WAVE-TRANSFORMING MICROWAVE METAMATERIALS WITH OPTICALLY

INVISIBLE INTERNAL STRUCTURE

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

[0001] This patent application claims the benefit under 35 U.S. C. § 119(e) of U.S. Patent Application Serial No. 63/359,542, entitled “WAVE-TRANSFORMING MICROWAVE METAMATERIALS WITH OPTICALLY INVISIBLE INTERNAL STRUCTURE,” filed on July 8, 2022, which is incorporated herein by reference in its entirety.

FIELD OF THE INVENTION

[0002] The present application relates to microwave technology and wireless communications. More particularly, the present application relates to wireless power transfer devices, transparent wave-transforming devices, and methods for fabricating the same.

BACKGROUND OF THE INVENTION

[0003] Microwave antennas are used to broadcast microwave transmissions between two or more locations. In addition to broadcasting, antennas are also used in radar, radio astronomy, wireless power transmissions, and electronic warfare. The antennas may be reflector antennas, such as parabolic reflectors having a curved surface with the cross- sectional shape of a parabola, to direct the radio waves. The antennas can act as transmitting antennas, receiving antennas, or both.

[0004] Affordable large-aperture (greater than 10 wavelengths) and ultralow profile (less than 1 wavelength) centimeter (cm) or millimeter (mm) wave antennas currently do not exist. Conventional dish antennas are approximately parabolic and use large curved surfaces, leading to their thick profile (i.e., the thickness of an enclosing parallelepiped). Phased array and active metasurface-like antennas are still not currently at a price point where they could be deployed by hundreds of millions. In addition, making any of such devices visually transparent and usable as windows, display coatings, screens, aircraft/vessel illuminators or optically -transparent radomes is a difficult challenge. [0005] Furthermore, with the advent of millimeter-wave communications to radio access networks (RANs), such as 5 ^th generation (5G) cellular networks, a new challenge has emerged: extending or improving wireless coverage in indoor environments, which are largely shielded from millimeter waves by conventional building construction materials, and in some cases, by conductor-coated low-emission window glass.

Thus, the need remains for optically transparent wave-transforming devices that can be used instead of, or combined with, conventional windows.

SUMMARY OF THE INVENTION

[0006] It has been discovered that large-aperture mm-wave antennas with flat geometry and ultralow profde, with the additional benefit of being visual, can replace window glasses in offices and residential buildings and enable highly efficient wireless links using geostationary satellite communications or 5G wireless communication.

[0007] This discovery has been exploited to develop the present disclosure, which, in part, is directed to optically transparent wave-transforming devices including metamaterials operating at microwave or mm-wave bands.

[0008] In one aspect, a structure is provided for at least one electromagnetic wave transformation at one or more operational frequencies. The structure includes a first layer of a first dielectric material having a top structured surface and a bottom surface. The structure also includes a second layer of a second dielectric material having a top surface opposite and substantially parallel to the bottom surface of the first layer and a bottom structured surface conforming with the top structured surface of the first layer.

[0009] In some examples, which may be combined with each of the disclosed examples, either or both of the first and second dielectric materials are at least partially optically transparent.

[0010] In some examples, which may be combined with each of the disclosed examples, the bottom structured surface of the second layer conforming with the top structured surface of the first layer is structured to achieve an electromagnetic wave transformation.

[0011] In some examples, which may be combined with each of the disclosed examples, the first dielectric material comprises a material having a first dielectric constant Ei at the one or more operational frequencies of the at least one electromagnetic wave transformation, and the second dielectric material comprises a material having a second dielectric constant £2 different from the first dielectric constant £1 at the one or more operational frequencies of the at least one electromagnetic wave transformation.

[0012] In some examples, which may be combined with either or both of the examples described herein, the first and the second dielectric materials have a dielectric loss tangent of less than 0. 1 at the one or more operational frequencies of the at least one electromagnetic wave transformation.

[0013] In some examples, which may be combined with each of the disclosed examples, the structure is periodic in one or two dimensions.

[0014] In some examples, which may be combined with each of the disclosed examples, the structure includes a linear grating or a two-dimensional grating.

[0015] In some examples, which may be combined with each of the disclosed examples, the structure includes a metamaterial or a metasurface at the one or more operational frequencies of the at least one electromagnetic wave transformation.

[0016] In some examples, which may be combined with each of the disclosed examples, the first dielectric material and the second dielectric material are refractive index-matched for at least one wavelength of visible light.

[0017] In some examples, which may be combined with each of the disclosed examples, the first dielectric material and the second dielectric material are refractive index-matched throughout at least one spectral band of visible light.

[0018] In some examples, which may be combined with each of the disclosed examples, the one band of visible light includes the visible spectrum having wavelengths ranging from about 380 nm to about 750 nm.

[0019] In some examples, which may be combined with each of the disclosed examples, the bottom surface is a first outer surface of the structure and the top surface is a second outer surface of the structure. Each of the first and second outer surfaces is substantially flat.

[0020] In some examples, which may be combined with each of the disclosed examples, each of the first and second dielectric materials is optically transparent such that the structure has a transmittance at a normal incidence of at least about 80% within a wavelength of about 400 nm to about 750 nm.

[0021] In some examples, which may be combined with each of the disclosed examples, the free-space wavelength for electromagnetic wave transformations ranges from about 0. 1 mm to about 1.0 cm. [0022] In some examples, which may be combined with each of the disclosed examples, the total thickness of the structure equals 1/4 or 1/3 of an effective wavelength of electromagnetic waves at the at least one operating frequency in a medium having a dielectric constant of E _a v = (Ei + E2)/2.

[0023] In some examples, which may be combined with each of the disclosed examples, the structure provides wave transformations including beam deflection, beam broadening, beam collimation, or beam splitting.

[0024] In some examples, which may be combined with each of the disclosed examples, the structure is configured for deflecting an incident plane wave at a predetermined angle. [0025] In some examples, which may be combined with each of the disclosed examples, the structure is configured for beam broadening or beam spreading suitable for wireless communications.

[0026] In some examples, which may be combined with each of the disclosed examples, the structure is configured for beam collimation or focusing suitable for wireless communications.

[0027] In some examples, which may be combined with each of the disclosed examples, the structure is configured for beam splitting by converting a single incident beam into multiple beams suitable for wireless communications.

[0028] In some examples, which may be combined with each of the disclosed examples, the structure provides beam concentration suitable for wireless power transfer devices.

[0029] In some examples, which may be combined with each of the disclosed examples, the largest diameter of the structure is between about 37 mm and about 52 mm, and at least one of a contour and shapes of the structure is configured to fit into an eyewear frame.

[0030] In some examples, which may be combined with each of the disclosed examples, the structure is between about 5 cm and about 10 cm in width and between about 10 cm and about 15 cm in height, and at least one of a contour and shape of the structure is configured to fit into a frame of a portable handheld device.

[0031] In some examples, which may be combined with each of the disclosed examples, the structure is between about 15 cm and about 40 cm in width and between about 10 cm and about 30 cm in height, and at least one of a contour and shape of the structure is configured to fit into a frame of a portable or stationary computer display. [0032] In some examples, which may be combined with each of the disclosed examples, wherein the structure is between about 40 cm and 240 cm in width and between about 30 and about 180 cm in height and at least one of a contour and shape of the structure is configured to fit into a frame of a TV display.

[0033] In some examples, which may be combined with each of the disclosed examples, the structure is between about 1 m and about 10 m in width and between about 0.7 m and about 7 m in height, and at least one of a contour and shape of the structure is configured to fit into a frame of a billboard screen or billboard-size display.

[0034] In some examples, which may be combined with each of the disclosed examples, the structure is between about 0.5 m and about 3 m in width and between about 0.5 m and about 5 m in height, and at least one of a contour and shape of the structure is configured to fit into a frame of a residential, industrial or office building.

[0035] In some examples, which may be combined with each of the disclosed examples, the structure is between about 1 m and about 3 m in width and between about 1 m and about 2 m in height, and at least one of a contour and shape of the structure is configured to fit onto an automotive windshield.

[0036] In some examples, which may be combined with each of the disclosed examples, the structure is between about 20 cm and about 50 cm in diameter, and at least one of a contour and shapes of the structure is configured to fit onto an illuminator of an aircraft or vessel or to serve as such an illuminator.

[0037] In some examples, which may be combined with each of the disclosed examples, the structure is between about 5 cm and about 50 cm in diameter, and at least one of a contour and shapes of the structure is configured to fit onto a radome of an aircraft or vessel which houses at least one optical device or to serve as a radome.

[0038] In some examples, which may be combined with each of the disclosed examples, a pair of the first dielectric material and the second dielectric material includes SiCh-bascd glass with additives, the SiCh-bascd glass having a dielectric constant ranging from about 3.8 to about 14.5, and polyethylene having a dielectric constant of about 2.25, and the pair having a matched refractive index of about 1.58.

[0039] In some examples, which may be combined with each of the disclosed examples, a pair of the first dielectric material and the second dielectric material includes polycarbonate having a dielectric constant of about 2.9 and polyethylene having a dielectric constant of about 2.25, and the pair having a matched refractive index of about 1.58.

[0040] In some examples, which may be combined with each of the disclosed examples, a pair of the first dielectric material and the second dielectric material includes PET having a dielectric constant of about 3. 1 and silica-based glass having a dielectric constant ranging of about 4.0, the pair having a matched refractive index of about 1.63.

[0041] In some examples, which may be combined with each of the disclosed examples, a pair of the first dielectric material and the second dielectric material includes doped silica glass having a dielectric constant greater than about 6.0 and PMMA having a dielectric constant of about 3.4, the pair having a matched refractive index of about 1.49.

[0042] In some examples, which may be combined with each of the disclosed examples, a pair of the first dielectric material and the second dielectric material includes glycerin having a dielectric constant of about 42.5, and silica glass having a dielectric constant of about 4.0, the pair having a matched refractive index of about 1.47.

[0043] In some examples, which may be combined with each of the disclosed examples, a pair of the first dielectric material and the second dielectric material includes silica glass or polymer glass plus index-matched immersion liquid.

[0044] In some examples, which may be combined with each of the disclosed examples, the index-matched immersion liquid includes oils having a dielectric constant higher than about 4.0.

[0045] In some examples, which may be combined with each of the disclosed examples, the second layer of dielectric material includes the immersion liquid. The structure further includes a substrate supporting the second layer of the second dielectric material.

[0046] In some examples, which may be combined with each of the disclosed examples, the first layer of the first dielectric material or the second layer of the second dielectric material is discontinuous. The structure further includes a substrate supporting the second layer of the second dielectric material.

[0047] In some examples, which may be combined with each of the disclosed examples, the first layer having the first thickness zi is filled uniformly with the first dielectric material. [0048] In some examples, which may be combined with each of the disclosed examples, the second layer having the second thickness Z2is filled uniformly with the second dielectric material. [0049] In some examples, which may be combined with each of the disclosed examples, dimensions of the structure along an x-axis and a y-axis form a rectangular shape.

[0050] In some examples, which may be combined with each of the disclosed examples, the structure includes a layer of optically transparent and microwave-reflective material over one of the bottom surface or the top surface such that the structure transforms incident waves in a reflection mode.

[0051] In some examples, which may be combined with each of the disclosed examples, the optically transparent and microwave-reflective material includes an optically transparent conductor having a microwave reflectivity of at least about 80%.

[0052] In some examples, the optically transparent and microwave-reflective material includes a nanostructured metal-dielectric composite or metamaterial having a microwave reflectivity of at least about 80%.

[0053] In some examples, which may be combined with each of the disclosed examples, the structure is used for one of the wireless relay windows, geostationary satellite links, and wireless backhaul links.

[0054] In some examples, which may be combined with each of the disclosed examples, the structure is used for industrial environments including factories or assembly lines where multiple devices or robots communicate with each other.

[0055] In some examples, which may be combined with each of the disclosed examples, the bottom surface of the first layer and the top surface of the second layer are curved surfaces.

[0056] In some examples, which may be combined with each of the disclosed examples, a method is provided for designing the structure for electromagnetic wave transformation. The method includes determining a type of wave transformation. The method also includes using a quantitative figure of merit for the type of wave transformation. The method further includes performing shape optimization of the conforming structured surfaces to increase the figure of merit to exceed a threshold.

[0057] In some examples, which may be combined with each of the disclosed examples, the type of wave transformation is beam deflecting, and the figure of merit is transmissivity into a diffraction order configured to occur at a selected angle of deflection. [0058] In some examples, the type of wave transformation is beam deflecting, and the figure of merit is directivity in the direction of a selected axis of a deflected beam, propagation.

[0059] In some examples, which may be combined with each of the disclosed examples, the type of wave transformation is electromagnetic beam splitting, and the figure of merit comprises a weighted combination of directivity in the directions of selected axes of the split beams.

[0060] In some examples, which may be combined with each of the disclosed examples, the structure has an optical transmissivity of at least about 80% in an about 400 nm to about 750 nm band and produces two beams of an angle ranging from 10° to 170° apart in an about 26-28 GHz band.

[0061] In some examples, which may be combined with each of the disclosed examples, the type of wave transformation is beam concentrating, and the figure of merit is power density at a predefined point or total power incident within a predefined area.

[0062] In some examples, which may be combined with each of the disclosed examples, the type of wave transformation is beam broadening, and the figure of merit is a total coverage area in which a resulting power exceeds a predefined threshold.

[0063] In some examples, which may be combined with each of the disclosed examples, the total thickness of the structure is predefined.

[0064] In some examples, which may be combined with each of the disclosed examples, a method is provided for fabricating the structure for electromagnetic wave transformation.

The method includes fabricating the first layer of the first dielectric material. The method may also include fabricating the second layer of the second dielectric material complementary to the first layer. The method may further include joining the first layer and the second layer at their conforming surface.

[0065] In some examples, which may be combined with each of the disclosed examples, the method may further include wetting the surfaces of the first layer and the second layer with a layer of refractive index-matching liquid before joining the first and the second layers together.

[0066] In some examples, which may be combined with each of the disclosed examples, fabricating the first layer of the first dielectric material includes patterning or casting the first layer of the first dielectric material into a predefined shape. [0067] In some examples, which may be combined with each of the disclosed examples, fabricating the second layer of the second dielectric material includes patterning or casting the second layer of the first dielectric material into a predefined shape.

[0068] In some examples, which may be combined with each of the disclosed examples, a method is provided for fabricating the structure. The method includes fabricating the first layer of the first dielectric material. The method may also include fabricating the second layer of the second dielectric material from a liquified form of the second material using the fabricated first layer as a mold.

[0069] In some examples, which may be combined with each of the disclosed examples, a method is provided for fabricating the structure. The method includes fabricating the first layer of the first dielectric material. The method may also include fabricating the second layer of the second dielectric material using the fabricated first layer as a mold by filling the mold with a liquid precursor of the second material.

[0070] In some examples, which may be combined with each of the disclosed examples, the liquid precursor of the second material is transformed into a solid form of the second material by photopolymerization or thermal polymerization.

[0071] In some examples, which may be combined with each of the disclosed examples, a method is provided for using the structure for electromagnetic wave transformation. The method includes relaying wireless communications in industrial environments where multiple devices or robots communicate with each other.

[0072] In some examples, which may be combined with each of the disclosed examples, the industrial environments include one or more factories or assembly lines.

BRIEF DESCRIPTION OF THE DRAWING

[0073] The foregoing and other objects of the present disclosure, the various features thereof, as well as the disclosure itself, may be more fully understood from the following description when read together with the accompanying drawings which:

[0074] FIG. 1A is a schematic representation delineating a top view of a transparent beam deflector with a pair of dielectric materials according to an embodiment of the disclosure;

[0075] FIG. IB is a schematic reorientation showing a cross-sectional view of one period of the beam deflector of FIG. 1 A according to an embodiment of the disclosure; [0076] FIG. 2A is a schematic representation delineating an alternative cross-sectional view of one period of the beam deflector of FIG. 1 A including a discontinuous dielectric layer and a substrate for supporting according to an embodiment of the disclosure;

[0077] FIG. 2B is a schematic representation delineating an alternative cross-sectional view of one period of the beam deflector of FIG. 1 A including a liquid dielectric layer and a substrate for supporting according to an embodiment of the disclosure;

[0078] FIG. 2C is a schematic representation delineating an alternative cross-sectional view of one period of the beam deflector of FIG. 1 A including a top substrate and a bottom substrate that sandwich the two layers of dielectric materials according to an embodiment of the disclosure;

[0079] FIG. 3 is a schematic representation delineating a top view of a transparent beam splitter with a pair of dielectric materials according to an embodiment of the disclosure;

[0080] FIG. 4 is a schematic representation delineating a top view of a transparent beam broadening device with a pair of dielectric materials according to an embodiment of the disclosure;

[0081] FIG. 5 is a schematic representation delineating a top view of a transparent beam collimation device with a pair of dielectric materials according to an embodiment of the disclosure;

[0082] FIG. 6 is a flow chart illustrating the steps for forming according to an embodiment of the disclosure;

[0083] FIG. 7A is a schematic representation delineating a cross-sectional view of one period of the beam deflector of FIG. 1A having a thickness of 1.6 mm according to an embodiment of the disclosure;

[0084] FIG. 7B is a representation of a convergence graph for the design of the beam deflector shown in FIG. 7A according to an embodiment of the disclosure;

[0085] FIG. 7C is a schematic representation of an image of the electric field distribution in a transparent beam deflector illuminated from the bottom by a normally incident plane wave according to an embodiment of the disclosure;

[0086] FIG. 8A is a schematic representation delineating a cross-sectional view of one period of the beam deflector of FIG. 1A having a thickness of 1. 1 mm according to an embodiment of the disclosure; [0087] FIG. 8B is a schematic representation of a convergence graph for the design of the beam deflector shown in FIG. 8A according to an embodiment of the disclosure;

[0088] FIG. 8C is a schematic representation of an image of the electric field distribution in a transparent beam deflector illuminated from the bottom by a normally incident plane wave according to an embodiment of the disclosure; and

[0089] FIG. 9 is a schematic representation of curved surfaces approximated with polyhedral surfaces including piecewise-flat polygons according to an embodiment of the disclosure.

DETAILED DESCRIPTION

[0090] The disclosures of the following patents, patent applications, and publications in their entirety are hereby incorporated by reference into this application to more fully describe the state of the art as known to those skilled therein as of the date of the invention described and claimed herein. The instant disclosure will govern in the instance that there is any inconsistency between the patents, patent applications, and publications and this disclosure. [0091] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. The initial definition provided for a group or term herein applies to that group or term throughout the present specification individually or as part of another group unless otherwise indicated.

[0092] To explain the well-known features of optical technology known to those skilled in the art have been omitted or simplified in order not to obscure the basic principles of the invention. Parts of the following description will be presented using terminology commonly employed by those skilled in the art of optical design. It should also be noted that in the following description of the invention repeated usage of the phrase “in one embodiment” does not necessarily refer to the same embodiment.

[0093] “Artificially-structured materials” are materials whose electromagnetic or acoustic properties are derived from their structural configurations, rather than or in addition to their material composition.

[0094] ‘ ‘Metamaterials” are a type of artificially structured material that includes subwavelength elements. Subwavelength elements can include structural elements with portions having spatial length scales smaller than an operating wavelength of the metamaterial. Further, the subwavelength elements have a collective response to waves or radiation that corresponds to an effective continuous medium response. For example, in the case of electromagnetic metamaterials, the collective response may be characterized by an effective permittivity, effective permeability, an effective magnetoelectric coefficient, or any combination thereof. For example, electromagnetic radiation may induce charges and/or currents in the subwavelength elements, and the subwavelength elements can acquire nonzero electric and/or magnetic dipole moments. Some metamaterials provide an artificial magnetic response. For example, split-ring resonators (SRRs) and other plasmonic resonators can exhibit an effective magnetic permeability. Some metamaterials have “hybrid” electromagnetic properties that emerge partially from the structural characteristics of the metamaterial, and partially from the intrinsic properties of the constituent materials. For example, a metamaterial consisting of a wire array embedded in a nonconducting ferrimagnetic host medium can exhibit the effects of both the wire array and the host medium.

[0095] ‘ ‘Metamaterials” can be designed and fabricated to exhibit selected permittivity, permeability, and/or magnetoelectric coefficient values that depend upon material properties of the constituent materials as well as shapes, chirality, configurations, positions, orientations, and couplings between the subwavelength elements. The selected permittivity, permeabilities, and/or magnetoelectric coefficients values can be positive or negative, complex (having loss or gain), anisotropic, variable in space (as in a gradient index lens), variable in time (e.g., in response to an external or feedback signal), variable in frequency (e.g., in the vicinity of a resonant frequency of the metamaterial), or any combination thereof. The selected electromagnetic properties can be provided at wavelengths that range from radio wavelengths to visible wavelengths and beyond.

[0096] ‘ ‘Metamaterials” can include either or both discrete elements or structures and nondiscrete elements or structures. For example, a metamaterial may include discrete structures, such as split-ring resonators. In another example, a metamaterial may include non-discrete elements that are inclusions, exclusions, layers, or other variations along with some continuous structure.

[0097] Further, “metamaterials” can include extended structures having distributed electromagnetic responses, such as distributed inductive responses, distributed capacitive responses, and distributed inductive-capacitive responses. For example, metamaterials can include structures consisting of loaded and/or interconnected transmission lines, artificial ground plane structures, and/or interconnected/extended nanostructures.

[0098] A “metasurface” is a thin layer of a metamaterial. A thin layer of a metamaterial can include a subset of the total volume of the metamaterial. A metasurface can be approximated as an infinitely thin sheet having a surface impedance, or surface impedances for anisotropic responses. When approximated as an infinitely thin sheet the metasurface can lack a refractive index, as waves do not propagate or refract "inside" of the metasurface. Instead, the metasurface can act as a discontinuity in space.

[0099] Dielectric constant (e) is defined as the ratio of the electric permeability of the material to the electric permeability of free space (i.e., vacuum).

[00100] Transmittance is the fraction of incident light that is transmitted through a material. It is defined as the intensity ratio of the transmitted light over the incident light.

[00101] Diffraction is defined as the interference or bending of waves around the comers of an obstacle or through an aperture into the region of the geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating wave.

[00102] A diffraction grating includes a regular pattern. The form of the light diffracted by the diffraction grating depends on the structure of the elements and the number of elements present, but all gratings have intensity maxima at angles 9 which are given by the grating equation: d (sin 9 — sin 9t) = n X where d is the separation of grating elements, X is the free-space wavelength, 9 _t is the incidence angle, and n is an integer called diffraction order.

[00103] As used herein, the articles “a” and “an” refer to one or more than one (i.e., to at least one) of the grammatical object of the article. By way of example, “an element” means one element or more than one element. Furthermore, the use of the term “including” as well as other forms, such as “include,” “includes,” and “included,” is not limiting.

[00104] As used herein, the term “about” will be understood by persons of ordinary skill in the art and will vary to some extent on the context in which it is used. As used herein when referring to a measurable value such as an amount, a temporal duration, and the like, the term “about” is meant to encompass variations of ±20% or ±10%, including ±5%, ±1%, and ±0. 1% from the specified value, as such variations are appropriate to perform the disclosed methods. [00105] Reference will now be made to specific examples illustrating the disclosure. It is to be understood that the examples are provided to illustrate exemplary embodiments and that no limitation to the scope of the disclosure is intended thereby.

[00106] The disclosure provides optically transparent microwave or millimeter-wavetransforming devices (e.g., but not limited to, beam deflector, beam splitter, beam concentrator, or beam broadening device) having a visual appearance like a conventional layer of glass. The disclosure also provides methods for fabricating wave-transforming devices. The disclosure presents a commercially feasible solution for an optically transparent passive relay antenna, having a large aperture and high aperture efficiency and operating in a selected band (or bands) in the centimeter or millimeter wave spectrum. The wavetransforming devices are essentially invisible to the naked eye. These large-aperture, wireless relay devices can be deployed as optically transparent windows and perform wave transformations of incident signals from a wireless base station and/or from an indoor/outdoor wireless device.

[00107] The wave -transforming devices generate wave transformations, which may include beam deflection, i.e., redirection of the beam originating from the signal transmitter towards a region of the room more suitable for the placement of wireless modems. The wave transformations may also include beam broadening, i.e., spreading (de-collimation) of the beam over a predefined region of the room to provide substantially uniform wireless coverage in that region. The wave transformations may also include beam concentration, i.e., focusing (collimation) of the beam towards a specific location, such as a predefined position of a wireless modem, to increase signal strength and consequently data throughput. The wave transformations may also include beam splitting, i.e., converting a single incident beam into multiple beams, each directed toward a receiver.

[00108] In some examples, wave transformations including beam deflection, beam broadening or widening, beam collimation or concentration, and beam splitting may be useful for wireless communications.

[00109] In some examples, beam collimation may also be suitable for wireless power transfer devices, as the beam concentration increases the power flux irradiating a receiver. [00110] In some examples, the wave-transforming devices can operate in a reflection mode in which the incident wave or energy and the transmitted wave or energy are on the same side of the wave-transforming device. [00111] In some examples, the wave-transformation devices can operate in a transmission mode in which the incident wave or energy and the transmitted wave or energy are on opposite sides of the wave-transforming device.

[00112] In some examples, wave transformation devices can operate in a combination of the reflection mode and the transmission mode. For example, some waves or energy may be emitted toward the incident side of the wave-transforming device, and some waves or energy may be transmitted towards the opposite side of the wave-transforming device.

[00113] Each of these types of wave -transforming devices can be constructed using the same building blocks, e.g., but not limited to, sections of a metamaterial transmitting and deflecting an incident plane wave at a predefined angle. For example, a transparent beam deflector is illustrated in FIGS. 1A-1B and FIGS. 2A-2C. A transparent beam splitter is illustrated in FIG. 3. A representative transparent beam collimation device is illustrated in FIG. 5. A transparent beam broadening device is illustrated in FIG. 4.

[00114] A top view of a transparent beam deflector with a pair of dielectric materials is depicted in FIG. 1 A according to an embodiment of the disclosure. As illustrated in FIG. 1 A, a beam deflector 102 has a periodic structure like a linear grating extending along an x-axis with a plurality of periods 106. The beam deflector 102 has a constant thickness of T along a y-axis perpendicular to the x-axis. An incident wave 104 arrives at a back surface 112B of the beam deflector 102 from the left side and transmits through a front surface 112A of the beam deflector 102 to the right side. A transmitted beam 108 is deflected at an angle 0 from a central line 110 along the y-axis. The beam deflector 106 may include two optically matched complementary dielectric layers having sufficiently high contrast at microwave frequencies. [00115] A cross-sectional view of one period of the beam deflector of FIG. 1 A is depicted in FIG. IB according to an embodiment of the disclosure. As illustrated in FIG. IB, the beam deflector 102 may be a flat sandwich including a top surface 112A (referred to as a front surface in FIG. 1A) and a bottom surface 112B (referred to as a back surface in FIG. 1A). The beam deflector 102 may also include two stacked layers of optically transparent dielectric materials between the top surface 112A and the bottom surface 112B. In some embodiments, either or both of the layers are at least partially optically transparent. The transparent dielectric materials have different dielectric constants (E) at the microwave frequency of operation, yet closely matched refractive indexes (RIs) at the center of the visible spectrum. [00116] The beam deflector 102 may include a first structured layer 114A of the first dielectric material, which may have a flat bottom surface 112B and a structured top surface 116. The beam deflector 102 may also include a second structured layer of a second dielectric material, which may have a flat top surface 112A and a structured bottom surface 116 that is conforming with, or complementary to the structured top surface 116 of the first structured layer 114A. The structured top surface 116 or the structured bottom surface 116 is also referred to as an interface or a boundary between the first structured layer 114A and the second structured layer 114B.

[00117] The structured top surface 116 of the first structured layer of the first dielectric material can be any arbitrary surface, which can be described as z=F(x,y) in Cartesian coordinates, where coordinates (x,y) are bounded to a rectangle corresponding to a window area, and z is bounded to the interval [0, T], where T is the thickness of the beam deflector or sandwiched structure 102. All space with 0 < z < F(x,y) is uniformly filled with a first dielectric material having a first dielectric constant, and all space with F(x,y) < z < T is uniformly filled with a second dielectric material having a second dielectric constant. The densities of the first and second dielectric materials do not change with the coordinates, which results in uniformly distributed dielectric materials in structure 102.

[00118] The structured top surface 116 may look like a series of linear grooves including narrow channels or narrow recess regions. Mathematically, the surface function F(x,y) = F(x) does not vary with the y coordinate along the y-axis. Furthermore, the structure can be further simplified by assuming that F(x) is periodic along the x-axis, which allows the modeling of one period along the x-axis.

[00119] In some examples, F(x,y) can be periodic along either the x-axis or y-axis. Alternatively, F(x,y) can be periodic along both the x-axis and y-axis. In yet another example, F(x,y) can be constant in either x or y. When F(x,y) = constant, the surface is flat. [00120] In some examples, the device may include an optional substrate(s) (A and/or B) when one of the first or second dielectric materials is a liquid, or if either the first or second dielectric layer or both are discontinuous. In both these cases, the device would include mechanic al/structural support. Various embodiments are illustrated in FIGs. 2A-2C.

[00121] An alternative cross-sectional view of one period of the beam deflector of FIG. 1 A including a discontinuous dielectric layer and a supporting substrate is depicted in FIG. 2A according to an embodiment of the disclosure. As illustrated in FIG. 2A, the first layer 202B of the first dielectric material is discontinuous near region 208, while the second layer 202A of the second dielectric material may be continuous. The device 106A may include a substrate 204 to support the first layer 202B.

[00122] An alternative cross-sectional view of one period of the beam deflector of FIG. 1 A including a liquid dielectric layer and a supporting substrate is depicted in FIG. 2B according to an embodiment of the disclosure. As illustrated in FIG. 2B, the first layer 203B of the first dielectric material is formed of a liquid, while the second layer 203A of the second dielectric material may be continuous. Device 106B may include a substrate 204 to support the first layer 203A.

[00123] An alternative cross-sectional view of one period of the beam deflector of FIG. 1 A including a top substrate and a bottom substrate that sandwich the two layers of dielectric materials is depicted in FIG. 2C according to an embodiment of the disclosure. The device 106C may optionally include substrate 204B beneath the structured layer 205B of the first dielectric material, whereas the substrate 204B may include a flat layer of the first dielectric material or the second dielectric material. The device 106C may optionally include substrate 204A on top of the structured layer 205A of the second dielectric material, whereas the substrate 204A may include a flat layer of the first dielectric material or the second dielectric material. The optional substrates 204A and/or 204B may be used if one of the dielectric materials is a liquid, or if either the first dielectric layer or the second dielectric layer (or both) are discontinuous, or may need mechanical or structural support.

[00124] The wave-transforming device includes an internally refractive index-matched structure such that the device is visually transparent. The internally refractive index-matched structure introduces little visual distortions that could provide visual cues of the underlying structure inside. The optical transparency can be understood from the following considerations. From the geometrical optics perspective, the internally refractive index- matched structure may be identical to a uniform flat layer, because the refractive index is constant across the structure. Therefore, transmitted rays can propagate without deflections although there can be a finite lateral shift identical to a shift produced by a homogeneous layer of a material with the same refractive index.

[00125] Reflected rays are reflected in a specular fashion from the front and back surfaces, in a way that is indistinguishable from the reflections from a homogeneous-index layer of a constant thickness. The interface between the refractive index-matched materials may not produce reflections regardless of its orientation relative to an incident ray, which can be seen from Fresnel formulas for reflectance:

When the two refractive indexes on the two sides of the interface between media are equal (n2=ni), by Snell’s law we have 0 _t = di (refracted angle equals incidence angle), and consequently, both R _s (reflectance for s-polarization) and reflectance for p-polarization R _p become zero. Therefore, the interface may have zero reflectance for unpolarized as well as arbitrarily polarized light.

[00126] Consequently, both the reflective and transmissive appearance of the internally refractive index-matched structure is generally identical to that of a uniform slab of the same thickness having the same optical refractive index. For example, the two dielectric materials can be paired to have nearly the same refractive index, e.g., but not limited to, within about 1.4 to about 1.6.

[00127] The two different dielectric constants useful for the wave-transforming devices are achievable with the example materials listed in Table 1. The exemplary clear materials along with their dielectric constants and refractive indexes are shown in Table 1.

TABLE 1

[00128] In some embodiments, Neoprene has lower optical transparency than most other materials listed so it is suitable in thin layers (e.g., for millimeter-wavelength applications with mm-scale metamaterial thicknesses).

[00129] Various pairs of clear materials may be used. In some aspects, the pair may include crystalline or amorphous SiCfi with various dopants (E: about 3.8-14.5) and polyethylene (e about 2.25), both with a refractive index is about 1.58.

[00130] In some embodiments, the pair may include polyethylene (E: about 2.25) and polycarbonate (E: about 2.9), both with a refractive index of about 1.58. Alternatively, the pair may include silica glass (E: about 4.0) and polyethylene terephthalate (PET) (E: about 3.1), both with a refractive index of about 1.63.

[00131] In some embodiments, the first material is a conventional transparent material with a known refractive index in the range of about 1.49 to about 1.64 (see examples of such materials in Table 1), and the second material is obtained by fine-tuning the refractive index of a transparent polymer to match the RI of the first material with high accuracy (at or better than about 1%). The manufacturing solution for the fine-tuning of a refractive index of a transparent polymer is available commercially through Promerus, 225 W. Bartges St., Akron, Ohio (a subsidiary of Sumitomo Bakelite Co., Ltd.), which supplies their PDM-5004 family of polymer materials with refractive index tunable throughout the range 1.49-1.64. Promerus PDM-5004 materials have high optical transparency (>92%) and other optical properties suitable for their use in optical components, such as LED display materials, glass lenses, and equipment windows, and they feature a dielectric constant in the range of about 2.2 to about 2.7. This means that pairing them with a first material from Table 1 having a dielectric constant of about 3 or higher (for example, PET, PMMA, Neoprene) achieves a sufficiently high dielectric contrast suitable for low-thickness wave transformation devices. Furthermore, for a batch of PDM-5004 having a dielectric constant of about 2.2, almost all example materials in Table 1 (except PE) are suitable for pairing with it for a reasonably thin (less than 5 free-space wavelengths of electromagnetic waves being transformed) wave transformation device.

[00132] The silica glass may be doped or mixed with inorganic nanoparticles to increase its dielectric constant. Alternatively, the pair may include doped silica glass (E > 6) and plexiglass or poly(methyl methacrylate) (PMMA) (E: about 3.4), both with a refractive index of about 1.49, or may include silica glass (E of about 4) and glycerin (a.k.a. glycerol) (E: about 42.5), both with a refractive index of about 1.47. In some embodiments, the pair may include silica or polymer glass and index-matched immersion liquid, as frequently used in microscopy. The immersion liquid may be oils used as the oils typically have a dielectric constant E substantially higher than 4 (the typical E of silica glass), and therefore provide excellent E contrast with many types of inorganic or polymer glasses.

[00133] In some variations, the variations of the dielectric constant may be due to variations in additives.

[00134] Nonlimiting examples of cost functions for the present functional metamaterial design are as follows.

[00135] A two-dimensional (2D) simulator can be used to design a one -dimensional (ID) grating or a linear grating with a sophisticated unit cell.

[00136] In terms of its microwave behavior, the wave-transforming device can be selected to perform wave transformations, e.g., of type A, B, or C, or any combination thereof over the area of the device.

[00137] To design metamaterials having an internally refractive index-matched structure, geometric optimization can be used. The boundary or interface between the two dielectric layers of spatially variable thickness is a function that can be discretized on a mesh, with the nodal values including the parameters. These parameters may be bounded to keep the boundary within the two-layer sandwich of a predefined thickness.

[00138] In some aspects, for wave-transforming devices, the cost function can be defined as the transmissivity into the desired waveform. For example, for type A (e.g., beam deflector, as illustrated in FIG. 1A), the cost function can be the transmissivity into a diffraction order designed to occur at a desired angle of deflection.

[00139] In some cases, for type A (e.g., beam splitter as illustrated in FIG. 3), the cost function for a transparent beam splitter may include optical as well microwave transmissivity parameters, so that the microwave and optical energy distributions can be optimized simultaneously. For example, an internally refractive index-matched structure may be optimized to have 80% optical transmissivity in the visible spectrum, e.g., the wavelength of about 400 nm to about 700 nm, and also act as a microwave beam splitter producing two transmitted microwave beams about 45° apart in a frequency band, e.g., a band from about 26 GH to about 28 GHz.

[00140] A top view of a transparent beam splitter with a pair of dielectric materials is depicted in FIG. 3 according to an embodiment of the disclosure. As illustrated in FIG. 3, an incident beam 304 transforms into two beams 308A and 308B through a transparent beam splitting device 202, which has a periodic structure like a grating. The two beams 308A and 308B are apart by an angle 0. The incident wave is a superposition of different plane waves. [00141] In some examples, other cost functions may be useful, i.e., due to the ease of computing. For type B (e.g., beam broadening device as illustrated in FIG. 4), the cost function can be the total coverage area, i.e., the area in which the resulting power density exceeds a predefined threshold.

[00142] Atop view of a transparent beam broadening device with a pair of dielectric materials is depicted in FIG. 4 according to an embodiment of the disclosure. The beam broadening can be achieved by conceptually splitting the aperture into segments, each segment deflecting the portion of the wave by a different deflection angle, the collection of the angles chosen to maximize the total angular coverage. As illustrated in FIG. 4, the narrow incident beam 404 transforms into a concentrated beam 408 through a transparent beam broadening device 402, which has a periodic structure like a grating. The concentrated beam 408 is configured to focus on point 410.

[00143] For type C (e.g., beam collimation device as illustrated in FIG. 5), the cost function can be the power density at a predefined point or within a predefined area. A top view of a transparent beam collimation device with a pair of dielectric materials is depicted in FIG. 5 according to an embodiment of the disclosure. The beam collimation can be achieved in a way Fresnel lenses work, e.g., by splitting the aperture into segments and using a deflecting metamaterial that deflects the sub-beam by an angle, such that all sub-beams are deflected towards the same point. As illustrated in FIG. 5, the narrow incident beam 504 transforms into a wide beam 508 through a transparent beam broadening device 502, which has a periodic structure like a grating. The wide beam 508 is configured to cover region 510 within boundary 512. [00144] The disclosure also provides wave-transforming devices with alternative functionality. Wave transformations can be performed on a wavefront being reflected into the half-space from which the incident wave arrives. Accordingly, the devices operate in a reflecting mode, rather than a transmitting mode. The reflection functionality can be achieved by adding a layer of optically transparent, microwave-reflective material, such as a transparent conductor.

[00145] In some examples, the transparent conductor may be ultrathin (less than 50 microns in thickness), and too thin to be visible to the human eye, while simultaneously highly reflective (reflectance >99%) for RF waves. The transparent conductor of this nature may include nanowire mesh, e.g., Nanoweb®, a metamaterial fabricated using rolling mask lithography (RML). Some dielectric materials, such as glass and PMMA, may be suitable for RML-based deposition of nanowire mesh on flat surfaces.

[00146] In some examples, the wave-transforming devices can additionally be coated on either side with anti-reflection layers (e.g., thin-fdm coatings), to reduce reflections in the visible or optical wavelength bands. The anti-reflection layers may further reduce visual distortions. Anti-reflection multilayer coatings are typically about 1 to 100 microns in thickness, with individual layers of about 0. 1 to 5 microns thick.

[00147] Certain manufacturing techniques, particularly, machining, benefit from the absence of curved surfaces. To simplify manufacturing, the design algorithm can be modified to generate piecewise-flat surfaces, which may not be parallel to the overall flat, top, and bottom surfaces. Each structured layer, such as the first dielectric layer or the second dielectric layer, can be split into sections, each section having a flat surface.

[00148] A flow chart illustrating the steps for forming the structure for electromagnetic wave transformation is depicted in FIG. 6 according to an embodiment of the disclosure. Method 600 may include fabricating the first layer of the first dielectric material at operation 602 and fabricating the second layer of the second dielectric material complementary to the first layer at operation 604. In some examples, the first layer and the second layer with entirely flat surfaces can be fabricated separately, and then assembled or joined. For example, the structured layer, such as the first dielectric layer having a flat top surface or the second dielectric layer having a flat bottom surface (e.g., dielectric layers 114A and 114B), can be fabricated separately and then joined together. 1 [00149] In some examples, some manufacturing techniques may benefit from the absence of two-dimensional (Gaussian) curvature and can handle constant one-dimensional curvature (e.g., cylindrical curvature). In that case, the design algorithm can be modified to generate piecewise -constant cylindrical curvature surfaces. In this case, the two flat surfaces are replaced with cylindrically curved surfaces, i.e., surfaces having some curvature in one direction (X) and zero curvature in the perpendicular direction (Y).

[00150] In some examples, the pieces having piecewise-constant curvature or piecewiseconstant linear slope can be optimized to be polygons, for example, rectangles, trapezoids, or hexagons, such that the overall shape is a tiling for such polygons. Curved surfaces (e.g., spheres or spherical sectors) can be approximated with polyhedral surfaces, each including piecewise-flat polygons which are non-flat, as depicted in FIG. 9. Those curved surfaces may be used in roofs, aircraft illuminators, wireless equipment radomes, and camera windows, among others.

[00151] Any errors arising from any such geometric constraints can be compensated using the following technique. Either the top, the bottom, or both flat surfaces of the complementary dielectric layers can be patterned with a thin layer of an optically transparent material having a large complex dielectric constant. Examples of such materials include, but are not limited to, germanium (a high E transparent dielectric), and a broad class of transparent conducting materials, which have a large complex E at microwave frequencies due to their high conductivity. Examples of transparent conductors include, but are not limited to, Indium tin oxide (ITO), nanoparticle-doped silica, and nanowire mesh, e.g., Nanoweb®, which may be manufactured using the RML. These thin layers act separately as metasurfaces or collectively as metamaterial to provide corrections to the phase of the wavefront being transmitted through the structure.

[00152] A useful feature size in the structured surfaces described herein is dependent on the operational wavelength of between about 0.1 mm and about 1 cm. For example, features on the order of about 1 mm are typical for a K or Ka-band device suitable for 5G wireless, Satcom, or K-band wireless power transfer.

[00153] In some examples, patterning of glasses and solid polymers can be performed on such scales using any methods known in the art of machining and micromachining techniques, including, but not limited to, computer numerical control (CNC) machining, laser etching, sandblasting, chemical etching, reactive ion etching, and/or glass reflow. [00154] In some examples, amorphous silica glass and polymer glasses can also be cast into the desired shape using conventional molding techniques.

[00155] Three-dimensional (3D) printing techniques can be used for transparent or clear thermoplastic polymers by commercially available machines based on 3D printing with multiple materials. Transparent or clear photopolymers can be molded and cured or solidified using UV light or thermal curing.

[00156] The two complementary layers are fabricated separately, e.g., using the above techniques. To help eliminate an air gap between the two layers, and/or improve refractive index matching, the surfaces being joined can be covered with a thin layer of an indexmatching liquid.

[00157] Method 600 may also include joining the first layer and the second layer by using a layer of index-matching liquid at operation 606. The index-matching liquids can be commercially obtained (e.g., from Cargille Laboratories, 55 Commerce Rd., Cedar Grove, NJ 07009), which provide specialized optical coupling (index matching) liquids that closely match the refractive index of common materials (e.g., but not limited to, fused silica, and water) at given wavelengths. To further assist this process, the surfaces being joined can be processed or coated with an agent that increases their wetting with the liquid to be used.

[00158] Alternatively, one layer of the structure, for example, a silica glass layer, can be manufactured using one technique, and then used as a mold for the making of the complementary layer.

[00159] For example, any wavefront curving system, such as a focusing lens, is aperiodic. For plane-wave to plane-wave transforming devices, a periodic arrangement may be used. [00160] The structures of the present disclosure can be used in the following nonlimiting applications, including 5G assist windows for residential and business users, industrial environments (e.g., but not limited to, factories or assembly lines) where multiple devices or robots need to be communicated to and from, geostationary satellite links for residential and business users (e.g., but not limited to, satellite TV, satellite phone, satellite internet), wireless backhaul with weather-resistant antennas (snow-repellent, rain-repellent, etc.), among others. EXAMPLES

[00161] Reference will now be made to specific fabrication examples illustrating the disclosure. It is to be understood that the examples are provided to illustrate exemplary embodiments and that no limitation to the scope of the disclosure is intended thereby.

[00162] Exemplary structures according to the disclosure shown in FIGs. 7A-7C and 8A- 8C were designed using a 2D simulator (e.g., software) based on the figure of merit of transmittance. Simulation software COMSOL Multiphysics is used with RF Module.

[00163] The figure of merit (a.k.a. objective or objective function) in FIGs. 7A-7C and FIGs. 8A-8C is transmittance into the first diffraction order. In the 2D simulator, the transmittance is known as a S Ji-parameter, where the state “i” corresponds to the incident plane wave, and state “j” to a transmitted mode, which is the first diffraction order of the periodic structure of the beam deflector of FIG. 1. The objective or objective function are synonymous with the figure of merit.

[00164] The material distribution does change during the design optimization, but only to the extent that the shape of the boundary or interface between the first and second dielectric materials can change during the iterations. During the iterations, the two dielectric materials are fixed. Also, the flat top and bottom surfaces of the beam deflector remain unchanged. Also, the dimensions of the unit cell, i.e., one period of the grating, are constant.

EXAMPLE 1

Beam Deflector Having a Thickness of 1.6 mm

[00165] A cross-sectional view of one period of a transparent beam deflector having a thickness of 1.6 mm is depicted in FIG. 7A according to an embodiment of the disclosure. As illustrated in FIG. 7A, dark areas 704 represent the dielectric material with a lower dielectric constant (E _X = 2.5), and light gray areas 702 represent the dielectric material with a higher dielectric constant (E ₂ = 8). The dark areas 704 and the light areas 702 have an interface or boundary 706. Both materials are distributed uniformly over the areas indicated in dark and gray regions, respectively.

[00166] The design parameters for the beam deflector of FIG. 7A include an operational frequency of 27 GHz (free-space wavelength A _o = 11 mm), dielectric constants of 2.5 and 8 at the operational frequency, a period of 13.3 mm which is 1.2 A _o , and a thickness of 1.6 mm. The thickness corresponds to one-third (1/3) of an effective wavelength in a “median” medium, the latter defined as having a dielectric constant E _av = + E ₂ )/2.

[00167] In FIG. 7A, the horizontal axis corresponds to the y coordinate in meters while the vertical axis corresponds to the z coordinate in meters. As illustrated, the thickness of the beam deflector is 1.6 mm.

[00168] The beam deflector in FIGs. 1 and 7A is obtained after the convergence of the design optimizer, which corresponds to the points with nearly 100% transmittance to the right end of the graph in FIG. 7B.

[00169] A representation of a convergence graph for design optimization in FIG. 7A is depicted in FIG. 7B. The horizontal axis represents the number of iterations, while the vertical axis represents the diffraction efficiency or transmittance into the first diffraction order is obtained at the desired angle of deflection. Note that the design achieves about 100% diffraction efficiency and nearly 100% transmittance, which implies negligible radio frequency (RF) reflectivity.

[00170] FIG. 7C is presented to illustrate light propagation and the deflection of a plane wave by the beam deflector of FIGs. 1 and 7A. A schematic representation of an image of the electric field distribution in a transparent beam deflector illuminated from the bottom by a normally incident plane wave is depicted in FIG. 7C according to an embodiment of the disclosure. The arrows indicate the direction of the local power flow (Poynting vector). As shown in FIG. 7C, the plane wave is deflected by approximately 56°.

EXAMPLE 2

Beam Deflector Having a Thickness of 1.1 mm

[00171] FIGs. 8A-8C illustrate a similar beam deflector to FIGs. 7A-7C, but with a thickness of 1. 1 mm corresponding to A _o , which is different from the thickness of 1.6 mm corresponding to 1/3 A _o of FIGs. 7A-7C.

[00172] A cross-sectional view of one period of a transparent beam deflector having a thickness of 1. 1 mm is depicted in FIG. 8A according to an embodiment of the disclosure. As illustrated, dark areas 804 represent the material with a lower dielectric constant, and light gray areas 802 represent the material with a higher dielectric constant. The dark areas 804 and the light areas 802 have an interface or boundary 806. Both materials are distributed uniformly over the areas indicated in dark and gray regions, respectively. The shape of interface 806 between the dark regions and the light gray regions is different from the shape of interface 706 shown in FIG. 7A.

[00173] The design parameters for the beam deflector of FIG. 8A include an operational frequency of 27 GHz (free-space wavelength A _o = 11 mm), dielectric constants of 4 and 9 at the operational frequency, a period of 13.3 mm, or 1.2 A _o , a thickness of 1. 1 mm. This thickness corresponds to 1/4 of the effective wavelength in a “median” medium, the latter defined as having a dielectric constant E _av = (eq + E ₂ )/2.

[00174] A representation of a convergence graph for a design in FIG. 8A is depicted in FIG. 8B according to an embodiment of the disclosure. The diffraction efficiency in the first diffraction order corresponds to the desired angle of deflection. The transmittance and diffraction efficiency are approximately 90% in the final design or the end of the iterations. The transmittance of about 90% at the end of the iteration is less than nearly 100% as illustrated in FIG. 7B.

[00175] FIG. 8C includes a larger free-space domain, which is a better illustration of wave deflection than FIG. 7C. A schematic representation of an image of the electric field distribution in a transparent beam deflector illuminated from the bottom by a normally incident plane wave is depicted in FIG. 8C according to an embodiment of the disclosure. The arrows indicate the direction of the local power flow (Poynting vector). The plane wave is deflected by approximately 56°, and the formation of a pure plane wave in the transmitted domain is visible in this picture.

EXAMPLE 3 Frequencies of Various Radio Bands

[00176] The radio bands where microwave antennas are used include the C band, X band, Ku-band, Ka-band, Q band, and W band. The frequencies of these bands are listed in Table 2 below.

Table 2

EXAMPLE 4

Dimensions and Uses for Structures for Electromagnetic Wave Transformation [00177] In one embodiment, the largest diameter of the structure for electromagnetic wave transformation is between about 37 mm and about 52 mm, and its contour and shape are configured to fit into an eyewear frame.

[00178] In another embodiment, the structure for electromagnetic wave transformation is between about 5 cm and about 10 cm in width and between about 10 cm and about 15 cm in height, and its contour is configured to fit into a frame of a portable handheld device.

[00179] In yet another embodiment, the structure for electromagnetic wave transformation is between about 15 cm and about 40 cm in width and between about 10 cm and about 30 cm in height, and its contour is configured to fit into a frame of a portable or stationary computer display.

[00180] In still another embodiment, the structure for electromagnetic wave transformation is between about 40 cm and 240 cm in width and between about 30 and about 180 cm in height, and its contour is configured to fit into a frame of a TV display.

[00181] In further embodiments, the structure for electromagnetic wave transformation is between about 1 m and about 10 m in width and between about 0.7 m and about 7 m in height, and its contour is configured to fit into a frame of a billboard screen or billboard-size display.

[00182] In other embodiments, the structure for electromagnetic wave transformation is between about 0.5 m and about 3 m in width and between about 0.5 m and about 5 m in height, and its contour is configured to fit into a frame of a residential, industrial or office building.

[00183] In another embodiment, the structure for electromagnetic wave transformation is between about 1 m and about 3 m in width and between about 1 m and about 2 m in height, and its contour and shape are configured to fit onto an automotive windshield.

[00184] In yet another embodiment, the structure for electromagnetic wave transformation is between about 20 cm and about 50 cm in diameter, and its contour and shape are configured to fit onto an illuminator of an aircraft or vessel or to serve as such an illuminator. [00185] In some embodiments, the structure for electromagnetic wave transformation is between about 5 cm and about 50 cm in diameter, and its contour and shape are configured to fit onto a radome of an aircraft or vessel which houses at least one optical device or to serve as a radome.

EQUIVALENTS

[00186] Those skilled in the art will recognize, or be able to ascertain, using no more than routine experimentation, numerous equivalents to the specific embodiments described specifically herein. Such equivalents are intended to be encompassed in the scope of the following claims.

STATEMENTS

[00187] Numerous examples are provided herein to enhance understanding of the present disclosure. A specific set of statements are provided as follows.

[00188] Statement 1. A structure for electromagnetic wave transformations, the structure comprising: a first layer of a first dielectric material having a bottom surface and a top structured surface; and a second layer of a second dielectric material having a top surface opposite and substantially parallel to the bottom surface and a bottom structured surface conformal with the top structured surface of the first layer, wherein each of the first and second dielectric materials is partially optically transparent.

[00189] Statement 2. The structure of statement 1, wherein the bottom structured surface of the second layer conformal with the top structured surface of the first layer is structured to achieve an electromagnetic wave transformation.

[00190] Statement 3. The structure of statements 1-2, wherein the first dielectric material comprises a first dielectric constant El and the second dielectric material comprises a second dielectric constant £2 different from the first dielectric constant £1, both at an at least one wavelength for electromagnetic wave transformations.

[00191] Statement 4. The structure of statements 1-3, wherein the first and the second dielectric materials have a dielectric loss tangent of less than 0. 1 at an at least one wavelength for electromagnetic wave transformations.

[00192] Statement 5. The structure of statements 1-4, wherein the structure is periodic in one or two dimensions. [00193] Statement 6. The structure of statements 1-5, wherein the structure comprises a linear grating or a two-dimensional grating.

[00194] Statement 7. The structure of statements 1-6, wherein the structure comprises a metamaterial or a metasurface at operational frequencies of electromagnetic wave transformations.

[00195] Statement 8. The structure of statements 1-7, wherein the first dielectric material and the second dielectric material are refractive index-matched for an at least one wavelength of visible light.

[00196] Statement 9. The structure of statements 1-8, wherein the first dielectric material and the second dielectric material are refractive index-matched throughout at least one spectral band of visible light.

[00197] Statement 10. The structure of statements 1-9, wherein the one band of visible light comprises the visible spectrum having wavelengths ranging from about 380 nm to about 750 nm.

[00198] Statement 11. The structure of statements 1-10, wherein each of the top surface of the top layer and the bottom surface of the bottom layer is substantially flat.

[00199] Statement 12. The structure of statements 1-11, wherein each of the first and second dielectric materials is optically transparent such that the structure has a transmittance at normal incidence of at least about 80% within a wavelength of about 400 nm to about 750 nm.

[00200] Statement 13. The structure of statements 1-12, wherein the free-space wavelength for electromagnetic wave transformations ranges from about 0. 1 mm to about 1.0 cm.

[00201] Statement 14. The structure of statements 1-13, wherein the total thickness of the structure equals about 1/4 or about 1/3 of an effective wavelength in a medium having a dielectric constant of Eav = (El + £2)/2.

[00202] Statement 15. The structure of statements 1-14, wherein the structure provides wave transformations comprising beam deflection, beam broadening, beam collimation, or beam splitting.

[00203] Statement 16. The structure of statements 1-15, wherein the structure is configured for deflecting an incident beam or a plane wave at a predetermined angle. [00204] Statement 17. The structure of statements 1-16, wherein the structure is configured for beam broadening or beam spreading for wireless communications, wherein the structure provides beam concentration suitable for wireless power transfer devices.

[00205] Statement 18. The structure of statements 1-17, wherein the structure is configured for beam collimation or focusing for wireless communications.

[00206] Statement 19. The structure of statements 1-18, wherein the structure is configured for beam splitting by converting a single incident beam into multiple beams suitable for wireless communications.

[00207] Statement 20. The structure of statements 1-19, wherein a pair of the first dielectric material and the second dielectric material comprises SiO2-based glass with additives, the SiO2-based glass having a dielectric constant ranging from about 3.8 to about 14.5, the variations of the dielectric constant being due to variations in additives, and polyethylene having a dielectric constant of about 2.25, and the pair having a matched refractive index of about 1.58.

[00208] Statement 21. The structure of statements 1-20, wherein a pair of the first dielectric material and the second dielectric material comprises polycarbonate having a dielectric constant of about 2.9 and polyethylene having a dielectric constant of about 2.25, and the pair having a matched refractive index of about 1.58.

[00209] Statement 22. The structure of statements 1-21, wherein a pair of the first dielectric material and the second dielectric material comprises PET having a dielectric constant of about 3.1 and silica-based glass having a dielectric constant ranging of about 4.0, the pair having a matched refractive index of about 1.63.

[00210] Statement 23. The structure of statements 1-22, wherein a pair of the first dielectric material and the second dielectric material comprises doped silica glass having a dielectric constant greater than about 6.0 and PMMA having a dielectric constant of about 3.4, the pair having a matched refractive index of about 1.49.

[00211] Statement 24. The structure of statements 1-23, wherein a pair of the first dielectric material and the second dielectric material comprises glycerin having a dielectric constant of about 42.5 and silica glass having a dielectric constant of about 4.0, the pair having a matched refractive index of about 1.47. [00212] Statement 25. The structure of statements 1-24, wherein a pair of the first dielectric material and the second dielectric material comprises silica glass or polymer glass plus index- matched immersion liquid.

[00213] Statement 26. The structure of statements 1-25, wherein the index-matched immersion liquid comprises oils having a dielectric constant higher than about 4.0.

[00214] Statement 27. The structure of statements 1-26, wherein the second layer of dielectric material comprises the immersion liquid, the structure further comprising a substrate supporting the second layer of the second dielectric material.

[00215] Statement 28. The structure of statements 1-27, wherein the first layer of the first dielectric material or the second layer of the second dielectric material is discontinuous, the structure further comprising a substrate supporting the second layer of the second dielectric material.

[00216] Statement 29. The structure of statements 1-28, wherein the first thickness zl= F(x, y) and the second thickness z2 = T-F(x, y) are both non-negative and do not exceed the total thickness T.

[00217] Statement 30. The structure of statements 1-29, wherein the first layer having 0 < zl < F(x,y) is filled uniformly with the first dielectric material.

[00218] Statement 31. The structure of statements 1-30, wherein the second layer having F(x,y) < z2 <T is filled uniformly with the second dielectric material.

[00219] Statement 32. The structure of statements 1-31, wherein the dimensions of the structure along the x-axis and the y-axis form a rectangular shape.

[00220] Statement 33. The structure of statements 1-32, further comprising a layer of optically transparent and microwave-reflective material over one of the bottom surface or the top surface such that the structure transforms incident waves in a reflection mode.

[00221] Statement 34. The structure of statement 1-33, wherein the optically transparent and microwave-reflective material comprises an optically transparent conductor having a microwave reflectivity of at least about 80%.

[00222] Statement 35. The structure of statements 1-34, wherein the optically transparent and microwave-reflective material comprises a nanostructured metal-dielectric composite or metamaterial having a microwave reflectivity of at least about 80%.

[00223] Statement 36. The structure of statements 1-35, wherein the structure is used for one of the wireless relay windows, geostationary satellite links, or wireless backhaul links. [00224] Statement 37. The structure of statements 1-36, wherein the structure is used for industrial environments comprising factories or assembly lines where multiple devices or robots communicate with each other.

[00225] Statement 38. The structure of statements 1-37, wherein the bottom surface of the first layer and the top surface of the second layer are curved surfaces.

[00226] Statement 39. A method for designing the structure of statement 1 for electromagnetic wave transformation, the method comprising: determining a type of wave transformation; using a quantitative figure of merit for the type of wave transformation; and performing shape optimization of the conformal structured surfaces to increase the figure of merit to exceed a threshold.

[00227] Statement 40. The method of statement 39, wherein the type of wave transformation is beam deflecting, and the figure of merit is transmissivity into a diffraction order configured to occur at a selected angle of deflection.

[00228] Statement 41. The method of statements 39-40, wherein the type of wave transformation is beam deflecting, and the figure of merit is directivity in the direction of a selected axis of a deflected beam propagation.

[00229] Statement 42. The method of statements 39-41, wherein the type of wave transformation is electromagnetic beam splitting, and the figure of merit comprises a weighted combination of directivity in the directions of selected axes of the split beams. [00230] Statement 43. The method of statements 39-42, wherein the structure has an optical transmissivity of at least about 80% in an about 400 run to about 750 nm band and producing two beams of an angle ranging from 10° to 170° apart in an about 26-28 GHz band.

[00231] Statement 44. The method of statements 39-43 wherein the type of wave transformation is beam concentrating, and the figure of merit is power density at a predefined point or total power incident within a predefined area.

[00232] Statement 45. The method of statements 39-44, wherein the type of wave transformation is beam broadening, and the figure of merit is a total coverage area in which a resulting power exceeds a predefined threshold.

[00233] Statement 46. The method of statements 39-45, wherein the total thickness of the structure is predefined.

[00234] Statement 47. A method for fabricating the structure of statement 1, the method comprising: fabricating the first layer of the first dielectric material; fabricating the second layer of the second dielectric material complementary to the first layer; and joining the first layer and the second layer at their conformal surfaces.

[00235] Statement 48. The method of statement 47, further comprising wetting the surfaces of the first layer and the second layer with a layer of refractive index-matching liquid before joining the first and the second layers together.

[00236] Statement 49. The method of statements 47-48, wherein fabricating the first layer of the first dielectric material comprises patterning or casting the first layer of the first dielectric material into a predefined shape.

[00237] Statement 50. The method of statements 47-49, wherein fabricating the second layer of the second dielectric material comprises patterning or casting the second layer of the first dielectric material into a predefined shape.

[00238] Statement 51. A method for fabricating the structure of statement 1, the method comprising: fabricating the first layer of the first dielectric material; and fabricating the second layer of the second dielectric material from a liquified form of the second material using the fabricated first layer as a mold.

[00239] Statement 52. A method for fabricating the structure of statement 51, the method comprising: fabricating the first layer of the first dielectric material; and fabricating the second layer of the second dielectric material using the fabricated first layer as a mold by filling the mold with a liquid precursor of the second material.

[00240] Statement 53. The method of statements 51-52, wherein the liquid precursor of the second material is transformed into a solid form of the second material by photopolymerization or thermal polymerization.