Planar optical metalens and optical connector comprising same

Abstract

An optical metalens includes a planar substrate, a plurality of nanostructures extending from a surface of the planar substrate, and a cladding extending from the surface of the planar substrate and encompassing the plurality of nanostructures. A cladding thickness is greater than the nanostructure height of each nanostructure of the plurality of nanostructures and a planar cladding surface opposite the planar substrate. The cladding thickness and at least one of a nanostructure dimension and a nanostructure height of each nanostructure of the plurality of nanostructures are configured such that the optical metalens imparts a target phase to light passing through the optical metalens and the optical metalens includes a transmittance greater than or equal to 80% at a wavelength of the light greater than or equal to 800 nm and less than or equal to 1600 nm.

Description

SP24-264PLANAR OPTICAL METALENSES AND OPTICAL CONNECTORS COMPRISING SAMECross-reference to Related Applications

[0001] This application claims the benefit of priority under 35 U.S.C. §119 of U.S.Provisional Application Serial No. 63 / 707839 filed on October 16, 2024, the content of which is relied upon and incorporated herein by reference in its entirety.Field

[0002] The present specification generally relates to optical metalenses and, in particular, to planar optical metalenses enabling physical contact operation and deposition of a coating while maintaining efficiency.Technical Background

[0003] Optical communication systems are widely deployed to provide various types of information content, such as voice content, video content, packet data, messaging, and broadcast content. Optical communication systems utilize a variety of adjustments and modifications to optical signals provided to common transmission optical fiber to increase the amount of information that may be transmitted over the transmission optical fiber.

[0004] Optical components including metasurfaces, such as metalenses, are a source of significant interest in optical communication systems because they have the ability to manipulate various aspects of incoming light (e.g., amplitude, phase, and polarization) to achieve a wide range of useful functions (e.g., beam steering, focusing, polarization multiplexing / de-multiplexing, spectral filtering, and others). However, conventional metalenses may not be subjected to physical contact (e.g., with other connectors or tools) as the nanostructures thereon may be fragile. Moreover, a conventional metalens may not have a planar surface to which a coating (e.g., anti-reflective coating) may be applied.

[0005] Therefore, a continuing need exists for optical metalenses enabling physical contact operation and deposition of a coating while maintaining efficiency.SP24-264SUMMARY

[0006] According to a first aspect Al, and optical metalens comprises: a planar substrate; a plurality of nanostructures extending from a surface of the planar substrate, the plurality of nanostructures arranged in a plurality of unit cells, each nanostructure of the plurality of nanostructures comprising a nanostructure dimension and a nanostructure height; and a cladding extending from the surface of the planar substrate and encompassing the plurality of nanostructures, the cladding having a cladding thickness greater than the nanostructure height of each nanostructure of the plurality of nanostructures and a planar cladding surface opposite the planar substrate; wherein the cladding thickness and at least one of the nanostructure dimension and the nanostructure height of each nanostructure of the plurality of nanostructures are configured such that the optical metalens imparts a target phase to light passing through the optical metalens and the optical metalens comprises a transmittance greater than or equal to 80% at a wavelength of the light greater than or equal to 100 nm and less than or equal to 10000 nm.

[0007] A second aspect A2 includes the optical metalens of the first aspect Al, wherein the cladding thickness is greater than or equal to 0.05 pm and less than or equal to 0.5 pm.

[0008] A third aspect A3 includes the optical metalens of the first aspect Al or the second aspect A2, wherein the cladding comprises silicon dioxide, silicon nitride, SU-8, hydrogen silsesquioxane, or a combination thereof.

[0009] A fourth aspect A4 includes the optical metalens of any one of the first through third aspects Al -A3, wherein each nanostructure of the plurality of nanostructures comprises a cylindrical shape, a rectangular shape, a hexagonal shape, or an irregular shape.

[0010] A fifth aspect A5 includes the optical metalens of any one of the first through fourth aspects A1-A4, wherein the nanostructure dimension of each nanostructure of the plurality of nanostructures may be greater than or equal to 0.02Z / RInto less than or equal to 50Z / RIn, wherein “X” refers to the wavelength of the light and “RIn” refers to the refractive index of the nanostructure.

[0011] A sixth aspect A6 includes the optical metalens of any one of the first through fifth aspects A1-A5, wherein the nanostructure dimension of one of the plurality of nanostructures differs from the nanostructure dimension of another one of the plurality of nanostructures.SP24-264

[0012] A seventh aspect A7 includes the optical metalens of any one of the first through sixth aspects A1-A6, wherein the nanostructure height of each nanostructure of the plurality of nanostructures may be greater than or equal to 0. l' / 7RInto less than or equal to 51 / RIn, wherein “X” refers to the wavelength of the light and “RIn” refers to the refractive index of the nanostructure.

[0013] An eighth aspect A8 includes the optical metalens of any one of the first through seventh aspects A1-A7, wherein each nanostructure of the plurality of nanostructures comprises a refractive index greater than or equal to 1.3.

[0014] A ninth aspect A9 includes the optical metalens of any one of the first through eighth aspects A1-A8, wherein each nanostructure of the plurality of nanostructures comprises amorphous silicon, crystalline silicon, silicon nitride, chalcogenide glasses, titanium oxide, optical resins, or combinations thereof.

[0015] A tenth aspect A10 includes the optical metalens of any one of the first through ninth aspects A1-A9, wherein the plurality of unit cells are arranged in a two-dimensional pattern covering an area of the surface of the substrate.

[0016] An eleventh aspect Al l includes the optical metalens of any one of the first through tenth aspects Al -A 10, wherein each unit cell of the plurality of unit cells comprises a single nanostructure of the plurality of nanostructures.

[0017] A twelfth aspect A 12 includes the optical metalens of any one of the first through eleventh aspects Al -Al 1, wherein each unit cell of the plurality of unit cells comprises at least two nanostructures of the plurality of nanostructures.

[0018] A thirteenth aspect A13 includes the optical metalens of any one of the first through twelfth aspects A1-A12, further comprising a coating disposed on the cladding.

[0019] A fourteenth aspect A14 includes the optical metalens of any one of the first through thirteenth aspects Al -A 13, wherein the planar substrate comprises a refractive index greater than or equal to 1.3.

[0020] A fifteenth aspect Al 5 includes the optical metalens of any of the first through fourteenth aspects Al -A 14, wherein the planar substrate comprises a glass or a polymer.SP24-264

[0021] A sixteenth aspect A 16 includes the optical metalens of any one of the first through fifteenth aspects A1-A15, wherein the planar substrate comprises a thickness greater than or equal to 50 pm and less than or equal to 5 mm.

[0022] According to a seventeenth aspect A 17, an optical connector comprises : a first optical fiber configured to transmit light; a first optical metalens coupled to and positioned to receive the light from the first optical fiber; a second optical fiber configured to receive the light; and a second optical metalens coupled to the second optical fiber, the second optical metalens positioned to receive the light from the first optical metalens and transmit the light to the second optical fiber; wherein each of the first optical metalens and the second optical metalens comprises the optical metalens of any one of the first through sixteenth aspects A1-A16.

[0023] An eighteenth aspect Al 8 includes the optical connector of the seventeenth aspect A 17, wherein at least one of the first optical fiber and the second optical fiber comprises a plurality of fibers.

[0024] A nineteenth aspect A 19 includes the optical connector of the seventeenth aspect A 17 or the eighteenth aspect A 18, wherein the wavelength of the light is greater than or equal to 850 nm and less than or equal to 1550 nm.

[0025] A twentieth aspect A20 includes the optical connector of any one of the seventeenth through nineteenth aspects A17-A19, wherein the light comprises a single wavelength.

[0026] A twenty-first aspect A21 includes the optical connector of any one of the seventeenth through twentieth aspects A17-A20, wherein the light comprises at least 2 wavelengths.

[0027] A twenty-second aspect A22 includes the optical connector of any one of the seventeenth through twenty-first aspects Al 7-A21, wherein the optical connector comprises an insertion loss less than or equal to 2.0 dB at the wavelength of the light.

[0028] Additional features and advantages of the optical elements and methods of making same described herein will be set forth in the detailed description which follows, and in part will be readily apparent to those skilled in the art from that description or recognized by practicing the embodiments described herein, including the detailed description which follows, the claims, as well as the appended drawings.SP24-264

[0029] It is to be understood that both the foregoing general description and the following detailed description describe various embodiments and are intended to provide an overview or framework for understanding the nature and character of the claimed subject matter. The accompanying drawings are included to provide a further understanding of the various embodiments, and are incorporated into and constitute a part of this specification. The drawings illustrate the various embodiments described herein, and together with the description serve to explain the principles and operations of the claimed subject matter.BRIEF DESCRIPTION OF THE DRAWINGS

[0030] FIG. 1 is a schematic view of an optical metalens, according to embodiments described herein;

[0031] FIG. 2 is a schematic view of nanostructures, according to embodiments described herein;

[0032] FIG. 3 is a schematic view of an optical connector, according to embodiments described herein;

[0033] FIG. 4 is a scanning electron microscope (SEM) image of nanostructures, according to embodiments described herein;

[0034] FIG. 5 is a SEM image of other nanostructures, according to embodiments described herein;

[0035] FIG. 6 is a SEM image of other nanostructures, according to embodiments described herein;

[0036] FIG. 7 is a plot of transmittance (y-axis) versus pillar diameter (x-axis; in nanometers (nm)) for various pillar heights (in microns (pm)) and cladding thicknesses (in microns (pm)), according to embodiments described herein;

[0037] FIG. 8 is a plot of transmittance (y-axis) versus pillar diameter (x-axis; in nanometers (nm)) for various pillar heights (in microns (pm)) and cladding thicknesses (in microns (pm)), according to embodiments described herein;SP24-264

[0038] FIG. 9 is a plot of transmittance (y-axis) versus pillar diameter (x-axis; in nanometers (nm)) for various pillar heights (in microns (pm)) and cladding thicknesses (in microns (pm)), according to embodiments described herein;

[0039] FIG. 10 is a plot of transmittance (y-axis) versus pillar diameter (x-axis; in nanometers (nm)) for various pillar heights (in microns (pm)) and cladding thicknesses (in microns (pm)), according to embodiments described herein;

[0040] FIG. 11 is a plot of transmittance (y-axis) versus pillar diameter (x-axis; in nanometers (nm)) for various pillar heights (in microns (pm)) and cladding thicknesses (in microns (pm)), according to embodiments described herein;

[0041] FIG. 12 is a plot of transmittance (y-axis) versus pillar diameter (x-axis; in nanometers (nm)) for various pillar heights (in microns (pm)) and cladding thicknesses (in microns (pm)), according to embodiments described herein;

[0042] FIG. 13 is a plot of transmittance (y-axis) versus pillar diameter (x-axis; in nanometers (nm)) for various pillar heights (in microns (pm)) and cladding thicknesses (in microns (pm)), according to embodiments described herein;

[0043] FIG. 14 is a plot of transmittance (y-axis) versus pillar diameter (x-axis; in nanometers (nm)) for various pillar heights (in microns (pm)) and cladding thicknesses (in microns (pm)), according to embodiments described herein;

[0044] FIG. 15 is a plot of transmittance (y-axis) versus pillar diameter (x-axis; in nanometers (nm)) for various pillar heights (in microns (pm)) and cladding thicknesses (in microns (pm)), according to embodiments described herein;

[0045] FIG. 16 is a plot of average transmittance of a range of pillar diameters (y-axis) versus pillar height (x-axis; in microns (pm)) for various cladding thicknesses (in microns (pm)), according to embodiments described herein;

[0046] FIG. 17 is a plot of 2TI phase coverage (y-axis) versus pillar diameter (x-axis; in nanometers (nm)) in nanometers for various cladding thicknesses (in microns (pm)), according to embodiments described herein;SP24-264

[0047] FIG. 18 is a plot of 2TI phase coverage (y-axis) versus pillar diameter (x-axis; in nanometers (nm)) in nanometers for various cladding thicknesses (in microns (pm)), according to embodiments described herein;

[0048] FIG. 19 is a plot of 2TI phase coverage (y-axis) versus pillar diameter (x-axis; in nanometers (nm)) in nanometers for various cladding thicknesses (in microns (pm)), according to embodiments described herein;

[0049] FIG. 20 is a plot of 2TI phase coverage (y-axis) versus pillar diameter (x-axis; in nanometers (nm)) in nanometers for various cladding thicknesses (in microns (pm)), according to embodiments described herein;

[0050] FIG. 21 is a plot of 2TI phase coverage (y-axis) versus pillar diameter (x-axis; in nanometers (nm)) in nanometers for various cladding thicknesses (in microns (pm)), according to embodiments described herein;

[0051] FIG. 22 is a plot of 2TI phase coverage (y-axis) versus pillar diameter (x-axis; in nanometers (nm)) in nanometers for various cladding thicknesses (in microns (pm)), according to embodiments described herein;

[0052] FIG. 23 is a plot of 2TI phase coverage (y-axis) versus pillar diameter (x-axis; in nanometers (nm)) in nanometers for various cladding thicknesses (in microns (pm)), according to embodiments described herein;

[0053] FIG. 24 is a plot of 2TI phase coverage (y-axis) versus pillar diameter (x-axis; in nanometers (nm)) in nanometers for various cladding thicknesses (in microns (pm)), according to embodiments described herein;

[0054] FIG. 25 is a plot of 2TI phase coverage (y-axis) versus pillar diameter (x-axis; in nanometers (nm)) in nanometers for various cladding thicknesses (in microns (pm)), according to embodiments described herein;

[0055] FIG. 26 is a plot of transmittance coefficient and 2n phase coverage (y-axis) as a function of pillar diameter (x-axis; in microns (pm)), according to embodiments described herein;SP24-264

[0056] FIG. 27 is a plot of transmittance (y-axis) versus 2TI phase coverage (x-axis), according to embodiments described herein;

[0057] FIG. 28 is a schematic view of an optical connector used in a Finite-Difference Time- Domain (FDTD) simulation, according to embodiments described herein;

[0058] FIG. 29 is a plot of intensity (y-axis; in atomic units (a.u.)) versus a substrate surface (x-axis; in microns (pm)), according to embodiments described herein;

[0059] FIG. 30 is a plot of 2TI phase coverage (y-axis) versus a substrate surface (x-axis; in microns (pm)), according to embodiments described herein;

[0060] FIG. 31 is a plot of efficiency (y-axis; in percentage (%)) versus wavelength (x-axis; in microns (pm)), according to embodiments described herein;

[0061] FIG. 32 is a schematic view of a unit cell, according to embodiments described herein;

[0062] FIG. 33 is a plot of 2n phase coverage at a given wavelength across the surface of an optical metalens, according to embodiments described herein;

[0063] FIG. 34 is a plot of 2n phase coverage at a given wavelength across the surface of an optical metalens, according to embodiments described herein;

[0064] FIG. 35 is a plot of transmittance at a given wavelength across the surface of an optical metalens, according to embodiments described herein;

[0065] FIG. 36 is a plot of transmittance at a given wavelength across the surface of an optical metalens, according to embodiments described herein;

[0066] FIG. 37 is a target 2n phase coverage (y-axis) across the surface of an optical metalens(x-axis; in microns (pm)), according to embodiments described herein;

[0067] FIG. 38 is 2TI phase coverage (y-axis) at a given wavelength across the surface of an optical metalens (x-axis; in microns (pm)), according to embodiments described herein;

[0068] FIG. 39 is 2TI phase coverage (y-axis) at a given wavelength across the surface of an optical metalens (x-axis; in microns (pm)), according to embodiments described herein;SP24-264

[0069] FIG. 40 is a plot of intensity (y-axis; in atomic units (a.u.)) versus a substrate surface (x-axis; in microns (pm)) at a given wavelength, according to embodiments described herein;

[0070] FIG. 41 is a plot of intensity (y-axis; in atomic units (a.u.)) versus a substrate surface (x-axis; in microns (pm)) at a given wavelength, according to embodiments described herein;

[0071] FIG. 42 is a plot of 2TI phase coverage (y-axis) versus a substrate surface (x-axis; in microns (pm)), according to embodiments described herein;

[0072] FIG. 43 is a plot of 2TI phase coverage (y-axis) versus a substrate surface (x-axis; in microns (pm)), according to embodiments described herein;

[0073] FIG. 44 is a plot of integral transmittance and overlap transmittance (y-axis; in percentage (%)) versus wavelength (x-axis; in microns (pm)), according to embodiments described herein; and

[0074] FIG. 45 is a plot of efficiency (y-axis; in percentage (%)) versus wavelength (x-axis; in microns (pm)).DETAILED DESCRIPTION

[0075] Reference will now be made in detail to various embodiments of planar optical metalenses enabling physical contact operation and deposition of a coating while maintaining efficiency.

[0076] According to embodiments, an optical metalens includes a planar substrate, a plurality of nanostructures extending from a surface of the planar substrate, and a cladding extending from the surface of the planar substrate and encompassing the plurality of nanostructures. The plurality of nanostructures are arranged in a plurality of unit cells. Each nanostructure of the plurality of nanostructures includes a nanostructure dimension and a nanostructure height. The cladding has a cladding thickness greater than the nanostructure height of each nanostructure of the plurality of nanostructures and a planar cladding surface opposite the planar substrate. The cladding thickness and at least one of the nanostructure dimension and the nanostructure height of each nanostructure of the plurality of nanostructures are configured such that the optical metalens imparts a target phase to light passing through the optical metalens and the optical metalens comprises a transmittance greater than or equal toSP24-26480% at a wavelength of the light greater than or equal to 100 nm and less than or equal to 10000 nm.

[0077] Various embodiments of planar optical metalenses and optical connectors comprising same will be described herein with specific reference to the appended drawings.

[0078] Ranges may be expressed herein as from “about” one particular value, and / or to “about” another particular value. When such a range is expressed, another embodiment includes from the one particular value and / or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms another embodiment. It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint.

[0079] Directional terms as used herein - for example up, down, right, left, front, back, top, bottom - are made only with reference to the figures as drawn and are not intended to imply absolute orientation.

[0080] Unless otherwise expressly stated, it is in no way intended that any method set forth herein be construed as requiring that its steps be performed in a specific order, nor that with any apparatus specific orientations be required. Accordingly, where a method claim does not actually recite an order to be followed by its steps, or that any apparatus claim does not actually recite an order or orientation to individual components, or it is not otherwise specifically stated in the claims or description that the steps are to be limited to a specific order, or that a specific order or orientation to components of an apparatus is not recited, it is in no way intended that an order or orientation be inferred, in any respect. This holds for any possible non-express basis for interpretation, including: matters of logic with respect to arrangement of steps, operational flow, order of components, or orientation of components; plain meaning derived from grammatical organization or punctuation, and; the number or type of embodiments described in the specification.

[0081] As used herein, the singular forms “a,” “an” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a” component includes aspects having two or more such components, unless the context clearly indicates otherwise.SP24-264

[0082] The term “metalens,” as used herein, refers to a planar lens with metasurfaces disposed thereon to perform an optical function (e.g., collimate, deflect, or refocus light).

[0083] The term “transmittance,” as used herein, refers to the ratio of light energy that travels through a material to the total light energy incident on the substrate.

[0084] The term “insertion loss,” as used herein, refers to the amount of optical power that is lost when a signal is transmitted through a fiber optic component, such as a connector, splice, or coupler. It is measured in decibels (dB). Lower insertion loss may be desirable as it indicates less power loss and better transmission efficiency. In high-speed and long-distance fiber optic systems, minimizing insertion loss is desirable to ensure reliable and efficient signal transmission.

[0085] As described herein, optical metasurfaces, such as metalenses, are a source of significant interest in optical communication systems because they have the ability to manipulate various aspects of incoming light (e.g., amplitude, phase, and polarization) to achieve a wide range of useful functions (e.g., beam steering, focusing, polarization multiplexing / de-multiplexing, spectral filtering, and others). For example, metalenses may be formed by an array of nanostructures disposed on a substrate to shape incoming light. Metalenses are attractive for their ability to perform functions typically served through traditional optical elements, like lenses, polarizers, and beam splitters, while being much lighter in weight, more compact, and less expensive.

[0086] However, conventional metalenses may not be subjected to physical contact (e.g., with other connectors or tools) as the nanostructures thereon may be fragile. Moreover, a conventional metalens may not have a planar surface to which a coating (e.g., anti-reflective coating) may be applied.

[0087] Disclosed herein are optical metalenses which mitigate the aforementioned problems. Specifically, the optical metalenses described herein include a cladding encompassing a plurality of nanostructures disposed on a planar substrate. The cladding comprises a planar cladding surface opposite the planar substrate. The thickness of the cladding and the dimension and / or height of each of the nanostructures are configured such that the optical metalens imparts a target phase to light passing through the optical metalens and the optical metalens comprises a transmittance greater than or equal to 80% at a wavelength of the light greater than or equalSP24-264 to 100 nm and less than or equal to 10000 nm. As such, the optical metalenses described herein enable physical contact operation and deposition of a coating while maintaining efficiency.

[0088] Referring now to FIG. 1, an optical metalens is shown at 100. The optical metalens 100 generally comprises a planar substrate 102, a plurality of nanostructures 104, and a cladding 106. The combination of the plurality of nanostructures 104 and the cladding 106 may be referred to herein as a metasurface 108.

[0089] The planar substrate 102 allows for inclusion of the cladding 106, thereby enabling physical contact operation and deposition of a coating on the optical metalens 100, as described in further detail below. The planar substrate 102 may be transparent to a wavelength of light of, for example, an input optical fiber. The term ‘transparent,” as used herein, means that the material has a linear optical absorption of less than 20% per mm of material depth, such as less than 10% per mm of material depth for a wavelength, or such as less than 1% per mm of material depth for a wavelength. Each of the planar substrates 102 described herein may be transparent within a wavelength operating window of optical signals propagating therethrough.

[0090] The planar substrate 102 may comprise a refractive index the same as or similar to the refractive index of the plurality of nanostructures 104. In embodiments, the planar substrate 102 may comprise a refractive index greater than or equal to 1.3. In embodiments, the planar substrate 102 may comprise a refractive index greater than or equal to 1.3 or even greater than or equal to 1.5. In embodiments, the planar substrate 102 may comprise a refractive index less than or equal to 3.7, less than or equal to 3.5, less than or equal to 3.0, less than or equal to 2.5, or even less than or equal to 2.0. In embodiments, the planar substrate 102 may comprise a refractive index greater than or equal to 1.3 and less than or equal to 3.7, greater than or equal to 1.3 and less than or equal to 3.5, greater than or equal to 1.3 and less than or equal to 3.0, greater than or equal to 1.3 and less than or equal to 2.5, greater than or equal to 1.3 and less than or equal to 2.0, greater than or equal to 1.5 and less than or equal to 3.7, greater than or equal to 1.5 and less than or equal to 3.5, greater than or equal to 1.5 and less than or equal to 3.0, greater than or equal to 1.5 and less than or equal to 2.5, or even greater than or equal to 1 .5 and less than or equal to 2.0, or any and all sub-ranges formed from any of these endpoints.

[0091] In embodiments, the planar substrate 102 may comprise a glass, a polymer (e.g., SU8), or other suitable transparent material. For example, in embodiments, the planar substrate 102 may comprise fused silica.SP24-264

[0092] In embodiments, the planar substrate 102 may comprise a thickness greater than or equal to 50 pm and less than or equal to 5 mm. In embodiments, the planar substrate 102 may comprise a thickness greater than or equal to 50 pm, greater than or equal to 100 pm, greater than or equal to 250 pm, greater than or equal to 500 pm, or even greater than or equal to 1 mm. In embodiments, the planar substrate 102 may comprise a thickness less than or equal to 5 mm, less than or equal to 3 mm, less than or equal to 1 mm, less than or equal to 500 pm, or even less than or equal to 100 pm. In embodiments, the planar substrate 102 may comprise a thickness greater than or equal to 50 pm and less than or equal to 5 mm, greater than or equal to 50 pm and less than or equal to 3 mm, greater than or equal to 50 pm and less than or equal to 1 mm, greater than or equal to 50 pm and less than or equal to 500 pm, greater than or equal to 50 pm and less than or equal to 100 pm, greater than or equal to 100 pm and less than or equal to 5 mm, greater than or equal to 100 pm and less than or equal to 3 mm, greater than or equal to 100 pm and less than or equal to 1 mm, greater than or equal to 100 pm and less than or equal to 500 pm, greater than or equal to 250 pm and less than or equal to 5 mm, greater than or equal to 250 pm and less than or equal to 3 mm, greater than or equal to 250 pm and less than or equal to 1 mm, greater than or equal to 250 pm and less than or equal to 500 pm, greater than or equal to 500 pm and less than or equal to 5 mm, greater than or equal to 500 pm and less than or equal to 3 mm, greater than or equal to 500 pm and less than or equal to 1 mm, greater than or equal to 1 mm and less than or equal to 5 mm, or even greater than or equal to 1 mm and less than or equal to 3 mm, or any and all sub-ranges formed from any of these endpoints.

[0093] Referring back to FIG. 1, the plurality of nanostructures 104 extend from a surface 102a of the planar substrate 102. The plurality of nanostructures 104 may be formed on or within the planar substrate 102. The plurality of nanostructures 104 are positive features where a layer is deposited on the planar substrate 102 and subsequently patterned (e.g., via nanolithography) to form the plurality of nanostructures 104.

[0094] Referring now to FIG. 2, an optical metalens 200 includes a plurality of nanostructures 204 disposed on a planar substrate 202. Each nanostructure of the plurality of nanostructures 204 comprise a nanostructure dimension and a nanostructure height. “Nanostructure dimension,” as used herein, refers to a largest dimension of the nanostructure extending parallel to the planar substrate 202 and orthogonal to the nanostructure height. For example, the nanostructure dimension of a cylindrical (i.e., pillar) nanostructure is theSP24-264 nanostructure diameter. As another example, the nanostructure dimension of a rectangular nanostructure is the nanostructure length or width. “Nanostructure height,” as used herein, refers to the distance the nanostructure extends away from the planar substrate, orthogonal to the nanostructure dimension.

[0095] The plurality of nanostructures 204 may introduce phase changes into an optical signal (i.e., light) interacting therewith. In embodiments, the phase response or phase coverage at a particular location of the optical metalens 200 may be dependent on structural parameters (e.g., nanostructure dimension, nanostructure height, arrangement of unit cells, geometric orientation relative to the light propagation) of the plurality of nanostructures 204.

[0096] The plurality of nanostructures 204 may be a variety of different sizes and shapes to alter a phase profde of an optical signal. In embodiments, each nanostructure of the plurality of nanostructures 204 may comprise a cylindrical shape, a rectangular shape, a hexagonal shape, or an irregular shape. For example, referring back to FIG. 2, the first, second, third, and fourth nanostructures 214, 216, 218, and 220 are substantially cylindrical-shaped, but have varying diameters to induce a spatially varying phase change in incoming optical signals. The fifth and sixth nanostructures 222 and 224 are substantially rectangular-shaped, but having varying side lengths to induce a spatially varying phase change in incoming optical signals. The seventh, eighth, and ninth nanostructures 226, 228, and 230 are hexagonal-shaped pillars, but have varying heights to induce a spatially varying phase change in an incoming optical signal. In embodiments, nanostructures comprising any cross-sectional profile, such as circle, triangle, square, rectangle, pentagon, hexagon, v-shaped, other shaped cross-sectional profile, or any combination thereof may be used.

[0097] As described herein, at least one of the nanostructure dimension and the nanostructure height of each nanostructure of the plurality of nanostructures 204, along with the cladding thickness, are configured such that the optical metalens 200 imparts a target phase to light passing through the optical metalens 200 and the optical metalens comprises a transmittance greater than or equal to 80% at a wavelength of the light greater than or equal to 100 nm and less than or equal to 10000 nm. As used herein, “target phase” means that the optical metalens 200 imparts a phase that collimates, deflects, or refocuses the light passing therethrough. For example, in embodiments, the optical metalens 200 may impart a conjugate phase to light passing through the optical metalens.SP24-264

[0098] In embodiments, the nanostructure dimension of each nanostructure of the plurality of nanostructures 204 may be greater than or equal to 0.02X / RInto less than or equal to 5 OX / RIn, wherein “X” refers to the wavelength of the light and “RIn” refers to the refractive index of the nanostructure. For example, in embodiments, the nanostructure dimension of each nanostructure of the plurality of nanostructures 204 may be greater than or equal to 50 nm and less than or equal to 400 pm. In embodiments, the nanostructure dimension of each nanostructure of the plurality of nanostructures 204 may be greater than or equal to 50 nm, greater than 100 nm, greater than or equal to 500 nm, greater than or equal to 1 pm, greater than or equal to 5 pm, greater than or equal to 10 pm, greater than or equal to 50 pm, or even greater than or equal to 100 pm. In embodiments, the nanostructure dimension of each nanostructure of the plurality of nanostructures 204 may be less than or equal to 400 pm, less than or equal to 100 pm, less than or equal to 50 pm, less than or equal to 10 pm, less than or equal to 5 pm, less than or equal to 1 pm, or even less than or equal to 500 nm. In embodiments, the nanostructure dimension of each nanostructure of the plurality of nanostructures 204 may be greater than or equal to 50 nm and less than or equal to 400 pm, greater than or equal to 50 nm and less than or equal to 100 pm, greater than or equal to 50 nm and less than or equal to 50 pm, greater than or equal to 50 nm and less than or equal to 10 pm, greater than or equal to 50 nm and less than or equal to 50 pm, greater than or equal to 50 nm and less than or equal to 1 pm, greater than or equal to 50 nm and less than or equal to 500 nm, greater than or equal to 100 nm and less than or equal to 400 pm, greater than or equal to 100 nm and less than or equal to 100 pm, greater than or equal to 100 nm and less than or equal to 50 pm, greater than or equal to 100 nm and less than or equal to 10 pm, greater than or equal to 100 nm and less than or equal to 50 pm, greater than or equal to 100 nm and less than or equal to 1 pm, greater than or equal to 100 nm and less than or equal to 500 nm, greater than or equal to 500 nm and less than or equal to 400 pm, greater than or equal to 500 nm and less than or equal to 100 pm, greater than or equal to 500 nm and less than or equal to 50 pm, greater than or equal to 500 nm and less than or equal to 10 pm, greater than or equal to 500 nm and less than or equal to 50 pm, greater than or equal to 500 nm and less than or equal to 1 pm, greater than or equal to 1 pm and less than or equal to 400 pm, greater than or equal to 1 pm and less than or equal to 100 pm, greater than or equal to 1 pm and less than or equal to 50 pm, greater than or equal to 1 pm and less than or equal to 10 pm, greater than or equal to 1 pm and less than or equal to 5 pm, greater than or equal to 5 pm and less than or equal to 400 pm, greater than or equal to 5 pm and less than or equal to 100 pm, greater than or equal to 5 pm and less than or equal to 50 pm, greater than or equal to 5 pm and less than or equal to 10 pm, greater than or equal to 10SP24-264 qm and less than or equal to 400 qm, greater than or equal to 10 qm and less than or equal to 100 qm. greater than or equal to 10 qm and less than or equal to 50 qm, greater than or equal to 50 qm and less than or equal to 400 qm, greater than or equal to 50 qm and less than or equal to 100 qm, or even greater than or equal to 100 qm and less than or equal to 400 qm, or any and all sub-ranges formed from any of these endpoints.

[0099] In embodiments, the nanostructure dimension of one of the plurality of nanostructures 204 may differ from the nanostructure dimension of another one of the plurality of nanostructures 204.

[0100] In addition to imparting a target phase and achieving a relatively high transmittance, the nanostructure height, along with the cladding thickness, may enable manufacturability of the optical metalens 200.

[0101] In embodiments, the nanostructure height of each nanostructure of the plurality of nanostructures 204 may be greater than or equal to 0. I / RInto less than or equal to 51 / RIn, wherein “X” refers to the wavelength of the light and “RIn” refers to the refractive index of the nanostructure. For example, in embodiments, the nanostructure height of each nanostructure of the plurality of nanostructures 204 may be greater than or equal to 0.7 pm and less than or equal to 1.8 pm. In embodiments, the nanostructure height of each nanostructure of the plurality of nanostructures 204 may be greater than or equal to 0.7 qm, greater than 0.8 qm, or even greater than or equal to 0.9 qm. In embodiments, the nanostructure height of each nanostructure of the plurality of nanostructures 204 may be less than or equal to 1.8 qm, less than or equal to 1.6 qm, less than or equal to 1.4 qm, less than or equal to 1 .2 qm, or even less than or equal to 1.0 qm. In embodiments, the nanostructure height of each nanostructure of the plurality of nanostructures 204 may be greater than or equal to 0.7 qm and less than or equal to 1.8 qm, greater than or equal to 0.7 qm and less than or equal to 1.6 qm, greater than or equal to 0.7 qm and less than or equal to 1.4 qm, greater than or equal to 0.7 qm and less than or equal to 1.2 qm, greater than or equal to 0.7 qm and less than or equal to 1.0 qm, greater than or equal to 0.8 qm and less than or equal to 1.8 qm, greater than or equal to 0.8 qm and less than or equal to 1.6 qm, greater than or equal to 0.8 qm and less than or equal to 1.4 qm, greater than or equal to 0.8 qm and less than or equal to 1.2 qm, greater than or equal to 0.8 qm and less than or equal to 1.0 qm, greater than or equal to 0.9 qm and less than or equal to 1.8 qm, greater than or equal to 0.9 qm and less than or equal to 1.6 qm, greater than or equal to 0.9 qm and less than or equal to 1.4 qm, greater than or equal to 0.9 qm and less than orSP24-264 equal to 1.2 pm, or even greater than or equal to 0.9 pm and less than or equal to 1.0 pm, or any and all sub-ranges formed from any of these endpoints.

[0102] Each nanostructure of the plurality of nanostructures 204 may comprise a refractive index the same as or similar to the refractive index of the planar substrate 202. In embodiments, each nanostructure of the plurality of nanostructures 204 may comprise a refractive index greater than or equal to 1.3 or even greater than or equal to 1.5. In embodiments, each nanostructure of the plurality of nanostructures 204 may comprise a refractive index less than or equal to 4.0, less than or equal to 3.5, less than or equal to 3.0, less than or equal to 2.5, or even less than or equal to 2.0. In embodiments, each nanostructure of the plurality of nanostructures 204 may comprise a refractive index greater than or equal to 1.3 and less than or equal to 4.0, greater than or equal to 1 .3 and less than or equal to 3.5, greater than or equal to 1.3 and less than or equal to 3.0, greater than or equal to 1.3 and less than or equal to 2.5, greater than or equal to 1.3 and less than or equal to 2.0, greater than or equal to 1.5 and less than or equal to 4.0, greater than or equal to 1.5 and less than or equal to 3.5, greater than or equal to 1.5 and less than or equal to 3.0, greater than or equal to 1.5 and less than or equal to 2.5, or even greater than or equal to 1.5 and less than or equal to 2.0, or any and all sub-ranges formed from any of these endpoints.

[0103] In embodiments, each nanostructure of the plurality of nanostructures 204 may be formed of material that is dependent on an operating wavelength window. For example, in embodiments where light is in the O band (1260-1360 nm), C band (1530-1565 nm), L band (1565-1625 nm), each nanostructure of the plurality of nanostructures 204 may comprise amorphous silicon, crystalline silicon, silicon nitride, and chalcogenide glasses. In embodiments, where light is in a shorter wavelength window (e.g., 850-940 nm), other suitable materials like titanium oxide and silicon nitride may be used for the plurality of nanostructures 204. In embodiments, the plurality of nanostructures 204 may comprise optical resins. In embodiments, different ones of the plurality of nanostructures 204 may be constructed of different materials.

[0104] Referring again to FIG. 2, the plurality of nanostructures 204 may be arranged in a plurality of unit cells 232. In embodiments, the plurality of unit cells 232 may be arranged in a two-dimensional pattern covering an area of the surface of the substrate 202, leveraging a given arrangement (e.g., a waveguide propagation phase, a Pancharatnam-Berry phase, or complex Bloch mode engineering). In embodiments, the plurality of unit cells 232 may beSP24-264 arranged such that a distribution of the plurality of nanostructures 204, relative to a central nanostructure, achieves a desired global phase.

[0105] In the depicted embodiment, each one of the plurality of nanostructures 204 is disposed in a unit cell such that each unit cell of the plurality of unit cells 232 comprises a single nanostructure of the plurality of nanostructures 204. In such embodiments, each of the plurality of nanostructures 204 is centrally disposed within a unit cell of the plurality of unit cells 232. In embodiments, the unit cells of the plurality of unit cells 232 are square-shaped such that the centers of each one of the plurality of nanostructures 204 are separated from one another by a length of the unit cell 232. In other embodiments, each unit cell of the plurality of unit cells 232 may comprise at least two nanostructures of the plurality of nanostructures 204, such as in broadband applications. Relatively smaller unit cells 232 may include taller nanostructures 204 to ensure full phase coverage. In unit cells 232 including at least two nanostructures, the nanostructures within the unit cell may have the same of different nanostructure dimensions and / or nanostructure heights.

[0106] Referring back to FIG. 1, the cladding 106 extends from the surface 102a of the planar substrate 102 and encompasses the plurality of nanostructures 104. The cladding 106 has a cladding thickness and a planar cladding surface 106a opposite the planar substrate 102. The cladding thickness, extending away from the surface 102a of the planar substrate 102, may be greater than the nanostructure height of each nanostructure of the plurality of nanostructures 104, thereby protecting the plurality of nanostructures 104 from damage and enabling physical contact operation and deposition of a coating.

[0107] The cladding thickness of the cladding 106, along with at least one of the nanostructure dimension and the nanostructure height of each nanostructure of the plurality of nanostructures 104, are configured such that the optical metalens 100 imparts a target phase and achieves a desired transmittance (e.g., a transmittance greater than or equal to 80% at a wavelength of the light greater than or equal to 100 nm and less than or equal to 10000 run). Operating wavelength, dimensions of the plurality of nanostructures 104, refractive index of the plurality of nanostructures 104, and the material of the cladding 106 may effect the cladding thickness of the cladding 106. In embodiments, the cladding thickness may be greater than or equal to 0.05 pm and less than or equal to 0.5 pm. In embodiments, the cladding thickness may be greater than or equal to 0.05 pm, greater than or equal to 0. 1 pm, greater than or equal to 0.15 pm, or even greater than or equal to 0.2 pm. In embodiments, the cladding thickness maySP24-264 be less than or equal to 0.5 pm. less than or equal to 0.4 qm, or even less than or equal to 0.3 qm. In embodiments, the cladding thickness may be greater than or equal to 0.05 qm and less than or equal to 0.5 qm, greater than or equal to 0.05 qm and less than or equal to 0.4 qm, greater than or equal to 0.05 qm and less than or equal to 0.3 qm, greater than or equal to 0. 1 qm and less than or equal to 0.5 qm, greater than or equal to 0. 1 qm and less than or equal to 0.4 qm, greater than or equal to 0. 1 qm and less than or equal to 0.3 qm, greater than or equal to 0. 15 qm and less than or equal to 0.5 qm, greater than or equal to 0. 15 qm and less than or equal to 0.4 qm, greater than or equal to 0. 15 qm and less than or equal to 0.3 qm, greater than or equal to 0.2 qm and less than or equal to 0.5 qm, greater than or equal to 0.2 qm and less than or equal to 0.4 qm, or even greater than or equal to 0.2 qm and less than or equal to 0.3 qm, or any and all sub-ranges formed from any of these endpoints.

[0108] The cladding 106 may comprise a material that is transparent at the operating window and have a refractive index different from the refractive index of the plurality of nanostructures 104. Differing refractive indices between the cladding 106 and the plurality of nanostructures 104 enables the modulation of a wavefront of incident light. For example, the cladding 106 may have a relatively low refractive index (e.g., 1.3) and each of the plurality of nanostructures 104 may have a relatively high refractive index (e.g., 2.0) or vice versa. If the refractive indices of the cladding 106 and the plurality of nanostructures 104 were the same, the cladding 106 and the plurality of nanostructures 104 would form an optically homogenous medium that would not modulate the waveform of the incident light, and, thus, would not perform the intended optical functionality. For example, in embodiments, the cladding 106 may comprise silicon dioxide, silicon nitride, SU-8, hydrogen sisequioxane, or a combination thereof. As noted herein, the cladding 106 protects the plurality of nanostructures 104, thereby enabling physical contact operation. As such, conventional cladding materials such as air or some other environmental gas may not be applicable to the present application.

[0109] Referring back to FIG. 1, the optical metalens 100 may further comprise a coating 110. As described herein, the planar substrate 102 and the cladding 106 enable deposition of a coating 110. In embodiments, the coating 110 may serve an anti -reflective function and / or a mechanical protection function. For example and not by way of limitation, the coating 110 may comprise silicon, silicon oxide, silicon nitride, aluminum oxide, titanium oxide, polymer, or a combination thereof.SP24-264

[0110] To impart a target phase to light passing through the optical metalens 100, the cladding thickness and at least one of the nanostructure dimension and the nanostructure height of each nanostructure of the plurality of nanostructures 104 are configured to ensure full phase coverage (e.g., 0 to 2TI phase).

[0111] The thickness of the cladding 106 and the dimension and / or height of each of the nanostructures 104 are configured such that the optical metalens comprises a transmittance greater than or equal to 80% at a wavelength of the light greater than or equal to 100 nm and less than or equal to 10000 nm. In embodiments, the optical metalens 100 may comprise a transmittance greater than or equal to 80%, greater than or equal to 85%, greater than or equal to 90%, or even greater than or equal to 95%, at a wavelength of the light greater than or equal to 100 nm and less than or equal to 10000 nm.

[0112] The present optical metalenses 100 may be used in UV, visible, near infrared, and mid-infrared applications. As such, in embodiments, the wavelength of light may be greater than or equal to 100 nm and less than or equal to 10000 nm. In embodiments, the wavelength of light may be greater than or equal to 100 nm, greater than or equal to 250 nm, greater than or equal to 500 nm, greater than or equal to 750 nm, or even greater than or equal to 1000 nm. In embodiments, the wavelength of light may be less than or equal to 10000 nm, less than or equal to 7500 nm, less than or equal to 5000 nm, less than or equal to 2500 nm, or even less than or equal to 1000 nm. In embodiments, the wavelength of light may be greater than or equal to 100 nm and less than or equal to 10000 nm, greater than or equal to 100 nm and less than or equal to 7500 nm, greater than or equal to 100 nm and less than or equal to 5000 nm, greater than or equal to 100 nm and less than or equal to 2500 nm, greater than or equal to 100 nm and less than or equal to 1000 nm, greater than or equal to 250 nm and less than or equal to 10000 nm, greater than or equal to 250 nm and less than or equal to 7500 nm, greater than or equal to 250 nm and less than or equal to 5000 nm, greater than or equal to 250 nm and less than or equal to 2500 nm, greater than or equal to 250 nm and less than or equal to 1000 nm, greater than or equal to 500 nm and less than or equal to 10000 nm, greater than or equal to 500 nm and less than or equal to 7500 nm, greater than or equal to 500 nm and less than or equal to 5000 nm, greater than or equal to 500 nm and less than or equal to 2500 nm, greater than or equal to 500 nm and less than or equal to 1000 nm, greater than or equal to 750 nm and less than or equal to 10000 nm, greater than or equal to 750 nm and less than or equal to 7500 nm, greater than or equal to 750 nm and less than or equal to 5000 nm, greater than or equal toSP24-264750 nm and less than or equal to 2500 nm, greater than or equal to 750 nm and less than or equal to 1000 nm, greater than or equal to 1000 nm and less than or equal to 10000 nm, greater than or equal to 1000 nm and less than or equal to 7500 nm, greater than or equal to 1000 nm and less than or equal to 5000 nm, or even greater than or equal to 1000 nm and less than or equal to 2500 nm, or any and all sub-ranges formed from any of these endpoints.

[0113] In embodiments, for a UV application, the wavelength of light may be greater than or equal to 200 nm and less than or equal to 380 nm. In embodiments, for a visible application, the wavelength of light may be greater than 380 nm and less than or equal to 800 nm. In embodiments, for a near infrared application, the wavelength of light may be greater than 800 nm and less than or equal to 2500 nm. In embodiments, for a mid-infrared application, the wavelength of light may be greater than 2500 nm and less than or equal to 10000 nm.

[0114] In embodiments, the present optical metalenses 100 may be used in telecommunication applications. As such, the wavelength of the light may be greater than or equal to 800 nm and less than or equal to 1600 nm. In embodiments, the wavelength of the light may be greater than or equal to 850 nm and less than or equal to 1550 nm. In embodiments, the wavelength of the light may be greater than or equal to 800 nm, greater than or equal to 850 nm, greater than or equal to 900 nm, greater than or equal to 950 nm, greater than or equal to 1000 nm, greater than or equal to 1050 nm, greater than or equal to 1100 nm, greater than or equal to 1150 nm, or even greater than or equal to 1200 nm. In embodiments, the wavelength of the light may be less than or equal to 1600 nm, less than or equal to 1550 nm, less than or equal to 1500 nm, less than or equal to 1450 nm, or even less than or equal to 1400 nm. In embodiments, the wavelength of the light may be greater than or equal to 800 nm and less than or equal to 1600 nm, greater than or equal to 800 nm and less than or equal to 1550 nm, greater than or equal to 800 nm and less than or equal to 1500 nm, greater than or equal to 800 nm and less than or equal to 1450 nm, greater than or equal to 800 nm and less than or equal to 1400 nm, greater than or equal to 850 nm and less than or equal to 1600 nm, greater than or equal to 850 nm and less than or equal to 1550 nm, greater than or equal to 850 nm and less than or equal to 1500 nm, greater than or equal to 850 nm and less than or equal to 1450 nm, greater than or equal to 850 nm and less than or equal to 1400 nm, greater than or equal to 900 nm and less than or equal to 1600 nm, greater than or equal to 900 nm and less than or equal to 1550 nm, greater than or equal to 900 nm and less than or equal to 1500 nm, greater than or equal to 900 nm and less than or equal to 1450 nm, greater than or equal to 900SP24-264 nm and less than or equal to 1400 nm, greater than or equal to 1000 nm and less than or equal to 1600 nm, greater than or equal to 1000 nm and less than or equal to 1550 nm, greater than or equal to 1000 nm and less than or equal to 1500 nm, greater than or equal to 1000 nm and less than or equal to 1450 nm, greater than or equal to 1000 nm and less than or equal to 1400 nm, greater than or equal to 1050 nm and less than or equal to 1600 nm, greater than or equal to 1050 nm and less than or equal to 1550 nm, greater than or equal to 1050 nm and less than or equal to 1500 nm, greater than or equal to 1050 nm and less than or equal to 1450 nm, greater than or equal to 1050 nm and less than or equal to 1400 nm, greater than or equal to 1100 nm and less than or equal to 1600 nm, greater than or equal to 1100 nm and less than or equal to 1550 nm, greater than or equal to 1100 nm and less than or equal to 1500 nm, greater than or equal to 1100 nm and less than or equal to 1450 nm, greater than or equal to 1100 nm and less than or equal to 1400 nm, greater than or equal to 1150 nm and less than or equal to 1600 nm, greater than or equal to 1150 nm and less than or equal to 1550 nm, greater than or equal to 1150 nm and less than or equal to 1500 nm, greater than or equal to 1150 nm and less than or equal to 1450 nm, greater than or equal to 1150 nm and less than or equal to 1400 nm, greater than or equal to 1200 nm and less than or equal to 1600 nm, greater than or equal to 1200 nm and less than or equal to 1550 nm, greater than or equal to 1200 nm and less than or equal to 1500 nm, greater than or equal to 1200 nm and less than or equal to 1450 nm, or even greater than or equal to 1200 nm and less than or equal to 1400 nm, or any and all sub-ranges formed from any of these endpoints. In embodiments, the wavelength of the light may be 850 nm. In embodiments, the wavelength of the light may be 980 nm. In embodiments, the wavelength of the light may be 1310 nm. In embodiments, the wavelength of the light may be 1550 nm.

[0115] The optical metalenses described herein may be integrated into a fiber-to-fiber connector. For example, referring now to FIG. 3, an optical connector is shown at 300. As depicted, the optical connector 300 may be an expanded beam connector that expands, collimates, and refocuses light from a first optical fiber 302 to a second optical fiber 304. The first and second optical fibers 302, 304 may comprise fiber core 302a, 304a disposed in a fiber cladding 302b, 304b. The first optical fiber 302 may be configured to transmit light. The second optical fiber 304 may be configured to receive the light. In embodiments, the light may comprise a single wavelength. In other embodiments, the light may comprise at least 2 wavelengths, such as in broadband applications.SP24-264

[0116] A first optical metalens 310 may be coupled to and positioned to receive light from the first optical fiber 302. The first optical metalens 310 may comprise an optical metalens as described herein, configured such that the first optical metalens 310 imparts a target phase to light passing through the first optical metalens 310 (e.g., thereby collimating or deflecting the light) and the first optical metalens 310 comprises a transmittance greater than or equal to 80% at a wavelength of the light greater than or equal to 800 nm and less than or equal to 1600 nm. A second optical metalens 312 may be coupled to the second optical fiber 304. The second optical metalens 312 may be positioned to receive the light from the first optical metalens 310 and transmit the light to the second optical fiber 304. The second optical metalens 312 may comprise an optical metalens as described herein, configured such that the second optical metalens 312 imparts a target phase to light passing through the second optical metalens 312 (e.g., thereby refocusing the light) and the second optical metalens 312 comprises a transmittance greater than or equal to 80% at a wavelength of the light greater than or equal to 800 nm and less than or equal to 1600 nm. The first and second optical metalenses 310, 312 may be coupled to the respective first and second optical fibers 302, 304 via, for example, glue or laser welding.

[0117] In some embodiments, the optical metalenses 310, 312 may be in physical contact with each other (not shown). In other embodiments, as shown in FIG. 3, a free-space region 320 is disposed between the first and second optical metalenses 310, 312. Due to the free- space region 320, the first and second optical fibers 302 and first and second optical metalenses 310, 312 do not touch. As such, the optical connector 300 may withstand a greater amount of mating cycles without frequent cleaning and is more resistant to damage from vibration and other mechanical forces. In embodiments, the free-space region 320 may be greater than 0 mm and less than or equal to 10 mm, greater than 0 mm and less than or equal to 8 mm, greater than 0 mm and less than or equal to 6 mm, greater than 0 mm and less than or equal to 4 mm, greater than 0 mm and less than or equal to 2 mm, greater than 0 mm and less than or equal to 1 mm, greater than or equal to 0. 1 mm and less than or equal to 10 mm, greater than or equal to 0. 1 mm and less than or equal to 8 mm, greater than or equal to 0.1 mm and or equal to 6 mm, greater than or equal to 0. 1 mm and less than or equal to 4 mm, greater than or equal to 0.1 mm and less than or equal to 2 mm, greater than or equal to 0. 1 mm and less than or equal to 1 mm, greater than or equal to 0.5 mm and less than or equal to 10 mm, greater than or equal to 0.5 mm and less than or equal to 8 mm, greater than or equal to 0.5 mm and or equal to 6 mm, greater than or equal to 0.5 mm and less than or equal to 4 mm, greater than or equal to 0.5 mmSP24-264 and less than or equal to 2 mm, greater than or equal to 0.5 mm and less than or equal to 1 mm, greater than or equal to 1 mm and less than or equal to 10 mm, greater than or equal to 1 mm and less than or equal to 8 mm, greater than or equal to 1 mm and or equal to 6 mm, greater than or equal to 1 mm and less than or equal to 4 mm, or even greater than or equal to 1 mm and less than or equal to 2 mm, or any and all sub-ranges formed from any of these endpoints.

[0118] In embodiments, the optical connector 300 may be a multi -fiber connector that collimates an array of fibers. For example, at least one of the first optical fiber 302 and the second optical fiber 304 may comprise a plurality of fibers.

[0119] The efficiency of the first and second optical metalenses 310, 312 (i.e., imparts a target phase to light passing through the optical metalens and the optical metalens comprises a transmittance greater than or equal to 80% at a wavelength of the light greater than or equal to 800 nm and less than or equal to 1600 nm) limits the insertion loss of the optical connector 300. In embodiments, the optical connector 300 may comprise an insertion loss less than or equal to 2 dB, less than or equal to 1 .75 dB, less than or equal to 1.5 dB, less than or equal to 1.25 dB, less than or equal to 1 dB, or even less than or equal to 0.75 dB.Examples

[0120] In order that various embodiments be more readily understood, reference is made to the following examples, which are intended to illustrate various embodiments of the optical metalenses according to embodiments described herein.

[0121] Plurality of Nanostructures

[0122] The plurality of nanostructures of the optical metalenses described herein may comprise a combination of materials, shapes, and optical functions. For example, referring now to FIG. 4, from Oh, Jaewon, et al., "Adjoint-optimized metasurfaces for compact modedivision multiplexing." ACS photonics 9.3 (2022): 929-937, which is incorporated by reference herein in its entirety, circular pillars on a glass substrate leveraging a waveguide propagation phase are shown. Referring now to FIG. 5, from M. Khorasaninejad and F. Capasso, “Metalenses: Versatile multifunctional photonic components.” Science (2017), which is incorporated by reference herein in its entirety, rectangular pillars of titanium dioxide leveraging Pancharatnam-Berry phase are shown. Referring now to FIG. 6, from D. Sell et al, “Large-Angle, Multifunctional Metagratings Based on Freeform Multimode Geometries.”SP24-264Nano Letters (2017), which is incorporated by reference herein in its entirety, inverse designed titanium dioxides structures leveraging complex Bloch mode engineering are shown.

[0123] Configuration of Cladding Thickness and Nanostructure Dimension and / or Nanostructure Height

[0124] The following are examples of evaluating various cladding thicknesses, nanostructure dimensions, and nanostructure heights to determine the parameters that result in an optical metalens that imparts a target phase to light passing through the optical metalens and the optical metalens comprises a transmittance greater than or equal to 80% at a wavelength of the light greater than or equal to 800 nm and less than or equal to 1600 nm, as described herein.

[0125] Note that the values for transmittance are provided as transmittance coefficient (i.e., transmittance (in percentage (%)) = transmittance coefficient x 100)

[0126] Library Approach

[0127] Cladding thicknesses, nanostructure dimensions, and nanostructure heights were evaluated using amorphous silicon circular pillar nanostructures and silicon dioxide cladding. The spacing between the pillars was fixed at 500 nm. The wavelength of light was 1310 nm.

[0128] Referring now to FIGS. 7-14, transmittance as a function of pillar diameter (i.e., nanostructure dimension; in nm) for a range of pillar heights (i.e., nanostructure height; in pm) and a range of cladding thicknesses (in pm) are shown. As exemplified, more resonances and, thus, lower transmittance s, were exhibited at certain pillar diameters.

[0129] Referring now to FIG. 16, the average transmittances across all pillar diameters shown in FIGS. 7-14 as a function of pillar height (in pm) for a range of cladding thicknesses (in pm) are shown. As exemplified, a pillar height of 0.75 pm to 1 pm and a cladding thickness of greater than 0 pm to 0.5 pm resulted in a transmittance greater than or equal to 80%. As also exemplified, a pillar height of 0.85 pm to 0.95 pm and a cladding thickness of 0.15 pm to 0.35 pm results in a transmittance greater than or equal to 90%.

[0130] Referring now to FIGS. 17-25, 2n phase coverage as a function of pillar diameter (i.e., nanostructure dimension; in nm) for a range of pillar heights (i.e., nanostructure height; in pm) and a range of cladding thicknesses (in pm) are shown. As exemplified, a pillar height of greater than 0.95 pm resulted in 2n phase coverage across the evaluated range of pillarSP24-264 diameters. However, as shown in FIG. 16, the average transmittance of these relatively taller pillars was lower compared to the pillars having a pillar height of 0.9 pm to 0.95 pm. For pillar heights less than 0.8 pm, there was no complete 2TI phase coverage for the range of pillar diameters evaluated. As also exemplified, cladding thickness did not effect the phase coverage within the cladding thicknesses evaluated.

[0131] Referring now to FIG. 26, transmittance coefficient and 2n phase coverage as a function of pillar diameter in microns (pm) at 1310 nanometers is shown. In view of the data shown in FIGS. 7-25, pillar height was set at 0.95 pm and cladding thickness was set at 0.25 pm. As exemplified, sharp resonances were exhibited with low transmission, due to the various pillar diameters across the evaluate range of pillar diameters.

[0132] Referring now to FIG. 27, transmittance is depicted as a function of the global phase shift imparted by the metalens onto the incident beam. As described herein, the distribution of pillar diameters on a planar substrate of an optical metalens may be determined by the target phase profile of the incident Gaussian beam and global phase of the optical metalens (i.e., distribution of pillars relative to a central pillar). For a given global phase, the pillar diameter distribution was determined. At each nanostructure, the output intensity was calculated by multiplying the input intensity with the transmittance for the corresponding pillar diameter. The total transmittance was then calculated by integrating the intensity of the Gaussian beam (normalized to the input power), as shown in FIG. 27. The desired constant phase shift was 0.6 * 2TI, corresponding to a central pillar diameter equal to 294 nm. The transmittance of such an optical metalens was about 96%.

[0133] Optical Connector Simulation

[0134] To verify performance of an optical connector, an expanded beam connector was simulated using the data obtained in the Library Approach described hereinabove. In particular, a Finite -Difference Time-Domain (FDTD) simulation using open-source MIT Electromagnetic Equation Propagation (MEEP) was implemented. Because of the size of the simulation (i.e., 100 pm x 100 pm in the transverse plane and >1 mm in the propagation direction), the simulation domain was divided in 5 sections along the propagation direction as shown in FIG. 28. Section 1 was an input planar substrate between an input fiber and a metasurface. Section 3 was a free-space region between two metasurfaces having a length of 20 pm. Section 5 was an output plane substrate between a metasurface and an output fiber.SP24-264Sections 2 and 4 were the metasurfaces including the plurality of nanostructures and the cladding. The metasurfaces had the following properties: pillar height of 0.95 pm, pillar diameters in a range of 50 nm to 400 nm, with a central pillar diameter of 294 nm, cladding thickness of 0.25 pm, and a unit cell size of 500 pm x 500 pm.

[0135] The Rayleigh-Sommerfeld propagation method (plane-wave decomposition) in regions containing only a uniform medium (i.e., sections 1, 3, and 5). Sections 2 and 4 were propagated using FDTD. The output field after section 5 was projected into a fiber mode (through an overlap integral calculation). This approach captured the response of the metasurfaces, including phase errors and reflection, and captured mode mismatch. This approach did not capture reflection effects.

[0136] Referring now to FIGS. 29 and 30, simulated intensity (in a.u.) and phase profile (phase normalized to 2TI phase) of fiber-expanded mode (approximated with Gaussian beam) as a function of the lateral coordinate along a surface of the first optical metalens (in microns (pm)) after interacting with the first optical metalens (i.e., Sections 1 and 2) are shown. As shown in FIG. 30, the 2TI phase coverage was flattened out, indicating collimation. As shown by the ripples in the field, there was some phase error that caused undesired diffraction. This is a common limitation of a library approach and may be corrected using a shape-optimization algorithm. Nevertheless, the first optical metalens had a transmittance of 94.3%. The second optical metalens (i.e., Sections 4 and 5) had a transmittance of 94.7%. The overlap loss representing mode mismatch was 95.0%. This resulted in a total fiber to fiber coupling efficiency of 84.0% or 0.75 dB insertion loss.

[0137] For a complete FDTD modeling of the device, a trial version of GPU implementation by Tidy 3D was used. Referring now to FIG. 31, fiber to fiber efficiency (in %) as a function of wavelength (in microns (pm)) is shown. As used herein, “efficiency” is defined as the ratio of optical power coupled to the fundamental mode of the second fiber to the optical power in the fundamental mode of the first fiber. As shown, the peak efficiency was 85%, corresponding to 0.74 dB insertion loss. The 3 dB bandwidth was approximately 200 nm. The peak efficiency was slightly shifted from the target of 1310 nm to 1322 nm (a 0.9% shift). This is also common in a library approach and tuning the pillar may be conducted to shift the peak back to 1310 nm. Overall, the result of the complete FDTD modeling was in alignment with the segmented modeling procedure of FIG. 28.SP24-264

[0138] Broadband Optical Metalens and Connector Library Approach and Simulation

[0139] A broadband optical metalens for a bandwidth of 1.31 pm to 1.51 pm (1310 nm to 1510 nm) was evaluated. Amorphous silicon circular pillar nanostructures and silicon dioxide cladding were used. A similar library approach as described above was used.

[0140] The building block of the optical metalens was a square unit cell with 4 pillars, as shown in FIG. 32. The pillars along the diagonal and the antidiagonal had the same diameter. As shown in FIGS. 33-36, a library was built for this unit cell (i.e., simulated dependence of intensity transmission and relative phase shift on the diameters of the pillars along the diagonal and anti -diagonal). The size of the unit cell and the heights of the pillars were selected to ensure full 2TI phase coverage for the range of pillar diameters.

[0141] The broadband optical metalens evaluated collimated the divergent beam at two wavelengths, 1.31 pm and 1.51 pm, resulting in the optical metalens imprinting a wavelengthdependent square phase on the beam, as shown in FIGS. 37-39.

[0142] Referring now to FIGS. 40-43, a FDTD simulation was conducted, simulating intensity and phase distributions of the fiber expanded mode (approximated by a Gaussian beam) after interaction with the broadband optical metalens. The phase profile of the Gaussian beam was flattened out after interaction with the broadband optical metalens, indicating collimation at both wavelengths.

[0143] Referring now to FIG. 44, two integral characteristics of the broadband optical metalens as a function of wavelength are shown. The first is the integral intensity transmittance of the expanding Gaussian mode through the metalens. The second characteristic is the overlap of the transmitted field with the field of the perfectly collimated Gaussian beam (i.e. the Gaussian beam with the flat phase profile). This characterizes the collimation property of the broadband optical metalens. The metalens collimated not only at the target wavelengths of 1.31 pm and 1.55 pm, but also at the intermediate wavelengths.

[0144] The efficiency of the expanded beam connector, based on the two broadband metalenses, was estimated as follows:Efficiency = Integral transmission2x Overlap integralSP24-264

[0145] Referring now to FIG. 45, the estimated efficiency of the broadband connector is shown. The broadband connector had a larger bandwidth at the cost of the reduced efficiency as compared to the example optical connector (i.e. narrowband) simulated hereinabove.

[0146] It will be apparent to those skilled in the art that various modifications and variations may be made to the embodiments described herein without departing from the spirit and scope of the claimed subject matter. Thus, it is intended that the specification cover the modifications and variations of the various embodiments described herein provided such modification and variations come within the scope of the appended claims and their equivalents.

Claims

SP24-264CLAIMSWhat is claimed is:1 . An optical metalens comprising: a planar substrate; a plurality of nanostructures extending from a surface of the planar substrate, the plurality of nanostructures arranged in a plurality of unit cells, each nanostructure of the plurality of nanostructures comprising a nanostructure dimension and a nanostructure height; and a cladding extending from the surface of the planar substrate and encompassing the plurality of nanostructures, the cladding having a cladding thickness greater than the nanostructure height of each nanostructure of the plurality of nanostructures and a planar cladding surface opposite the planar substrate; wherein the cladding thickness and at least one of the nanostructure dimension and the nanostructure height of each nanostructure of the plurality of nanostructures are configured such that the optical metalens imparts a target phase to light passing through the optical metalens and the optical metalens comprises a transmittance greater than or equal to 80% at a wavelength of the light greater than or equal to 100 nm and less than or equal to 10000 nm.

2. The optical metalens of claim 1, wherein the cladding thickness is greater than or equal to 0.05 pm and less than or equal to 0.5 pm.

3. The optical metalens of claim 1 or claim 2, wherein the cladding comprises silicon dioxide, silicon nitride, SU-8, hydrogen silsesquioxane, or a combination thereof.

4. The optical metalens of any one of claims 1-3, wherein each nanostructure of the plurality of nanostructures comprises a cylindrical shape, a rectangular shape, a hexagonal shape, or an irregular shape.

5. The optical metalens of any one of claims 1-4, wherein the nanostructure dimension of each nanostructure of the plurality of nanostructures may be greater than or equal to 0.02X / RInto less than or equal to 5 OX / RIn, wherein “X” refers to the wavelength of the light and “RIn” refers to the refractive index of the nanostructure.SP24-2646. The optical metalens of any one of claims 1-5, wherein the nanostructure dimension of one of the plurality of nanostructures differs from the nanostructure dimension of another one of the plurality of nanostructures.

7. The optical metalens of any one of claims 1-6, wherein the nanostructure height of each nanostructure of the plurality of nanostructures may be greater than or equal to 0. 1 Z / R Into less than or equal to 51 / RIn, wherein “X” refers to the wavelength of the light and “RIn” refers to the refractive index of the nanostructure.

8. The optical metalens of any one of claims 1-7, wherein each nanostructure of the plurality of nanostructures comprises a refractive index greater than or equal to 1.3.

9. The optical metalens of any one of claims 1-8, wherein each nanostructure of the plurality of nanostructures comprises amorphous silicon, crystalline silicon, silicon nitride, chalcogenide glasses, titanium oxide, optical resins, or combinations thereof.

10. The optical metalens of any one of claims 1-9, wherein the plurality of unit cells are arranged in a two-dimensional pattern covering an area of the surface of the substrate.

11. The optical metalens of any one of claims 1-10, wherein each unit cell of the plurality of unit cells comprises a single nanostructure of the plurality of nanostructures.

12. The optical metalens of any one of claims 1-11, wherein each unit cell of the plurality of unit cells comprises at least two nanostructures of the plurality of nanostructures.

13. The optical metalens of any one of claims 1-12, further comprising a coating disposed on the cladding.

14. The optical metalens of any one of claims 1-13, wherein the planar substrate comprises a refractive index greater than or equal to 1.3.

15. The optical metalens of any one of claims 1-14, wherein the planar substrate comprises a glass or a polymer.SP24-26416. The optical metalens of any one of claims 1-15, wherein the planar substrate comprises a thickness greater than or equal to 50 pm and less than or equal to 5 mm.

17. An optical connector comprising: a first optical fiber configured to transmit light; a first optical metalens coupled to and positioned to receive the light from the first optical fiber; a second optical fiber configured to receive the light; and a second optical metalens coupled to the second optical fiber, the second optical metalens positioned to receive the light from the first optical metalens and transmit the light to the second optical fiber; wherein each of the first optical metalens and the second optical metalens comprises the optical metalens of any one of claims 1-16.

18. The optical connector of claim 17, wherein at least one of the first optical fiber and the second optical fiber comprises a plurality of fibers.

19. The optical connector of claim 17 or claim 18, wherein the wavelength of the light is greater than or equal to 850 nm and less than or equal to 1550 nm.

20. The optical connector of any one of claims 17-19, wherein the light comprises a single wavelength.

21. The optical connector of any one of claims 17-20, wherein the light comprises at least 2 wavelengths.

22. The optical connector of any one of claims 17-21, wherein the optical connector comprises an insertion loss less than or equal to 2.0 dB at the wavelength of the light.

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