Distributed optimization for metasurface development

Abstract

A method for designing a metasurface may include selecting a first metamaterial structure from a plurality of metamaterial structures of the metasurface, generating a forward light propagation model for the first metamaterial structure, generating a reverse light propagation model for the first metamaterial structure using a light manipulation function for the metasurface, determining a first electromagnetic response difference between the forward light propagation model and the reverse light propagation model, and determining a first property range for the first metamaterial structure such that the first electromagnetic response difference is optimized.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to U.S. Application No. 63 / 379992, filed October 18, 2022, and U.S. Application No. 18 / 486262, filed October 13, 2023, the contents of which are incorporated herein by reference in their entireties.

[0002] Various embodiments relate to devices, systems, and methods related to optimization in developing metasurfaces that may be used in signal manipulation to alter the properties of, for example, optical beams and / or electromagnetic waves. [Background technology]

[0003] When developing a metasurface, modeling every individual metasurface element in the final metasurface array can be computationally expensive. Therefore, the effects of metasurface elements are typically modeled during a library generation step prior to modeling the final metasurface phased array. However, metasurface elements may function differently in the phased array than in the library-generated modeling. The optical or wave performance of the metasurface may be affected or degraded due to conflicts between the phased array function and the library-generated modeling. Through dedicated effort, ingenuity, and innovation, many deficiencies in such systems have been addressed by developing solutions structured in accordance with embodiments of the present invention, many examples of which are described in detail herein. Summary of the Invention [Means for solving the problem]

[0004] Exemplary embodiments provide methods, systems, apparatus, computer program products, etc. for designing a metasurface. In an exemplary embodiment, the method includes selecting a first metamaterial structure from a plurality of metamaterial structures of the metasurface, generating a forward light propagation model for the first metamaterial structure using a light manipulation function for the metasurface, generating a reciprocal light propagation model for the first metamaterial structure using the light manipulation function for the metasurface, determining a first phase delay difference in the forward light propagation model and the reverse light propagation model, and determining a first characteristic range for the first metamaterial structure such that the first phase delay difference is optimized.

[0005] In certain exemplary embodiments, the light manipulation functionality of the metasurface includes any of refractive and / or reflective light manipulation functionality.

[0006] In an exemplary embodiment, a backward light propagation model models the interaction of backward-propagating light with the first metamaterial structure, and a forward light propagation model models the interaction of forward-propagating light with the first metamaterial structure, where in the forward light propagation model, the forward angle of the light remains unchanged, and in the backward light propagation model, the backward angle of the light remains unchanged, where the backward angle is determined using the light manipulation function for the metasurface and the forward angle.

[0007] In certain exemplary embodiments, the refractive or reflective light manipulation function comprises a focusing and / or collimating function.

[0008] In an exemplary embodiment, the method further includes determining a first amplitude difference in the forward light propagation model and the reverse light propagation model, and determining a first property range of the first metamaterial structure such that the first amplitude difference is optimized.

[0009] In an exemplary embodiment, the method further includes determining a first polarization difference in the forward light propagation model and the reverse light propagation model, and determining a first property range of the first metamaterial structure such that the first polarization difference is optimized.

[0010] In an exemplary embodiment, the first property range of the first metamaterial structure includes any of a first shape and / or size range of the first metamaterial structure, hi an exemplary embodiment, the first metamaterial structure is located at the periphery of the metasurface.

[0011] In an exemplary embodiment, the method further includes selecting a second metamaterial structure from the plurality of metamaterial structures; generating a forward light propagation model for the second metamaterial structure; generating a reverse light propagation model for the second metamaterial structure using the light manipulation function for the metasurface; determining a second phase delay difference in the forward light propagation model and the reverse light propagation model; and determining a second characteristic range for the second metamaterial structure such that the second phase delay difference is optimized.

[0012] In an exemplary embodiment, the method further includes determining a first property value within a first property range and a first location for a first metamaterial structure on a first unit cell of the metasurface, and determining a second property value within a second property range and a second location for a second metamaterial structure on a second unit cell adjacent to the first unit cell, wherein the first and second property values ​​and locations are determined to satisfy a geometric constraint of the metasurface.

[0013] In an exemplary embodiment, the geometric constraint includes any of the distance between the first metamaterial structure and the second metamaterial structure and / or the fill factor of the local region.

[0014] Certain embodiments herein provide an apparatus comprising at least one processor and a memory storing computer-executable instructions, the computer-executable instructions being configured, when executed by the at least one processor, to cause the apparatus to perform a method of any of the embodiments described above.

[0015] Certain embodiments herein provide a computer program product comprising at least one non-transitory computer-readable medium storing computer-executable instructions, the computer-executable instructions being configured, when executed by a processor of the device, to cause the device to perform the method of any of the embodiments described above.

[0016] An exemplary embodiment provides a method for designing a metasurface, the method including the steps of selecting a reference metamaterial structure of a plurality of metamaterial structures of the metasurface; determining a relationship between a reference forward phase delay and a property of the reference metamaterial structure for a forward angle of incidence; determining a relationship between a reference reverse phase delay and a property of the reference metamaterial structure for a reverse angle of incidence; and determining the property of the reference metamaterial structure such that a difference between the forward and reverse phase delays is optimized, wherein the forward and reverse phase delays are offset by a fixed phase value.

[0017] In an exemplary embodiment, the method includes determining the forward and reverse angles of incidence using a phase mask of the metasurface. In an exemplary embodiment, the method includes determining the phase mask of the metasurface using a light manipulation function for the metasurface.

[0018] In an exemplary embodiment, the method includes selecting the reference metamaterial structure such that the difference between the forward and reverse angles of incidence is minimized. In an exemplary embodiment, the method includes determining a characteristic of the other metamaterial structure by referencing the forward phase delay of the other metamaterial structure with the reference forward phase delay and the reverse phase delay of the other metamaterial structure with the reference reverse phase delay.

[0019] In an exemplary embodiment, the method includes iteratively repeating the steps of determining properties of other metamaterial structures until the metasurface is optimized.

[0020] An exemplary embodiment provides a method for designing a metasurface, the method including: determining an optical response of the metamaterial structure for each value of one or more configuration parameters of the metamaterial structure while holding constant one or more global parameters of the metamaterial structure of the metasurface; determining an optical response of the metamaterial structure for each value of one or more shape parameters of the metamaterial structure while holding constant one or more global parameters of the metamaterial structure for each value of the one or more configuration parameters; and recording the optical response for each value of the one or more configuration parameters and each of the one or more shape parameters.

[0021] In an exemplary embodiment, the method includes keeping global parameters constant for all metamaterial structures of the metasurface, hi an exemplary embodiment, the global parameters include a height, a local filling fraction, and / or a wavelength associated with each metamaterial structure.

[0022] In an exemplary embodiment, the configuration parameters include a forward angle of incidence of a forward optical beam on the metamaterial structure of the metasurface, the forward angle of incidence being determined using the optical manipulation function of the metasurface, and a backward angle of incidence of a backward optical beam on the metamaterial structure of the metasurface, the backward angle of incidence being determined using the optical manipulation function of the metasurface.

[0023] In an exemplary embodiment, the configuration parameters include a forward polarization of a forward optical beam relative to the metamaterial structure of the metasurface, the forward polarization being determined using the optical manipulation function of the metasurface, and a reverse polarization of a reverse optical beam relative to the metamaterial structure of the metasurface, the reverse polarization being determined using the optical manipulation function of the metasurface.

[0024] In an exemplary embodiment, the method includes updating a metasurface master library by recording the optical response for each value of one or more configuration parameters and each value of one or more shape parameters, and optimizing the metasurface in forward and reverse directions using the master library by determining optimal values ​​of the one or more configuration parameters and optimal values ​​of the one or more shape parameters that optimize an aggregate metric for the metasurface.

[0025] An exemplary embodiment provides a method for designing a metasurface, the method including determining a forward transformation function for one or more metamaterial structures of the metasurface; determining an inverse transformation function for one or more metamaterial structures of the metasurface; calculating a forward transformed beam by transforming a field of a forward incident light according to the forward transformation function; calculating an inverse transformed beam by transforming a field of a reverse incident beam according to the inverse transformation function; comparing the forward transformed beam with a forward target beam and using the comparison to determine a forward gradient; comparing the inverse transformed beam with a reverse target beam and using the comparison to determine a reverse gradient; and modifying one or more shape parameters of the metamaterial structures of the metasurface using the forward gradient and the inverse gradient.

[0026] In an exemplary embodiment, the forward gradient maps to a forward shape gradient in one or more shape parameters of one or more metamaterial structures of the metasurface, and the reverse gradient maps to a reverse shape gradient in one or more shape parameters of one or more metamaterial structures of the metasurface.

[0027] In an exemplary embodiment, the method includes determining forward shape parameters of metamaterial structures of the metasurface using a forward gradient; determining reverse shape parameters of metamaterial structures of the metasurface using an inverse gradient; determining a shape convergence gradient, where the shape convergence gradient is the difference between the forward shape parameters and the inverse shape parameters for each metamaterial structure of the metasurface; and iteratively repeating the steps of determining the forward and inverse shape parameters until the difference between the forward transformed beam and the forward target beam is optimized and the difference between the inverse transformed beam and the inverse target beam is optimized, thereby determining the shape convergence gradient for each metamaterial structure of the metasurface.

[0028] In an exemplary embodiment, the method includes optimizing a design of the metasurface by modifying one or more metamaterial structures of the metasurface using forward and reverse gradients such that the difference between the forward transformed beam and the forward target beam is optimized and the difference between the reverse transformed beam and the reverse target beam is optimized. In an exemplary embodiment, the modification includes modifying a forward shape parameter and a reverse shape parameter.

[0029] In an exemplary embodiment, the method includes minimizing a shape convergence gradient, prioritizing the minimization of the shape convergence gradient when iteratively repeating the steps of determining forward and inverse shape parameters, and completing the optimization when the shape convergence gradient for each metamaterial structure of the metasurface is zero.

[0030] In an exemplary embodiment, the method includes making a forward shape parameter of a metamaterial structure of the metasurface equal to a reverse shape parameter of the metamaterial structure of the metasurface.

[0031] In an exemplary embodiment, the method includes optimizing the design of the metasurface by modifying one or more metamaterial structures of the metasurface using forward and reverse gradients such that the combination of the forward and reverse gradients is minimized.

[0032] In an exemplary embodiment, modifying one or more metamaterial structures of the metasurface includes modifying equal forward and reverse shape parameters of each metamaterial structure of the metasurface, where the combination is a weighted average of the forward and reverse gradients.

[0033] Having thus generally described the invention, reference is now made to the accompanying drawings, which are not necessarily drawn to scale. [Brief explanation of the drawings]

[0034] [Figure 1] FIG. 1 is a schematic diagram illustrating a metasurface in accordance with an exemplary embodiment. [Figure 2] FIG. 10 is a schematic diagram illustrating a forward light propagation model for a metasurface in accordance with an example embodiment. [Figure 3] FIG. 10 is a schematic diagram illustrating a reverse light propagation model for a metasurface, according to an example embodiment. [Figure 4A] FIG. 1 is a schematic diagram illustrating a forward light propagation model for a metamaterial structure, according to an example embodiment. [Figure 4B] FIG. 1 is a schematic diagram illustrating a reverse light propagation model for a metamaterial structure, according to an example embodiment. [Figure 5] FIG. 1 is a schematic diagram illustrating a metasurface in accordance with an exemplary embodiment. [Figure 6] 1 is a flowchart illustrating a method according to an example embodiment. [Figure 7] 1 is a flowchart illustrating a method according to an example embodiment. [Figure 8]1 is a flowchart illustrating a method according to an example embodiment. [Figure 9] 1 is a flowchart illustrating a method according to an example embodiment. [Figure 10] 1 is a flowchart illustrating a method according to an example embodiment. [Figure 11] 1 is a flowchart illustrating a method according to an example embodiment. [Figure 12] 1 is a schematic diagram of an exemplary computing entity that may be used in accordance with an embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0035] The present inventions will now be described in more detail below with reference to the accompanying drawings, in which some, but not all, of the inventions are shown. Indeed, the present invention may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will satisfy applicable legal requirements. The term "or" (also indicated as " / ") is used herein in both an alternative and connective sense unless otherwise specified. The terms "exemplary" and / or "example" are used as examples without any indication of quality level. The terms "generally," "substantially," and "approximately" refer to within engineering and / or manufacturing tolerances and / or within the user's measurement capabilities, unless otherwise specified. Like numbers refer to like elements throughout.

[0036] A metasurface can include an array of metamaterial structures (or elements), each disposed within a unit cell of the metasurface. Each metamaterial structure can have a unique set of properties. The set of properties can include any of the metamaterial structure's mechanical and / or electromagnetic properties, such as height, local area fill factor, wavelength, polarization, beam angles (altitude and azimuth) of forward and reverse light, and / or cross-sectional shape.

[0037] In various embodiments, each metamaterial structure may manipulate the electromagnetic properties of an incident signal using the metamaterial structure's electromagnetic response. For example, the metamaterial structure may manipulate any of the phase, amplitude, and / or polarization of the incident signal in a unique manner. In various embodiments, the metamaterial structure's electromagnetic response may include linear and / or nonlinear interactions with the incident signal to provide frequency shifting or frequency generation. Cumulatively, the metamaterial structures may provide optical manipulation functions for the incident signal.

[0038] In various approaches used, the phase provided by a metamaterial structure is mapped to a parameter of the metamaterial structure, such as the diameter of a cylindrical metamaterial structure. Thus, a single unit cell and a single shape of the metamaterial structure within the unit cell can be modeled. The modeled library can then provide the diameter needed for the metamaterial structure to provide the phase shift required to achieve the light manipulation function of the metasurface.

[0039] The generated library may provide the electromagnetic response of the metamaterial structure based on various properties of the metamaterial structure. Using the desired light manipulation function of the metasurface, the computing entity can determine the electromagnetic response of the metamaterial structure, and using the modeled library, the computing entity determines the physical and / or electromagnetic properties of the metamaterial structure. In one example, the library may include a set of phase, amplitude, and / or polarization modifiers, mappings, or complex numbers corresponding to each material structure that are multiplied with an input electromagnetic field to determine the output electromagnetic field generated by the metamaterial structure.

[0040] In one example, the light manipulation function of a metasurface may include the electromagnetic response of the metasurface. The light manipulation function may therefore describe how an input light beam is transformed by the metasurface in either the forward or reverse direction. In various embodiments, the phase curve of the metasurface may be determined using the light manipulation function of the metasurface. The phase curve may include the phase transformation that each point on the metasurface needs to provide to the input optical beam to perform the light manipulation function. For example, when the light manipulation function of the metasurface is focusing in the forward direction and collimating in the reverse direction, the phase curve of the metasurface provides the phase manipulation required at each point on the metasurface to provide the focusing and collimating functions in the corresponding directions. A phase mask may refer to the discretized values ​​of the phase curve in each unit cell. Thus, the phase mask of the metasurface provides the phase manipulation value that each metamaterial structure needs to provide to the forward and / or reverse optical beam to perform the light manipulation function of the metasurface in the corresponding direction.

[0041] Metasurfaces can be developed and / or designed using optimization methods that take into account various properties of each of the metamaterial structures. For example, one or more properties of the metasurface to be formed and / or manufactured are determined through implementation of the optimization method. These properties of the metamaterial structures can be described in a modeled library. In an exemplary embodiment, the modeled library can be generated during or prior to the optimization process.

[0042] For example, a metamaterial structure model may be generated and / or determined (e.g., by a computing entity) for a new metamaterial structure of a metasurface during optimization, design, and / or development of the metasurface, incorporating relevant properties (e.g., material properties of the metamaterial structure, geometric properties of the metamaterial structure, electromagnetic properties of the metamaterial structure, etc.). The metamaterial structure model may then be added to a modeled library (e.g., stored in a memory of the computing entity) for future use the next time similar metamaterial structures and / or elements are added to the optimization, design, and / or development of the metasurface.

[0043] In various embodiments, a modeled library of metasurfaces and phase masks can be used to determine one or more properties of the metamaterial structure to be achieved in the design of the metasurface.

[0044] However, while generating a library by modeling each single unit cell with periodic boundary conditions may not be computationally expensive, metamaterial structures may function differently in a phased array when disposed on a metasurface than the generated library model. An exemplary cause of this discrepancy may be that neighboring metamaterial structures on a metasurface may not all be uniform in practice. Another exemplary cause of this discrepancy may be that interactions with two different angles of beam, wave, or signal incidence may not be accounted for in the library modeling.

[0045] Therefore, unless the metasurface is uniform (e.g., includes uniform properties, such as disposing all metamaterial structures where all neighboring metamaterial structures are identical) and / or all angles of the forward and reverse beams are similar, the metasurface may not perform as well as library models with varying properties exhibit when disposed on the metasurface.

[0046] For example, the geometric refractive index or near-field coupling of elements may be altered when there is a variable filling fraction of the unit cell, or when neighboring metamaterial structures have different shapes or locations within the unit cell, etc. Therefore, if such library modeling alone is used to determine an array of metamaterial structures, the performance of the resulting metasurface may be degraded.

[0047] When using modeled libraries in developing and optimizing metasurfaces, it should be considered that variable filling ratios or fill factors of adjacent unit cells can result in variable near-field coupling of adjacent metamaterial structures within those cells, affecting the local effective refractive index of the metasurface. Accounting for all these variations in metasurface optimization and development can make full metasurface optimization computationally expensive, and modeling may need to be limited to metasurfaces of small areas. Thus, technical challenges exist for metasurface design. For example, technical challenges exist in being able to adequately model the properties of a metasurface and its response to an incident beam in order to design a metasurface with an accurate response that is computationally tractable.

[0048] Various embodiments provide technical solutions to these technical problems. For example, in various embodiments, a distributed optimization strategy using element-wise inverse design and inverse modeling is used to design and develop metamaterial structures. In various embodiments, an iterative process is used to generate and / or optimize a multidimensional library. In various embodiments, an aggregate optimization process is provided to design metasurfaces using the multidimensional library. For example, aggregate performance criteria of the metasurfaces may be optimized. In various examples, the distributed optimization strategy of various embodiments results in the design of metasurfaces that are computationally tractable and have accurate responses.

[0049] FIG. 1 illustrates a metasurface 100 according to an exemplary embodiment. In various embodiments, the metasurface 100 includes metamaterial structures 102_1, 102_2, ..., 102_N. Each metamaterial structure 102_1, 102_2, ..., 102_N may be disposed within a corresponding unit cell 104_1, 104_2, ..., 104_N of the metasurface 100. In exemplary embodiments, the metasurface 100 may include any number of metamaterial structures and / or unit cells. In some exemplary embodiments, a unit cell may not include a metamaterial structure.

[0050] In various embodiments, metasurface 100 provides a manipulation function to an incident signal, such as incident light and / or an electromagnetic beam. For example, metasurface 100 can focus, diverge, collimate, and / or redirect incident signals of various other forms and shapes.

[0051] In exemplary embodiments, so that metasurface 100 provides an appropriate manipulation function on an incident signal, each metamaterial structure 102_1, 102_2, ..., 102_N may perform a unique manipulation on the signal. For example, each metamaterial structure 102_1, 102_2, ..., 102_N may alter and / or shift the phase of the incident signal by a certain amount. In some examples, each metamaterial structure 102_1, 102_2, ..., 102_N may alter and / or shift the frequency and / or amplitude of the incident signal by a certain amount.

[0052] In various embodiments, various characteristics for each of the metamaterial structures 102_1, 102_2, ..., 102_N determine how each metamaterial structure manipulates a signal. In an exemplary embodiment, the metamaterial structures 102_1, 102_2, ..., 102_N may each be a strut, a cylinder, etc. The various characteristics of the metamaterial structures may include, for example, the shape, size, geometry, fill factor, orientation, or location of the metamaterial structures (struts, cylinders, etc.) within the unit cells 104_1, ..., 104_N of the metasurface. In the exemplary embodiment of FIG. 1, the shape, orientation, location, size, and fill factor of the metamaterial structures 102_1, 102_2, ..., 102_N may each be different.

[0053] 2 illustrates an exemplary embodiment of a metasurface 100 configured to steer an incident beam 202 into a focused beam 204, according to various embodiments herein. FIG. 3 illustrates an exemplary embodiment of a metasurface 100 configured to steer a backward incident beam 304 into a collimated beam 302, according to various embodiments herein. In various examples, signals 202 and 302 have opposite directions relative to each other, are parallel, and overlap. Similarly, in various examples, signals 204 and 304 have opposite directions relative to each other, and are parallel and overlap.

[0054] In various embodiments, metasurface 100 is expected to provide symmetrical steering functions for the incoming and outgoing signals, for example, as shown in Figures 2 and 3. Various embodiments herein use the symmetry requirements for steering functions to determine the properties of each of the metamaterial structures in a distributed manner and to design metasurface 100 to provide the desired steering functions.

[0055] 4(a) and 4(b) are schematic diagrams used to illustrate distributed optimization for designing metasurfaces, according to various embodiments herein. In various embodiments, a computing entity, such as computing entity 10 shown in FIG. 12 and described further below, is used to perform various steps of the optimization method.

[0056] In various embodiments herein, computing entity 10 selects metamaterial structure 402 from the metamaterial structures of the metasurface. In various embodiments, metamaterial structure 402 is located within unit cell 401. In various embodiments, computing entity 10 generates a forward light propagation model for metamaterial structure 402. For example, computing entity 10 uses a simulation-based model to model how metamaterial structure 402 manipulates any of the phase, amplitude, and / or polarization of a light beam, such as forward incident light beam 403_1. Metamaterial structure 402 manipulates forward incident light beam 403_1 into forward incident light beam 403_2. In various embodiments, when simulating an individual metamaterial structure, such as metamaterial structure 402, in distributed optimization, the forward light passes through without changing its angle. For example, as shown in FIG. 4a, the angles of forward incident light beam 403_1 and forward incident light beam 403_2 remain the same.

[0057] In various embodiments, computing entity 10 uses the light manipulation function to generate a reverse light propagation model for metamaterial structure 402. For example, computing entity 10 generates a reverse light propagation model for reverse incident light beam 405_1 and reverse light beam 405_2. For example, computing entity 10 uses a simulation-based model to model how metamaterial structure 402 manipulates any of the phase, amplitude, and / or polarization of a light beam, such as reverse incident light beam 405_1. In various embodiments, when simulating an individual metamaterial structure, such as metamaterial structure 402, in distributed optimization, the reverse light passes through without changing its angle. For example, as shown in FIG. 4b, the angles of reverse incident light beam 405_1 and reverse incident light beam 405_2 remain the same. In various embodiments, the angle of incidence of reverse incident light beam 405_1 is determined by the light manipulation function for the metasurface and the angle of the incident light beam. For example, the angle of the reverse incident light beam 405_1 is determined using the light manipulation function for the metasurface and the angle of incidence of the forward incident light beam 403_1. For example, the angle of the reverse incident light beam 405_1 is any angular change that the light manipulation function causes to the forward incident light beam 403_1 on the metasurface as a whole. For example, if the light manipulation function is a focused light manipulation function, such as the examples of FIGS. 2 and 3, the reverse incident light beam has the same angle as beam 304 shown in FIG. 3.

[0058] In various embodiments, due to the symmetry requirements of the metasurface, the electromagnetic response for the forward and reverse light propagation directions is equal. In various embodiments, computing entity 10 determines an electromagnetic response difference between the forward and reverse light propagation models. In various embodiments, computing entity 10 determines an optimized property range for metamaterial structure 402 such that the electromagnetic response difference is optimized. In various embodiments, the electromagnetic response difference is optimized such that the aggregate performance criteria of the metasurface is optimized. In various embodiments, the electromagnetic response may be a phase delay, amplitude, and / or polarization change induced by the metamaterial structure.

[0059] For example, computing entity 10 determines the phase delay difference in a forward light propagation model and a reverse light propagation model. In various embodiments, computing entity 10 determines an optimized characteristic range for metamaterial structure 402 so that the phase delay difference is optimized. For example, computing entity 10 determines the shape and / or physical dimension range of metamaterial structure 402 so that the phase delay difference is optimized. For example, if metamaterial structure 402 is a cylindrical metamaterial structure, computing entity 10 determines the diameter range of metamaterial structure 402 so that the phase delay difference is optimized.

[0060] In various embodiments, due to symmetry requirements of the metasurface, the amplitudes for the forward light propagation direction and the reverse light propagation direction are equal. In various embodiments, computing entity 10 determines an amplitude difference in the forward light propagation model and the reverse light propagation model. In various embodiments, computing entity 10 determines an optimized property range for metamaterial structure 402 such that the amplitude difference is optimized. For example, computing entity 10 determines a shape and / or physical dimension range for metamaterial structure 402 such that the amplitude difference is optimized. For example, if metamaterial structure 402 is a cylindrical metamaterial structure, computing entity 10 determines a diameter range for metamaterial structure 402 such that the amplitude difference is optimized.

[0061] In various embodiments, due to the symmetry requirements of the metasurface, the polarizations for the forward and reverse light propagation directions are equal. In various embodiments, computing entity 10 determines the polarization difference in the forward and reverse light propagation models. In various embodiments, computing entity 10 determines an optimized property range for metamaterial structure 402 such that the polarization difference is optimized. For example, computing entity 10 determines a shape and / or physical dimension range for metamaterial structure 402 such that the polarization difference is optimized. For example, if metamaterial structure 402 is a cylindrical metamaterial structure, computing entity 10 determines a diameter range for metamaterial structure 402 such that the polarization difference is optimized.

[0062] In various embodiments, the light manipulation function of the metasurface is a refractive light manipulation function or a reflective light manipulation function. For example, the metasurface can function as a signal focusing and / or diverging lens and / or reflector. In one example, the metasurface can be spherical, cylindrical, and / or a combination of lenses and / or reflectors.

[0063] Metamaterial structures at or near the periphery of the metasurface may have the most drastic effect on the phase of the incident signal, and their optimization may be more error-prone. In various embodiments, when the light manipulation function of the metasurface is a refractive light manipulation function, metamaterial structures at or near the periphery of the metasurface may be more important to optimize than the remaining metamaterial structures, as these metamaterial structures may benefit most from the optimization methods provided herein. In various embodiments, computing entity 10 selects metamaterial structures 402 from the periphery of the metasurface. In various embodiments, computing entity 10 selects metamaterial structures 402 from a portion of the metasurface that is closer to the periphery of the metasurface than, for example, 75% of the other metamaterial structures. In various embodiments, computing entity 10 selects metamaterial structures 402 from a portion of the metasurface that is closer to the periphery of the metasurface than, for example, 50% of the other metamaterial structures.

[0064] In an embodiment, signals 403_1, 403_2, 405_3, and / or 405_2 are simulated signals. In an embodiment herein, a simulation program may be stored in non-volatile memory 24 of computing entity 10, as shown in FIG. 12 below, to provide a simulation including the simulated signals.

[0065] 5 is a schematic diagram illustrating a metasurface 100 according to various embodiments herein. In various embodiments, computing entity 10 selects metamaterial structure 102_1 as the metamaterial structure 402 for performing the simulation function for optimizing metasurface 10, described above with respect to FIGS. 4a and 4b. In various embodiments, computing entity 10 determines optimized property ranges for first metamaterial structure 102_1 such that any of the phase delay difference, amplitude difference, and / or polarization difference is optimized in the forward light propagation model and the reverse light propagation model.

[0066] In various embodiments, the computing entity 10 selects a second metamaterial structure 102_2 from the plurality of metamaterial structures of the metasurface 100. In various embodiments, the computing entity 10 generates forward and reverse light propagation models using light manipulation functions for the second metamaterial structure 102_2, e.g., as also described above with respect to Figures 4a and 4b.

[0067] In various embodiments, computing entity 10 determines a phase delay difference in the forward light propagation model and the reverse light propagation model for metamaterial structure 102_2. In various embodiments, computing entity 10 determines an optimized property range for second metamaterial structure 102_2 such that the phase delay difference is optimized. For example, computing entity 10 determines a shape and / or physical dimension range for metamaterial structure 102_2 such that the phase delay difference is optimized. In various embodiments, computing entity 10 may determine an optimized property range such that either the amplitude difference and / or the polarization difference in the forward light propagation model and the reverse light propagation model for metamaterial structure 102_2 is optimized.

[0068] In various embodiments herein, the computing entity 10 determines a first property value within a first property range for the metamaterial structure 102_1. For example, the computing entity 10 determines a diameter for the metamaterial structure 102_1. In various embodiments, the computing entity 10 determines a first location for the metamaterial structure 104_1 on the unit cell 104_1 of the metasurface 100.

[0069] In various embodiments herein, the computing entity 10 determines a second property value within a second property range for the metamaterial structure 102_2. For example, the computing entity 10 determines a diameter for the metamaterial structure 102_2. In various embodiments herein, the computing entity 10 determines a second location for the metamaterial structure 102_2 on a second unit cell 104_2 adjacent to the first unit cell 104_1.

[0070] In various embodiments, the first and second property values ​​and locations for metamaterial structures 102_1 and 102_2 are determined to satisfy geometric constraints of the metasurface. For example, the geometric constraints may be minimum and / or maximum distance requirements for each of the metamaterial structures from the perimeter of the unit cell and / or from each other. For example, the geometric constraints for metamaterial structures 102_1 and 102_2 may be a constraint on the distance d1 between the two metamaterial structures 102_1 and 102_2 and / or constraints on the distances d2 and d3 from the edges of unit cells 104_1 and 104_2. For example, each of the distances, e.g., d1, d2, and d3, may be constrained to a minimum and / or a maximum.

[0071] In various embodiments, the geometric constraints may include constraints on the filling factor of each metamaterial structure within its corresponding unit cell. For example, the geometric constraints may include a minimum and / or maximum ratio of the two-dimensional surface area of ​​a cross-section of metamaterial structure 102_1 or 102_2 to the corresponding unit cell 104_1 or 104_2. The cross-section of the metamaterial structure may lie in a plane parallel to or on the surface of the corresponding unit cell.

[0072] In various embodiments, when placing a metamaterial structure, for example, metamaterial structure 102_2 within unit cell 104_2 is adjusted during the optimization process, which may affect and / or change the phase delay caused by metamaterial structure 102_2. To optimize the phase delay, a second property value of metamaterial structure 102_2 (e.g., its diameter) may need to be updated. Thus, various embodiments provide for sub-optimization of determining and / or updating property values ​​for the metamaterial structure when the placement of the metamaterial structure within the unit cell is determined.

[0073] In various embodiments, geometric constraints are used to account for local coupling between metamaterial structures on a metasurface. For example, by limiting the distance between two metamaterial structures 102_1 and 102_2, the local coupling between the two metamaterial structures can be limited. In various embodiments, by limiting the distance between the two metamaterial structures 102_1 and 102_2, the local coupling between the two metamaterial structures is minimized. In various embodiments, by limiting the distance between the two metamaterial structures 102_1 and 102_2 and / or by any geometric constraint, the local coupling between neighboring metamaterial structures, such as metamaterial structures 102_1 and 102_2, is kept constant.

[0074] In various embodiments herein, the optimization process performs the steps described above following the last metamaterial structure, e.g., metamaterial structure 102_N in unit cell 104_N, taking into account all other previously placed metamaterial structures.

[0075] In various embodiments, after a metasurface is designed using any of the distributed modeling and / or sub-optimization methods described above, the arrangement of the metamaterial structures may no longer form a geometric pattern, such as a geometric lattice, based on the unit cell arrangement. Various embodiments may use the fill factor of a local region and / or local density of the metamaterial structures to complete the metasurface design. For example, various embodiments may complete the metasurface design and / or optimization using an optimization process using geometric constraints based on a constant fill factor of a local region of metamaterial structures connecting adjacent metamaterial structures. In an exemplary embodiment, a local region may include two neighboring metamaterial structures. In an exemplary embodiment, a local region may include three neighboring metamaterial structures. In an exemplary embodiment, a local region may include four neighboring metamaterial structures. In an exemplary embodiment, a local region may include five or more neighboring metamaterial structures.

[0076] 6 is a flowchart illustrating a method 600 according to various embodiments herein. According to various embodiments herein, the computing entity 10 comprises means, such as a processing device 22, memories 26, 24, etc., used to initiate the metasurface optimization and / or various other steps of the method 600, for example, as shown in FIG. 12 herein.

[0077] In various embodiments, in step 602, computing entity 10 selects a first metamaterial structure of a plurality of metamaterial structures of the metasurface. For example, computing entity 10 selects metamaterial structure 102_1 of metasurface 100, with reference to FIG. 1 and / or FIG. 5. In an exemplary embodiment, selecting the first metamaterial structure includes selecting the height, shape, width, length, radius / diameter, and location of the metamaterial structure within a corresponding unit cell. In various embodiments, the first metamaterial structure is selected based on a default initial metamaterial structure, user input (e.g., received via a user input device of computing entity 10), the intended function of the metasurface, etc.

[0078] In various embodiments, in step 604, the computing entity 10 generates a forward light propagation model for the first metamaterial structure. For example, the computing entity 10 generates the forward light propagation model as shown and described with respect to FIG. 4a. The forward light propagation model may be based on a light manipulation function for the metasurface, which describes the intended function the metasurface performs on incident light. For example, the light manipulation function may be any of a focusing function, a diverging function, a collimating function, and / or any other beamforming function. For example, the computing entity 10 simulates the response of a forward incident light beam 403_1 interacting with the first material structure to derive a forward light beam 403_2. In an exemplary embodiment, determining the forward light propagation model for the first metamaterial structure includes determining one or more characteristics (e.g., phase delay, polarization, amplitude, frequency, etc.) of the forward light beam 403_2.

[0079] In various embodiments, in step 606, computing entity 10 generates a reverse light propagation model for the first metamaterial structure using the light manipulation function for the metasurface. For example, computing entity 10 simulates the reverse light propagation model shown and described with respect to FIG. 4b on the selected first metamaterial structure. In various examples, the reverse light propagation model includes a beam of light incident with an angle determined based on the light manipulation function of the metasurface. For example, computing entity 10 simulates the response of the reverse incident light beam 405_1 interacting with the first metamaterial structure to derive reverse light beam 405_2. In an exemplary embodiment, determining the reverse light propagation model for the first metamaterial structure includes determining one or more characteristics (e.g., phase delay, polarization, amplitude, frequency, etc.) of the reverse light beam 405_2.

[0080] In various embodiments, in step 608, the computing entity 10 determines a first phase delay difference in the forward light propagation model and the reverse light propagation model. For example, the computing entity 10 determines the difference in the phase delay caused with respect to the forward light propagation model (e.g., see FIG. 4a) and the phase delay caused with respect to the reverse light propagation model (e.g., see FIG. 4b) as applied to the first material structure. For example, the computing entity 10 determines the forward phase delay, or the change in phase between the forward incident light beam 403_1 and the forward incident light beam 403_2, caused by the interaction of the forward incident light beam 403_1 with the first metamaterial structure. The computing entity 10 also determines the reverse phase delay, or the change in phase between the reverse incident light beam 405_1 and the reverse incident light beam 405_2, caused by the interaction of the reverse incident light beam 405_1 with the first metamaterial structure. The computing entity 10 determines the first phase delay difference by determining the difference between the forward phase delay and the reverse phase delay.

[0081] In various embodiments, in step 610, computing entity 10 determines a first property range of the first metamaterial structure such that the first phase delay difference is optimized. For example, the first property of the first metamaterial structure may be a diameter of the first metamaterial structure. In an exemplary embodiment, computing entity 10 executes an optimization framework to determine the diameter (or a range of diameters) of the first metamaterial structure while optimizing the first phase delay difference. In various examples, the first property of the first metamaterial structure may be other parameters, such as a shape (e.g., a shape of a cross section of the first metamaterial structure taken in a plane perpendicular to a normal to a surface on which the first metamaterial structure is modeled), a perimeter, a refractive index, or other physical parameters and / or dimensions of the first metamaterial structure.

[0082] In various embodiments, in step 610, computing entity 10 determines whether the first property range of the first metamaterial structure may indeed optimize the first phase delay difference. If in step 610 the first property range of the first metamaterial structure does not optimize the first phase delay difference, method 600 repeats steps 604 through 608 by updating the first property and / or property range of the first metamaterial structure, as described above.

[0083] In various embodiments, if in step 610 the first characteristic range of the first metamaterial structure optimizes the first phase delay difference, the computing entity 10 in step 612 selects another metamaterial structure from the plurality of metamaterial structures of the metasurface and repeats the optimization process for the other metamaterial structure, e.g., as described below with reference to FIG. 7 .

[0084] FIG. 7 is a flowchart illustrating a method 700 according to various embodiments herein. In various embodiments, at step 702, computing entity 10 selects a second metamaterial structure of a plurality of metamaterial structures of a metasurface. For example, computing entity 10 selects metamaterial structure 102_2 with reference to FIGS. 1 and / or 5 . In an exemplary embodiment, selecting the second metamaterial structure includes selecting a height, shape (e.g., a shape of a cross section of the second metamaterial structure taken in a plane perpendicular to a normal to the surface on which the first metamaterial structure is modeled to be formed), width, length, radius / diameter, location of the second metamaterial structure within a corresponding unit cell, etc. In various embodiments, the second metamaterial structure is selected based on a default initial metamaterial structure, user input (e.g., received via a user input device of computing entity 10), the intended function of the metasurface, etc.

[0085] In various examples, in step 704, the computing entity 10 generates a forward light propagation model for the second metamaterial structure. For example, the computing entity 10 generates the forward light propagation model as shown and described with respect to FIG. 4a. The forward light propagation model may be based on a light manipulation function for the metasurface, which describes the intended function the metasurface performs on incident light. For example, the computing entity 10 simulates the response of a forward incident light beam 403_1 interacting with the second metamaterial structure to derive a forward light beam 403_2. In an exemplary embodiment, determining the forward light propagation model for the second metamaterial structure includes determining one or more characteristics (e.g., phase delay, polarization, amplitude, frequency, etc.) of the forward light beam 403_2.

[0086] In various embodiments, in step 706, computing entity 10 generates a reverse light propagation model for the second metamaterial structure using the light manipulation function for the metasurface. For example, computing entity 10 simulates the reverse light propagation model shown and described with respect to FIG. 4b on the selected second metamaterial structure. In various examples, the reverse light propagation model includes a beam of light incident with an angle determined based on the light manipulation function of the metasurface. For example, computing entity 10 simulates the response of the reverse incident light beam 405_1 interacting with the second metamaterial structure to derive reverse light beam 405_2. In an exemplary embodiment, determining the reverse light propagation model for the second metamaterial structure includes determining one or more characteristics (e.g., phase delay, polarization, amplitude, frequency, etc.) of the reverse light beam 405_2.

[0087] In various embodiments, in step 708, the computing entity 10 determines a second phase delay difference in the forward light propagation model and the reverse light propagation model. For example, the computing entity 10 determines the difference in the phase delay induced with respect to the forward light propagation model (e.g., see FIG. 4a) and the phase delay induced with respect to the reverse light propagation model (e.g., see FIG. 4b) applied to the second metamaterial structure. For example, the computing entity 10 determines the forward phase delay induced by the interaction of the forward incident light beam 403_1 with the second metamaterial structure, or the change in phase between the forward incident light beam 403_1 and the forward incident light beam 403_2. The computing entity 10 also determines the reverse phase delay induced by the interaction of the reverse incident light beam 405_1 with the second metamaterial structure, or the change in phase between the reverse incident light beam 405_1 and the reverse incident light beam 405_2. The computing entity 10 determines the second phase delay difference by determining the difference between the forward phase delay and the reverse phase delay.

[0088] In various embodiments, in step 710, computing entity 10 determines a range of a second property of the second metamaterial structure such that the second phase delay difference is optimized. For example, the second property of the second metamaterial structure may be a diameter of the second metamaterial structure. In an exemplary embodiment, computing entity 10 executes an optimization framework to determine the diameter (or a range of diameters) of the second metamaterial structure while optimizing the second phase delay difference. In various examples, the second property of the second metamaterial structure may be other parameters, such as a shape (e.g., a shape of a cross section of the first metamaterial structure taken in a plane perpendicular to a normal to the surface on which the first metamaterial structure is modeled to be formed), a perimeter, a refractive index, or other physical parameters and / or dimensions of the second metamaterial structure.

[0089] Note that in various embodiments, instead of the first or second phase delay difference, a first or second amplitude and / or polarization difference between the forward and reverse light propagation models may be calculated. The optimization model may then determine first and / or second properties for the first and / or second metamaterial structures while optimizing the amplitude and / or polarization difference.

[0090] In various embodiments, in step 710, computing entity 10 determines whether the second property range of the second metamaterial structure may indeed optimize the second phase delay difference. If in step 710 the second property range of the second metamaterial structure does not optimize the second phase delay difference, method 700 repeats steps 704 through 708 by updating the second property and / or property range of the second metamaterial structure, as described above.

[0091] In various embodiments, if in step 710 the second property range of the second metamaterial structure optimizes the second phase delay difference, then in step 712 the computing entity 10 selects another metamaterial structure from the plurality of metamaterial structures of the metasurface and repeats the optimization process for the other metamaterial structures until the last metamaterial structure is selected, its property ranges determined, and optimized to optimize the corresponding phase delay difference.

[0092] FIG. 8 is a flowchart illustrating a method 800 according to various embodiments herein. In various embodiments, in step 802, computing entity 10 determines a first property value within a first property range for a first metamaterial structure. In various embodiments, computing entity 10 may determine a first location for the first metamaterial structure on a first unit cell of the metasurface. For example, computing entity 10 determines one or more properties of a first metamaterial structure (e.g., metamaterial structure 102_1, with reference to FIG. 5 ) in a unit cell corresponding to the first metamaterial structure of the metasurface (e.g., corresponding unit cell 104_1, with reference to FIG. 5 ). In various embodiments, determining one or more properties of the metamaterial structure may include determining any of the shape (e.g., struts), size, perimeter, refractive index, geometry, fill factor, orientation, and / or location of the metamaterial structure in the corresponding unit cell.

[0093] In various embodiments, in step 804, computing entity 10 determines a second property value within the second property range and a second location for a second metamaterial structure (e.g., with reference to FIG. 5, metamaterial structure 102_2) on a second unit cell adjacent to the first unit cell (e.g., with reference to FIG. 5, corresponding unit cell 104_2). In various embodiments, computing entity 10 determines the second property value and location such that geometric constraints on the metasurface are satisfied, e.g., as described with respect to FIG. 5. For example, the second property of the second metamaterial structure is determined such that minimum distance requirements for the first and second metamaterial structures from edges of the corresponding first and second unit cells are satisfied.

[0094] In various embodiments, when optimizing the properties of a metasurface for a particular phase mask of the metasurface, the target phase delay provided by the forward response of the metamaterial structures may not be the same as the reverse response. This may not be due to relative phase characteristics. Thus, for a given phase curve or phase mask of the metasurface, the forward phase response of each metamaterial structure of the metasurface may be offset from the reverse phase response by a fixed phase value.

[0095] Thus, in various embodiments, the relative phase response of the metamaterial structure in each direction is a design target, and thus, in various embodiments, the forward and reverse phase delays may not be equal to each other, but may be offset from each other.

[0096] In various embodiments, the optimization process begins with a desired phase curve for the metasurface. The phase curve may be based on the desired light manipulation function of the metasurface, such as a focusing or collimating function for a lens. By discretizing the phase curve for each unit cell, a phase mask may be created. In various embodiments, the phase mask may provide the relative phase response requirements of each metamaterial structure with respect to its neighboring metamaterial structures. In various embodiments, the phase masks for the forward and reverse directions may be shifted from each other by a fixed value.

[0097] In various embodiments, the optimization process can select one metamaterial structure and optimize its properties to achieve optimal phase responses in the forward and reverse directions. Each forward and reverse phase delay response can then serve as a reference phase value for the remaining optimization processes in each direction. However, the physical properties of the metamaterial structure remain the same regardless of the direction in which it is used. For example, the diameter of a cylindrical metamaterial structure remains the same regardless of the direction in which it is used.

[0098] In various embodiments, the reference metamaterial structure is selected so that the forward and reverse phase delays of the metamaterial structure are the same or are minimized. In the example of a focusing / collimating lens, the metamaterial structures in the metasurface bender may have the same forward and reverse phase delays.

[0099] After selecting a metamaterial structure with a near-zero or minimal difference between the forward and reverse phases, the forward phase delay provided by the reference metamaterial structure can be used as a reference for the optimization process to create the remaining metasurface phase curves or phase masks in the forward direction, and the reverse phase delay can be used as a reference for the optimization process to create the metasurface phase curves or phase masks in the reverse direction. However, as previously mentioned, all forward and reverse phase delays can be offset from each other by a fixed value.

[0100] 9 is a flowchart illustrating a method 900 for designing a metasurface according to various embodiments herein. In various embodiments, in step 902, the computing entity 10 selects a reference metamaterial structure from the metamaterial structures of the metasurface.

[0101] In various embodiments, in step 904, computing entity 10 models the reference forward phase delay. Computing entity 10 may determine a relationship between the reference forward phase delay and the characteristics of the reference metamaterial structure with respect to the forward angle of incidence. For example, when the metamaterial structure is cylindrical, computing entity 10 may provide a model that represents the forward phase delay provided by the relationship between the reference metamaterial structure and the diameter of the metamaterial structure.

[0102] In various embodiments, in step 906, computing entity 10 models the reference reverse phase delay. Computing entity 10 may determine a relationship between the reference reverse phase delay and the characteristics of the reference metamaterial structure with respect to the reverse incidence angle. For example, when the metamaterial structure is cylindrical, computing entity 10 may provide a model that represents the reverse phase delay provided by the relationship between the reference metamaterial structure and the diameter of the metamaterial structure.

[0103] In various embodiments, computing entity 10 optimizes the reference metamaterial structure in step 908. Computing entity 10 may determine the properties of the reference metamaterial structure such that the difference between the forward phase delay and the reverse phase delay is optimized.

[0104] In various embodiments, the computing entity 10 optimizes the aggregate performance criterion of the metasurface to optimize the forward and / or reverse phase delay for the metamaterial structure. For example, the computing entity 10 may maximize the aggregate performance criterion of the metasurface to optimize the forward and / or reverse phase delay for the metamaterial structure. For example, the computing entity 10 may minimize the aggregate performance criterion of the metasurface to optimize the forward and / or reverse phase delay for the metamaterial structure.

[0105] In an exemplary embodiment, computing entity 10 selects the reference metamaterial structure such that the difference between the forward and backward angles of incidence is minimized.

[0106] In various embodiments, the forward and reverse phase delays can be offset by a fixed phase value. This may be because the relative forward and reverse phase delays determine the light manipulation function of the metasurface. Thus, the optimized forward and reverse phase delays can be offset by a fixed phase value as the metasurface is optimized.

[0107] In various embodiments, computing entity 10 determines the forward and reverse angles of incidence using a phase mask of the metasurface. Computing entity 10 may determine the phase mask of the metasurface using a light manipulation function for the metasurface. In various embodiments, computing entity 10 determines a phase curve of the metasurface and discretizes the phase curve at every unit cell to determine a phase mask including discrete phase values ​​corresponding to each unit cell.

[0108] In various embodiments, the computing entity 10 determines the properties of the other metamaterial structures by referencing the forward phase delay of the other metamaterial structures with the reference forward phase delay and the antiphase delay of the other metamaterial structures with the reference antiphase delay. The computing entity 10 can iteratively repeat the steps of determining the properties of the other metamaterial structures until the metasurface is optimized.

[0109] In various embodiments, one or more design libraries are generated that map any of the phase delay, amplitude variation, and / or polarization shift of the metamaterial structure to one or more properties of the metamaterial structure. Various embodiments increase the speed of the distributed optimization procedure by performing all or some of the model generation and pre-creating a library of optimization procedures.

[0110] In various embodiments, the model development and optimization processes can be performed together (e.g., with various model development and optimization steps in parallel or interleaved) while designing a metasurface. The library generated using the model development can be stored in a storage system (e.g., memory) and can be used in later optimization for new metasurfaces.

[0111] In various embodiments, a master library can be generated and maintained that can be used in optimizing new metasurfaces. Thus, the master library can be pre-calculated prior to a new optimization process. In various embodiments, the optimization process can select various properties of metamaterial structures and / or specific types of metamaterial structures from the master library while accounting for forward and reverse angles during the optimization process.

[0112] In various embodiments, the parameters for the metamaterial structure may include global parameters, geometry parameters, and shape parameters.

[0113] In various embodiments, the global parameters include height, either unit cell or local area fill factor, and wavelength. In various embodiments, the global parameters are kept constant during the optimization process and / or are equal for all elements in the metasurface.

[0114] In various embodiments, the shape parameters of the metamaterial structure determine the shape of the metamaterial structure. For example, for a cylindrical structure, the shape parameter is the diameter of the metamaterial structure (while, in various embodiments, its height remains constant). For example, for an elliptical metamaterial structure, the shape parameters are the two diameters and the angle of rotation of the elliptical cross section. In various embodiments, the shape parameters indicate the shape of a two-dimensional cross section of the metamaterial structure.

[0115] In various embodiments, the configuration parameters of the metamaterial structure determine the forward and / or reverse incident angles, including the elevation angle and the azimuth angle. The elevation angle may determine the deviation from normal, and the azimuth angle may determine the rotation about the normal axis. Thus, the configuration parameters include the k-vector of the incident light (in the forward and / or reverse directions). In various embodiments, the configuration parameters also include the polarization shift provided by the metamaterial structure in the forward and / or reverse directions.

[0116] In various embodiments, when compiling a master library, the photonic response to various possible situations is evaluated and recorded. In various embodiments, the optical response of the metamaterial structure in response to various geometry and shape parameters is evaluated and recorded. For example, the phase delay and / or amplitude variation in response to various geometry and / or shape parameters may be evaluated and recorded.

[0117] For example, metamaterial structures on a metasurface can be selected. The metamaterial structures can have fixed global parameters (e.g., their height and their spacing are fixed). In various embodiments, the placement parameters are determined by knowing the light manipulation function of the metasurface (which can indicate how the metasurface is expected to manipulate light). For example, in a focusing / collimating metasurface, knowing the focal point of the metasurface will know the placement parameters for various metamaterial structures at various locations on the metasurface. However, the metamaterial structures can have any shape. Thus, various embodiments model all possible shapes to build a master library.

[0118] Thus, in various embodiments, to have a complete master library that can be used for any given design, the optical response (e.g., phase delay) is determined and recorded in a library for various combinations of incident elevation and azimuthal angles, forward and reverse polarization shifts, and metamaterial structure shapes. Thus, in various embodiments, the master library is a multidimensional library.

[0119] In various examples, after the master library is designed, computing entity 10 may use the light manipulation capabilities of the metasurface to determine the maximum range for the angle of incidence (forward and reverse) and polarization requirements for each metamaterial structure. Computing entity 10 may then determine the phase delay for each such possibility, and then all the shape parameters for each such possibility, in order to build various entries into the master model.

[0120] In various embodiments, computing entity 10 may use various machine learning methods in constructing the library. For example, the computing entity may determine the optical response for several geometry and / or shape parameters and use interpolation to determine the optical response for the geometry or shape parameters. For example, the computing entity may determine the phase delay for incident light elevation angles with a granularity of 1° and use machine learning to determine the phase delay for incident light elevation angles with a granularity of 0.1°. In exemplary embodiments, doing so may accelerate the creation of the master library.

[0121] 10 is a flowchart illustrating a method 1000 for designing a metasurface according to various embodiments herein. In various embodiments, in step 1002, the computing entity 10 determines the optical response of the metamaterial structure for various configuration parameters. The computing entity 10 may determine the optical response of the metamaterial structure of the metasurface for each value for one or more configuration parameters of the metamaterial structure while holding one or more global parameters of the metamaterial structure constant. In various embodiments, the optical response may include variations in phase delay, polarization, and / or amplitude.

[0122] In various embodiments, in step 1004, computing entity 10 determines the optical response of the metamaterial structure for various geometric parameters. Computing entity 10 may determine the optical response of the metamaterial structure for each value for one or more geometric parameters of the metamaterial structure while holding one or more global parameters of the metamaterial structure constant for each value of the one or more configuration parameters. For example, for each selected and evaluated angle of incidence and / or polarization parameter, the computing entity determines the optical response for the one or more geometric parameters.

[0123] In various embodiments, in step 1006, computing entity 10 updates the master design library. Computing entity 10 may record the optical response for each value of one or more geometry parameters and for each value of one or more shape parameters. For example, computing entity 10 may create a lookup table or database that maps the phase delay of the metamaterial structure to some or all possible values ​​of the geometry parameters. Computing entity 10 may create the mapping in two steps: first for the geometry parameters, and then for each geometry parameter value (or vice versa). Computing entity 10 may do so while keeping global parameters constant for all metamaterial structures of the metasurface.

[0124] In various embodiments, the global parameters include a height, a local fill factor, and / or a wavelength associated with each metamaterial structure. In various embodiments, the configuration parameters include a forward incidence angle of a forward optical beam on the metamaterial structure of the metasurface, a backward incidence angle of a backward optical beam on the metamaterial structure of the metasurface, a forward polarization of a forward optical beam on the metamaterial structure of the metasurface, and / or a backward polarization of a backward optical beam on the metamaterial structure of the metasurface.

[0125] In various embodiments, the forward and / or reverse incidence angles of the optical beam are determined using the optical manipulation capabilities of the metasurface. In various embodiments, the forward and / or reverse polarizations are determined using the optical manipulation capabilities of the metasurface.

[0126] In various embodiments, when the forward and reverse polarizations are not the same, the metasurface will locally impart a polarization shift, however the forward and reverse beams themselves are independently defined.

[0127] In various embodiments, computing entity 10 optimizes the metasurface using the master design library in step 1008. In various embodiments, computing entity 10 optimizes the metasurface in the forward and reverse directions using the master library by determining optimal values ​​of one or more geometry parameters and highest values ​​of one or more shape parameters that optimize an aggregation criterion for the metasurface.

[0128] Various embodiments of the present disclosure use adjoint optimization to optimize metasurfaces. In some examples, using adjoint optimization can further optimize metasurfaces that may be optimized using other methods.

[0129] In various embodiments, a design library, such as a master library as previously described, may be used in the adjoint optimization. In various embodiments, the adjoint optimization may use a design library that does not reveal configuration parameters.

[0130] In various embodiments, an aggregate optimization process is provided. For example, adjoint optimization can be used to optimize the metasurface for both forward and backward incident beams. Adjoint optimization can be used for the forward and backward directions simultaneously.

[0131] The adjoint optimization method can compare the fields produced by metasurface test iterations operating on predefined incident fields to predefined fields that represent the optimization target. The comparison of these fields can result in a calculated response gradient for every metamaterial structure of the metasurface, which can then be used to update the metamaterial structure array for subsequent iterations.

[0132] Adjoint methods can be more computationally efficient than direct search or gradient descent methods, which may require N+1 calculations per iteration, where N is the number of parameters being optimized. Adjoint optimization methods, however, may run a single test point M(P), where the metasurface response M is a function of all possible parameters (denoted by the vector P) considered by the optimizer. From one response, the adjoint optimization method may calculate the gradient for each parameter in P. However, direct search or gradient descent methods run a series of test points (e.g., N+1) to visualize an N-dimensional surface of the response, which is then used to calculate the gradient for each parameter. These approaches can work well for problems with a small number of parameters. However, metasurfaces can have a very large number of parameters (e.g., arbitrary shape parameters multiplied by each element in the array), and therefore using direct search or gradient descent methods may not be computationally feasible. However, adjoint optimization methods allow optimization over a large parameter space.

[0133] When using adjoint optimization, the metasurface design may not be known initially, but for a known incident field, the expected target field is known. In various embodiments, either the electric and / or electromagnetic fields of the incident target field or the expected target field may be used in various other steps, either for simulation, comparison, calculation, etc.

[0134] In various embodiments, the field of each incident beam in the forward direction is multiplied by the electromagnetic response of the corresponding metamaterial structure to calculate the field transformed by the metasurface. The transformed field may then be compared to the target field. Using the comparison, a gradient for each metamaterial structure is determined. The metamaterial structure gradient indicates a change in one or more parameters of the metamaterial structure required for the transformed field to approximate the target field. In various embodiments, the metamaterial structure gradient indicates a change in one or more geometric parameters of the metamaterial structure required for the transformed field to approximately equal the target field. The parameters of the metamaterial structure are then iteratively changed based on the metamaterial structure gradient, and the transformed field is recalculated until the transformed field approximately equals the target field and / or the metasurface is optimized. In various embodiments, the aggregate performance criterion used to optimize the metasurface is for the transformed field to approximately equal the target field. For example, the difference between the transformed field and the target field may be minimized.

[0135] In various embodiments, an aggregate optimization process is performed, accounting for both the forward and reverse beams and using the master library as previously described.

[0136] In various embodiments, a first adjoint optimization process is performed in a forward direction using a library that reveals known geometry parameters for the forward incident light. A second adjoint optimization process can be performed in a backward direction using a library that reveals geometry parameters for the reverse incident light. In various embodiments, a constraint on the optimization is that the two separate calculations must converge to the same metasurface design over time. For example, the same shape parameters must be determined for the metamaterial structure.

[0137] In various embodiments, the forward adjoint optimization process is performed in parallel and / or intermittently with the backward adjoint optimization process, with the constraint that the shape parameters determined in the forward and backward processes must converge to the same shape parameters.

[0138] In various embodiments, during the adjoint forward optimization process, the geometry parameters are determined using the forward incident beam. For example, in a focusing metasurface, when the forward incident beam is parallel, the elevation and azimuthal angles and polarization parameters are known and are the same for all metamaterial structures. Iterations of the adjoint optimization process are performed in the forward direction to determine the shape parameters.

[0139] However, in various embodiments, a backward adjoint optimization is performed before the shape parameters are updated for the metamaterial structures based on the determined gradient. In the example of a focusing metasurface, the backward incident beam is a diverging beam and the target field is a collimated beam. The geometry parameters for the various metamaterial structures of the metasurface can then have a wide range of values ​​because the incident beam is diverging and does not impinge on all metamaterial structures on the metasurface at the same angle.

[0140] Thus, adjoint optimization is performed in both forward and reverse directions using a master design library containing geometry parameters. The gradients for the metamaterial structure in the forward direction and the gradients for the metamaterial structure in the reverse direction are determined, and the adjoint optimization iterates through the metasurface design and proceeds to the next loop. However, because the metasurface is the same device in both directions, the determined shape parameters for both directions must converge.

[0141] Thus, in various embodiments, adjoint optimization is performed in both the forward and backward directions using known geometry parameters, including the constraint that the shape parameters in both the forward and backward directions are the same. In various embodiments, the forward and backward adjoint optimization iterations are subject to the constraint that the shape parameters must converge to the same parameters for the forward and backward directions.

[0142] In various embodiments, the fixed configuration parameters for each of the forward and reverse directions are determined using any of the light manipulation functions, phase curves, and / or phase masks of the metasurface.

[0143] In various embodiments, during adjoint optimization, two calculations are completed using two different library mappings, as described above for the forward and backward directions, and two gradients are calculated (as part of the adjoint optimization procedure). However, the metasurface shape map (metamaterial structure shape parameters) remains the same for both the forward and backward calculations. The two gradients can be evaluated together (e.g., using a weighted average, etc.) to calculate the changes that need to be made to the metasurface shape map (which remains the same for both directions) between each iteration.

[0144] Thus, in various embodiments, from the start of the adjoint optimization, the array of shapes is asserted to be the same for the forward and reverse calculations. Thus, after the gradients for the forward metamaterial structures and the gradients for the reverse metamaterial structures are determined, information from both of those gradients is used to make a single set of changes to the shape parameters of the metamaterial structures of the metasurface.

[0145] Thus, in various embodiments, the adjoint optimization considers both forward and backward calculations, but at every iteration, the metasurface shape designs are the same for both calculations, thus forcing these shapes to always remain the same, rather than allowing them to start as different designs and converge to the same design.

[0146] In exemplary embodiments, adjoint optimization allows for the evaluation of the response of the entire metasurface by assessing the extent to which the target field is achieved using provisional shape parameters. In some instances, adjoint optimization is an aggregate optimization because the effect of the entire metasurface is taken into account. In exemplary embodiments, aggregate optimization can therefore reveal the response of elements located at a distance from each other relative to the overall design and function of the metasurface.

[0147] 11 is a flowchart illustrating a method 1100 for designing a metasurface according to various embodiments herein. In various embodiments, in step 1102, the computing entity 10 determines a forward transform function for one or more metamaterial structures of the metasurface. In step 1104, the computing entity 10 determines an inverse transform function for one or more metamaterial structures of the metasurface. In step 1106, the computing entity 10 calculates a forward transformed beam by transforming the field of a forward incident beam according to the forward transform function. In step 1108, the computing entity 10 calculates an inverse transformed beam by transforming the field of a backward incident beam according to the inverse transform function.

[0148] In step 1110, the computing entity 10 determines the forward gradient. In various embodiments, the computing entity 10 compares the forward transformed beam with the forward target beam and uses the comparison to determine the forward gradient.

[0149] In step 1112, the computing entity 10 determines the reverse gradient. In various embodiments, the computing entity 10 compares the reverse transformed beam with the reverse target beam and uses the comparison to determine the reverse gradient.

[0150] In step 1114, the computing entity 10 uses the forward and backward gradients to modify one or more shape parameters of the metamaterial structure of the metasurface.

[0151] In various embodiments, the forward gradient maps to a forward shape gradient within one or more shape parameters of one or more metamaterial structures of the metasurface, and the reverse gradient maps to a reverse shape within one or more shape parameters of one or more metamaterial structures of the metasurface, in various embodiments, the mapping can be a unity function.

[0152] In various embodiments, method 1100 may further determine forward shape parameters of the metamaterial structures of the metasurface using the forward gradient. Method 1100 may determine reverse shape parameters of the metamaterial structures of the metasurface using the reverse gradient. Method 1100 may determine a shape convergence gradient, which is the difference between the forward and reverse shape parameters for each metamaterial structure of the metasurface.

[0153] In various embodiments, method 1100 may further iteratively repeat the steps of determining the forward and reverse shape parameters and determine a shape convergence gradient for each metamaterial structure of the metasurface until the difference between the forward transformed beam and the forward target beam is optimized and the difference between the reverse transformed beam and the reverse target beam is optimized. In various embodiments, as described further below, the difference between the forward transformed beam and the forward target beam and the difference between the reverse transformed beam and the reverse target beam are optimized when the shape parameters are the same in the forward and reverse directions or the shape convergence gradient is zero.

[0154] In various embodiments, method 1100 may optimize the design of a metasurface by modifying one or more metamaterial structures of the metasurface using forward and reverse gradients such that the difference between the forward transformed beam and the forward target beam is optimized and the difference between the reverse transformed beam and the reverse target beam is optimized.

[0155] In various embodiments, the modification includes modifying the forward and inverse shape parameters. In various embodiments, the method 1100 includes minimizing a shape convergence gradient, prioritizing the minimization of the shape convergence gradient when iteratively determining the forward and inverse shape parameters, and completing the optimization when the shape convergence gradient for each metamaterial structure of the metasurface is zero.

[0156] In various embodiments, the method 1100 includes making a forward shape parameter of the metamaterial structure of the metasurface equal to a reverse shape parameter of the metamaterial structure of the metasurface.

[0157] In various embodiments, the method 1100 includes optimizing the design of the metasurface by modifying one or more metamaterial structures of the metasurface using forward and reverse gradients such that the combination of the forward and reverse gradients is minimized.

[0158] In various embodiments, modifying one or more metamaterial structures of the metasurface includes modifying equal forward and reverse shape parameters of each metamaterial structure of the metasurface using a combination of forward and reverse gradients. In various embodiments, the combination is a weighted average. In various embodiments, the combination includes unequal weighting of the forward and reverse gradients. For example, a weighted average of the determined forward and reverse gradients is used to make the same change to the shape parameters of one or more metamaterial structures of the metasurface.

[0159] As described above, in various embodiments, metasurfaces are designed and / or optimized that include multiple metamaterial structures. For example, the metasurfaces may perform functions that manipulate signals such as light for applications in quantum computers, light detection and ranging systems (lidar), cameras, etc.

[0160] Technical Issues and Benefits Optimizing metasurfaces can require the use of modeled libraries of metasurfaces, but with various previously used approaches, computationally modeling large-area metasurfaces can be computationally prohibitive due to excessive computational memory and time requirements.

[0161] Various embodiments provide technical solutions to technical problems related to the computational difficulty of designing metasurfaces with accurate responses (e.g., accurately modeling the response of the metasurface). Various embodiments provide systems and methods for metasurface optimization without computationally prohibitive modeling. These various technical solutions provide a computationally feasible manner for optimizing and developing metasurfaces, including metasurfaces with dimensions of 10 × 10 microns or greater. These solutions further avoid the prohibitive memory requirements and significant processing costs of modeling large metasurface arrays while providing metasurface models that more accurately predict the behavior of each metasurface.

[0162] Exemplary Computing Entity 12 provides an exemplary schematic diagram depicting an exemplary computing entity 10 that may be used in connection with embodiments of the present invention. In various embodiments, computing entity 10 may be configured to allow a user to provide input to a quantum computer (e.g., via a user interface of computing entity 10) and receive, display, analyze, etc. output from the quantum computer. In various embodiments, computing entity 10 may be configured to compute any step or calculation provided in accordance with various embodiments of the present disclosure.

[0163] 12 , computing entity 10 may include an antenna 12, a transmitter 14 (e.g., wireless), a receiver 16 (e.g., wireless), and a processing element 22 that provides signals to and receives signals from transmitter 14 and receiver 16, respectively. The signals provided to and received from transmitter 14 and receiver 16, respectively, may include signaling information / data according to an applicable wireless system air interface standard for communicating with various entities, such as controllers, other computing entities 10, etc. In this regard, computing entity 10 may be capable of operating with one or more air interface standards, communication protocols, modulation types, and access types. For example, computing entity 10 may be configured to receive and / or provide communications using a wired data transmission protocol, such as fiber distributed data interface (FDDI), digital subscriber line (DSL), Ethernet, asynchronous transfer mode (ATM), frame relay, data over cable service interface specification (DOCSIS), or any other wired transmission protocol.Similarly, the computing entity 10 may be configured to communicate using any of a variety of protocols, including General Packet Radio Service (GPRS), Universal Mobile Telecommunications System (UMTS), Code Division Multiple Access 2000 (CDMA2000), CDMA2000 1X (1xRTT), Wideband Code Division Multiple Access (WCDMA), Global System for Mobile Communications (GSM), Enhanced Data rates for GSM Evolution (EDGE), Division-Synchronous Code Division Multiple Access (TD-SCDMA), Long Term Evolution (LTE), Evolved Universal Terrestrial Radio Access Network (E-UTRAN), Evolution-Data Optimized (EVDO), High Speed ​​Packet Access (HSPA), High Speed ​​Downlink Packet Access (HSDPA), IEEE 802.11a / b / g / n, IEEE 802.1 ... It may be configured to communicate via a wireless external communication network, such as 802.11 (Wi-Fi), Wi-Fi Direct, 802.16 (WiMAX), Ultra Wideband (UWB), Infrared (IR) protocol, Near Field Communication (NFC) protocol, Wibree, Bluetooth protocol, Wireless Universal Serial Bus (USB) protocol, and / or any other wireless protocol.Computing entity 10 may communicate using such protocols and standards, such as Border Gateway Protocol (BGP), Dynamic Host Configuration Protocol (DHCP), Domain Name System (DNS), File Transfer Protocol (FTP), Hypertext Transfer Protocol (HTTP), HTTP over TLS / SSL / Secure, Internet Message Access Protocol (IMAP), Network Time Protocol (NTP), Simple Mail Transfer Protocol (SMTP), Telnet, Transport Layer Security (TLS), Secure Sockets Layer (SSL), Internet Protocol (IP), Transmission Control Protocol (TCP), User Datagram Protocol (UDP), Datagram Congestion Control Protocol (DCCP), Stream Control Transmission Protocol (SCTP), Hypertext Markup Language (HTML), and the like.

[0164] Through these communication standards and protocols, computing entity 10 may communicate with various other entities using concepts such as Unstructured Supplementary Service information / data (USSD), Short Message Service (SMS), Multimedia Messaging Service (MMS), Dual-Tone Multi-Frequency Signaling (DTMF), and / or Subscriber Identity Module Dialer (SIM dialer). Computing entity 10 may also download modifications, add-ons, and updates to, for example, its firmware, software (including, for example, executable instructions, applications, program modules), and operating system.

[0165] In various embodiments, computing entity 10 may comprise a network interface 28 for interfacing and / or communicating with another entity, device, or module, e.g., a controller, memory, a user, etc. For example, computing entity 10 may comprise a network interface 28 for providing executable instructions, command sets, etc. for receipt by the other entity, device, or module, and / or for receiving output provided by the other entity, device, or module and / or results of processing of the output. In various embodiments, computing entity 10 and the other entity, device, or module may communicate via direct wired and / or wireless connections and / or via one or more wired and / or wireless networks.

[0166] Computing entity 10 may comprise user interface devices comprising one or more user input / output interfaces (e.g., a display 18 and / or speakers / speaker drivers coupled to processing element 22, and a touchscreen, keyboard, mouse, and / or microphone coupled to processing element 22). For example, the user output interface may be configured to provide an application, browser, user interface, interface, dashboard, screen, web page, page, and / or similar terms used interchangeably herein executing on and / or accessible via computing entity 10 to cause a display or audible presentation of and interaction with information / data via one or more user input interfaces. The user input interface may comprise any of several devices that enable computing entity 10 to receive data, such as a keypad 20 (hard or soft), a touch display, a voice / audio or motion interface, a scanner, reader, or other input device. In embodiments including a keypad 20, the keypad 20 may include (or display) conventional numeric (0-9) and related keys (#, *), as well as other keys used to operate computing entity 10, and may include a full set of alphabetic keys, or a set of keys that can be activated to provide a full set of alphanumeric keys. In addition to providing input, the user input interface may be used to activate or deactivate certain functions, such as, for example, a screen saver and / or sleep mode. Through such input, computing entity 10 may collect information / data, user interaction / input, etc.

[0167] Computing entity 10 may include volatile storage or memory 26 and / or non-volatile storage or memory 24, which may be embedded and / or removable. For example, non-volatile memory may be ROM, PROM, EPROM, EEPROM, flash memory, MMC, SD memory card, memory stick, CBRAM, PRAM, FeRAM, RRAM, SONOS, racetrack memory, etc. Volatile memory may be RAM, DRAM, SRAM, FPM DRAM, EDO DRAM, SDRAM, DDR SDRAM, DDR2 SDRAM, DDR3 SDRAM, RDRAM, RIMM, DIMM, SIMM, VRAM, cache memory, registered memory, etc. Volatile and non-volatile storage or memory may store databases, database instances, database management system entities, data, applications, programs, program modules, scripts, source code, object code, byte code, compiled code, interpreted code, machine code, executable instructions, etc. for implementing the functionality of computing entity 10.

[0168] conclusion

[0023] Many modifications and other embodiments of the inventions described herein will come to mind to one skilled in the art to which these inventions pertain having the benefit of the teachings presented in the foregoing descriptions and the associated drawings. It is to be understood, therefore, that the invention is not to be limited to the specific embodiments disclosed, and that modifications and other embodiments are intended to be included within the scope of the appended claims. Although specific terms are employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation.

Claims

1. A method for designing a metasurface, comprising: selecting a first metamaterial structure from a plurality of metamaterial structures of the metasurface; generating a forward light propagation model for the first metamaterial structure using light manipulation functions for the metasurface; and generating a reverse light propagation model for the first metamaterial structure using light manipulation functions for the metasurface; and determining a first electromagnetic response difference between the forward light propagation model and the reverse light propagation model; determining a first characteristic range of the first metamaterial structure such that the first electromagnetic response difference is optimized.

2. 10. The method of claim 1, wherein the light manipulation functionality of the metasurface comprises refractive and / or reflective light manipulation functionality.

3. 3. The method of claim 2, wherein the backward light propagation model models the interaction of backward-propagating light with the first metamaterial structure, and the forward light propagation model models the interaction of forward-propagating light with the first metamaterial structure, wherein in the forward light propagation model, a forward angle of light remains unchanged, and in the backward light propagation model, a backward angle of light remains unchanged, and wherein the backward angle is determined using a light manipulation function for the metasurface and a forward angle.

4. The method of claim 2 , wherein the refractive or reflective light manipulation function comprises a focusing and / or collimating function.

5. The method of claim 1 , wherein the electromagnetic response of the first electromagnetic response difference comprises a phase delay, an amplitude, or a polarization.

6. 10. The method of claim 1, wherein optimizing the first electromagnetic response difference comprises minimizing an aggregate performance criterion of the metasurface.

7. 10. The method of claim 1, wherein a first range of properties of the first metamaterial structure comprises a first range of shapes and / or dimensions of the first metamaterial structure.

8. 10. The method of claim 1, wherein the first metamaterial structure is located at the periphery of the metasurface.

9. selecting a second metamaterial structure from the plurality of metamaterial structures; generating a forward light propagation model for the second metamaterial structure; generating a reverse light propagation model for the second metamaterial structure using light manipulation functions for the metasurface; and determining a second electromagnetic response difference between the forward light propagation model and the reverse light propagation model; 10. The method of claim 1, further comprising: determining a second characteristic range of the second metamaterial structure such that the second electromagnetic response difference is optimized.

10. determining a first property value within the first property range and a first location for the first metamaterial structure on a first unit cell of the metasurface; 10. The method of claim 9, further comprising: determining a second property value within the second property range and a second location for the second metamaterial structure on a second unit cell adjacent to the first unit cell, wherein the first and second property values ​​and the first and second locations are determined to satisfy a geometric constraint of the metasurface.

11. The method of claim 10 , wherein the geometric constraints include a distance between the first metamaterial structure and the second metamaterial structure and / or a fill factor of a local region.

12. 10. An apparatus comprising at least one processor and a memory storing computer-executable instructions, the computer-executable instructions being configured, when executed by the at least one processor, to cause the apparatus to perform the method of claim 1.

13. 10. A computer program product comprising at least one non-transitory computer-readable medium storing computer-executable instructions, the computer-executable instructions being configured, when executed by a processor of the device, to cause the device to perform the method of claim 1.

14. A method for designing a metasurface, comprising: selecting a reference metamaterial structure of the plurality of metamaterial structures of the metasurface; determining the characteristics and computational complexity of the reference metamaterial structure for a reference forward phase delay and a forward angle of incidence; determining a relationship between a reference reverse phase retardation and a characteristic of the reference metamaterial structure for a reverse angle of incidence; determining characteristics of the reference metamaterial structure such that the difference between the forward phase delay and the reverse phase delay is optimized; The method, wherein the forward phase delay and the reverse phase delay are offset by a fixed phase value.

15. 15. The method of claim 14, comprising determining the forward and reverse angles of incidence using a phase mask of the metasurface.

16. 16. The method of claim 15, comprising using a light manipulation function for the metasurface to determine a phase mask of the metasurface.

17. 15. The method of claim 14, comprising selecting the reference metamaterial structure such that a difference between the forward and backward angles of incidence is minimized.

18. 20. The method of claim 17, comprising determining a characteristic of another metamaterial structure by referencing a forward phase delay of the other metamaterial structure with the reference forward phase delay and by referencing an antiphase delay of the other metamaterial structure with the reference antiphase delay.

19. 20. The method of claim 18, comprising iteratively repeating the step of determining properties of other metamaterial structures until the metasurface is optimized.

20. A method for designing a metasurface, comprising: determining an optical response of a metamaterial structure of the metasurface for each value of one or more configuration parameters of the metamaterial structure while holding one or more global parameters of the metamaterial structure constant; determining an optical response of the metamaterial structure for each value of one or more geometric parameters of the metamaterial structure while holding one or more global parameters of the metamaterial structure constant for each value of the one or more geometric parameters; and recording the optical response for each value of the one or more configuration parameters and for each value of the one or more shape parameters.

21. 21. The method of claim 20, comprising keeping the global parameters constant for all the metamaterial structures of the metasurface.

22. 22. The method of claim 21 , wherein the global parameters include a height, a local filling fraction, and / or a wavelength associated with each metamaterial structure.

23. The configuration parameters are: a forward incident angle of a forward optical beam to the metamaterial structure of the metasurface, the forward incident angle being determined using an optical steering function of the metasurface; and and a retrograde angle of incidence of a retrograde optical beam on the metamaterial structure of the metasurface, the retrograde angle of incidence being determined using an optical steering function of the metasurface.

24. The configuration parameters are: a forward polarization of the forward optical beam relative to the metamaterial structure of the metasurface, the forward polarization being determined using an optical manipulation function of the metasurface; and and a reverse polarization of the reverse optical beam relative to the metamaterial structure of the metasurface, the reverse polarization being determined using an optical manipulation function of the metasurface.

25. updating a metasurface master library by recording the optical response for each value of the one or more configuration parameters and for each value of the one or more shape parameters; and optimizing the metasurface in a forward and reverse direction using the metasurface master library by determining optimal values ​​of the one or more configuration parameters and optimal values ​​of the one or more shape parameters that optimize an aggregation criterion for the metasurface.

26. A method for designing a metasurface, comprising: determining a forward transformation function for one or more metamaterial structures of the metasurface; determining a reverse transformation function for one or more metamaterial structures of the metasurface; calculating a forward transformed beam by transforming the field of the forward incident beam according to the forward transformation function; calculating an inverse transformed beam by transforming the field of the inverse incident beam according to the inverse transform function; comparing the forward transformed beam to a forward target beam and using the comparison to determine a forward gradient; comparing the reverse transformed beam with a reverse target beam and using the comparison to determine a reverse gradient; and using the forward gradient and the reverse gradient to modify one or more shape parameters of a metamaterial structure of the metasurface.

27. 27. The method of claim 26, wherein the forward gradient maps to a forward shape gradient in one or more shape parameters of the one or more metamaterial structures of the metasurface, and the reverse gradient maps to a reverse shape gradient in one or more shape parameters of the one or more metamaterial structures of the metasurface.

28. using the forward gradient to determine forward shape parameters of the metamaterial structure of the metasurface; determining inverse shape parameters of the metamaterial structure of the metasurface using an inverse gradient; determining a shape convergence gradient, the shape convergence gradient being the difference between a forward shape parameter and a reverse shape parameter for each metamaterial structure of the metasurface; and iteratively repeating the steps of determining the forward shape parameters and the reverse shape parameters until a difference between the forward transformed beam and the forward target beam is optimized and a difference between the reverse transformed beam and the reverse target beam is optimized, and determining the shape convergence gradient for each metamaterial structure of the metasurface.

29. 30. The method of claim 28, comprising optimizing a design of the metasurface by using the forward gradient and the reverse gradient to modify the one or more metamaterial structures of the metasurface such that a difference between the forward transformed beam and the forward target beam is optimized and a difference between the reverse transformed beam and the reverse target beam is optimized.

30. 30. The method of claim 29, wherein said modifying comprises modifying said forward shape parameters and said reverse shape parameters.

31. minimizing the shape convergence gradient; prioritizing the step of minimizing the shape convergence gradient when iteratively repeating the steps of determining the forward shape parameters and the backward shape parameters; completing the optimization when the shape convergence gradient for each metamaterial structure of the metasurface is zero.

32. 27. The method of claim 26, comprising: making a forward shape parameter of the metamaterial structure of the metasurface equal to a reverse shape parameter of the metamaterial structure of the metasurface.

33. 33. The method of claim 32, comprising optimizing a design of the metasurface by using the forward gradient and the reverse gradient to modify the one or more metamaterial structures of the metasurface such that a combination of the forward gradient and the reverse gradient is minimized.

34. 34. The method of claim 33, wherein modifying the one or more metamaterial structures of the metasurface comprises modifying equal forward and reverse shape parameters of each metamaterial structure of the metasurface.

35. 35. The method of claim 34, wherein the combination of the forward gradient and the backward gradient is a weighted average of the forward gradient and the backward gradient.

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