Automatic super lens design system

Abstract

A method for designing a superlens includes receiving a description of an optical system including (i) a superatom to be used in a first lens in the optical system and (ii) a first distance from the first lens, receiving a description of an optical signal including (i) an incident optical signal to the optical system and (ii) a target optical signal of the optical system, and determine a first layout of the plurality of superatoms on the first lens. The method further includes determining a first output optical signal of the optical system based at least in part on the incident optical signal and a first layout of the plurality of superatoms on the first lens, and setting a design of the first lens using the first layout.

Description

Technical Field

[0001] The present invention relates to the design of optical systems. In particular, the present invention relates to a system and method for providing automated metalens design. Background Art

[0002] Optical systems can include lenses for redirecting or refocusing light signals. The relatively flat surface topology used for metasurfaces and mature semiconductor manufacturing techniques make metasurfaces ideal for a wide range of applications, including lens design (e.g., for optical systems operating in transmission or reflection modes). Summary of the invention

[0003] Systems and methods for designing metalenses are described herein. According to one embodiment, a method for designing a metalens includes receiving a description of an optical system. The description of the optical system indicates (i) characteristics of a first lens in the optical system, (ii) meta-atoms to be used in the first lens, and (iii) a first distance from the first lens. The method also includes receiving a description of a light signal, the description of the light signal describing (i) an incident light signal to the optical system and (ii) a target light signal for the optical system, and determining a first layout of a plurality of meta-atoms on the first lens based at least in part on the characteristics of the first lens, the meta-atoms, and the first distance. The method also includes determining a first output light signal of the optical system based at least in part on the incident light signal and the first layout of the plurality of meta-atoms on the first lens, and setting a design of the first lens using the first layout based on whether a difference between the first output light signal and the target light signal satisfies a threshold.

[0004] The method may include, based on the difference between the first output light signal and the target light signal not satisfying a threshold, determining a second layout of the plurality of meta-atoms on the first lens based at least in part on the characteristics of the first lens, the meta-atom, the first distance, and the first layout. The method may also include determining a second output light signal of the optical system using the incident light signal and using the second layout of the plurality of meta-atoms on the first lens, and setting a design of the first lens using the second layout based on whether the difference between the second output light signal and the target light signal satisfies the threshold.

[0005] The description of the optical system may indicate a characteristic of a second lens in the optical system and a second distance from the second lens. The first distance may be between the first lens and the second lens in the optical system, and determining the first layout may be based on the characteristic of the second lens and the second distance.

[0006] Determining the first layout may include determining a geometric design parameter for each of the plurality of meta-atoms on the first lens.

[0007] The first layout may be based on a different incident angle for each of the plurality of meta-atoms.

[0008] The first layout may be based on polarization of the optical signal and a response of each of the plurality of meta-atoms to the polarization.

[0009] The first output light signal may be based at least in part on an absorptive boundary condition of a space within a first distance from the first lens.

[0010] The difference may include a difference between an intensity distribution of the first output optical signal and an intensity distribution of the target optical signal scaled by the scaling factor.

[0011] The difference may be based on a phase of the first output optical signal and a phase of the target optical signal.

[0012] According to another embodiment, a system includes a memory and a processor communicatively coupled to the memory. The processor receives (i) characteristics of a first lens in an optical system, (ii) meta-atoms to be used in the first lens, and (iii) a first distance from the first lens, and receives (i) an incident light signal to the optical system and (ii) a description of a target light signal for the optical system. The processor also determines a first layout of a plurality of meta-atoms on the first lens based at least in part on the characteristics of the first lens, the meta-atoms, and the first distance, and determines a first output light signal of the optical system based at least in part on the incident light signal and the first layout of the plurality of meta-atoms on the first lens. The processor also sets a design of the first lens using the first layout based on whether a difference between the first output light signal and the target light signal satisfies a threshold.

[0013] The processor may determine a second layout of the plurality of meta-atoms on the first lens based at least in part on the characteristics of the first lens, the meta-atom, the first distance, and the first layout based on the difference between the first output light signal and the target light signal not satisfying a threshold. The processor may also determine a second output light signal of the optical system using the incident light signal and using the second layout of the plurality of meta-atoms on the first lens, and set the design of the first lens using the second layout based on whether the difference between the second output light signal and the target light signal satisfies the threshold.

[0014] The processor may receive a characteristic of a second lens in the optical system and a second distance from the second lens. The first distance may be between the first lens and the second lens in the optical system. Determining the first layout may be based on the characteristic of the second lens and the second distance.

[0015] Determining the first layout may include determining a geometric design parameter for each of the plurality of meta-atoms on the first lens.

[0016] The first layout may be based on a different incident angle for each of the plurality of meta-atoms.

[0017] The first layout may be based on polarization of the optical signal and a response of each of the plurality of meta-atoms to the polarization.

[0018] The first output light signal may be based at least in part on an absorptive boundary condition of a space within a first distance from the first lens.

[0019] The difference may include a difference between an intensity distribution of the first output optical signal and an intensity distribution of the target optical signal scaled by the scaling factor.

[0020] The difference may be based on a phase of the first output optical signal and a phase of the target optical signal.

[0021] According to another embodiment, a non-transitory computer-readable medium stores instructions for designing a metalens, which, when executed by a processor, causes the processor to receive (i) properties of a first lens in an optical system, (ii) meta-atoms to be used in the first lens, and (iii) a first distance from the first lens, and receive a description of (i) an incident light signal to the optical system and (ii) a target light signal for the optical system. The processor also determines a first layout of a plurality of meta-atoms on the first lens based at least in part on the properties of the first lens, the meta-atoms, and the first distance, determines a first output light signal of the optical system based at least in part on the incident light signal and the first layout of the plurality of meta-atoms on the first lens, and sets a design of the first lens using the first layout based on whether a difference between the first output light signal and the target light signal satisfies a threshold.

[0022] The processor can determine a second layout of the plurality of meta-atoms on the first lens based at least in part on the characteristics of the first lens, the meta-atoms, the first distance, and the first layout based on the fact that a difference between the first output light signal and the target light signal does not satisfy a threshold, determine a second output light signal of the optical system using the incident light signal and using the second layout of the plurality of meta-atoms on the first lens, and set the design of the first lens using the second layout based on whether the difference between the second output light signal and the target light signal satisfies a threshold. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The present disclosure will be more fully understood from the detailed description given below and the accompanying drawings of the embodiments of the present disclosure. These drawings are used to provide knowledge and understanding of the embodiments of the present disclosure, and do not limit the scope of the present disclosure to these specific embodiments. In addition, these drawings are not necessarily drawn to scale.

[0024] Figure 1 An example optical system is illustrated.

[0025] Figure 2 Picture shows Figure 1 Example metalens in an optical system.

[0026] Figure 3A An example superatom array is illustrated.

[0027] Figure 3B An example superatom array is illustrated.

[0028] Figure 3C An example superatom array is illustrated.

[0029] Figure 4 Illustration for design Figure 1 An example process of using a metalens in an optical system.

[0030] Figure 5 is a flow chart of an example method for designing a metalens.

[0031] Figure 6 A diagram of an example computer system is depicted in which embodiments of the present disclosure may operate. DETAILED DESCRIPTION

[0032] Aspects of the present disclosure relate to automated metalens design systems. An optical system may include a lens that redirects or refocuses an optical signal. The relatively flat surface topology used for metasurfaces and mature semiconductor manufacturing techniques make metasurfaces ideal for a wide range of applications, including lens design (e.g., for optical systems operating in transmission or reflection modes). For example, including a metalens in an optical system can reduce the size of the optical system and can reduce alignment challenges.

[0033] Each metalens in the optical system is formed using an array of meta-atoms on a surface. A meta-atom is a sub-wavelength structure that can have any suitable shape and size. For example, a meta-atom can be a rectangular column with any suitable width. As another example, a meta-atom can be a cylinder with any suitable width.

[0034] Computational simulations have been used to examine the underlying physics of metasurfaces and provide insights into the design of optical systems that include both metalenses and typical lenses. Due to the wide range of sizes of the geometries involved in these optical systems, where the size of the system itself as well as the metalenses can be centimeters, and the size of the meta-atoms that form the metalenses can be sub-micrometers, various numerical techniques can be used to efficiently and accurately analyze the performance and optimize efficiency. However, due to the limitations of geometric optics, traditional (e.g., ray tracing-based) optical design methods may not be able to accurately simulate such optical systems. In addition, more rigorous electromagnetic simulation methods are resource intensive and may not be used to optimize these systems due to the large number of sub-wavelength structures in these metalenses.

[0035] This disclosure describes a system for automatically determining the design of a metalens in an optical system. Typically, a user provides the system with a description of the optical system (e.g., the types of lenses in the optical system, the meta-atoms to be used by one or more metalens in the optical system, and the distances between the lenses) and a description of the light signal in the system (e.g., the characteristics of the incident light signal and the characteristics of the desired target light signal to be output by the optical system). The system then applies an optimization process based on an adjoint method to determine the layout of the metalens in the optical system (e.g., the size or arrangement of the meta-atoms that form the metalens) so that the optical system outputs a light signal within the target light signal threshold for a given incident light signal.

[0036] In certain embodiments, the present system provides several technical advantages over traditional design processes. For example, the present system takes into account non-uniform transmission, different angles of incidence, and polarization when determining the layout of the metalens, which improves the accuracy of the system simulation and optimizes the optical system behavior. In addition, the present system allows the optical system to include both metalenses and typical lenses. Therefore, the present system can be used to design optical systems for multi-wavelength applications, multifunctional devices, larger fields of view, and polarization-sensitive devices.

[0037] Figure 1 An example optical system 100 is shown. Figure 1 As seen in FIG. 1 , optical system 100 includes an arrangement of lenses and metalenses. Optical system 100 may include any suitable number of lenses and metalenses arranged in any suitable manner. INC ) passes through the optical system 100. The lenses and metalenses split or redirect the incident light signal to produce one or more output light signals (E OUT ). The properties and arrangement of the lenses and metalenses can be set so that the optical system 100 produces a desired optical signal.

[0038] exist Figure 1 In the example of FIG. 1 , the optical system 100 includes a plurality of lenses and metalenses. In particular, the optical system 100 includes a first metalenses 102, a first lens 104, a lens 106, and a second metalenses 108. The optical system 100 may include additional lenses and metalenses. It should also be understood that the optical system may include any number and arrangement of lenses and metalenses without departing from the scope of the present disclosure. The first metalenses 102 is spaced a distance D from the first lens 104. 1 The distance between the first lens 104 and the second lens 106 is D 2The lenses and metalens may be positioned with any desired distance between them. An incident light signal passes through first metalens 102, first lens 104, second lens 106, and second metalens 108. As the light signal passes through first metalens 102, first lens 104, second lens 106, and second metalens 108, first metalens 102, first lens 104, second lens 106, and second metalens 108, the light signal is split or redirected by first metalens 102, first lens 104, second lens 106, and second metalens 108. Second metalens 108 generates one or more output light signals E of optical system 100. OUT The first metalens 102, the first lens 104, the second lens 106, and the second metalens 108 may be arranged such that one or more output optical signals are at a distance D from the metalens 108. 3 In other words, the properties of the first metalens 102, the first lens 104, the second lens 106, and the second metalens 108 can be selected, and the distance D can be set 1 , D 2 and D 3 , so that one or more output optical signals are generated at a distance D from the metalens 108 3 One or more desired intensity distributions at.

[0039] Lenses 104 and 106 can be typical thin lenses, whose thickness is much smaller than their radius of curvature. As a result, lenses 104 and 106 can be modeled by phase transfer functions. Metalenses 102 and 108 can be formed using meta-atoms, which are underlying sub-wavelength structures. Each metalens 102 or 108 includes an array of meta-atoms.

[0040] Figure 2 Picture shows Figure 1 1. Example metalens 102 in optical system 100 of FIG. 1. In general, metalens 102 is formed using an array of meta-atoms. The meta-atoms can be any suitable shape or size. For example, the meta-atoms can be cylindrical, square, or cross-shaped. The geometric design parameters of the meta-atoms can be adjusted to control how the metalens splits or redirects an incoming light signal. For example, the width or diameter of the meta-atoms can be adjusted to control how the metalens splits or redirects an incoming light signal.

[0041] like Figure 2 As seen in FIG. 1 , the metalens 102 includes an array of meta-atoms 202. For clarity, Figure 2 Not all meta-atoms 202 in first metalens 102 are labeled. The meta-atoms 202 in the array may have different widths or diameters. For example, some meta-atoms 202 may have smaller widths or diameters relative to other meta-atoms 202 in the array. These widths or diameters may be selected so that metalens 102 splits or redirects an incident light signal in a desired manner.

[0042] Figure 3A An example array 300 of superatoms is shown. Figure 3A As seen in FIG. 3 , array 300 is formed using cylindrical meta-atoms 302. For clarity, Figure 3A Not all superatoms 302 in array 300 are labeled. Figure 3B An example array 304 of superatoms is shown. Figure 3B As seen in FIG. 3 , array 304 includes rectangular pillars of superatoms 306. For clarity, Figure 3B Not all superatoms 306 in array 304 are labeled. Figure 3C An example array 308 of superatoms is shown. Figure 3C , array 308 includes cross-shaped column meta-atoms 310. For clarity, not all of the meta-atoms 310 in array 308 are labeled. Although the previous figures show meta-atoms for a metalens having a particular shape, the meta-atoms for a metalens may be any suitable shape.

[0043] Figure 4 Illustration for design Figure 1 An example process for a metalens in an optical system 100 of FIG. 10 is shown in FIG. 10 . A computer system (such as Figure 6 The computer system 600 may execute Figure 4 In general, the computer system uses the specified arrangement of the optical system 100 and the specified characteristics of the incident and output light signals to determine the structure of the meta-atoms on the metalens in the optical system 100. In a particular embodiment, the computer system generates a design for the metalens in the optical system 100 to allow the optical system 100 to generate an output light signal that is closer to the desired light signal.

[0044] The computer system receives an optical system file 402. The optical system file 402 includes a description of the optical system 100, including characteristics of lenses and metalenses (e.g., size and shape of the lenses or metalenses), and specifies the arrangement of lenses and metalenses in the optical system 100. For example, the optical system file 402 may indicate the order / arrangement of lenses and metalenses in the optical system 100. Additionally, the optical system file 402 may indicate distances between metalenses and arrangements of lenses in the optical system 100. Furthermore, the optical system file 402 may specify distances at which desired characteristics of an output optical signal of the optical system 100 should be measured. For example, the optical system file 402 may indicate a distance at which the intensity distribution of the output optical signal should be measured. The computer system may use the information in the optical system file 402 to determine the design of the metalenses specified in the optical system file 402.

[0045] In addition, optical system file 402 may specify particular meta-atoms to be used for metalenses. For example, optical system file 402 may specify that a metalens in optical system 100 should use cylindrical meta-atoms. As another example, optical system file 402 may specify that another metalens in optical system 100 should use rectangular cylindrical meta-atoms. Optical system file 402 may specify that any suitable number of metalens in optical system 100 should use any suitable type of meta-atom.

[0046] As an example, the optical system file 402 may define the optical system as a series of metalenses and typical thin lenses, with specified distances between each lens, and the final distance being the distance to the image plane. The optical system file 402 may be a plain text file defining one or more lens specifications, one lens per line, as follows:

[0047] <Specifications for Lens #0>

[0048] <Specifications for Lens #1>

[0049] …

[0050] Each lens specification may include a sequence of keyword-value pairs. If the lens is a metalens (rather than a typical lens), the computer system may use a database library that contains performance characteristics of each metaatom as a function of wavelength, angle of incidence, polarization, metaatom design parameters, etc. The database used for the metalens may be specified via the "database" keyword by setting database= on the corresponding line in the optical system file 402.<user_defined_dbname> If no database keyword is specified for a metalens, a virtual idealized atomic database is used, which has one parameter, a linear phase response over 360 degrees and perfect transmission. A typical thin lens can be specified by setting the "thinlens" keyword to 1, and its focal length can be specified by the "flens" keyword.

[0051] The distance to the next lens, or the distance to the final image plane for the last lens, can be specified via the "length" keyword. The final image distance can be overridden in each individual test case. The size of the lens (i.e., the region in which the meta-atoms for the metalens are to be placed, or the diameter of a typical lens) is specified via the "size" keyword, and the lens is ideally apertured outside of this region (e.g., transmittance is 0). The shape of the lens is specified via the "shape" keyword, and can be set to circular (which produces a circular aperture), and can default to rectangular. The orientation of the database that specifies which side (substrate or background) the light is incident from can be specified via the "swapfb" keyword. The refractive index of the medium on both sides of the lens is inferred from the "database", which contains information about the meta-atom substrate or background index. If the database does not exist, the refractive index on both sides of the lens can be specified via the "nin" and "nout" keywords. The value ranges to which the meta-atom parameters are constrained are inferred from the database, but can be overridden via the "pmin" and "pmax" keywords for each design parameter of the meta-atom.

[0052] An example optical system file 402 is shown below, which describes a doublet lens having a diameter of 300 separated by 500 μm thick glass. μ A circular aperture of 1.3 m with the same meta-atom pattern on both sides and focused at a distance of 1000 μm from the second lens:

[0053] database=meta_atom_bsdf_datalength=500 size=300 shape=circleswapfb=1

[0054] database=meta_atom_bsdf_datalength=1000size=300 shape=circle

[0055] The computer system also receives an optical signal file 404. The optical signal file can specify characteristics of an incident optical signal to the optical system 100. For example, the optical signal file 404 can specify a wavetype and / or a wavelength of the incident optical signal. In addition, the optical signal file 404 can specify desired characteristics of one or more output optical signals of the optical system 100. For example, the optical signal file can specify a desired wavelength or a desired intensity distribution of one or more output optical signals of the optical system 100. The computer system can use the optical signal file 404 to determine a design of a metalens in the optical system 100.

[0056] As an example, the optical signal file 404 defines multiple objectives that the optical system is to satisfy simultaneously. The optical signal file 404 may be a plain text file that defines one or more objectives, one objective per line, as follows:

[0057] <Specifications for test case #0>

[0058] <Specifications for test case #1>

[0059] …

[0060] Each objective specification consists of a sequence of keyword-value pairs. Objectives can be defined by multiple wavelengths, multiple polarizations, and multiple input modes / emission angles. The "Einc" keyword specifies the incident field that illuminates the optical system. This can be specified by the file name or by a prefix or expression in brackets ("[]"). The "[]" syntax can also be used to run any command line utility or Python script, which can generate field files that allow users to customize them. The desired intensity distribution is specified by the "Ides" keyword. Alternatively, the desired field distribution can be specified by the "Edes" keyword. They support the same options as the "Einc" specified above. The wavelength at which the simulation will be performed is specified by the "lambda" keyword. The relative weight of this objective compared to other objectives is specified by the "weight" keyword. The "length" keyword can be used to cover the distance from the image plane after the last lens. For the polarization case, the "Einc", "Edes" and "Ides" keywords can have a "_y" suffix to indicate the y component of the field.

[0061] An example optical signal file 404 is shown below, which describes the diffraction limited spot as the desired image for three wavelengths (0.64 μm, 0.54 μm, and 0.46 μm) with a plane wave input, and each objective has the same weight:

[0062] Einc=[--type=planewave]Ides=[--type=airy]lambda=0.64

[0063] Einc=[--type=planewave]Ides=[--type=airy]lambda=0.54

[0064] Einc=[--type=planewave]Ides=[--type=airy]lambda=0.46

[0065] The computer system analyzes the information in the optical system file 402 and the light signal file 404 and uses an optimization process based on the adjoint method to determine the characteristics of the metalens in the optical system 100. The computer system uses the information in the optical system file 402 and the light signal file 404 as input to the optimization process 406. The optimization process 406 analyzes the information in the optical system file 402 and the light signal file 404 to determine the metalens layout 408. The metalens layout 408 can indicate the design parameters of the meta-atoms in the metalens in the optical system 100. The optimization process 406 can predict any suitable number of metalens layouts 408 for any suitable number of metalens in the optical system 100. The metalens layout 408 can specify any suitable design perimeter for the meta-atoms in the metalens. For example, the metalens layout 408 can specify the width or diameter of the meta-atoms in the metalens. As previously discussed, the metalens layout 408 can specify different widths or diameters for different meta-atoms in the metalens.

[0066] The computer system uses the metalens layout 408 determined by the optimization process 406 to determine an output light signal 410. The output light signal 410 is the light signal output by the optical system 100 when the metalens in the optical system 100 use the metalens layout 408. The computer system can use any suitable technique to determine the output light signal 410 of the optical system 100. For example, the computer system can simulate the path of the incident light signal specified in the light signal file 404 through the optical system 100, where the metalens are arranged according to their respective predicted metalens layouts 408. Then, after the incident light signal passes through the lenses and metalens of the optical system 100, the computer system determines the output light signal 410 of the optical system 100. In some embodiments, the computer system retrieves information about the behavior and characteristics of the expected meta-atoms for the metalens from a database. The computer system can use this information to determine how the metalens in the metalens layout 408 will split or redirect the light signal when simulating the path of the light signal.

[0067] The computer system then compares the output light signal 410 to a target light signal 412. The target light signal 412 may have been specified by the light signal file 404. The target light signal 412 may be a desired output light signal specified in the light signal file 404. For example, the target light signal 412 may include a desired intensity distribution at a particular distance from the optical system 100. The computer system may simulate the output light signal 410 at the distance from the optical system 100 and compare the output light signal 410 to the target light signal 412 to determine a difference 414 between the output light signal 410 and the target light signal 412. Before determining the difference 414, the desired intensity distribution of the target light signal 412 is scaled by a scaling factor. The scaling factor is automatically determined by the computer system as part of the optimization process 406.

[0068] The computer system analyzes the difference 414 to determine whether the metalens layout 408 is acceptable. The computer system compares the difference 414 to a threshold 416. The threshold 416 can be pre-selected and set according to the needs for the optical system 100. For example, the threshold 416 can be set to 0.001, which is dimensionless and can be interpreted as a fraction of the total intensity. If the difference 414 is within the threshold 416, the computer system can set the layout of the metalens in the optical system 100 to the metalens layout 408. If the difference 414 exceeds the threshold 416, the computer system re-evaluates the metalens layout 408. The computer system provides the difference 414 as an additional input to the optimization process 406. The optimization process 406 then re-evaluates the information in the optical system file 402 and the optical signal file 404 based on the difference 414 to determine a new metalens layout 408. The computer system then evaluates the new metalens layout 408 to see if the new difference 414 meets the threshold 416. This process continues until the difference 414 meets the threshold 416. The computer system then sets the design parameters of the metalens according to the metalens layout 408.

[0069] As an example, a computer may determine one or more geometric design parameters (e.g., width or diameter) of a meta-atom of a metalens in the following manner. In this design approach, the physical parameters of the meta-atoms are directly optimized and their effects on the behavior of non-uniform transmission, different angles of incidence, and polarization are directly incorporated. In addition, the design approach allows the design of an optical system consisting of a mixture of multiple typical thin lenses and multiple metalenses with unique metasurfaces. The design approach employs an adjoint method to effectively determine the gradients of all physical parameters for each independent meta-atom in the system. By determining the physical parameters of the meta-atoms in the system, the computer system determines the layout for each metalens in the system. The metric used for optimization consists of a plurality of test cases specified via the optical signal file 404, including the incident field and the corresponding expected output field at the image plane (e.g., the distance from the optical system at which the output optical signal 410 is measured). The metric M is mathematically described as follows:

[0070]

[0071] Among them I out (x, y) and I des (x, y) are the current intensity and the desired intensity at position (x, y) on the image plane, and the integral is evaluated over a region A corresponding to the lateral simulation domain or a subset thereof (as desired by the user). The field is discretized on a grid and the integral is done numerically. N tc is the total number of test cases, and the weight assigned to the test case is w tc In the case of polarization, two options can be considered for the metric: the first is to use I out (x, y) is considered as the sum of the intensities due to Ex and Ey, and the second is to have a value for (I out -scale*I des ) 2 In addition, if you use E des Specifying the desired target as a field, the metric can be adjusted appropriately to account for the phase.

[0072] The computer system introduces the scaling factors and automatically picks the scaling factors to use for each test case. This eliminates the need for a priori scaling expectations. The scaling factors can be picked using one of two techniques. First, they can be picked by directly optimizing the metric with respect to the scaling factor, keeping all other conditions constant, and alternating between optimizing the scaling factor and optimizing the design parameters in a co-optimization loop. Direct optimization of the scaling factors is performed by analytically computing Set it to 0, and then solve for the scaling analytically. Second, the scaling factor can be directly part of the optimization variable set.

[0073] The field E at the image plane out is based on the incident field E inc Calculated:

[0074]

[0075] The index L corresponds to the lens (thin lens or super lens) in the optical system, where N L is the total number of lenses. Note that the product sign indicates the ordering, where the terms are ordered in such a way that the lower index is on the left and the upper index is on the right. If the lens is a typical thin lens, its transfer matrix can be defined in a number of ways, i.e., via analytical phase shifts, user-defined amplitude / phase distributions, or via the transfer matrix obtained by Zernike polynomials. If the lens is a metalens, the computer system uses the general non-unitary transfer matrix T L , whose elements are functions of (p,λ,φ,θ), where p represents the set of design parameters of the meta-atom of the metalens, λ denotes the wavelength of the test case being simulated, and and θ are the local polar and azimuthal angles at each lateral site. For example, in the absence of scalar nearest neighbor interactions, the transmission matrix T L Will be diagonal, as follows:

[0076]

[0077] The above can be easily extended to allow T L becomes a block diagonal (the Jones matrix represents each block) to combine polarizations and by allowing T L becomes a more general but still sparse matrix to incorporate the nearest neighbor effect. T in (Equation 2) L With N A ×N A Dimension, where N A is (Nx*Ny), with Nx and Ny being the number of lateral field values. However, to simplify notation examples such as Error! Reference source not found, we will refer only to the active area of ​​the lens, understanding that the transmission is fixed externally.

[0078] Back to the special case of Error! Reference source not found, N AL is the total number of effective superatom sites on the Lth lens, and arrive is a vector of design parameters corresponding to the meta-atoms at each lateral site of the Lth metalens. The computer system determines the local angle based on the field incident at the Lth metalens by one of two methods: and The first is to fit the phase distribution in the neighborhood of the point to a smooth function, and then and The local k-vector is determined, from which the angle can be easily calculated. Before fitting, it is important to first wrap the phase, and the order of the fitting function should be reasonably low compared to the number of points in order to smooth out insignificant fluctuations in the phase and detect the main angles of incidence. A simple linear fit was found to be sufficient. Another approach is to perform a local Fourier analysis in a neighborhood of the point and then find the peak in k-space using a weighted average of the spectra in k-space or by fitting.

[0079] The effective region of the lens may be different from the simulation domain, outside which the lens is apertured and the transmission has a fixed value. The complex transmission coefficients a(p, λ, φ, θ)e of the metaatom are calculated using electromagnetic simulations over the desired range of design parameters, wavelengths, and angles. iφ(p，λ，φ，θ) This information can be stored in a pre-built database that can be quickly accessed during the optimization process. The above transmission coefficients become a Jones-type matrix when dealing with polarization and can also include the effects of multiple orders and reflections.

[0080] For propagation in the uniform region between the lenses and from the last lens to the image plane, the computer system uses a non-unitary free-space propagator D L , which is based on Fourier optics and incorporates the absorbing boundary condition (ABC) in the formula. The propagation matrix D L is defined as:

[0081]

[0082] Among them, F and F -1 They are fast Fourier transform (FFT) and its inverse, K L is the matrix defining the phase change for each plane wave in k-space, A L is the matrix defining ABC, and N s Lis the number of propagation steps. Without ABC, the free space propagator would be implemented with a discrete Fourier transform (DFT) over a finite domain, and an FFT algorithm would be employed to improve performance. The DFT (rather than the FFT itself) suffers from two problems. First, artificial reflections from the boundaries of the simulation domain produce significant errors in the field inside the domain of interest. Second, the power cannot escape the domain, and the efficiency of the lens cannot be accurately measured. The simulation domain can be artificially extended beyond the aperture of the lens and the data in this extended region is ignored. But in order to be effective, the extension may need to be quite large, significantly increasing the size and cost of the FFT. As an alternative, a computer system can use a small extension of the simulation domain and place a custom absorber in the extended region, and replace the normal free space propagator with an FFT-based beam propagation method in this region, as indicated in (Equation 3). The absorber characteristics and the propagation step size are automatically selected based on the simulation domain and diffraction considerations related to the aperture. Using this ABC effectively removes artifacts in the domain of interest and allows the power to be easily calculated. Both the propagation and transmission mechanisms can be easily replaced with other technologies without changing the proposed design flow.

[0083] The optimization strategy adopts an adjoint approach to efficiently determine the optimal solution for a given test case M with respect to all physical parameters of the meta-atom. tc The gradient of the optimization metric:

[0084]

[0085] where the conjugate transpose of the matrix A is denoted by Re denotes the real part, r is the index of the solution vector of the hyperatom design parameter p, and the associated domain a is defined as:

[0086]

[0087] and is a representation relative to For example, in the context of the scalar case without nearest neighbor interactions, the matrix will be a diagonal matrix with a single nonzero element based on the derivatives of the transmission coefficient with respect to the metaatom design parameters, which is given by

[0088]

[0089] The above equation can be easily extended to becomes a block diagonal matrix, the Jones matrix derivative represents a single non-zero block, thereby combining polarizations, and by allowing becomes a more general but still sparse matrix, thereby incorporating the nearest neighbor effect. When the gradient is evaluated in descending order of L in (Eq. 4), then bL can be effectively updated to

[0090]

[0091] And E H，L-1 It can be stored when (Equation 2) is applied in ascending order of L.

[0092] The above process can be used with any gradient-based optimizer. For example, the optimizer can be a limited memory Broyden–Fletcher–Goldfarb–Shanno algorithm (L-BFGS-B) with box constraints. By constraining the design parameter ranges for unique meta-atoms and using them as box constraints in the optimizer, manufacturing design rules can be incorporated. The computer system uses several heuristics as input to the optimizer for initial guesses. By default, it sets the initial design parameters uniformly on the surface of each metalens and at the center of the maximum transmission range, although there are multiple options to control this specification. Once the optimization reaches the desired tolerance, the computer system captures the final optimized design parameters onto a discrete grid based on the manufacturing resolution. The default value for this is 0.001 μm (e.g., 1 nm resolution). The final performance is evaluated with the captured solution.

[0093] Figure 5 is a flow chart of an example method 500 for designing a metalens. In certain embodiments, a computer system (such as Figure 6 The computer system 600 in the optical system 100 performs the method 500. By performing the method 500, the computer system determines one or more design constraints for one or more metalenses in the optical system 100.

[0094] In 502, the computer system receives the optical system file 402. The optical system file 402 specifies the arrangement of metalenses and lenses in the optical system 100. For example, the optical system file 402 may specify the order of lenses and metalenses in the optical system 100. In addition, the optical system file 402 may specify the type of meta-atom used in the metalenses of the optical system 100. In addition, the optical system file 402 may specify the distance between the metalenses and lenses in the optical system 100.

[0095] At 504, the computer system receives the optical signal file 404. The optical signal file 404 specifies characteristics of an optical signal in the optical system 100. For example, the optical signal file 404 may specify characteristics of an incident optical signal to the optical system 100. The optical signal file 404 may specify a wave type or wavelength of the incident optical signal. Additionally, the optical signal file 404 may specify a target optical signal 412 for the optical system 100. The optical signal file 404 may indicate a desired wavelength or intensity distribution of the target optical signal 412.

[0096] At 506, the computer system determines an initial layout 408 for a metalens in the optical system 100. The computer system may use an optimization process to determine the layout 408. For example, the computer system may provide the optical system file 402 and the optical signal file 404 as inputs to the optimization process 406. The optimization process 406 analyzes the information in the optical system file 402 and the optical signal file 404 to determine the initial layout 408 of the metalens. For example, the optimization process 406 may determine design parameters such as the width or diameter of the meta-atoms in the metalens.

[0097] At 508, the computer system determines an output optical signal 410 of the metalens used by the layout 408 determined at 506. The computer system may determine the output optical signal 410 using any suitable technique. For example, the computer system may simulate the path of the incident optical signal specified in the optical signal file 404 through the optical system 100. The computer system may determine how the different lenses and metalens (including the meta-atoms in the metalens) split or redirect the incident optical signal as the optical signal passes through the lenses and metalens. By simulating the path of the optical signal, the computer system determines the output optical signal 410 of the optical system 100.

[0098] In 510, the computer system determines a difference 414 between the output light signal 410 and the target light signal 412 specified by the light signal file 404. For example, the computer system can determine a difference in intensity distribution between the output light signal 410 and the target light signal 412. Prior to determining the difference 414, the intensity distribution of the target light signal 412 is scaled by the scaling factor. In 512, the computer system compares the difference 414 to a threshold 416. The threshold 416 may have been pre-selected by a designer of the optical system. For example, the threshold 416 may be 0.001.

[0099] If the difference 414 exceeds the threshold 416, the computer system proceeds to adjust the layout of the metalens in 514. For example, the computer system can provide the difference 414 as an input to the optimization process 406. The optimization process 406 then re-evaluates the information in the optical system file 402 and the optical signal file 404 based on the difference 414. The optimization process 406 then determines a new layout 408 for the metalens. The computer system then evaluates the new layout 408 to determine whether the new difference 414 satisfies the threshold 416.

[0100] If the difference satisfies the threshold 416, the computer system sets the design of the metalens in 516. For example, the computer system may set the design of the metalens using the layout 408 having the difference 414 that satisfies the threshold 416. In this manner, the computer system sets the design parameters for the meta-atoms in the metalens so that the optical system 100 outputs an optical signal that is within the threshold 416 of the target optical signal 412. As a result, the computer system finds the best selection of the set of design parameters for each metalens in the optical system 100 to achieve the desired target optical signal 412 that exploits the structural symmetry to increase the speed.

[0101] Figure 6 An example machine of a computer system 600 is illustrated in which a set of instructions may be executed to cause the machine to perform one or more of the methodologies discussed herein. In alternative implementations, the machine may be connected (e.g., networked) to other machines in a LAN, an intranet, an extranet, and / or the Internet. The machine may operate in the capacity of a server or a client machine in a client-server network environment, as a peer machine in a peer-to-peer (or distributed) network environment, or as a server or a client machine in a cloud computing infrastructure or environment.

[0102] The machine may be a personal computer (PC), a tablet PC, a set-top box (STB), a personal digital assistant (PDA), a cellular phone, a network appliance, a server, a network router, a switch or a bridge, or any machine capable of executing a set of instructions (sequential or otherwise) that specify actions to be taken by the machine. In addition, while a single machine is illustrated, the term "machine" should also be interpreted to include any collection of machines that individually or jointly execute a set (or multiple sets) of instructions to perform one or more of the methods discussed herein.

[0103] The example computer system 600 includes a processing device 602, a main memory 604 (e.g., read-only memory (ROM), flash memory, dynamic random access memory (DRAM), such as synchronous DRAM (SDRAM), a static memory 606 (e.g., flash memory, static random access memory (SRAM), etc.), and a data storage device 618, which communicate with each other via a bus 630.

[0104] Processing device 602 represents one or more processors, such as a microprocessor, a central processing unit, etc. More specifically, the processing device can be a complex instruction set computing (CISC) microprocessor, a reduced instruction set computing (RISC) microprocessor, a very long instruction word (VLIW) microprocessor, or a processor that implements other instruction sets, or a processor that implements a combination of instruction sets. Processing device 602 can also be one or more special processing devices, such as an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a digital signal processor (DSP), a network processor, etc. Processing device 602 can be configured to execute instructions 626 to perform the operations and steps described herein.

[0105] The computer system 600 may also include a network interface device 608 to communicate over a network 620. The computer system 600 may also include a video display unit 610 (e.g., a liquid crystal display (LCD) or a cathode ray tube (CRT)), an alphanumeric input device 612 (e.g., a keyboard), a cursor control device 614 (e.g., a mouse), a graphics processing unit 622, a signal generating device 616 (e.g., a speaker), a graphics processing unit 622, a video processing unit 628, and an audio processing unit 632.

[0106] The data storage device 618 may include a machine-readable storage medium 624 (also referred to as a non-transitory computer-readable medium) on which is stored one or more sets of instructions 626 or software embodying one or more of the methodologies or functions described herein. The instructions 626 may also reside, completely or at least partially, within the main memory 604 and / or within the processing device 602 during execution thereof by the computer system 600, the main memory 604 and the processing device 602 also constituting machine-readable storage media.

[0107] In some implementations, the instructions 626 include instructions for implementing functionality corresponding to the present disclosure. Although the machine-readable storage medium 624 is shown as a single medium in the example implementation, the term "machine-readable storage medium" should be interpreted as including a single medium or multiple media (e.g., a centralized or distributed database and / or associated caches and servers) that store one or more sets of instructions. The term "machine-readable storage medium" should also be interpreted as including any medium capable of storing or encoding a set of instructions for machine execution and causing the machine and processing device 602 to perform any one or more methods of the present disclosure. Therefore, the term "machine-readable storage medium" should be considered to include, but is not limited to, solid-state memory, optical media, and magnetic media.

[0108] Some portions of the foregoing detailed description have been presented in the form of algorithms and symbolic representations of operations on data bits within a computer memory. These algorithmic descriptions and representations are the means by which those skilled in the art of data processing most effectively communicate their work to other skilled in the art. An algorithm may be a series of operations that lead to a desired result. These operations are those that require physical manipulation of physical quantities. These quantities may take the form of electrical or magnetic signals that can be stored, combined, compared, and otherwise manipulated. These signals may be referred to as bits, values, elements, symbols, characters, terms, numbers, and the like.

[0109] It should be remembered, however, that all of these and similar terms are to be associated with the appropriate physical quantities and are merely convenient labels applied to these quantities. Unless otherwise expressly stated as apparent from the present disclosure, it should be understood that throughout the description certain terms refer to the actions and processes of a computer system or similar electronic computing device that manipulates data represented as physical (electronic) quantities within the computer system's registers and memories and converts it into other data similarly represented as physical quantities within the computer system's memories or registers or other such information storage devices.

[0110] The present disclosure also relates to an apparatus for performing the operations herein. The apparatus may be specially constructed for the intended purpose, or it may include a computer selectively activated or reconfigured by a computer program stored in the computer. Such a computer program may be stored in a non-transitory computer-readable storage medium, such as but not limited to any type of disk, including a floppy disk, an optical disk, a CD-ROM and a magneto-optical disk, a read-only memory (ROM), a random access memory (RAM), an EPROM, an EEPROM, a magnetic card or an optical card, or any type of medium suitable for storing electronic instructions, each of which is coupled to a computer system bus.

[0111] The algorithms and displays presented herein are essentially independent of any particular computer or other device. Various other systems may be used together with the programs taught herein, or it may prove convenient to construct more specialized devices to perform the method. In addition, the present disclosure is not described with reference to any particular programming language. It should be appreciated that a variety of programming languages ​​may be used to implement the teachings of the present disclosure described herein.

[0112] The present disclosure may be provided as a computer program product or software, which may include a machine-readable medium having instructions stored therein, and the instructions may be used to program a computer system (or other electronic device) to perform a process according to the present disclosure. A machine-readable medium includes any mechanism for storing information in a machine (e.g., computer) readable form. For example, a machine-readable (e.g., computer-readable) medium includes a machine (e.g., computer) readable storage medium, such as a read-only memory ("ROM"), a random access memory ("RAM"), a disk storage medium, an optical storage medium, a flash memory device, etc.

[0113] In the foregoing disclosure, the implementation of the present disclosure has been described with reference to its specific example implementation. Obviously, various modifications may be made thereto without departing from the broader spirit and scope of the implementation of the present disclosure as set forth in the following claims. When the present disclosure refers to certain elements in the singular tense, multiple elements may be depicted in the figures, and the same elements are marked with the same numbers. Therefore, the present disclosure and the accompanying drawings should be regarded as illustrative, not restrictive.

Claims

1. A method for designing a metalens, comprising: receiving a description of an optical system, the description of the optical system indicating (i) properties of a first lens in the optical system, (ii) meta-atoms to be used in the first lens, and (iii) a first distance from the first lens; receiving a description of an optical signal, the description of the optical signal describing (i) an incident optical signal to the optical system and (ii) a target optical signal for the optical system; determining a first layout of a plurality of meta-atoms on the first lens based at least in part on a characteristic of the first lens, the meta-atom, and the first distance; determining the first output light signal of the optical system based at least in part on the incident light signal and the first arrangement of the plurality of meta-atoms on the first lens; as well as The design of the first lens is set using the first layout based on whether a difference between the first output light signal and the target light signal satisfies a threshold.

2. The method according to claim 1, further comprising: determining, based on the difference between the first output light signal and the target light signal not satisfying the threshold, a second layout of the plurality of super-atoms on the first lens based at least in part on a characteristic of the first lens, the meta-atom, the first distance, and the first layout; determining a second output light signal of the optical system using the incident light signal and the second layout of the plurality of meta-atoms on the first lens; as well as The design of the first lens is set using the second layout based on whether a difference between the second output light signal and the target light signal satisfies the threshold.

3. The method according to claim 1, wherein: The description of the optical system further indicates characteristics of a second lens in the optical system and a second distance from the second lens; The first distance is between the first lens and the second lens in the optical system; as well as Determining the first layout is also based on characteristics of the second lens and the second distance. 4 . The method of claim 1 , wherein determining the first layout comprises determining a geometric design parameter for each of the plurality of meta-atoms on the first lens. 5 . The method of claim 1 , wherein the first layout is further based on a different angle of incidence for each of the plurality of superatoms. 6 . The method of claim 1 , wherein the first layout is further based on a polarization of the optical signal and a response of each of the plurality of meta-atoms to the polarization.

7. The method of claim 1, wherein the first output optical signal is based at least in part on an absorptive boundary condition of space within the first distance from the first lens.

8. The method of claim 1, wherein the difference comprises a difference between an intensity distribution of the first output optical signal and an intensity distribution of the target optical signal scaled by a scaling factor.

9. The method of claim 1, wherein the difference is further based on a phase of the first output optical signal and a phase of the target optical signal.

10. A system for designing a metalens, comprising: Memory; as well as a processor communicatively coupled to the memory, the processor being configured to: receiving (i) characteristics of a first lens in an optical system, (ii) a metaatom to be used in the first lens, and (iii) a first distance from the first lens; receiving a description of (i) an incident light signal to the optical system and (ii) a target light signal for the optical system; determining a first layout of a plurality of meta-atoms on the first lens based at least in part on a characteristic of the first lens, the meta-atom, and the first distance; determining a first output light signal of the optical system based at least in part on the incident light signal and the first arrangement of the plurality of meta-atoms on the first lens; as well as The design of the first lens is set using the first layout based on whether a difference between the first output light signal and the target light signal satisfies a threshold.

11. The system of claim 10, wherein the processor is further configured to: determining, based on the difference between the first output light signal and the target light signal not satisfying the threshold, a second layout of the plurality of super-atoms on the first lens based at least in part on a characteristic of the first lens, the super-atom, the first distance, and the first layout; determining a second output light signal of the optical system using the incident light signal and the second layout of the plurality of meta-atoms on the first lens; as well as The design of the first lens is set using the second layout based on whether a difference between the second output light signal and the target light signal satisfies the threshold.

12. The system of claim 10 , wherein the processor is further configured to receive characteristics of a second lens in the optical system and a second distance from the second lens, wherein the first distance is between the first lens and the second lens in the optical system, and wherein determining the first layout is also based on the characteristics of the second lens and the second distance.

13. The system of claim 10, wherein determining the first layout comprises determining a geometric design parameter for each of the plurality of meta-atoms on the first lens.

14. The system of claim 10, wherein the first layout is further based on a different angle of incidence for each of the plurality of meta-atoms.

15. The system of claim 10, wherein the first layout is further based on a polarization of the optical signal and a response of each of the plurality of meta-atoms to the polarization.

16. The system of claim 10, wherein the first output optical signal is based at least in part on an absorptive boundary condition of a space within the first distance from the first lens.

17. The system of claim 10, wherein the difference comprises a difference between an intensity distribution of the first output optical signal and an intensity distribution of the target optical signal scaled by a scaling factor.

18. The system of claim 10, wherein the difference is further based on a phase of the first output optical signal and a phase of the target optical signal.

19. A non-transitory computer-readable medium storing instructions for designing a metalens, the instructions, when executed by a processor, causing the processor to: receiving (i) characteristics of a first lens in an optical system, (ii) a metaatom to be used in the first lens, and (iii) a first distance from the first lens; receiving a description of (i) an incident light signal to the optical system and (ii) a target light signal for the optical system; determining a first layout of a plurality of meta-atoms on the first lens based at least in part on a characteristic of the first lens, the meta-atom, and the first distance; determining a first output light signal of the optical system based at least in part on the incident light signal and the first arrangement of the plurality of meta-atoms on the first lens; as well as The design of the first lens is set using the first layout based on whether a difference between the first output light signal and the target light signal satisfies a threshold.

20. The non-transitory computer readable medium of claim 19, wherein the instructions, when executed by the processor, further cause the processor to: determining, based on the difference between the first output light signal and the target light signal not satisfying the threshold, a second layout of the plurality of super-atoms on the first lens based at least in part on a characteristic of the first lens, the meta-atom, the first distance, and the first layout; determining a second output light signal of the optical system using the incident light signal and the second layout of the plurality of meta-atoms on the first lens; as well as The design of the first lens is set using the second layout based on whether a difference between the second output light signal and the target light signal satisfies the threshold.

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