Spectral Regulation Metasurface Design Method Based on Time-Domain Adjoint Topology Optimization

Abstract

The present invention discloses a method for designing a spectral regulation metasurface based on time-domain adjoint topology optimization, including: selecting an initial metasurface structure, and obtaining a first structural refractive index distribution according to a pixelated structure matrix; performing blurring processing and threshold filtering processing to obtain a second structural refractive index distribution; setting an incident source and a target plane to perform forward simulation to obtain forward electric field information and actual optical field time-domain information at the target plane; fitting to obtain ideal optical field time-domain information at the target plane according to the optical field time-domain information of the incident source; using the correlation between the actual optical field time-domain information and the ideal optical field time-domain information as an objective function, performing adjoint simulation to obtain adjoint electric field information; calculating the value of the objective function, calculating a gradient matrix according to the forward electric field information and the adjoint electric field information, and updating the pixelated structure matrix; repeating the above steps for iterative calculation until the value of the objective function converges, and obtaining a spectral regulation metasurface according to the finally updated pixelated structure matrix.

Description

Technical Field

[0001] The present invention belongs to the technical field of metasurface spectral regulation, and particularly relates to a metasurface design method for spectral regulation based on time-domain adjoint topology optimization. Background Art

[0002] With the rapid development of photonics and nanotechnology, many different resonant optical phenomena have emerged frequently, including Fano resonance, electromagnetically induced transparency, Kerker and Borrmann effects, and parity-time symmetry breaking, etc. These special spectra have extensive applications in optical switches and sensors, as well as other optical design fields. A metasurface is a planar metamaterial with a subwavelength thickness, or a planar material composed of a single layer or several layers of planar structures stacked together, which can be easily fabricated using lithography and nano-printing methods. The ultra-thin thickness in the wave propagation direction can greatly suppress unwanted losses. Using a metasurface can achieve spatially varying optical responses, shape the optical wavefront into a shape that can be designed arbitrarily, and facilitate the integration of functional materials to achieve active control and greatly enhanced nonlinear responses. Therefore, how to use metasurfaces to regulate spectra has become a research focus. In frequency-domain design, metasurfaces provide an extraordinary method to control light through spatially structured materials.

[0003] Traditional metasurface designs have always relied on intuitive methods. The motivation for new devices comes from prior physical effects, and then specific functions are matched with suitable applications by adjusting a small number of characteristic parameters. However, when the design scope expands to include large bandwidth or multi-frequency applications, nonlinear phenomena, and dense integration, continuing with this prototyping method faces more complex challenges. Based on the difficulties of the above forward design, the reverse design method of topology optimization has been introduced into metasurface design from the mechanical field. It can be based on finite element and finite difference type modeling in the frequency domain and time domain. The basic idea is to regard the material density of each element or grid point as a design variable, so the geometry can be parameterized in a pixel-like manner, and the optimization problem can be effectively solved using optimization methods based on mathematical programming and analytical gradient calculation.

[0004] In recent years, the research on topology optimization has mainly focused on the frequency domain. However, when performing spectral regulation or pulse shaping, it is found that traditional frequency-domain topology optimization cannot perform metasurface design well due to its complexity and limitations. For this situation, the present invention considers introducing time-domain topology optimization to solve this problem. Summary of the Invention

[0005] In view of the problem that it is difficult to select sampling points in frequency-domain topology optimization because the spectral sampling points move as the structure changes, and the number of sampling points represents the number of multi-objectives in the frequency domain, which involves multi-objective optimization and greatly increases the design difficulty, the present invention proposes a spectral regulation metasurface design method based on time-domain adjoint topology optimization. It is a method for realizing spectral regulation using time-domain adjoint topology optimization. By introducing the time domain in the field of topology optimization and realizing spectral regulation through adjoint calculation means, compared with the previous direct frequency-domain design, using this method reduces the difficulty and complexity of spectral regulation and provides a new idea for inverse design to optimize the spectrum.

[0006] One aspect of the present invention provides a spectral regulation metasurface design method based on time-domain adjoint topology optimization, including:

[0007] S1, select an initial metasurface structure, and obtain the first structural refractive index distribution according to the pixelated structure matrix obtained after pixelation processing;

[0008] S2, perform fuzzy processing and threshold filtering processing on the first structural refractive index distribution to obtain a second structural refractive index distribution;

[0009] S3, set an incident source and a target plane, and perform forward simulation according to the second structural refractive index distribution to obtain the forward electric field information in the structural layer and the actual optical field time-domain information at the target plane;

[0010] S4, according to the optical field time-domain information of the incident source, use time coupling simulation to obtain the ideal optical field time-domain information at the target plane;

[0011] S5, take the correlation between the actual optical field time-domain information and the ideal optical field time-domain information as the objective function, remove the incident source and set an adjoint source at the target plane to perform adjoint simulation to obtain the adjoint electric field information in the structural layer;

[0012] S6, calculate the value of the objective function, calculate the gradient matrix according to the forward electric field information and the adjoint electric field information in the structural layer, and update the pixelated structure matrix and the first structural refractive index distribution using the gradient matrix;

[0013] S7, repeat steps S2 to S6 for iterative calculation until the value of the objective function converges, and obtain a spectral regulation metasurface according to the finally updated pixelated structure matrix.

[0014] According to an embodiment of the present invention, in S1, it further includes setting optimization parameters, where the optimization parameters at least include a blur radius, a binarization parameter for threshold filtering processing, and a gradient update step size; the pixelated structure matrix is composed of only 0 and 1 and is expressed as a function ρ(x‘,y’) of coordinates, and the first structural refractive index distribution is n(x‘,y’) = n air +ρ(x‘,y’)·(n material -n air ), where n air is the refractive index of air, and n material is the refractive index of the material of the metasurface structure;

[0015] In S2, the blurring process is a linear blurring process or a Gaussian blurring process, and the second structural refractive index distribution is n‘(x‘,y’).

[0016] According to an embodiment of the present invention, in S3, it further includes calculating the transmittance distribution at the target plane through the finite-difference time-domain algorithm during the forward simulation process to obtain the actual spectral line, and performing a Fourier transform on the actual optical field time-domain information at the target plane to obtain the actual optical field frequency-domain information;

[0017] where the target plane is a transmission plane and / or a reflection plane, and the forward electric field information in the structure layer is x’ and t’ respectively represent the coordinates and time of the structure layer.

[0018] According to an embodiment of the present invention, in S4, the optical field time-domain information of the incident source is Fourier-transformed to obtain the optical field frequency-domain information of the incident source, the parameters of the ideal spectral line are determined by the time-domain coupled mode and fitted to obtain the ideal spectral line, the ideal optical field frequency-domain information at the target plane is calculated based on the optical field frequency-domain information of the incident source and the parameters of the ideal spectral line, and then after Fourier transform, the ideal optical field time-domain information at the target plane is obtained.

[0019] According to an embodiment of the present invention, in S5, the objective function is expressed as the inner product of the actual optical field time-domain information and the ideal optical field time-domain information, that is, the integral of the conjugate multiplication of the actual optical field time-domain information and the ideal optical field time-domain information, where T is the time domain, T = [0,t end ;, is the actual optical field time-domain information, is the ideal optical field time-domain information, * represents complex conjugate, t end is the simulation cut-off time, and i is the component in the three directions of xyz;

[0020] The adjoint source is defined as the derivative of the objective function with respect to the electric field, expressed as where x and t respectively represent the coordinates and time of the target plane; the adjoint electric field information in the structural layer is x’ and t’ respectively represent the coordinates and time of the structural layer.

[0021] According to an embodiment of the present invention, in S6, according to the forward electric field information in the structural layer and the adjoint electric field information in the structural layer calculate the gradient matrix using the following formula and update the pixelated structure matrix ρ(x‘,y’);

[0022]

[0023] where x’∈ψ, x’ represents the coordinates of the structural layer, that is, the region where the relative permittivity ε changes inside the structural layer; t0 represents the initial time, and t’ represents the time of the structural layer, that is, the time of the induced polarization effect before time t.

[0024] According to an embodiment of the present invention, in S7, determine whether the value of the objective function tends to converge or whether the current cumulative number of iterations is greater than the set value: if so, output the finally updated pixelated structure matrix and obtain the spectral modulation metasurface; otherwise, continue the iterative calculation.

[0025] According to an embodiment of the present invention, the method further includes S8: comparing the actual spectral line corresponding to the finally updated pixelated structure matrix with the ideal spectral line, and / or comparing the actual optical field frequency domain information corresponding to the finally updated pixelated structure matrix with the ideal optical field frequency domain information to verify the spectral modulation effect of the spectral modulation metasurface.

[0026] On the other hand, the present invention provides a spectral modulation metasurface, which is designed by using the above-mentioned spectral modulation metasurface design method based on time-domain adjoint topology optimization and is used for spectral modulation.

[0027] On yet another aspect, the present invention provides a spectral modulation device, including the above-mentioned spectral modulation metasurface and being used for spectral modulation.

[0028] On still another aspect, the present invention provides a spectral modulation method, which uses the above-mentioned spectral modulation metasurface or the above-mentioned spectral modulation device for spectral modulation.

[0029] Compared with the prior art, the time-domain adjoint topology optimization proposed by the present invention adds the regulation of the time domain on the basis of the frequency-domain topology optimization, solving the difficulties of upsampling in the frequency domain during spectral regulation and the problem of doubling the computational amount caused by the inability to achieve multi-objective optimization. The use of Fourier transform and inverse transform can cleverly achieve the mutual conversion between the frequency domain and the time domain, converting the frequency-domain problem into a time-domain problem. When the time-domain signal changes into spectral information, it has more information and higher simulation speed compared with the sampled frequency domain, greatly improving the optimization efficiency. At the same time, the arbitrary shape design gives the metasurface great freedom. Compared with the traditional metasurface, it can achieve performance and special properties that cannot be achieved by forward design, enabling the design of a spectral regulation metasurface and obtaining an ideal spectrum, greatly improving the design efficiency and performance compared with the traditional method. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly understand the structure and embodiments of the present invention, the following will explain the required drawings. The following drawings only represent some embodiments of the present invention.

[0031] Figure 1 FIG. is a flowchart of a method for designing a spectral regulation metasurface based on time-domain adjoint topology optimization according to an exemplary embodiment of the present invention.

[0032] Figure 2 FIG. is a schematic structural diagram of iteration and a change curve of FoM in an embodiment of the present invention.

[0033] Figure 3 FIG. is a comparison schematic diagram of the actual spectrum line and the ideal spectrum line in the simulation of an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0034] All features disclosed in this specification, or all steps in any method or process disclosed, except for mutually exclusive features and / or steps, can be combined in any manner.

[0035] Any feature disclosed in this specification, unless specifically recited, can be replaced by other equivalent or similar-purpose alternative features. That is, unless specifically recited, each feature is only an example of a series of equivalent or similar features.

[0036] In order to make the content of the present invention easy to understand, the following will be described in detail with reference to the drawings and specific embodiments. The listed embodiments are only partial embodiments of the present invention, and there can be other combination methods without departing from the present invention.

[0037] The present invention will be described in detail below with reference to the drawings.

[0038] Figure 1Flowchart of a spectral regulation metasurface design method based on time-domain adjoint topology optimization according to an exemplary embodiment of the present invention.

[0039] As Figure 1 shown, according to an exemplary embodiment of the present invention, the spectral regulation metasurface design method based on time-domain adjoint topology optimization of the present invention specifically includes the following multiple steps:

[0040] S1. Select an initial metasurface structure, and obtain a first structural refractive index distribution according to the pixelated structure matrix obtained after pixelization processing.

[0041] The initial metasurface structure here can be a structure designed forward or any random structure. Specifically, it is pixelized during the software calculation process, that is, the existing part of the structure is set to 1, and the non-existing part is set to 0. According to the set number of pixels, the pixelated structure matrix of this initial metasurface structure can be written, and its elements are only composed of 0 and 1. Writing the pixelated structure matrix as a function ρ(x‘,y’) of coordinates, the first structural refractive index distribution representing the structural information can be written as n(x‘,y’) = n air + ρ(x‘,y’)·(n material - n air ). Among them, n air is the refractive index of air, and n material is the material refractive index of the metasurface structure.

[0042] In addition, this step also includes a sub-step of setting optimization parameters, and the optimization parameters at least include a blur radius, a binarization parameter for threshold filtering processing, a gradient update step size, etc.

[0043] S2. Perform blur processing and threshold filtering processing on the above first structural refractive index distribution to obtain a second structural refractive index distribution.

[0044] From the perspective of image processing and physics, blur processing can not only denoise and make the image smoother, but also eliminate discontinuous points to make the dielectric constant continuous, thereby meeting the actual processing requirements. Therefore, blur processing is introduced in this step to obtain the structure entering the algorithm. The blur processing in this step can adopt two blur methods: linear blur processing or Gaussian blur processing. Since the actual structural refractive index is a binary distribution, that is, there are only two states, threshold filtering processing (i.e., binarization processing) is required after blur processing to meet its physical meaning, and the obtained second structural refractive index distribution is n‘(x‘,y’).

[0045] S3. Set the incident source and the target plane, and perform forward simulation according to the above second structural refractive index distribution to obtain the forward electric field information in the structural layer and the actual optical field time-domain information at the target plane.

[0046] The simulation process starting from the light source and passing through the structural layer is called forward simulation by the present invention. At this time, the forward electric field information in the structural layer can be obtained, denoted by where x' and t' respectively represent the coordinates and time of the structural layer. In the present invention, the target plane set can be a transmission plane and / or a reflection plane, specifically determined according to the designed ideal spectral line.

[0047] Import the refractive index distribution n'(x',y') of the second structure into the simulation software, calculate the current iteration transmittance distribution at the target plane through the finite-difference time-domain algorithm and obtain the actual spectral line. The final result obtained after several iterations is the required final result and the data is stored. At the same time, the actual light field time-domain information, that is, the time signal information, can be obtained at the target plane, and its Fourier transform can also be performed to obtain the actual light field frequency-domain information, that is, the spectral distribution, for comparing and evaluating the light field regulation result.

[0048] S4. According to the light field time-domain information of the incident source, use time-coupled simulation to obtain the ideal light field time-domain information at the target plane.

[0049] This step is used for inverse design to obtain the ideal target spectral line, that is, the ideal light field time-domain information at the target plane. To satisfy its underlying physical meaning, the present invention introduces the theory of time-domain coupled mode to fit the ideal spectral line. First, the light field time-domain information of the incident source is obtained through the simulation software, and its Fourier transform is also performed to obtain the light field frequency-domain information of the incident source. Then, the transmittance and group delay are quantitatively described by the time-domain coupled mode, the parameters of the ideal spectral line are determined by the time-domain coupled mode and the ideal spectral line is fitted. Based on the light field frequency-domain information of the incident source and the parameters of the ideal spectral line, the ideal light field frequency-domain information at the target plane is calculated, and after Fourier transform, the ideal light field time-domain information at the target plane can be obtained.

[0050] In the theory of time-domain coupled mode, the interaction between the free space and the response of the amplitude x of the metasurface resonance mode can be quantitatively described in a time-dependent form by the following dynamic equations: and where x1 and x2 respectively represent the mode amplitudes of the first oscillator (bright mode) with a resonant frequency of ω1 and the second oscillator (dark mode) with a resonant frequency of ω2, is the non-radiative decay (intrinsic damping loss); the bright mode coupling cavity can radiatively couple and decay into forward and backward propagating spatial electromagnetic waves to the free space through the radiation coupling path; μ represents the effective coupling coefficient between the first and second oscillators; κ is the bright mode dipole coupling strength of the external incident electromagnetic field |s+>=(E0exp(jωt),0); τ i2 represents the resonant lifetime of the dark mode; s iIt represents the incident wave or the outgoing wave. Both resonators are linearly coupled with the coupling strength, so the transmittance and reflectance functions of the vertically incident electric field can be obtained as follows:

[0051] and

[0052]

[0053] where the ± sign corresponds to the case where the resonant mode is even (odd) symmetric, r d (reflectance) and t d (transmittance) are the direct transmission coefficients, |r d | 2 +|t d | 2 =1, τ i and τ w are the cavity lifetimes related to the intrinsic loss and the radiation loss to free space respectively, and the total resonant cavity lifetime is 1 / τ = 1 / τ i +1 / τ w . The transmission efficiency T, the effective phase shift and the group delay t g can be obtained by T = abs(S 21 ) 2 , and respectively.

[0054] After determining the parameters of the ideal spectrum according to the above formulas, the frequency-domain information of the ideal optical field at the target plane can be calculated from the amplitude and phase and the frequency-domain information of the optical field of the incident source. Finally, the inverse Fourier transform can be performed to obtain the time-domain information of the ideal optical field at the target plane, which is used as the ideal spectrum.

[0055] S5. Using the correlation between the above actual optical field time-domain information and the above ideal optical field time-domain information as the objective function, removing the incident source and setting an adjoint source at the target plane for adjoint simulation to obtain the adjoint electric field information in the structural layer.

[0056] Removing the light source in the forward simulation and setting an adjoint source at the position of the target plane, this process of source reverse simulation is called adjoint simulation. According to the principle of adjoint optimization, through the reciprocity of the Green's function, the field distribution excited by the adjoint source set at the target plane can be used to update the gradient change of the structure. Therefore, the adjoint source here is defined as the derivative of the objective function with respect to the electric field, that is where x and t represent the coordinates and time of the target plane respectively, F(x,t) is the objective function, and E is the actual electric field, that is, the source of the adjoint simulation is driven by the time-dependent electric field.

[0057] The objective function in the present invention is expressed as the inner product of the actual optical field time-domain information and the ideal optical field time-domain information, that is, the integral of the conjugate multiplication of the actual optical field time-domain information and the ideal optical field time-domain information. where T is the time domain, T = [0, t end ; is the actual optical field time-domain information, is the ideal optical field time-domain information, * represents complex conjugate, and t end is the simulation cut-off time.

[0058] It should be noted here that in the adjoint optimization in the time domain, time also needs to be reverse-excited simultaneously, which cannot be realized in real life. Therefore, the concept of time reversal is introduced. Traditionally, if the evolution of a physical process in the backward direction (i.e., the reverse process of the original process) is also a real process, it is called time-reversal invariant or reversible. Only when the dissipative losses in the system can be ignored can the time-reversal symmetry of the field equation lead to the time reversibility of electromagnetic processes. At this time, the reverse electric field information in the structural layer is obtained, which is expressed as x' and t' represent the coordinates and time of the structural layer respectively.

[0059] S6. Calculate the value of the objective function, and calculate the gradient matrix according to the forward electric field information and the adjoint electric field information in the above structural layer. Use this gradient matrix to update the pixelized structure matrix and the first structural refractive index distribution in step S01.

[0060] From the simulation results in the forward simulation (step S03) and the adjoint simulation (step S05) and the gradient matrix of the structure can be calculated, that is where x' ∈ ψ, x' represents the coordinates of the structural layer, that is, the region where the dielectric constant ε changes inside the structural layer; t0 represents the initial time, and t' represents the time of the structural layer, that is, the time of the induced polarization effect before time t.

[0061] This gradient matrix is also the magnitude of the change in the optimization direction at each pixel point of the structure. Thus, it can be used to update the pixelized structure matrix ρ(x', y') and the first structural refractive index distribution. After updating, all pixel values are limited within the range of [0, 1] to ensure that the refractive index matrix conforms to the actual physical meaning. Among them, pixel values greater than 1 are set to 1, pixel values less than 0 are set to 0, and pixel values within the range of [0, 1] remain unchanged.

[0062] S7. Repeat steps S2 - S6 for iterative calculation until the value of the objective function converges. Obtain the spectral modulation metasurface according to the finally updated pixelized structure matrix.

[0063] Specifically, it is determined whether the value of the objective function tends to converge or whether the current cumulative number of iterations is greater than the set value: if so, the finally updated pixelated structure matrix is output and the spectral modulation metasurface is obtained; otherwise, iterative calculation continues. Among them, the determination of the convergence of the objective function generally starts from the image. If the objective function curve tends to be flat within a certain number of generations, it can be considered convergent.

[0064] In order to evaluate the spectral modulation effect of the obtained spectral modulation metasurface, the design method of the present invention may further include S08, that is, comparing the actual spectral line corresponding to the finally updated pixelated structure matrix with the ideal spectral line, and / or comparing the actual optical field frequency domain information corresponding to the finally updated pixelated structure matrix with the ideal optical field frequency domain information to verify the spectral modulation effect of the obtained spectral modulation metasurface.

[0065] The present invention also provides a spectral modulation metasurface, which is designed by using the above-mentioned design method of spectral modulation metasurface based on time-domain adjoint topology optimization and is used for spectral modulation. The present invention also provides a spectral modulation device, which includes the above-mentioned spectral modulation metasurface and is used for spectral modulation. The present invention also provides a corresponding spectral modulation method, which uses the above-mentioned spectral modulation metasurface or the above-mentioned spectral modulation device for spectral modulation.

[0066] The spectral modulation metasurface designed by the present invention can realize the modulation of any spectrum. Compared with the topological optimization method in the frequency domain, it greatly reduces the design difficulty and complexity and improves the design efficiency. The present invention realizes time-domain topological optimization by using time reversal, which is not only effective for the spectral modulation field, but also can be used in fields such as spatio-temporal shaping, providing a new option for the control of time. The inverse design means of the present invention can realize strange shapes that cannot be designed forward, improving the design freedom and making it easier to achieve better target effects.

[0067] The present invention will be further described below with reference to specific embodiments.

[0068] This embodiment is a high-Q resonance EIT metasurface designed by using the method steps S1-S7 of the present invention described above.

[0069] According to step S1, the initial metasurface structure is set as a typical bright-dark mode separation resonator, which is composed of dielectric Si and is arranged in a periodic structure. The size of each period is 750 nm, including a ring structure and a columnar structure. The length and width of the columnar structure are 720 nm and 150 nm respectively, the inner diameter of the ring is 110 nm, the outer diameter is 225 nm, and the distance between them is 70 nm. The thickness of all structures is set to 110 nm. Through the pixelation process of the structure, the first structure refractive index distribution is obtained.

[0070] According to step S2, the obtained refractive index distribution of the first structure is subjected to blurring processing and threshold filtering processing. The initial blurring radius is set to 0.1 μm, and the refractive index distribution of the second structure is obtained. As Figure 2 in the sub- Figure 1 st shown, the obtained refractive index distribution is between 0 and 1, which is reflected as an unclear pattern on the picture.

[0071] According to step S3, an incident source is set at a position 0.5 times the central wavelength λ0 below the structure. The wavelength range is set to 1.5 μm - 1.6 μm, where λ0 is 1.55 μm, and it is incident from below. At a position 0.5 times λ0 away from the structure in the outgoing direction, that is, the transmittance target plane, a time monitor is set. At a position 0.7 times λ0 away from the structure in the incident direction, that is, the reflectance target plane (which is below the incident source), a time monitor is set. At the same time, a monitor is set at the center of the structure. Forward simulation is performed according to the above refractive index distribution of the second structure, and the forward electric field information in the structure layer and the actual optical field time-domain information at the target plane are obtained through each monitor.

[0072] According to step S4, starting from the optical field time-domain information of the incident source, a physically meaningful target spectral line is simulated by time coupling. The mode is calculated from the initial structure, and the ideal optical field time-domain information at the target plane can be calculated through the target spectral line.

[0073] According to step S5, the correlation between the above actual optical field time-domain information and the above ideal optical field time-domain information is used as the objective function. Here, based on the model of this example, the objective function in this embodiment is set as the difference between the actual optical field time-domain information and the above ideal optical field time-domain information: is the actual optical field time-domain information, is the ideal optical field time-domain information, where i is the component in the xyz three directions. Thus, it can be proved that different objective functions can also achieve the functions that this theory wants to achieve. Therefore, the smaller the value of the objective function, the closer the actual spectral line is to the ideal spectral line, that is, the optimization proceeds in the desired direction, as Figure 2 shown. The magnitude of the adjoint source is calculated from the objective function, the incident source is removed, and the adjoint source is set at the target plane for adjoint simulation to obtain the adjoint electric field information in the structure layer.

[0074] According to step S6, the value of the objective function is calculated, and the gradient matrix is calculated based on the forward electric field information and the adjoint electric field information obtained from the structure layer monitor above. The pixelized structure matrix and the refractive index distribution of the first structure in step S1 are updated using this gradient matrix. The updated refractive index distribution is as Figure 2 shown in the subgraphs of each different iteration number in

[0075] According to step S7, steps S2 - S6 are repeated for iterative calculation until the value of the objective function converges. As Figure 2 shown, after 70 generations, the objective function converges. In this embodiment, the termination condition is set as the number of iterations. When the number of iterations reaches 150 generations, the process stops. The EIT metasurface is obtained according to the finally updated pixelized structure matrix. The ideal and actual transmission / reflection spectra simulated by this metasurface are as Figure 3 shown. It can be seen that the optimized spectral line is very close to the set ideal spectral line, generating EIT resonance.

[0076] Figure 2 is the curve of the structural change and FoM of the EIT metasurface used in this embodiment during the iterative process. Figure 3 is the comparison schematic diagram between the simulated actual spectral line and the ideal spectral line after time-domain topology optimization in this embodiment.

[0077] From Figure 2 it can be seen that Figure 2 the main part is the curve of the change in FoM. Here, FoM is designed as the difference between the actual spectral line and the ideal spectral line. Therefore, moving forward in the optimization direction means that the value of the objective function needs to be as small as possible until it approaches 0. It can be seen that due to the sensitivity of the spectral line to the structure, changing the structure will cause significant changes to the time-domain information. Therefore, during the early optimization process, the objective function has been oscillating up and down, but the trend is always downward. After 70 iterations, FoM tends to converge and approaches 0, demonstrating the correctness of the optimization direction and meeting the definition of gradient optimization.

[0078] Figure 2 The subgraph of shows the refractive index distribution at different iteration times, displayed every 30 generations, from the 1st generation to the 150th generation. It can be seen that the structure of the first generation is obtained by blurring and threshold filtering the initially forward-designed regular metasurface structure (i.e., a ring and a square), and the refractive index distribution is between 0 and 1. After multiple iterative designs, when reaching the 30th generation, it can still be seen that the situation is relatively blurred and the structure expands towards the edge; at the 60th generation, the clarity of the structure increases, and while expanding towards the edge, the non-uniformity of the ring becomes more obvious; at the 90th generation, the structure is already relatively clear and the degree of binarization is higher; at the 120th generation, the structure approaches complete binarization, and compared with the previous structure, only the corner positions are optimized; until the 150th generation, complete binarization is achieved, the structure is clear, and it is an asymmetric irregular structure distribution, which is the finally optimized structure form. It can be seen that as the number of iterations increases, the refractive index distribution changes continuously, and the pattern gradually becomes irregular (i.e., topological) and clear (i.e., binarized), which is the essence of topological optimization until complete binarization is achieved in the last generation.

[0079] From Figure 3 As can be seen, the dashed line is the ideal spectrum line, and the solid line is the actual spectrum line obtained by simulation. By using time-domain topology optimization, the simulated transmission spectrum line and reflection spectrum line can be made to approach the designed ideal spectrum line. T and R respectively represent the transmittance and reflectance varying with wavelength, with numerical values ranging from 0 to 1, and T + R = 1. The ideal resonance peak position appears at 1.540 μm, at which time T ≈ 1 and R ≈ 0; the actual resonance peak position also appears at 1.540 μm, which basically coincides. As the wavelength changes towards both sides, the ideal transmittance T drops to 0 at 1.530 μm and 1.552 μm and then rises towards both sides; the reflectance R is just the opposite, rising to 1 at 1.530 μm and 1.552 μm and then dropping towards both sides. The actual transmittance T drops to 0 at 1.529 μm and 1.551 μm and then rises towards both sides; the reflectance R is just the opposite, rising to 1 at 1.529 μm and 1.551 μm and then dropping towards both sides. In terms of the overall trend and resonance peak position, the ideal spectrum line and the actual spectrum line are almost the same. As can be seen from the spectrum, the Q value of the obtained actual simulated transmission / reflection spectrum is slightly lower than the designed ideal Q value, which is consistent with the FoM not satisfying being equal to 0. During the optimization process, it is impossible to achieve perfect overlap of the spectrum lines, but only approach the target direction, which is also the core of gradient optimization. In terms of the essence of gradient optimization, it is easy to fall into the situation of local optimum and it is difficult to reach the optimal solution. And for Figure 3 the spectrum in, it can be seen that EIT resonance is achieved and resonance peaks are generated. From the perspective of spectrum design, it is proved that the finally obtained metasurface structure achieves the purpose of the present invention, that is, to realize the regulation of the spectrum, that is, a metasurface structure meeting the requirements can be obtained by setting the ideal spectrum line and performing inverse design.

[0080] The description of the above embodiments is only used to help understand the method and core idea of the present invention. It should be pointed out that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and modifications can still be made to the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

[0081] The present invention is not limited to the foregoing specific embodiments. The present invention extends to any new feature or any new combination disclosed in this specification, as well as any new method or process step or any new combination disclosed.

Claims

1. A method for designing a spectral regulation metasurface based on time-domain adjoint topology optimization, characterized in that It includes the following steps: S1. Select an initial metasurface structure and obtain the first structural refractive index distribution according to the pixelated structure matrix obtained after pixelization processing; S2. Perform blurring processing and threshold filtering processing on the first structural refractive index distribution to obtain the second structural refractive index distribution; S3. Set an incident source and a target plane, and perform forward simulation according to the second structural refractive index distribution to obtain the forward electric field information in the structural layer and the actual optical field time-domain information at the target plane; S4. According to the optical field time-domain information of the incident source, use time-domain coupled simulation to obtain the ideal optical field time-domain information at the target plane; perform Fourier transform on the optical field time-domain information of the incident source to obtain the optical field frequency-domain information of the incident source, use time-domain coupled simulation to determine the parameters of the ideal spectrum line and fit to obtain the ideal spectrum line, calculate the ideal optical field frequency-domain information at the target plane based on the optical field frequency-domain information of the incident source and the parameters of the ideal spectrum line, and then perform Fourier transform to obtain the ideal optical field time-domain information at the target plane; S5. Use the correlation degree between the actual optical field time-domain information and the ideal optical field time-domain information as the objective function, remove the incident source and set an adjoint source at the target plane to perform adjoint simulation to obtain the adjoint electric field information in the structural layer; S6. Calculate the value of the objective function, calculate the gradient matrix according to the forward electric field information and the adjoint electric field information in the structural layer, and use the gradient matrix to update the pixelated structure matrix and the first structural refractive index distribution; S07. Repeat steps S2 to S6 for iterative calculation until the value of the objective function tends to converge, and obtain the spectral modulation metasurface according to the finally updated pixelated structure matrix.

2. The method for designing a spectral regulation metasurface based on time-domain adjoint topology optimization according to claim 1, characterized in that, In S1, it also includes setting optimization parameters, and the optimization parameters at least include a blur radius, a binarization parameter for threshold filtering processing, and a gradient update step size; the pixelated structure matrix is only composed of 0 and 1 and is expressed as a function of coordinates , and the first structural refractive index distribution is , where is the refractive index of air, is the material refractive index of the metasurface structure; In S2, the blurring process is a linear blurring process or a Gaussian blurring process, and the second structural refractive index distribution is .

3. The method for designing a spectral regulation metasurface based on time-domain adjoint topology optimization according to claim 1, wherein, In S3, it further includes calculating the transmittance distribution at the target plane and obtaining the actual spectrum line during the forward simulation process by using the finite-difference time-domain algorithm, and performing Fourier transform on the actual optical field time-domain information at the target plane to obtain the actual optical field frequency-domain information; Wherein, the target plane is a transmission plane and / or a reflection plane, and the forward electric field information in the structure layer is , and respectively represent the coordinates and time of the structure layer.

4. The method for designing a spectral regulation metasurface based on time-domain adjoint topology optimization according to claim 1, wherein In S5, the objective function is expressed as the inner product of the actual optical field time-domain information and the ideal optical field time-domain information, that is, the integral of the conjugate multiplication of the actual optical field time-domain information and the ideal optical field time-domain information. , where is the time domain, , is the actual optical field time-domain information, is the ideal optical field time-domain information, represents the complex conjugate, is the simulation cut-off time, and i is the component in the three directions of x, y, and z; The adjoint source is defined as the derivative of the objective function with respect to the electric field, expressed as , where and represent the coordinates and time of the target plane, respectively; The adjoint electric field information in the structural layer is , and respectively represent the coordinates and time of the structural layer.

5. The method for designing a spectral regulation metasurface based on time-domain adjoint topology optimization according to claim 1, wherein In S6, according to the forward electric field information in the structure layer and the accompanying electric field information in the structure layer , calculate the gradient matrix using the following formula and update the pixelated structure matrix ; Among them, , represents the coordinates of the structural layer, that is, the region where the relative permittivity inside the structural layer changes; , represents the initial time, represents the time of the structural layer, that is, the time of the induced polarization effect before the moment.

6. The method for designing a spectral regulation metasurface based on time-domain adjoint topology optimization according to claim 1, wherein In S7, judge whether the value of the objective function tends to converge or whether the current cumulative number of iterations is greater than the set value: if so, output the finally updated pixelated structure matrix and obtain the spectral modulation metasurface; otherwise, continue the iterative calculation.

7. The method for designing a spectral regulation metasurface based on time-domain adjoint topology optimization according to claim 1, wherein The method further includes S8: comparing the actual spectrum line corresponding to the finally updated pixelated structure matrix with the ideal spectrum line, and / or comparing the actual optical field frequency-domain information corresponding to the finally updated pixelated structure matrix with the ideal optical field frequency-domain information to verify the spectral modulation effect of the spectral modulation metasurface.

8. A spectral modulation metasurface, characterized in that, Designed by using the spectral modulation metasurface design method based on time-domain adjoint topology optimization according to any one of claims 1 to 7 and used for spectral modulation.

9. A spectral modulation device, characterized in that, It includes the spectral modulation metasurface according to claim 8 and is used for spectral modulation.

10. A spectral regulation method, characterized in that, Perform spectral modulation by using the spectral modulation metasurface according to claim 8 or the spectral modulation device according to claim 9.

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