensional array of pillars. This fabrication method may be used to fabricate each metalens pixel or metalens subpixel separately, and then the individual metalens pixels or metalens subpixels can be bonded together. Alternatively, this fabrication method can be used to fabricate a complete two-dimensional array of metalens pixels or metalens subpixels as a single unit.

[0163] 19A-19D show another exemplary method for fabricating a metalens having an array of passive deflector elements having varying diameters extending from a substrate, according to one embodiment. In FIG. 19A, a mold can be used to soft stamp a pattern of pillars having varying diameters into a resist that is sensitive to, for example, ultraviolet light. As shown in FIG. 19B, the resist can be cured or otherwise hardened. For example, a UV-sensitive photoresist can be exposed to ultraviolet light while a mold is soft stamped into the UV-sensitive photoresist.

[0164] As shown in FIG. 19C, the mold may be removed from the hardened resist, leaving behind a pillar-shaped plurality of deflector elements. Reactive ion etching may be used on the remaining layer to produce the final array of pillars extending from the substrate, as shown in FIG. 19D. Again, while the illustrated embodiment includes a one-dimensional row of several pillars, it will be understood that the described fabrication methods may be used to fabricate two-dimensional arrays of pillars or deflector elements having alternative shapes. Additionally, the fabrication methods may be used to fabricate complete two-dimensional arrays of metalens pixels or metalens subpixels, either as a single unit or as multiple sub-unit panels. Multiple such sub-unit panels may be bonded or otherwise configured to form a larger metalens.

[0165] FIG. 20A shows a simplified diagram of a subpixel of a CMOS digital imaging sensor, according to one embodiment. In the illustrated embodiment, red (solid line), green (dashed line), and blue (dotted line) optical radiation is received by a microlens 2035, which refracts it towards a phototransistor 2020 for detection. The refracted optical radiation is filtered by a color filter 2025 based on the color of the subpixel. In this example, the subpixel is a red subpixel of a digital sensing array. Thus, red optical radiation (solid line) passes through to the phototransistor 2020 for detection. Green and blue (dashed and dotted lines) optical radiation is filtered out by the color filter 2025. The exemplary diagram of the subpixel includes a light shielding layer 2015 and an electrode 2010, which may be utilized in some embodiments of a CMOS digital sensing array. In particular, due to limitations of conventional optics, light ray path 2001 is refracted by microlens 2035 towards phototransistor 2020 but is blocked by light blocking layer 2015 .

[0166] FIG. 20B illustrates a subpixel of a digital imaging sensor that uses a metalens 2050 to filter and refract optical radiation, according to one embodiment. As shown, the metalens 2050 may include a number of deflector elements extending from a substrate having a pattern of diameters, element spacings, and heights selected to perform the dual function of refracting red light toward the phototransistor 2020 and filtering out other wavelengths of optical radiation (e.g., green and blue optical radiation). By using the metalens 2050 instead of the microlenses 2035 and color filters 2025, the digital imaging sensor may be much thinner and potentially less expensive to manufacture. In particular, the metalens 2050 may also allow for more control over the deflection (e.g., reflection and / or refraction) of optical radiation. For example, the optical ray path 2002 has been refracted sufficiently (compared to the optical ray path 2001 in FIG. 20A) that it may be received by the phototransistor 2020.

[0167] The various embodiments of the metalenses (both refractive and reflective) described herein may be used in combination with a wide variety of imaging sensing arrays, including RGB imaging sensing arrays that employ CCD technology and RGB imaging sensing arrays that employ CMOS technology. One or more metalenses may be used to provide the functionality of traditional microlens focusing, color filtering, infrared filtering, and / or other filtering and refractive functions. In some embodiments, the same metalens or additional metalenses may be used as a primary focusing lens for an imaging device and / or may be used to supplement a conventional primary focusing lens of an imaging device.

[0168] The present disclosure has been made with reference to various embodiments, including the best mode. However, those skilled in the art will recognize that changes and modifications may be made to the various embodiments without departing from the scope of the present disclosure. While the principles of the present disclosure have been illustrated in various embodiments, many modifications of the structure, arrangement, proportions, elements, materials and components may be made to adapt to particular environments and / or operating requirements without departing from the principles and scope of the present disclosure. These and other changes or modifications are intended to be included within the scope of the present disclosure.

[0169] The present disclosure is to be regarded as illustrative and not in a limiting sense, and all such modifications are intended to be included within the scope of the present disclosure. Moreover, benefits, other advantages, and solutions to problems have been described above with respect to various embodiments. However, the benefits, advantages, solutions to problems, and any element(s) that may give rise to any benefit, advantage, or solution, or any element(s) that may make any benefit, advantage, or solution more significant, should not be construed as critical, essential, or essential features or elements. [Brief description of the drawings]

[0170] [Figure 1A] 1 illustrates examples of light paths through a concave optical lens, a convex optical lens, and a flat optical lens, according to various embodiments. [Figure 1B] 1 illustrates examples of light paths through a concave optical lens, a convex optical lens, and a flat optical lens, according to various embodiments. [Figure 1C] 1 illustrates examples of light paths through a concave optical lens, a convex optical lens, and a flat optical lens, according to various embodiments. [Figure 2A] FIG. 14 shows a top view of an exemplary representation of a pattern of deflector elements for a metalens structure, according to one embodiment. [Figure 2B]FIG. 2B shows an enlarged perspective view of an exemplary representation of a pattern of deflector elements in the metalens of FIG. 2A, in accordance with one embodiment. [Figure 3A] FIG. 13 shows an exemplary diagram of a side view of a metalens having a plurality of nanopillar deflectors disposed on a substrate in accordance with one embodiment. [Figure 3B] FIG. 3B shows an exemplary diagram of the metalens of FIG. 3A operative to reflect incident optical radiation, according to one embodiment. [Figure 3C] FIG. 3B shows an exemplary diagram of the metalens of FIG. 3A for transmitting and directing incident optical radiation, according to one embodiment. [Figure 4A] 1 illustrates a metalens for use in conjunction with a laser scanning subsystem, in accordance with various embodiments. [Figure 4B] 1 illustrates a metalens for use in conjunction with a laser scanning subsystem, in accordance with various embodiments. [Figure 5A] 1 illustrates an exemplary system having a metalens and a waveguide for use in conjunction with a laser scanning subsystem, according to one embodiment. [Figure 5B] FIG. 14 shows an exemplary display system that utilizes input and output metalenses in conjunction with a waveguide, according to one embodiment. [Figure 6A] FIG. 1 shows an example of a unit cell of a metalens having a cylindrical polarizer element for use with a red laser, according to one embodiment. [Figure 6B] FIG. 14 shows phase shift values ​​for various diameters of a cylindrical polarizer element in a unit cell of a metalens illuminated by a red laser, in accordance with one embodiment. [Figure 6C] FIG. 14 shows another example of a metalens unit cell in which a cylindrical cavity is formed in a cylindrical deflector element, in accordance with one embodiment. [Figure 6D] FIG. 6D illustrates a side cross-sectional view of the exemplary unit cell of FIG. 6C, according to one embodiment. [Figure 7A]FIG. 1 shows an example of a display system for forming a light field including a metalens with a plurality of rectangular polarizer elements, an array of light emitting diodes (LED array), and a polarizer, according to one embodiment. [Figure 7B] FIG. 1 shows an example of a display system that includes a metalens with multiple rectangular polarizer elements, an LED array, and a polarizer to split the light emission from each pixel of the LED array into two different directions for pupil replication, according to one embodiment. [Figure 8A] FIG. 1 shows an example of a display system that includes a metalens having multiple polarizer elements operating in a waveguide mode and an LED array, without a polarizer, according to one embodiment. [Figure 8B] FIG. 14 shows another example of a display system that includes a metalens having multiple polarizer elements operating in a waveguide mode and an LED array, without a polarizer, in accordance with one embodiment. [Figure 9] FIG. 1 illustrates a portion of an exemplary LED display and various levels of detail of a tuned metalens having multiple RGB (red, green, blue) sub-pixels, according to one embodiment. [Figure 10A] 1 illustrates an exemplary unit cell for a red metalens subpixel, according to one embodiment. [Figure 10B] FIG. 10B shows transmittance values ​​for various diameters of the cylindrical polarizer element in a unit cell for the exemplary red metalens subpixel of FIG. 10A in accordance with one embodiment. [Figure 10C] FIG. 10B illustrates phase shift values ​​for various diameters of cylindrical deflector elements in a unit cell for the exemplary red metalens subpixel of FIG. 10A , in accordance with one embodiment. [Figure 11A] 1 illustrates an exemplary unit cell for a green metalens subpixel, according to one embodiment. [Figure 11B] FIG. 11B shows transmittance values ​​for various diameters of the cylindrical deflector element in a unit cell for the exemplary green metalens subpixel of FIG. 11A in accordance with one embodiment. [Figure 11C] FIG. 11B illustrates phase shift values ​​for various diameters of cylindrical deflector elements in a unit cell for the exemplary green metalens subpixel of FIG. 11A , in accordance with one embodiment. [Figure 12A] 1 illustrates an exemplary unit cell for a blue metalens subpixel, according to one embodiment. [Figure 12B] FIG. 12B shows transmittance values ​​for various diameters of the cylindrical deflector element in a unit cell for the exemplary blue metalens subpixel of FIG. 12A in accordance with one embodiment. [Figure 12C] FIG. 12B illustrates phase shift values ​​for various diameters of cylindrical deflector elements in a unit cell for the exemplary blue metalens subpixel of FIG. 12A in accordance with one embodiment. [Figure 13A] 1 illustrates an example of a sub-unit cell deflector element having a dual frequency response, according to one embodiment. [Figure 13B] 1 illustrates an exemplary multi-cell deflector unit cell having dual frequency response, according to one embodiment. [Figure 14A] 1 illustrates an example of a sub-unit cell deflector element for an RGB display, according to one embodiment. [Figure 14B] 1 illustrates an exemplary multi-cell deflector unit cell for R, G and B frequency responses, according to one embodiment. [Figure 15A] 1 shows an example of a transmissive metalens filter for focusing narrow band optical radiation, according to one embodiment. [Figure 15B] 1 shows a graph of normalized power of filtered and focused optical radiation versus wavelength, according to one embodiment. [Figure 16A] 1 illustrates a reflective metalens filter for focusing narrowband optical radiation, according to one embodiment. [Figure 16B] 1 shows a graph of normalized power of filtered and focused optical radiation versus wavelength, according to one embodiment. [Figure 17A] 1 illustrates a unit cell of an exemplary narrowband frequency selective filter, according to one embodiment. [Figure 17B]13 shows a graph of magnitude versus radius selection for an array of multiple passive deflector elements, according to one embodiment. [Figure 17C] 13 shows a graph of phase shift for various radius selections of an array of multiple passive deflector elements, according to one embodiment. [Figure 17D] FIG. 1 illustrates an exemplary block diagram of an array of passive deflector elements for use in a unit cell of a frequency selective filter, according to one embodiment. [Figure 18A] FIG. 1 illustrates an exemplary method for fabricating a metalens having an array of passive deflector elements having various diameters extending from a substrate, according to one embodiment. [Figure 18B] FIG. 1 illustrates an exemplary method for fabricating a metalens having an array of passive deflector elements having various diameters extending from a substrate, according to one embodiment. [Figure 18C] FIG. 1 illustrates an exemplary method for fabricating a metalens having an array of passive deflector elements having various diameters extending from a substrate, according to one embodiment. [Figure 18D] FIG. 1 illustrates an exemplary method for fabricating a metalens having an array of passive deflector elements having various diameters extending from a substrate, according to one embodiment. [Figure 18E] FIG. 1 illustrates an exemplary method for fabricating a metalens having an array of passive deflector elements having various diameters extending from a substrate, according to one embodiment. [Figure 18F] FIG. 1 illustrates an exemplary method for fabricating a metalens having an array of passive deflector elements having various diameters extending from a substrate, according to one embodiment. [Figure 19A] FIG. 14 illustrates another exemplary method for fabricating a metalens having an array of passive deflector elements having various diameters extending from a substrate, according to one embodiment. [Figure 19B] FIG. 14 illustrates another exemplary method for fabricating a metalens having an array of passive deflector elements having various diameters extending from a substrate, according to one embodiment. [Figure 19C]FIG. 14 illustrates another exemplary method for fabricating a metalens having an array of passive deflector elements having various diameters extending from a substrate, according to one embodiment. [Figure 19D] FIG. 14 illustrates another exemplary method for fabricating a metalens having an array of passive deflector elements having various diameters extending from a substrate, according to one embodiment. [Figure 20A] 1 illustrates a subpixel of a complementary metal-oxide semiconductor (CMOS) digital imaging sensor with a microlens and a color filter, according to one embodiment. [Figure 20B] 1 illustrates a sub-pixel of a digital imaging sensor that uses a metalens to filter and refract optical radiation, according to one embodiment.

Claims

1. a multi-pixel light emitting diode (LED) display layer using a plurality of LED sub-pixels of at least three different colors to generate light emission of various wavelengths; a metalens layer for a plurality of metalens subpixels corresponding to a plurality of said LED subpixels, the metalens layer deflecting the light emission from each corresponding LED subpixel to a target deflection angle; An electronic display comprising: each metalens subpixel comprises a two-dimensional array of passive deflector elements having varying diameters extending from a substrate having a repeating pattern of center-to-center element spacings and deflector element diameters selected as a function of the wavelength of the optical radiation produced by the corresponding LED subpixel; each of said plurality of passive deflector elements comprises a cylinder having a diameter (D), a height (H) and a center-to-center nearest neighbor element spacing (P); an electronic display, wherein a plurality of passive deflector elements included in one of the plurality of metalens subpixels have a range of diameters (D) based on a phase shift range and a transmittance value of the light radiation produced by the LED subpixel corresponding to the one of the plurality of metalens subpixels.

2. 10. The electronic display of claim 1 , wherein said repeating pattern of deflector element diameters in each metalens subpixel comprises a plurality of passive deflector elements having at least six different diameters.

3. 3. An electronic display as claimed in claim 1 or 2, wherein each passive polarizer element comprises a polarization independent passive polarizer element.

4. the LED display layer includes RGB LED displays; 4. The electronic display of claim 3, wherein in the RGB LED display, each pixel of the LED display layer includes a red LED subpixel, a green LED subpixel and a blue LED subpixel.

5. the metalens subpixel for the red LED subpixel includes a pattern of a plurality of polarization independent passive deflector elements having diameters between 100 nanometers and 210 nanometers; the metalens subpixel for the green LED subpixel comprises a pattern of a plurality of polarization independent passive polarizer elements having diameters between 80 nanometers and 140 nanometers; 5. The electronic display of claim 4 , wherein the metalens subpixel for the blue LED subpixel comprises a pattern of a plurality of polarization independent passive polarizer elements having diameters between 40 nanometers and 140 nanometers.

6. 6. The electronic display of claim 5, wherein the height that each polarization independent passive deflector element extends from the substrate is greater than the maximum diameter of any deflector element in the metalens, such that each deflector element has a height:diameter aspect ratio greater than 1.

7. A multi-pixel light emitting diode (LED) display layer using a plurality of LED subpixels of at least three different colors to generate light radiation of various wavelengths; a metalens layer for a plurality of metalens subpixels corresponding to a plurality of said LED subpixels, the metalens layer deflecting the light emission from each corresponding LED subpixel to a target deflection angle; An electronic display comprising: each metalens subpixel comprises a two-dimensional array of passive deflector elements having varying diameters extending from a substrate having a repeating pattern of center-to-center element spacings and deflector element diameters selected as a function of the wavelength of the optical radiation produced by the corresponding LED subpixel; Each passive deflector element includes a polarization dependent passive deflector element; The electronic display further includes a polarizing layer between the LED display layer and the metalens layer, the polarizing layer polarizing the light radiation produced by the LED display layer.

8. the LED display layer includes RGB LED displays; 8. The electronic display of claim 7, wherein in the RGB LED display, each pixel of the LED display layer includes a red LED sub-pixel, a green LED sub-pixel and a blue LED sub-pixel.

9. 10. The electronic display of claim 8 , wherein each polarization-dependent passive deflector element extends from the substrate a height that is less than a maximum diameter of any deflector element in the metalens, such that each polarization-dependent deflector element has a height:diameter aspect ratio that is less than one.

10. 3. The electronic display of claim 1 or 2, wherein the passive deflector elements in each metalens subpixel have a substantially constant height.

11. 10. The electronic display of claim 1 , wherein the repeating pattern of deflector element diameters comprises a one dimensional repeating pattern of deflector element diameters that is repeated within the two dimensional array of deflector elements in each metalens subpixel.

12. An electronic display as described in claim 1, wherein the diameter (D) of each deflector element varies based on the relative position of the deflector element in the repeating pattern.

13. A multi-pixel light emitting diode (LED) display layer using a plurality of LED subpixels of at least three different colors to generate light radiation of various wavelengths; a metalens layer for a plurality of metalens subpixels corresponding to a plurality of said LED subpixels, the metalens layer deflecting the light emission from each corresponding LED subpixel to a target deflection angle; An electronic display comprising: each metalens subpixel comprises a two-dimensional array of passive deflector elements having varying diameters extending from a substrate having a repeating pattern of center-to-center element spacings and deflector element diameters selected as a function of the wavelength of the optical radiation produced by the corresponding LED subpixel; each of the plurality of deflector elements comprises a cylinder having a diameter (D), a height (H) and a center-to-center nearest neighbor element spacing (P); a diameter (D) of each deflector element varies based on the relative position of the deflector element in the repeating pattern; Each of the cylindrical deflector elements has a cavity formed therein, The cavity has a depth that is less than the height (H).

14. 14. The electronic display of claim 13, wherein the cavity formed in each cylindrical deflector element is cylindrical in shape and filled with air.

15. 1. An optical metalens comprising an array of passive deflector elements having varying diameters extending from a substrate having a repeating pattern of deflector element diameters, a plurality of center-to-center element spacings of the plurality of passive deflector elements are selected as a function of an operating wavelength of the optical metalens; each passive deflector element has a height that is smaller than a minimum wavelength within an operating bandwidth and a width that is smaller than the minimum wavelength within said operating bandwidth; each of said plurality of passive deflector elements comprises a cylinder having a diameter (D), a height (H) and a center-to-center nearest neighbor element spacing (P); an optical metalens, wherein the plurality of passive deflector elements have a range of diameters (D) based on a phase shift range and a transmittance value of optical radiation produced by a corresponding LED subpixel.

16. 16. The optical metalens of claim 15, wherein said repeating pattern of deflector element diameters comprises a plurality of passive deflector elements having at least six different diameters.

17. 17. The optical metalens of claim 15 or 16, wherein a plurality of the passive polarizer elements are polarization independent.

18. 20. The optical metalens of claim 17, wherein the height that each polarization independent passive deflector element extends from the substrate is greater than the maximum diameter of any deflector element in the metalens, such that each deflector element has a height:diameter aspect ratio greater than 1.

19. the optical metalens is configured to deflect red wavelengths of light; 18. The optical metalens of claim 17, wherein diameters of the polarization independent passive deflector elements in the repeating pattern of deflector element diameters range from 80 nanometers to 220 nanometers.

20. the optical metalens is configured to deflect light of green wavelengths; 18. The optical metalens of claim 17, wherein diameters of the polarization independent passive deflector elements in the repeating pattern of deflector element diameters range from 80 nanometers to 150 nanometers.

21. the optical metalens is configured to deflect blue wavelengths of light; 18. The optical metalens of claim 17, wherein diameters of the polarization independent passive deflector elements in the repeating pattern of deflector element diameters range from 80 nanometers to 140 nanometers.

22. An optical metalens comprising an array of passive deflector elements having varying diameters extending from a substrate having a repeating pattern of deflector element diameters, comprising: a plurality of center-to-center element spacings of the plurality of passive deflector elements are selected as a function of an operating wavelength of the optical metalens; each passive deflector element has a height that is smaller than a minimum wavelength within an operating bandwidth and a width that is smaller than the minimum wavelength within said operating bandwidth; 14. An optical metalens, further comprising a polarizer layer between said substrate and said array of passive polarizer elements, such that a plurality of said passive polarizer elements extend from said substrate through said polarizer layer.

23. 23. The optical metalens of claim 22, wherein the passive polarizer elements are polarization dependent.

24. 24. The optical metalens of claim 23, wherein the height that each polarization-dependent passive deflector element extends from the substrate is less than the maximum diameter of any deflector element in the metalens, such that each polarization-dependent deflector element has a height:diameter aspect ratio that is less than 1.

25. 17. The optical metalens of claim 15 or 16, wherein the array of passive deflector elements comprises a two-dimensional array of passive deflector elements.

26. 17. The optical metalens of claim 15 or 16, wherein each of the plurality of passive deflector elements extend to the same height.

27. The optical metalens of claim 15 or 16, wherein the diameter (D) of each deflector element varies based on the relative position of the deflector element in the repeating pattern.

28. An optical metalens comprising an array of passive deflector elements having varying diameters extending from a substrate having a repeating pattern of deflector element diameters, comprising: a plurality of center-to-center element spacings of the plurality of passive deflector elements are selected as a function of an operating wavelength of the optical metalens; each passive deflector element has a height that is smaller than a minimum wavelength within an operating bandwidth and a width that is smaller than the minimum wavelength within said operating bandwidth; each of the plurality of deflector elements comprises a cylinder having a diameter (D), a height (H) and a center-to-center nearest neighbor element spacing (P); a diameter (D) of each deflector element varies based on the relative position of the deflector element in the repeating pattern; Each of the cylindrical deflector elements has a cavity formed therein, The optical metalens, wherein the cavity has a depth that is less than the height (H).

29. 30. The optical metalens of claim 28, wherein the cavity formed in each cylindrical deflector element is cylindrical in shape and filled with air.

30. An optical metalens comprising an array of passive deflector elements having varying diameters extending from a substrate having a repeating pattern of deflector element diameters, comprising: a plurality of center-to-center element spacings of the plurality of passive deflector elements are selected as a function of an operating wavelength of the optical metalens; each passive deflector element has a height that is smaller than a minimum wavelength within an operating bandwidth and a width that is smaller than the minimum wavelength within said operating bandwidth; the array of passive deflector elements being configured for a dual frequency response; an optical metalens, wherein the array of passive deflector elements has a center-to-center element spacing of a first set of the passive deflector elements selected as a function of a first operating wavelength of the optical metalens, and a center-to-center element spacing of a second set of the passive deflector elements selected as a function of a second operating wavelength of the optical metalens.

31. An optical metalens comprising an array of passive deflector elements having varying diameters extending from a substrate having a repeating pattern of deflector element diameters, comprising: a plurality of center-to-center element spacings of the plurality of passive deflector elements are selected as a function of an operating wavelength of the optical metalens; each passive deflector element has a height that is smaller than a minimum wavelength within an operating bandwidth and a width that is smaller than the minimum wavelength within said operating bandwidth; the array of passive deflector elements being configured for a multiple frequency response; an optical metalens, wherein the array of passive deflector elements has a center-to-center element spacing of a first set of the passive deflector elements selected as a function of a first operating wavelength of the optical metalens, a center-to-center element spacing of a second set of the passive deflector elements selected as a function of a second operating wavelength of the optical metalens, and a center-to-center element spacing of a third set of the passive deflector elements selected as a function of a third operating wavelength of the optical metalens.

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