Superlens with corrected phase
Through computer-implemented methods, differentiable phase prediction function and Newton's iterative optimization technology are constructed, which solves the problem of unmodeled interactions in hyperlens, significantly improves focus efficiency and performance, and realizes an efficient hyperlens design.
Patent Information
- Application Number
- CN202380038602.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Priority Date
- 2022-05-11
- Filing Date
- 2023-02-03
- Publication Date
- 2024-12-17
AI Technical Summary
The existing superlenses have low focusing efficiency at high numerical apertures and have failed to effectively solve the problem of unmodeled photomatter interactions and resonant coupling between nanostructures, resulting in degradation in performance.
Through computer-implemented methods, differential phase prediction functions are constructed, and the overlapping neighborhood phase delay of the hyperlens is optimized using Newtonian iteration, the geometry of the nanostructure is adjusted to improve focus efficiency, and the CPU usage and power consumption are reduced through the data conversion system.
The focus efficiency of the ultra-lens is significantly improved, by 5%-9%, and the overall performance is improved by optimizing the design parameters, reducing the demand for computing resources.
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Figure CN119156344A_ABST
Abstract
Description
Technical Field
[0001] The present disclosure relates generally to metalens having a metasurface, and more particularly to systems and methods for designing metalens. Background Art
[0002] A metasurface is a planar arrangement of wavelength-scale structures that interact with electric and / or magnetic fields. Optical metasurfaces (i.e., metalenses) interact with visible and near-visible wavelengths and provide exquisite control over the wavefront, with the potential for substantial miniaturization of optoelectronics. In practice, metalenses completely lack the efficiency predicted by theory and are not yet competitive with conventional bulk lenses and mirrors. The main design strategy is to decompose the metalenses into a unit grid, calculate the expected optical phase delay for each grid cell, and select nanostructures that provide the appropriate phase delay from a library of pre-simulated nanostructures. For nanostructures that exhibit phase delays according to the predictions of Pancharatnam-Berry (PB) theory, the design problem is particularly simple: the relative phase delay is expected to vary linearly with the rotational orientation of the nanostructure. However, in practice, metalenses designed based on the unit cell principle suffer from unmodeled light-matter interactions and resonant coupling between nearby nanostructures, especially at high numerical apertures (NA). Therefore, a novel data processing (system) needs to be developed to address the above problems. Summary of the invention
[0003] The present disclosure is based on the recognition that rapid optimization of tuning all unit cells simultaneously can improve the near-field distribution and performance of optical devices primarily by correcting interactions between nearby units. This improves the focusing efficiency of high-NA metalenses by 5%-9%, as verified in high-resolution FDTD simulations.
[0004] Arrays of nanoscale waveguides have proven to be an attractive design motif for metalenses due to the high efficiency and simple design process (where the geometry of each waveguide is independently determined via the theory of Parabancham-Berry phase). We show that the phase delays are not actually independent and present corrections that result in significantly higher focusing efficiencies.
[0005] Some embodiments of the present invention are based on the recognition that extensive efforts have been made to find families of nanostructures that provide independent phase shifts as expected in the unit cell decomposition. However, in practice, the phase delays achieved by the unintended resonant couplings between nearby nanostructures perturb the expected values. The couplings and the resulting perturbations are not well understood but are observed to reduce the efficiency and overall performance of the metalens.
[0006] Some embodiments are based on the recognition that a computer-implemented method constructs a differentiable phase prediction function or electric field prediction function from simulations of a small neighborhood of a cell, and uses this function to jointly optimize the achieved phase delays of an overlapping neighborhood covering the entire metalens with Newton iterations, thereby obtaining a significant increase in focusing efficiency. The main insights are that (1) a differentiable predictor of the electric field above the middle cell of a small neighborhood can be constructed from simulation data; (2) this function is roughly separable into functions of overlapping smaller neighborhoods, so an exponential number of expensive simulations are not required to accurately model the unknown physics; and (3) the derivative of this function can be used to obtain a (locally) optimal metalens design by solving a short sequence of banded linear equations that correct for the nanostructure geometry in the overlapping neighborhood covering the metalens.
[0007] In addition, since the data conversion system and the computer-implemented method for data conversion according to an embodiment of the present invention provide a special computing strategy for determining the location of candidate tools, the data conversion system and the computer-implemented method of the present invention can reduce central processing unit (CPU) usage, power consumption and / or network bandwidth.
[0008] According to some embodiments of the present invention, a computer-implemented method for designing a metalens is provided. The metalens has a metasurface, the metasurface comprising nanostructures arranged on a substrate based on preliminary simulation data. The method uses a processor coupled to a memory storing a target near-field profile, preliminary simulation data of the metalens, and instructions for implementing the method, wherein the preliminary simulation data represents first design parameters, the first design parameters comprising a geometry and an orientation angle of the nanostructures on the metalens. The instructions, when executed by the processor, perform the steps of the method, the steps including: partitioning the nanostructure into overlapping d-unit supercells such that each non-peripheral nanostructure is located at the center of one d-unit supercell; calculating a differentiable mapping function for the d-unit supercell, the differentiable mapping function predicting the near field on the unit cell at the center of the supercell according to the design parameters of all nanostructures in the supercell by fitting an interpolator to preliminary simulation data of the d-unit supercell; jointly tuning the design parameters of all unit cells in the metalens to better approximate the target near-field distribution on the entire metalens by solving the local optimal corrections for all design parameters using the Jacobian matrix of partial derivatives provided by the mapping function; and generating a manufacturable design of the metalens based on the optimized parameters.
[0009] The presently disclosed embodiments will be further explained with reference to the accompanying drawings. The drawings shown are not necessarily drawn to scale, with emphasis instead generally being placed upon illustrating the principles of the presently disclosed embodiments. BRIEF DESCRIPTION OF THE DRAWINGS
[0010] [ Figure 1A ]
[0011] Figure 1A A fragment of a metalens comprising four oriented nanopillars on a substrate is shown.
[0012] [ Figure 1B ]
[0013] Figure 1B Shown is a top view of a metalens segment divided into four equally sized unit cells, where three of the unit cells each contain a nanopillar with a specified width, length, and orientation angle.
[0014] [ Figure 1C ]
[0015] Figure 1C A side view of a metalens segment is shown, where the lower arrow represents the incident plane electromagnetic wavefront and the upper line represents the scattering pattern provided by the nanopillars.
[0016] [ Figure 2A ]
[0017] Figure 2AShown is a top view of a metalens segment with two overlapping 3x3 neighborhoods of unit cells highlighted by grey squares, in accordance with an embodiment of the present invention.
[0018] [ Figure 2B ]
[0019] Figure 2B is a graph showing how the average phase retardation provided by a single unit cell varies when the nanopillar orientation angles of two neighboring cells in its neighboring cell vary.
[0020] [ Figure 2C ]
[0021] Figure 2C is a graph of the near-field phase provided by a high numerical aperture focusing metalens according to some embodiments of the present invention.
[0022] [ Figure 3 ]
[0023] Figure 3 A process for obtaining simulated data for training a predictor according to some embodiments of the present invention is shown.
[0024] [ Figure 4 ]
[0025] Figure 4 A metalens design system according to an embodiment of the present invention is shown.
[0026] [ Figure 5 ]
[0027] Figure 5 is a flow chart of a metalens design algorithm according to an embodiment of the present invention.
[0028] [ Fig. 6A ]
[0029] Fig. 6A The error caused when predicting the near-field phase delay on the unit cell via the Pancharatnam-Berry phase theory (PB) is shown.
[0030] [ Figure 6B ]
[0031] Figure 6B Shown is the error caused when predicting the near-field phase delay across a unit cell by selecting the closest 3-cell supercell in the simulation data set.
[0032] [ Figure 6C ]
[0033] Figure 6CShown is the error caused when predicting the near-field phase delay across a unit cell by averaging the two closest 3-cell supercells in the simulated data set.
[0034] [ Fig. 7A ]
[0035] Fig. 7A The error in the near field is shown in terms of the percentage error in the near field distribution predicted for a 3×3 supercell according to PB theory.
[0036] [ Figure 7B ]
[0037] Figure 7B Shown is the error caused when using an interpolator trained on 1×3 supercells.
[0038] [ Figure 7C ]
[0039] Figure 7C The error caused when averaging the interpolations from the 1x3 and 3x1 supercells is shown.
[0040] [ Fig.7D ]
[0041] Fig.7D The results of linear regression on these interpolations are shown. DETAILED DESCRIPTION
[0042] Although the drawings indicated above illustrate the embodiments of the present disclosure, other embodiments may be envisioned as noted in the discussion. The present disclosure presents illustrative embodiments by way of representation and not limitation. Those skilled in the art may devise many other modifications and embodiments that fall within the scope and spirit of the principles of the embodiments disclosed herein.
[0043] Detailed description
[0044] The following description provides only exemplary embodiments and is not intended to limit the scope, applicability or configuration of the present disclosure. Rather, the following description of the exemplary embodiments will provide a description of implementations for implementing one or more exemplary embodiments to those skilled in the art. Various changes may be made to the functions and arrangements of the elements without departing from the spirit and scope of the disclosed subject matter set forth in the appended claims.
[0045] Specific details are given in the following description to provide a thorough understanding of the embodiments. However, it will be appreciated by those skilled in the art that the embodiments may be practiced without these specific details. For example, the systems, processes, and other elements in the disclosed subject matter may be shown as components in block diagram form so as not to obscure the embodiments with unnecessary details. In other cases, well-known processes, structures, and techniques may be shown without unnecessary details to avoid obscuring the embodiments. In addition, the same reference numerals and designations in the various drawings indicate the same elements.
[0046] In addition, each embodiment can be described as a process, which is depicted as a flow chart, a process view, a data flow diagram, a structure diagram or a block diagram. Although a flow chart can describe an operation as a sequential process, many operations can be performed in parallel or concurrently. In addition, the order of the operations can be rearranged. A process can terminate when its operation is completed, but may have additional steps not discussed or included in the figure. In addition, not all operations in any particularly described process can occur in all embodiments. A process can correspond to a method, a function, a process, a subroutine, a subprogram, etc. When a process corresponds to a function, the termination of the function can correspond to the function returning to the calling function or the main function.
[0047] In addition, embodiments of the disclosed subject matter may be implemented at least in part manually or automatically. Manual or automatic implementation may be performed or at least assisted by the use of a machine, hardware, software, firmware, middleware, microcode, hardware description language, or any combination thereof. When implemented in software, firmware, middleware, or microcode, program code or code segments that perform the necessary tasks may be stored in a machine-readable medium. A processor may perform the necessary tasks.
[0048] Therefore, some embodiments of the present disclosure may reduce power consumption of a computer (processor) and improve the functionality of a computing system.
[0049] In some embodiments of the present disclosure, the system can perform efficiently and accurately in less time and with less computing power, thus using the methods or systems described in the present disclosure can reduce central processing unit usage and power consumption.
[0050] We introduce a fast joint optimization of unit cells across the entire metasurface, exploiting the interactions between nearby cells to produce a target (desired) near-field profile and improve overall device efficiency. Joint optimization means tuning all design parameters of the entire metasurface simultaneously to maximize the overall performance of the device, taking into account the interactions between different parts of the device; this is in contrast to local or greedy optimization, where only one or a small subset of parameters is tuned to improve performance in one part of the metasurface, but often degrades performance elsewhere.
[0051] Unit cell decomposition (UCD) has become the dominant design strategy for optical metalenses. UCD treats metalenses as a grid of nanostructures that can be independently selected to control the near field. UCD-designed lenses have been shown to steadily improve focusing efficiency, but have not met the expectations of theoretical predictions (and can be replaced by free-form designs once simulation and manufacturing challenges are resolved). One reason for the efficiency gap is that the electric field effects associated with a single nanostructure are typically based on periodic assumptions (i.e., the nanostructures tile the plane identically), but when they are placed in a heterogeneous neighborhood of varying nanostructures, unmodeled coupling effects can substantially change the response. Attempts to correct this typically use extended supercell simulations in a generation and test cycle to find alternative nanostructures that provide the target near field in the context of their neighbors. Even when pre-trained neural networks are used as agents for the simulator, these one-at-a-time search processes have limited effectiveness and are computationally very expensive.
[0052] We note that most simulator agents are differentiable with respect to their inputs (not just their parameters), and thus provide unexploited derivatives for direct tuning of unit cell parameters. More powerfully, this opens the door to jointly optimize all cells in a metalens to produce a target (desired) near-field distribution by solving a short sequence of linear equations, each with a special structure that achieves linear time and space complexity. Thus, metalenses of millions of cells can be rapidly optimized with modest computational resources. We apply this to the design of focusing TiO2 nanofin metalenses pre-engineered via UCD according to the Pancharatnam-Berry (PB) phase theory, and obtain significant improvements in focusing efficiency.
[0053] Figure 1A A fragment of a metalens comprising four oriented nanopillars on a substrate is shown. Figure 1B A top view of a metalens segment divided into four equally sized unit cells, where three of the unit cells each contain nanopillars of specified width, length, and orientation angle is shown. The figure shows a side view of a metalens segment, with the lower arrows representing the incident plane electromagnetic wavefront and the upper lines representing the scattering pattern provided by the nanopillars.
[0054] The nanofin 110 is usually formed on a substrate 120 ( Figure 1A ) is a directional rectangular column manufactured on a substrate 120, the substrate 120 being arranged in a large number of regular grids 130 ( Figure 1B ), each of which introduces a local phase delay so that the Figure 1C )'s plane wavefront 140 is reshaped in an optically useful manner, for example, into a spherical wavefront that diverges 150 or converges to a point on the far-field focal plane.
[0055] Figure 2A Shown is a top view of a metalens fragment with two overlapping 3×3 neighborhoods of a unit cell highlighted by grey squares. Figure 2B is a graph showing how the average phase retardation provided by a single unit cell varies when the nanopillar orientation angles of two neighboring cells in its neighboring cell vary. Figure 2C is a graph of the near-field phase provided by a high numerical aperture focusing metalens, wherein point 230 represents the ideal phase profile with high efficiency focusing as the goal (desired), the grey jagged curve 240 indicates the phase error incurred when designing the metalens using the prior art, and the straight line 250 at the top indicates the near zero phase error incurred when using the method according to the present invention.
[0056] Figure 2A An example of a method for designing a metalens according to some embodiments of the present invention is shown. The method is summarized as follows: (a) The metalens is divided into densely overlapping neighborhoods 210 and 220, here 3×3 ( Figure 2A ), each neighborhood is called a supercell. (b) A differentiable function f is fitted to the supercell simulation data to predict the near-field response of the intermediate cell of each neighborhood from the design parameters of the neighborhood (e.g., nanofin orientation). As an example, Figure 2B It is shown that when two adjacent nanofins are rotated, the average right circularly polarized phase retardation in the near field of the middle unit cell changes by more than 40°. (c) Finally, the design parameters of all units in the metalens are jointly optimized to produce the target near-field phase retardation pattern. Figure 2C An example is shown where the process improves a poorly focusing metalens to a perfectly focusing (within physical limits) metalens by tuning the orientation of all nanofins so that the average phase shift of each unit matches the target value of the focusing lens, thereby improving the focusing efficiency by >5%.
[0057] PB theory predicts that the phase shift provided by a properly shaped waveguide is simply twice its in-plane orientation angle, i.e., f(θ) = 2θ. For example, Khorasaninejad et al. in Science (Mohammadreza Khorasaninejad, Wei Ting Chen, Robert C. Devlin, Jaewon Oh, Alexander Y. Zhu, Federico Capasso, "Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging," Science, June 3, 2016, vol. 352 issue 6290) describe an extensive computational search in homogeneous local periodic unit cell simulations to find a nanofin geometry that provides a phase shift according to PB theory and also provides good transmission efficiency.
[0058] Some embodiments of the present invention are based on the following recognition: We found that f has nonlinearity and dependence on nearby nanofins, which can produce phase errors > ±20° (see Figure 2C ), as revealed in detailed finite-difference time-domain (FDTD) simulations of the heterogeneous supercell. Furthermore, there are nanofin geometries that provide excellent transfer efficiency but have large deviations from the ideal PB behavior. We use one such geometry here: 265×95×600nm TiO2 nanofins on a SiO2 substrate in a 325nm square grid. In general, we observe deviations from the PB phase when the corners of adjacent nanofins are close, indicating coupling effects, and when the phase shift varies significantly between adjacent fins, typically anywhere the superlens provides significant beam deflection. For example, in Figure 2C In , the PB phase error grows to >40° near the edge of the metalens, although the relative phase error between adjacent cells is more modest, providing a decreased beam deflection. Nevertheless, this leaves room for optimization.
[0059] Figure 3 The process of acquiring simulation data for training a predictor according to some embodiments of the present invention is shown. First, general device parameters such as size, band, and grid spacing are selected in step 321. A neighborhood size that is small enough to allow fast simulations but large enough to capture the physical interactions between the central nanostructure and those in its vicinity is selected in step 322. These interactions are typically pairwise and a 3×3 neighborhood is sufficient.
[0060] The nanopillar parameters to be varied are selected in step 323. Typically, these parameters control the shape and / or placement of the nanopillars in their grid cells. In step 324, the process samples the space of possible neighborhood configurations. For the sampled neighborhood configurations of the metalens' nanostructures, the process simulates electromagnetic field propagation by solving Maxwell's equations in step 325, and outputs electric field samples from a near-field plane outside the metasurface in step 326.
[0061] Figure 4 A block diagram of a metalens design system 400 according to some embodiments of the present disclosure is shown. The system 400 may include a human machine interface (HMI) 410 that may be connected to a keyboard 411 and a pointing device / medium 412, one or more processors 420, a storage device 430, a memory 440, a network interface controller 450 (NIC) that may be connected to a network 490 including a local area network, a wireless network, and an Internet network, a display interface 460 connected to a display device 465, and a printer interface 480 that may be connected to a printing device 485. Hereinafter, for convenience, one or more processors 420 may be referred to as processor 420.
[0062] The memory 440 may be one or more memory units that operate with the storage device 430 that stores a computer executable program (algorithm code) associated with the processor 420. The system 400 may receive input data including preliminary simulation data from a user 499 or a previous simulation database 495 via a network 490 connected to the NIC 450. The NIC 450 includes a receiver and a transmitter to connect to the network 490 via a wired network and via a wireless network (not shown). When the system 400 receives the input data, the system 400 uses the preliminary simulation data 402, the target near-field profile data 434, and the dynamic programming algorithm module to provide design parameters for the metalens by executing the metalens design algorithm 404 stored in the storage device 430 using the processor 420 and the memory 440. The storage device 430 may include an algorithm module 408 as a computer-implemented method configured to execute the metalens design algorithm 404 using the preliminary simulation data 402 and the target near-field profile data 434 including the target near-field phase distribution.
[0063] Figure 5 is a flowchart 500 describing the metalens design algorithm 404: We use a differentiable interpolator f(θ1, ..., θ) fitted to the simulated data 326 of a d-unit neighborhood supercell (d-unit supercell). d)510 to approximate the unknown true near-field function f*. The interpolator f provides us with local near-field values with respect to the neighborhood design parameters θ1,…,θ d We use f to compute the near-field error 520 for each overlapping neighborhood on the metasurface. We choose a differentiable penalty function P() for the difference between the target near-field radiation distribution and the near-field provided by the candidate metalens design, and use the derivative of f to compute its penalty function with respect to all design parameters Partial derivatives 530 of n>>d. For example, P can be the mean square error of the local phase delay integrated over the entire near field. The partial derivatives are arranged into a Jacobian matrix 540. At design time, we use this Jacobian matrix to minimize the penalty function through Newton iterations 550, which jointly optimize all design parameters 560. Assuming that the near field at any point depends on the finite neighborhood of the metalens, each Newton iteration can be reduced to solving a system of banded linear equations, which can be done in O(n) time and space complexity. All examples considered in this specification (each involving thousands of units) are fully optimized in <1 second, while the time spent simulating any of these metalenses can be hours or days. In other words, a step is performed to calculate a differentiable mapping function for a d-unit supercell, which predicts the near field on the unit cell at the center of the supercell according to the design parameters of all nanostructures in the supercell by fitting an interpolator to the preliminary simulation data of the d-unit supercell. In this case, the calculation step continues until the ratio of the design parameter correction drops below the manufacturing tolerance. Furthermore, in a calculation step, an interpolator function may be used to predict a near-field phase distribution over each unit cell, wherein the calculation step continues until the near-field phase distribution matches a target near-field phase distribution within a target error tolerance.
[0064] Furthermore, a d-unit supercell is a different combination of orientations of a collection of nanofins, wherein the interaction of each of the d-unit supercells with the incident wavefront is simulated by solving Maxwell's equations.
[0065] For example, Fig. 6A Depicted are the far-field propagation intensity from full FDTD simulations of a small NA=0.937 metalens designed via (from left to right): UCD with PB phase rule; optimization of near-field phase by the present invention (+7.8% focusing efficiency); and optimization of near-field phase phase and amplitude by the present invention (+8.1%). The optimization also results in a device with better depth of focus. Figure 6BThe achieved phase error and target phase distribution (thick dark line 630) for an optimized NA=0.8 metalens per 10 nm at the near-field point are depicted; in this case, the initial phase error (high amplitude sawtooth line 640) is minimized (low amplitude dark thin line 650) but not zeroed because the target phase oscillates faster than the device physics can provide. Nevertheless, Figure 6C The far field intensity distribution plotted in shows that the focusing efficiency is improved and is within 3% of the theoretical limit, with the ideal case 660, optimized case 670 and PB case 680 shown.
[0066] The metasurfaces described in this invention are arrangements of nanostructures in a grid of unit cells according to regular tilings (usually rectangular or hexagonal, less commonly triangular or phyllotactic (e.g., the double helix pattern seen in a sunflower). In other words, the metasurface is arranged into a grid of unit cells that divides the plane into rectangular, hexagonal, triangular, or phyllotactic shapes.
[0067] Each unit cell contains a photonic nanostructure located on or in a substrate. Typically, the nanostructure is a dielectric such as SiO2 or a waveguide such as TiO2. Typically, the planar dimensions of the cell are smaller than the operating wavelength of the device; there is no such restriction on the vertical dimensions of the nanostructure. The neighborhood around the central unit cell can be defined as that cell plus any edge neighbors and optionally corner neighbors, and possibly their neighbors if the device physics supports longer-range interactions. The accompanying figures show examples of TiO2 rectangular nanoprisms arranged in various orientations within their cells.
[0068] The physical nanostructure specified inside each cell can be a rectangular nanoprism, an elliptical nanopillar, a split-ring structure (e.g., a "c" shaped resonator), a hole in the substrate, an H or I beam-shaped nanopillar, a nanopillar with a cross-shaped cross section, or a more complex shape. Typically, the nanostructures are formed from a single material, but layers of multiple materials are possible. Each nanostructure is described by a small number of design parameters that specify its geometry and composition. The accompanying figure shows an example where the design parameters are the orientation angle and two of the three rectangular prism dimensions.
[0069] A differentiable interpolator function (differentiable mapping function) is used to predict the near fields at a unit cell from its design parameters and the design parameters of other cells in its neighborhood. The function is fit to the simulation data. Suitable functions include spline interpolators, re-dialed basis functions, neural networks, logistic regressors, rational polynomial approximators. The accompanying figure shows an example where the function is a barycentric interpolator (a very simple spline) applied to the simulation data point whose design parameters are closest to the interpolation query. For example, the space of possible neighborhood design parameters is is partitioned into simplifications (d-dimensional triangles) whose vertices coincide with the simulated neighborhood. Given a query about a novel neighborhood, we find a simplex containing its design parameters, and return a weighted average of the simulation results for the vertices attached to the simplex, with the weights determined by their distance from the similarity of each simulation to the query. Since the number of simulations required to train an interpolator can grow exponentially with the number of independent design parameters, in some cases it is useful to partition each 2D supercell into multiple overlapping 1D groups of unit cells, fit an interpolation function to predict their near fields, and combine the results using linear regression. For example, Fig. 7A The error in predicting the near field at the center of the 3×3 supercell near field distribution of the PB theory is shown; Figure 7B shows the error caused when using an interpolator trained on 1×3 supercells; Figure 7C shows the error caused when averaging interpolations from 1×3 and 3×1 supercells; and Fig.7D The results of a linear regression of these interpolations are shown. Darker is better. In this case, interpolation is performed on a one-dimensional subset of the d-unit supercell to obtain an interpolation function, and the obtained interpolation functions are averaged to provide predictions and gradients for the two-dimensional d-unit supercell.
[0070] The above-mentioned embodiments of the present disclosure can be implemented in any of a variety of ways. For example, hardware, software or a combination thereof can be used to implement the embodiments. The use of sequential terms such as "first", "second" and the like in the claims to modify the claim elements themselves does not imply any priority, precedence or order of one claim element relative to another claim element or the time sequence of the actions of the method of execution, but is only used as a label (but using sequential terms) to distinguish a claim element with a specific name from another element with the same name to distinguish the claim elements.
[0071] Although the present disclosure has been described with reference to certain preferred embodiments, it should be understood that various other changes and modifications may be made within the spirit and scope of the present disclosure. Therefore, the aspects of the appended claims cover all such changes and modifications that fall within the true spirit and scope of the present disclosure.
Claims
1. A computer-implemented method for designing a metalens having a metasurface comprising nanostructures arranged on a substrate based on preliminary simulation data, wherein: The method uses a processor coupled to a memory storing a target near-field profile, preliminary simulation data of the metalens, and instructions for implementing the method, wherein the preliminary simulation data represents design parameters including orientation angles and geometry of the nanostructures on the metalens, wherein the instructions, when executed by the processor, perform the steps of the method, the method comprising the steps of: dividing the nanostructure into overlapping d-unit supercells such that each non-peripheral nanostructure is located at the center of a d-unit supercell; calculating a differentiable mapping function for the d-unit supercell, the differentiable mapping function predicting a near field on a unit cell at a center of the supercell based on design parameters of all of the nanostructures in the supercell by fitting an interpolator to preliminary simulation data of the d-unit supercell; jointly tuning the design parameters of all unit cells in the metalens to better approximate a target near-field distribution across the entire metalens by solving for locally optimal corrections for all design parameters using the Jacobian matrix of partial derivatives provided by the mapping function; and A manufacturable design of the metalens is generated based on the optimized parameters.
2. The method according to claim 1, wherein: The metasurface is arranged into a grid of unit cells that divides the plane into rectangular, hexagonal, triangular, or phyllosy shapes.
3. The method according to claim 2, wherein: The phyllotaxy is formed by a double helical pattern.
4. The method according to claim 1, wherein: The substrate is made of silicon dioxide.
5. The method according to claim 1, wherein: The nanostructures are made of titanium dioxide.
6. The method according to claim 1, wherein: The calculation steps continue until the magnitude of the design parameter correction falls below manufacturing tolerances.
7. The method according to claim 1, wherein: In the calculation step, an interpolator function is used to predict the near-field phase distribution on each of the unit cells.
8. The method according to claim 7, wherein: The calculating step continues until the near-field phase distribution matches the target near-field phase distribution within a target error tolerance.
9. The method according to claim 1, wherein: Interpolation is performed on the one-dimensional subset of the d-unit supercell to obtain an interpolation function, and the obtained interpolation functions are averaged to provide a gradient and a prediction of the two-dimensional d-unit supercell.
10. The method according to claim 1, wherein: The d-unit supercells are different combinations of orientations of a collection of nanofins, wherein the interaction of each d-unit supercell with an incident wavefront is modeled by solving Maxwell's equations.