Metasurface structure design method and metasurface structure

Abstract

The invention provides a metasurface structure design method and a metasurface structure, and the method can comprise the steps: initializing a rotation angle of the metasurface structure; a first light field construction step: constructing a transmission light relation of the current metasurface structure based on the rotation angle; a second light field construction step: constructing a diffracted light relationship of the current metasurface structure based on the transmitted light relationship so as to determine the light intensity distribution of the image plane; an error construction step: calculating an iteration constraint value according to the image plane light intensity distribution and the target light intensity; wherein the target light intensity is a preposed parameter, the target light intensity is the light intensity corresponding to the target metasurface structure, and the target metasurface structure is a design target; if it is judged that the iteration constraint value is larger than the set value, the rotation angle is updated, the updated rotation angle is obtained, the first light field construction step, the second light field construction step and the error construction step are repeatedly executed till the iteration constraint value is not larger than the set value, and the target metasurface structure is determined based on the current rotation angle.

Description

Technical Field

[0001] This application relates to the field of metasurface design technology, and more specifically, to a metasurface structure design method and a metasurface structure. Background Technology

[0002] In the design of metasurfaces, especially in the field of reverse engineering, the traditional approach relies on iterative algorithms. However, current methods have slow convergence speeds, require a large number of iterations, and lack effective constraints, leading to discrepancies between the design results and actual conditions. Summary of the Invention

[0003] The purpose of this application is to provide a metasurface structure design method and a metasurface structure, which can improve the efficiency of metasurface structure design.

[0004] In a first aspect, embodiments of this application provide a metasurface structure design method, comprising: initializing the rotation angle of the metasurface structure; a first light field construction step: constructing the transmission light relationship of the current metasurface structure based on the rotation angle; a second light field construction step: constructing the diffraction light relationship of the current metasurface structure based on the transmission light relationship to determine the image plane light intensity distribution; an error construction step: calculating an iterative constraint value based on the image plane light intensity distribution and the target light intensity; wherein, the target light intensity is a pre-parameter, the target light intensity is the light intensity corresponding to the target metasurface structure, and the target metasurface structure is the design target; if it is determined that the iterative constraint value is greater than a set value, the rotation angle is updated to obtain the updated rotation angle, and the first light field construction step, the second light field construction step, and the error construction step are repeatedly executed until the iterative constraint value is not greater than the set value, and the target metasurface structure is determined based on the current rotation angle.

[0005] In the above implementation method, the metasurface structure is simulated by combining the transmission light relationship and the light intensity distribution of the image plane. Then, the update direction or progress of the metasurface structure is constrained based on the iterative constraint value, so that the target metasurface structure can better meet the actual design requirements.

[0006] In an optional implementation, the iterative constraint value includes: light intensity error and total variation (TV); the step of calculating the iterative constraint value based on the image plane light intensity distribution and the target light intensity includes: determining the light intensity error based on the difference between the image plane light intensity distribution and the target light intensity; and determining the total variation based on the rotation angle of each nanostructure of the current metasurface structure.

[0007] In the above implementation, the iterative constraint values ​​include constraints on light intensity error and rotation angle. It can simultaneously monitor the light intensity error and the rotation angle of each nanostructure of the current metasurface structure obtained at the current stage of design iteration. It takes into account various constraints of the metasurface from multiple perspectives, and the actual designed target metasurface structure can be more closely matched with actual needs.

[0008] In an optional implementation, determining the light intensity error based on the difference between the image plane light intensity distribution and the target light intensity includes: calculating, for a first coordinate, the square of the light intensity difference between the current light intensity of the current metasurface structure at the first coordinate and the target light intensity of the target metasurface structure at the first coordinate; wherein, the first coordinate is the coordinate of any nanostructure in the two-dimensional coordinate of the target metasurface structure; and calculating the sum of the squares of the light intensity differences in the coordinates of all nanostructures in the two-dimensional coordinate of the target metasurface structure to obtain the light intensity error.

[0009] In an optional implementation, the method for determining the light intensity error based on the difference between the image plane light intensity distribution and the target light intensity includes: ; Where L represents the light intensity error; N and M represent the number of nanostructures in the horizontal and vertical directions of the current metasurface structure, respectively; Indicates the target light intensity at At the strength, This represents the light intensity in the image plane of the current metasurface structure. The light intensity at that location.

[0010] In an optional implementation, determining the total variation loss based on the rotation angles of each nanostructure of the current metasurface structure includes: calculating the squared difference of the rotation angles of each nanostructure of the current metasurface structure at each adjacent coordinate; and determining the total variation loss of the current metasurface structure based on the squared difference of the rotation angles at each adjacent coordinate.

[0011] In an optional implementation, the method for determining the total variation loss based on the rotation angles of each nanostructure of the current metasurface structure includes: ; in, Indicates the adjustable weighting coefficient; Indicates in The rotation angle at the location; N and M represent the number of nanostructures in the horizontal and vertical directions of the current metasurface structure, respectively.

[0012] In an optional implementation, updating the rotation angle to obtain the updated rotation angle includes: calculating the updated rotation angle by combining the light intensity error, the total variation loss, and the current rotation angle.

[0013] In an optional implementation, the step of calculating the updated rotation angle by combining the light intensity error, the total variation loss, and the current rotation angle includes: differentiating the rotation angle by the sum of the light intensity error and the total variation loss to obtain an iterative difference; and calculating the updated rotation angle of the nanostructure based on the iterative difference and the rotation angle of the nanostructure on the current metasurface.

[0014] In an optional implementation, the method for determining the updated rotation angle by combining the light intensity error, the total variation loss, and the current rotation angle includes: ; in, Indicates the learning rate; The rotation angle of the nanostructure on the current metasurface in row m and column n is represented by ; k represents the current iteration number.

[0015] In the above implementation, by combining automatic differentiation technology to construct a differentiable physical model to update the rotation angle, convergence is accelerated and design efficiency is improved compared to the potential local optima problems that may occur with existing technologies. Furthermore, by introducing a phase smoothing term, i.e., total variation loss, into the rotation angle update method, phase jumps and Gibbs oscillations can be suppressed, thereby improving the uniformity of the optical field.

[0016] In an optional implementation, the step of constructing the transmission light relationship of the current metasurface structure based on the rotation angle includes: constructing a Jones matrix corresponding to each nanostructure of the current metasurface structure based on the rotation angle; and determining the transmission light relationship of the current metasurface structure based on the Jones matrix.

[0017] In an optional implementation, determining the transmission light relationship of the current metasurface structure based on the Jones matrix includes: determining the transmission light relationship of the current metasurface structure based on the incident light and the Jones matrix.

[0018] In an optional implementation, the Jones matrix corresponding to the nanostructure is represented in the following ways: ; ; in, This represents the Jones matrix corresponding to the nanostructure; Indicates transmittance; R represents the rotation angle of the nanostructure; C represents the representation transformation matrix; and i represents the imaginary unit. The transmission light relationship of the current metasurface structure is represented in the following ways: ; in, Indicates the relationship of transmitted light; This represents incident light.

[0019] In the above implementation, when determining the transmitted light relationship, the Jones matrix is ​​used to incorporate information such as the difference in transmittance between the two principal axes and the intensity of the incident light field into the phase optimization process, thereby improving energy utilization and light field contrast.

[0020] In an optional implementation, the step of constructing the diffraction relationship of the current metasurface structure based on the transmission relationship to determine the image plane intensity distribution includes: performing an integral calculation based on the product of the transmission relationship and the diffraction transfer function to obtain the Fresnel diffraction relationship; and determining the image plane intensity distribution according to the Fresnel diffraction relationship.

[0021] In an optional implementation, the step of constructing the diffraction relationship of the current metasurface structure based on the transmitted light relationship to determine the representation of the image plane intensity distribution includes: ; in, This represents the optical field modulated by the metasurface, i.e., the transmitted light relationship; Represents the diffraction transfer function; ; ; The light intensity distribution of the image plane represents: .

[0022] Secondly, embodiments of this application provide a metasurface structure designed using the metasurface structure design method described above. Attached Figure Description

[0023] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following is a brief introduction to the drawings required for use in the embodiments. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0024] Figure 1 A block diagram illustrating an electronic device provided in an embodiment of this application; Figure 2A flowchart illustrating the metasurface structure design method provided in this application embodiment; Figure 3 The embodiment provided in this application shows a schematic diagram of the error variation curve; Figure 4 The embodiment provided in this application shows another schematic diagram of error variation curve; Figure 5a A schematic diagram of a hologram calculated using existing technology; Figure 5b This is a schematic diagram of a hologram obtained based on the metasurface structure design method provided in the embodiments of this application. Detailed Implementation

[0025] The technical solutions in the embodiments of this application will now be described with reference to the accompanying drawings.

[0026] It should be noted that similar reference numerals and letters represent similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings. At the same time, in the description of this application, the terms "first", "second", etc. are only used to distinguish the description and should not be understood as indicating or implying relative importance.

[0027] Metasurfaces are artificial layered materials composed of periodic or aperiodic arrangements of subwavelength-scale structural units. Through precise design of these structural units, the optical properties of incident light waves, such as phase, amplitude, and polarization, can be accurately controlled. Among them, geometrically phase metasurfaces, by utilizing the rotation of anisotropic nanostructure units and introducing a geometrical phase delay related to the azimuth angle of the structural units through birefringence, demonstrate enormous application potential in the design of micro- and nano-optical devices.

[0028] In the design of metasurfaces, especially in the field of reverse engineering, the traditional approach relies on iterative algorithms. The core idea of ​​this method is: first, to determine the desired target light field distribution; then, to iteratively adjust the geometric parameters of the metasurface nanostructure units so that the calculated light field distribution gradually approaches the preset target light field distribution.

[0029] In the design of geometric phase metasurfaces, iterative optimization algorithms are employed to achieve the desired design by adjusting the geometric parameters of the metasurface nanostructure units within a pre-defined target light field distribution. Available iterative optimization algorithms include: 1. The Gerchberg-Saxton (GS) algorithm. The GS algorithm iteratively recovers the desired phase distribution by performing Fourier transforms between the object and image planes and applying corresponding amplitude constraints. In metasurface design, this algorithm is often used for holographic metasurface design to find the phase distribution that can generate specific holographic images. However, for complex target images or high-precision phase recovery, the GS algorithm has a slow convergence speed, requires a large number of iterations, and has high computational costs. Furthermore, the original GS algorithm mainly handles amplitude constraints; its performance significantly degrades when complex amplitude and phase constraints coexist. The GS algorithm has low correlation with the actual physical properties of the metasurface, easily leading to deviations between simulation and actual results. 2. Gradient Descent Method: The gradient descent method iteratively adjusts the metasurface design parameters along the negative gradient direction of the objective function to minimize the objective function and optimize the metasurface performance. However, the standard gradient descent method ignores constraints such as actual manufacturing process limitations and the physical properties of the metasurface material, leading to deviations between the design results and actual conditions.

[0030] To address the aforementioned research, this application provides solutions to the following main issues: 1. Correction of physical errors in the geometric phase model: The geometric phase metasurface design is based on different phase changes introduced by anisotropic structural units (meta-atoms) along the two principal axes. However, this design ignores the problem of inconsistent transmittance along the two principal axes in reality, leading to phase distortion and decreased energy utilization. This application calculates the transmittance along different principal axes using FDTD simulation and re-derives the Jones matrix, introducing a transmittance difference term along the two principal axes into the geometric phase model to correct the errors of the traditional ideal model, thereby improving phase control accuracy and optical field energy utilization. 2. Iterative phase optimization algorithm: Traditional GS algorithms and gradient descent methods suffer from drawbacks such as slow convergence speed, phase discontinuity, and lack of physical constraints. This application combines automatic differentiation techniques to construct a differentiable physical model (such as vector diffraction theory), directly optimizing the phase distribution through gradient backpropagation, avoiding the local optima problem of the GS algorithm, and accelerating convergence. Furthermore, a phase smoothing term is introduced into the objective function of the rotation angle for calculating the geometric phase parameters to suppress phase jumps and Gibbs oscillations, thereby improving the uniformity of the optical field.

[0031] Based on the above research, the metasurface structure design method and metasurface structure provided in this application effectively solve the problems existing in the prior art, such as phase distortion, low energy utilization, slow convergence speed, and poor optical field uniformity, by correcting the physical error of the geometric phase model and improving the iterative phase optimization algorithm. The metasurface structure design method and metasurface structure provided in this application are described below with reference to some embodiments.

[0032] To facilitate understanding of this embodiment, the electronic device that performs the metasurface structure design method disclosed in this application will first be described in detail.

[0033] like Figure 1 The diagram shown is a block illustration of an electronic device. The electronic device 100 may include a memory 111 and a processor 113. Those skilled in the art will understand that... Figure 1 The structure shown is for illustrative purposes only and does not limit the structure of the electronic device 100. For example, the electronic device 100 may also include components that are more... Figure 1 The more or fewer components shown, or having the same Figure 1 The different configurations shown.

[0034] The memory 111 and processor 113 described above are electrically connected to each other directly or indirectly to enable data transmission or interaction. For example, these components can be electrically connected to each other via one or more communication buses or signal lines. The processor 113 described above is used to execute executable modules stored in the memory.

[0035] The memory 111 can be, but is not limited to, Random Access Memory (RAM), Read Only Memory (ROM), Programmable Read-Only Memory (PROM), Erasable Programmable Read-Only Memory (EPROM), Electrically Erasable Programmable Read-Only Memory (EEPROM), etc. The memory 111 stores programs, and the processor 113 executes these programs upon receiving execution instructions. The methods executed by the electronic device 100 as defined in any embodiment of this application can be applied to the processor 113, or implemented by the processor 113.

[0036] The aforementioned processor 113 may be an integrated circuit chip with signal processing capabilities. The processor 113 may be a general-purpose processor, including a Central Processing Unit (CPU), a Network Processor (NP), etc.; it may also be a digital signal processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor may be a microprocessor or any conventional processor.

[0037] Optionally, the electronic device 100 may also run simulation software to simulate the metasurface structure based on the input geometric parameters of the metasurface structure. The electronic device 100 may also be equipped with a display unit to display the simulation results.

[0038] The electronic device 100 in this embodiment can be used to execute various steps in the various methods provided in the embodiments of this application. The implementation process of the metasurface structure design method is described below through several embodiments.

[0039] Please see Figure 2 This is a flowchart of a metasurface structure design method provided in an embodiment of this application. The metasurface structure design method provided in this application can be applied to electronic devices, through which the electronic devices execute the steps of the metasurface structure design method. The following will describe... Figure 2 The specific process shown will be explained in detail.

[0040] Step 210: Initialize the rotation angle of the metasurface structure.

[0041] The initial rotation angle can be randomly determined or based on historical experience. For example, the rotation angle to be initialized can be assigned based on the rotation angle of a pre-designed metasurface. Alternatively, the initial rotation angle can be determined based on the requirements of the target metasurface structure to be designed. For instance, the rotation angle of the pre-designed metasurface structure, which most closely matches the requirements of the target metasurface structure, can be compared with the phase control requirements of an existing metasurface structure and used as the initial rotation angle.

[0042] Step 220: Construct the transmission light relationship of the current metasurface structure based on the rotation angle.

[0043] For example, the current metasurface structure can be a metasurface structure based on the rotation angle determined in real time during the iteration process. As the iteration progresses, the specific value of the rotation angle will change, and the current metasurface structure will also change accordingly.

[0044] Alternatively, the metasurface structure can be simulated based on the current rotation angle, and the transmission light relationship can be constructed based on the simulation data. For example, the FDTD simulation tool can be used to perform the simulation.

[0045] Alternatively, experimental measurements can be used to determine the transmission light relationship of the current metasurface structure.

[0046] Step 230: Based on the transmission light relationship, construct the diffraction light relationship of the current metasurface structure to determine the light intensity distribution on the image plane.

[0047] Step 240: Calculate the iterative constraint value based on the image plane light intensity distribution and the target light intensity.

[0048] Among them, the target light intensity is a prerequisite parameter, the target light intensity is the light intensity corresponding to the target metasurface structure, and the target metasurface structure is the design target.

[0049] If the iterative constraint value is determined to be greater than the set value, then proceed to step 250.

[0050] For example, the iterative constraint value may include the error between the image plane light intensity determined by the current rotation angle and the target light intensity, the deflection between the current rotation angles, etc.

[0051] For example, the evaluation of the current iteration effect can be represented by mean squared error, peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM), serving as iteration constraint values. Depending on the desired outcome of the target metasurface structure, different iteration constraint values ​​may be selected. For instance, to achieve anisotropic nanopore deep ultraviolet holograms, the iteration constraint value may include the peak signal-to-noise ratio. To suppress Gibbs oscillations caused by phase abrupt changes, the iteration constraint value may also include the total variation loss.

[0052] For example, relative standard deviation (RSD), width penalty loss (WPL), and energy loss rate can also be used as iterative constraint values. Specifically, the relative standard deviation is used as the loss function to optimize the flat-top light uniformity, the width penalty loss as the loss function to optimize the edge steepness, and the energy loss rate as the loss function to optimize energy utilization.

[0053] Step 250: Determine whether the iterative constraint value is greater than the set value.

[0054] Step 260: Update the rotation angle to obtain the updated rotation angle.

[0055] Alternatively, the updated rotation angle can be obtained by combining the above-mentioned iterative constraint values ​​and the rotation angle obtained in the previous iteration.

[0056] Alternatively, particle swarm optimization (PSO) can be used to update the rotation angles. PSO leverages the collaborative and information-sharing mechanisms of swarm intelligence to optimize the phase distribution, and is particularly suitable for scenarios with non-convex objective functions. For example, W rotation angle distributions are first initialized. Each rotation angle distribution represents a candidate solution in the solution space. The iterative constraint values ​​mentioned above, i.e., the negatives of the loss function, are used as the fitness function: ; Update the formula based on speed: ; Update formula for rotation angle distribution: ; The optimal solution is obtained through multiple iterations. In the above formula, the superscript t indicates the t-th iteration, and the subscript w indicates the w-th rotation angle distribution; c1 and c2 represent learning factors, which can be adaptively adjusted based on actual needs. For example, they can be manually adjusted based on the update situation to obtain the best optimization effect.

[0057] Repeat steps 220 to 240 above until the iterative constraint value is no greater than the set value, and determine the target metasurface structure based on the latest rotation angle determined in step 260.

[0058] Furthermore, an upper limit can be set for the number of iterations. When the number of iterations reaches this upper limit, the process can be terminated even if the iteration constraint value is still greater than the set value.

[0059] In the above implementation, the incident light field is modulated by introducing a geometric phase. Specifically, by rotating the anisotropic nanostructure in the metasurface, the polarization state of the incident light relative to the nanostructure is changed, thereby causing the incident light to evolve along different paths on the Poincaré sphere, thus generating a corresponding geometric phase.

[0060] In one embodiment, the aforementioned iterative constraint values ​​may include: light intensity error and total variation loss.

[0061] Step 240 above may include steps 241 and 242.

[0062] Step 241: Determine the light intensity error based on the difference between the light intensity distribution on the image plane and the target light intensity.

[0063] Optionally, step 241 above may include: calculating the current light intensity of the current metasurface structure in the first coordinate and the square of the light intensity difference between the current light intensity of the current metasurface structure in the first coordinate and the target light intensity of the target metasurface structure in the first coordinate; wherein, the first coordinate is the coordinate of any nanostructure in the two-dimensional coordinate of the target metasurface structure; and calculating the sum of the squares of the light intensity differences in the coordinates of all nanostructures in the two-dimensional coordinate of the target metasurface structure to obtain the light intensity error.

[0064] For example, if we need to design a metasurface structure with N nanostructures in the horizontal direction and M nanostructures in the vertical direction, then theoretically, the target metasurface structure has N*M nanostructures, and the current metasurface structure also has N*M nanostructures. The first coordinate mentioned above represents values ​​where the horizontal axis is less than or equal to N, and the vertical axis is less than or equal to M.

[0065] Among them, the square of the light intensity difference can be represented by the square of the difference between the current light intensity and the target light intensity.

[0066] Step 242: Determine the total variation loss based on the rotation angle of each nanostructure in the current metasurface structure.

[0067] Optionally, step 242 above may include: calculating the squared difference of the rotation angles of each nanostructure of the current metasurface structure under each adjacent coordinate; and determining the total variation loss of the current metasurface structure based on the squared difference of the rotation angles under each adjacent coordinate.

[0068] Optionally, the method for determining the light intensity error described above may include: ; Where L represents the light intensity error; N and M represent the number of nanostructures in the horizontal and vertical directions of the current metasurface structure, respectively; Indicates the target light intensity at At the strength, This represents the light intensity in the image plane of the current metasurface structure. The light intensity at that location.

[0069] Optionally, the methods for determining the total variation loss mentioned above include: ; in, Indicates the adjustable weighting coefficient; Indicates in The rotation angle at the location; N and M represent the number of nanostructures in the horizontal and vertical directions of the current metasurface structure, respectively.

[0070] In one embodiment, step 250 described above may include: calculating an updated rotation angle by combining the light intensity error, the total variation loss, and the current rotation angle.

[0071] For example, step 250 above may include: performing a differential calculation on the rotation angle using the sum of the light intensity error and the total variation loss to obtain an iterative difference; and calculating the updated rotation angle of the nanostructure based on the iterative difference and the rotation angle of the nanostructure on the current metasurface.

[0072] Alternatively, the above-mentioned method for updating the rotation angle can be achieved using the following formula: ; in, Indicates the learning rate; The rotation angle of the nanostructure on the current metasurface in row m and column n is represented by ; k represents the current iteration number.

[0073] In the above implementation, the first derivative is used to constrain the iterative update term. Building upon this, the second derivative can also be used to constrain the iterative update term. By penalizing the second gradient of the phase distribution, phase jumps can be suppressed more effectively, resulting in a smoother phase distribution.

[0074] For example, the second derivative loss term can be expressed by the following formula: .

[0075] In the above implementation method, the iterative optimization algorithm is implemented through the above update method. By adding light intensity error and total variation loss to the iteration of rotation angle, iterative optimization is achieved.

[0076] In one embodiment, step 220 may include steps 221 and 222. Step 221: Based on the rotation angle, construct the Jones matrix corresponding to each nanostructure of the current metasurface structure.

[0077] Step 222: Based on the Jones matrix, determine the transmission light relationship of the current metasurface structure.

[0078] For example, step 222 above may include: determining the transmission light relationship of the current metasurface structure based on the incident light and the Jones matrix.

[0079] Optionally, the Jones matrix corresponding to the nanostructure can be represented in the following ways: ; ; in, This represents the Jones matrix corresponding to the nanostructure; Indicates transmittance; R represents the rotation angle of the nanostructure; C represents the rotation matrix; and C represents the representation transformation matrix.

[0080] Current methods for representing the transmission light relationship of metasurface structures include: ; in, Indicates the relationship of transmitted light; This represents the incident light. Understandably, this incident light may vary depending on the usage scenario.

[0081] In the above implementation formula, the influence of the incident light field intensity is also incorporated into the phase optimization process to improve energy utilization and light field contrast.

[0082] The Jones matrix above is derived below by combining the transmittance difference between the two principal axes: The Jones matrix of a nanostructure can be represented as: ; in, , These represent different complex amplitudes introduced into the nanostructure in two mutually perpendicular directions, where R represents the rotation matrix and C represents the representation transformation matrix.

[0083] In the above formula, different complex amplitudes are introduced into the nanostructure in two mutually perpendicular directions. , It is determined to be two independent parameters, so that it can be used to , This reflects the difference in transmittance between the two main axes.

[0084] The rotation matrix R can be expressed as: ; The representation transformation matrix C can be expressed as: Here, i represents the imaginary unit.

[0085] This represents the transformation of coordinates from the xy representation to the circularly polarized representation. In the circularly polarized coordinate system, the Jones matrix corresponding to the anisotropic nanostructure can be calculated as follows: .

[0086] In the above implementation, the difference in transmittance between the two principal axes can be represented by different complex amplitudes by combining the Jones matrix. , Introducing this will also increase the intensity of the incident light field. By incorporating information such as polarization distribution into the updating of the rotation angle during the metasurface design process, energy utilization and light field contrast can be improved, resulting in higher control precision and higher light field energy utilization of the designed metasurface.

[0087] Optionally, step 230 above may include: performing an integral calculation based on the product of the transmission light relation and the diffraction transfer function to obtain the Fresnel diffraction relation; and determining the image plane light intensity distribution based on the Fresnel diffraction relation.

[0088] The above representation of the target light field distribution formed by the image plane, combined with Fresnel diffraction theory, can be expressed as including: ; in, This represents the optical field modulated by the metasurface, i.e., the transmission light relationship; This represents the diffraction transfer function.

[0089] The transmission light relationship can be represented as a two-row, one-column vector, as shown below: .

[0090] Based on this, the target light field distribution formed by the image plane can also be represented as a vector with two rows and one column: ; The image plane light intensity distribution corresponding to the current rotation angle distribution can be represented as follows: .

[0091] In this embodiment, by incorporating the corresponding Jones matrix into the gradient descent method, a correlation between the diffraction light field distribution and transmittance is established, thereby optimizing the spatial distribution of the rotation angle. When the mean square error loss function value converges to a preset threshold, the obtained rotation angle distribution can generate the target light field distribution of the target metasurface structure.

[0092] In this embodiment, through specific simulation experiments, under the conditions of a metasurface pixel count of 600x600, a size of 1.8mm, a wavelength of 193nm, a distance of 50mm from the metasurface to the holographic image, and non-ideal light incidence, the advantages of the iterative optimization algorithm proposed in this invention were verified. The specific analysis is as follows: 1. The speed and computational accuracy were optimized, specifically as follows: Figure 3 As shown, it illustrates a schematic diagram of the error variation curve, with the horizontal axis representing the number of iterations and the vertical axis representing the error value. In one instance, the error value can be represented using the root mean square error (MSE). Figure 3 The error variation curves based on three algorithms are shown, namely the convergence curve diagrams of the Gerchberg-Saxton (GS) algorithm, the apprentice descent method, and the iterative optimization algorithm provided in the embodiments of this application. Among them, although the traditional Gerchberg-Saxton (GS) algorithm has the fastest convergence speed, its optimization accuracy is much lower than that of the iterative optimization algorithm provided in the embodiments of this application. Compared with the gradient descent method, the iterative optimization algorithm provided in the embodiments of this application can achieve a lower root mean square error, i.e., higher optimization accuracy, while maintaining a comparable convergence speed. It can be seen that by introducing physical information, the optimization process is effectively constrained in the embodiments of this application, thereby significantly improving optimization accuracy while maintaining optimization speed. 2. Advantages in adaptability to non-ideal incident light, specifically as follows... Figure 4 As shown, another error variation curve is illustrated, with the horizontal axis representing the energy proportion of left-hand circular polarization (LCP) and the vertical axis representing the error value. When the incident light deviates from the ideal right-hand circular polarization (RCP), the root mean square error (RMSE) of the image optimized by the gradient descent method increases rapidly with the increase of the left-hand circular polarization energy proportion. In contrast, the iterative optimization algorithm provided in this application maintains a low RMS error regardless of the change in the left-hand circular polarization energy proportion. Traditional gradient descent methods are based on the assumption of ideal incident light; when the actual incident light deviates from the ideal state, the optimization results deteriorate significantly. The iterative optimization algorithm provided in this application, by considering the characteristics of the actual incident light during the optimization process, effectively improves robustness to non-ideal incident light, thereby ensuring image quality in practical applications. 3. Advantages in improving image quality, specifically as follows... Figure 5a and Figure 5b As shown, it illustrates hologram diagrams under different examples. When the LCP energy percentage is 0.16, as... Figure 5aAs shown, the holograms calculated by the traditional phase optimization algorithm exhibit significant quality degradation, with a root mean square error of 0.0329. After using the iterative optimization algorithm proposed in this application, as shown... Figure 5b At any given time, the holographic image quality is significantly improved, with the root mean square error reduced to 0.0012. By introducing a phase smoothing term into the objective function, phase jumps and Gibbs oscillations are effectively suppressed, further improving the uniformity of the light field and reducing the total variation (TV) loss by approximately 17%. The iterative optimization algorithm proposed in this application not only optimizes the phase distribution more accurately but also effectively improves the continuity and uniformity of the holographic image by introducing a phase smoothing term, thereby significantly improving image quality.

[0093] This application also provides a metasurface structure, which is designed using the aforementioned metasurface structure design method.

[0094] Other details regarding this metasurface structure can be found in the descriptions of the foregoing embodiments, and will not be repeated here.

[0095] The metasurface structure provided in this application can be used in the field of holographic display. It can be applied to real-time hologram generation and dynamic display systems. Addressing the problems of large computational latency and low spatial bandwidth product in existing holographic algorithms, the parallelized phase optimization capability of the geometric phase metasurface structure provided in this application enables functions such as real-time rendering and resolution enhancement.

[0096] The metasurface structure provided in this application can be used in the field of Gaussian beam shaping into flat-top beams. It can also be used for phase optimization of beam-shaping metasurfaces. Flat-top beams, due to their uniform energy distribution and steep edges, exhibit unique advantages in many fields such as laser material processing, optical metrology and detection, and biomedicine. The metasurface structure provided in this application can achieve beam-shaping metasurfaces with high uniformity, high edge steepness, and high energy utilization.

[0097] The metasurface structure provided in this application embodiment can also be used in lithography systems. The metasurface structure provided in this application embodiment can be applied to the design of wavefront shaping and polarization modulation devices in semiconductor lithography machines. In high-NA lithography processes, wavefront distortion and polarization state inhomogeneity of the incident light field significantly reduce the resolution and linewidth consistency of the lithographic pattern. Based on the metasurface structure provided in this application embodiment, it can replace traditional refractive / diffractive optical elements, achieving light field shaping through high-precision phase gradient distribution design, effectively reducing phase modulation losses, reducing the size and complexity of the optical path system, and simultaneously reducing assembly and adjustment errors of multilayer optical elements.

[0098] The metasurface structure provided in this application can also be used in super-resolution microscopy imaging equipment. The iterative optimization algorithm proposed in this metasurface structure design method can improve the performance of super-resolution microscopy imaging equipment. Specifically, it can integrate phase difference imaging, fluorescence excitation, and structured light illumination functions in the same device through phase optimization design of metalenses, supporting simultaneous detection of multiple parameters of biological samples; and it can also break through the optical diffraction limit and improve resolution by utilizing Bessel beams or vortex light fields generated by the algorithm.

[0099] The metasurface structure provided in this application can also be used in the field of microparticle manipulation light sources. The metasurface structure provided in this application can optimize optical force-based micro / nano particle manipulation systems, enabling non-contact capture and manipulation of nanoscale particles. By optimizing the topology of the metasurface unit through iterative optimization algorithms, a high-modal-purity vortex beam is generated, supporting stable particle capture. Simultaneously, phase gradient optimization increases the optical tweezers capture force by 2-5 times, reducing laser power requirements and avoiding photothermal damage.

[0100] The design process of metasurface structures is described below using some actual data: In the first example, it is necessary to realize anisotropic deep ultraviolet holograms based on femtosecond laser-induced nanopores. To achieve this, the target metasurface structure needs to: use the target metasurface to phase-modulate incident 193nm deep ultraviolet light and reconstruct the target image on the image plane.

[0101] The design method provided in the embodiments of this application may include the following steps: First, the target image and actual physical parameters are determined: Before conducting computer simulation, the actual physical parameters need to be determined, including: wavelength 193nm, hologram size and simulation area size 600×600, single pixel size 3um, imaging plane distance from hologram 0.35m, target image is a designated marker, and incident light field distribution is planar light.

[0102] Secondly, the diffraction algorithm is determined based on the physical parameters. There are three commonly used diffraction calculation algorithms: Fraunhofer diffraction, Fresnel diffraction, and angular spectrum diffraction. These three algorithms can be applied to different scenarios. Fraunhofer diffraction is suitable when the observation screen is very far from the diffracting object; in this case, the diffracted wave propagating from the hologram to the observation screen can be approximated as a plane wave. Fresnel diffraction is suitable when the distance from the light source or observation screen to the diffracting object is finite, and the Fraunhofer far-field condition is not met. In this case, the second phase factor needs to be considered in the calculation to describe the bending of the wave during propagation. Angular spectrum diffraction is suitable for diffraction calculations at arbitrary propagation distances, including near-field, mid-field, and far-field. However, in computer simulations, it is usually based on Fourier transform for fast calculation. Attention needs to be paid to the sampling rate of the input and output planes to avoid frequency domain aliasing; therefore, it is usually used when calculating near-range diffraction. The physical parameters provided in the above example are not suitable for Fraunhofer diffraction but are suitable for Fresnel diffraction; therefore, Fresnel diffraction will be used in subsequent diffraction calculations.

[0103] Secondly, the physical parameters such as the bi-principal-axis complex transmittance of the actual structural unit were confirmed. Methods for obtaining the physical parameters of the actual structural unit include both numerical simulation of the electromagnetic field and experimental measurement. FDTD is a typical numerical simulation method that directly solves Maxwell's equations in the time domain. It discretizes space and time into a mesh and uses staggered meshes and time steps to iteratively calculate the propagation and interaction of the electromagnetic field in complex structures and materials. In this example, randomly distributed nanopores exist, making modeling difficult; therefore, experimental measurement was used to determine the bi-principal-axis transmittance.

[0104] Next, determine the loss function: First, it's necessary to define the optimization objective, including objectives related to holographic image quality and physical constraints. Commonly used metrics for evaluating holographic image quality include mean square error (MSE), peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM), each suitable for different scenarios. MSE measures the average of the squared differences between corresponding pixel values ​​in the distorted image and the original image; it's simple and direct to calculate, with a clear mathematical meaning. PSNR represents the ratio of the maximum possible power of a signal to the power of destructive noise that affects its representation accuracy; it's commonly used to measure the performance of image compression and reconstruction algorithms. SSIM measures the similarity between two images in terms of brightness, contrast, and structure, better aligning with human visual perception and reflecting the perceived quality of the image. In this example, we primarily evaluate the quality of the reconstructed hologram, and PSNR can be used as the evaluation metric for holographic image quality.

[0105] In this example, the main physical constraints to consider are the difference in transmittance between the two principal axes and the phase order (phase continuity). First, the Jones matrix corresponding to the complex transmittance of the current structural unit's two principal axes is calculated. Then, the incident light distribution is multiplied by the Jones matrix, thus introducing the complex transmittance of the two principal axes into the phase distribution optimization. Second, the phase order needs to be determined based on the actual processing scheme. Then, after each phase update, a mapping is performed to transform the continuous phase distribution into a discrete distribution. In this example, the phase is close to a continuous distribution, but excessively large differences between adjacent phases will lead to a mismatch between processing and design. Therefore, a total variation loss is introduced to make the phase distribution smoother.

[0106] Then, the iterative optimization algorithm provided in this application embodiment is used to calculate the hologram phase distribution: a single calculation consists of two parts: forward propagation and parameter update. Forward propagation includes first calculating the hologram image corresponding to the current hologram based on the aforementioned physical parameters and the determined diffraction calculation scheme, and then calculating the difference between the current hologram image and the target hologram image based on the loss function. Parameter update includes calculating the gradient of the current hologram phase distribution with respect to the loss based on the chain rule and the current loss, and updating the phase distribution of each point based on the gradient. The above process is repeated until the loss is lower than the set value or the number of iterations exceeds the upper limit.

[0107] Finally, hologram fabrication is achieved based on the determined metasurface structure: metasurface structure holograms can be fabricated using femtosecond laser processing technology. The high peak power of femtosecond lasers can induce nanoscale porous structures within transparent materials such as fused silica. By precisely controlling laser parameters such as energy, pulse number, and polarization direction, the arrangement and shape of the nanopores can be adjusted. The anisotropic nanopore structure leads to birefringence, thereby introducing geometric phase. After directly writing the corresponding phase distribution using ultrafast lasers, annealing further enhances the transmittance of the metasurface in the ultraviolet band.

[0108] The above describes the entire process of implementing the first example. The above method can be used to realize anisotropic nanopore deep ultraviolet holograms based on femtosecond laser-induced methods.

[0109] In the second example, there is a need to achieve flat-top beam shaping based on a phase metasurface. The objectives for this requirement are to convert an incident Gaussian laser beam (wavelength 808 nm) into a flat-top beam with high homogeneity and steep edges within the target plane, while achieving an energy efficiency of >90%.

[0110] In this example, the target parameters are defined as follows: Flat-top region size: square region, width 300μm; Uniformity index: light intensity fluctuation within the target plane ≤ ±5%; Edge steepness: 10%-90% intensity rise distance ≤ 3μm.

[0111] First, the structural unit is designed and simulated: the structural unit can be composed of a silicon dioxide substrate and gold nanopillars on it. The length and width of a single structural unit are both 400 nm, while the length and width of the nanopillars on the substrate are variable, ranging from 200 to 280 nm. The electromagnetic response corresponding to all nanopillar dimensions is simulated using FDTD, and two directions with a phase difference of [missing value] are selected. The set of parameters that has the highest average transmittance in both directions. The transmittance in the two directions can then be expressed as Ax and Ay.

[0112] Secondly, the loss function is determined: the quality of the flat-top beam is mainly quantified by the deviation of uniformity, edge steepness and energy utilization. In actual design, all three factors are considered.

[0113] The relative standard deviation (RSD) is used as the loss function to optimize the uniformity of the flat-top light: ; Where N represents the number of pixels. This represents the average light intensity.

[0114] Width-penalized loss (WPL) is used as the loss function to optimize edge steepness: ; Where M represents the number of pixels in the edge region. This represents the gradient value of the edge region.

[0115] Use the energy loss rate as the loss function to optimize energy utilization: ; in, This represents the total energy of the flat-top section. This represents the total energy of the incident light.

[0116] Then, the metasurface phase distribution is calculated based on an iterative optimization algorithm: based on actual physical parameters, simulated structural unit parameters, and a loss function, the optimal phase distribution is calculated using the iterative optimization algorithm provided in this application embodiment. After a certain number of iterations, the light intensity fluctuation in the flat-top region is 4.9%, the intensity rise distance from 10% to 90% is <3µm, and the energy utilization rate is 91.6%, all of which meet the target. The iteration terminates, and the phase distribution is output.

[0117] Finally, metasurface fabrication was performed based on the designed phase distribution. The metasurface fabrication process is as follows: First, a 1200 nm thick commercial silicon-on-insulator (SOI) wafer was transferred onto a glass substrate via adhesive wafer bonding and deep reactive ion etching (DRIE). Next, the device layer thickness was further reduced to 600 nm using inductively coupled plasma (ICP) technology. To fabricate the metasurface structure pattern, a 300 nm thick layer of hydrogen silsesquioxane (HSQ) was spin-coated onto the substrate at 4000 rpm and baked on a hot plate at 90°C for 5 minutes. Then, a 30 nm thick aluminum layer was deposited via thermal evaporation as a charge dissipation layer. Finally, the pattern was exposed using electron beam lithography (EBL). After exposure, the aluminum layer was removed using 5% phosphoric acid, and the sample was developed using tetramethylammonium hydroxide solution. Finally, the sample was etched using inductively coupled plasma (ICP) technology.

[0118] In this embodiment, a physical model for compensating for the transmittance difference between the two principal axes can be incorporated into the iterative optimization algorithm, thereby constructing an optimization framework that better reflects the actual fabrication of metasurfaces. This physical model can accurately predict the changes in the optical field caused by the transmittance difference between the two principal axes, thus enabling more accurate adjustment of the phase distribution of the metasurface during the optimization process. Furthermore, this physical model can provide effective gradient information or constraints, accelerating algorithm convergence and improving optimization accuracy. This combination of the physical model and the iterative optimization algorithm effectively solves the problem of performance degradation of traditional optimization algorithms in actual metasurface fabrication, providing strong support for high-quality metasurface design.

[0119] Furthermore, to improve the convergence speed and stability of the iterative optimization algorithm, a strategy combining momentum and adaptive learning rate adjustment is employed in the optimization process. This strategy independently adapts the learning rate for each parameter of the model by tracking the first moment (the mean used to calculate the light intensity error) and the second moment (the variance used to calculate the total variation loss). The first moment, acting as momentum, accelerates model convergence and effectively mitigates oscillations in parameter update directions; the second moment normalizes the gradient magnitude, ensuring smooth updates for sparse or frequently changing gradients. This adaptive learning rate adjustment strategy not only promotes rapid model convergence but also significantly reduces the reliance on manual learning rate adjustments, improving the algorithm's robustness and ease of use.

[0120] Furthermore, to improve the continuity and uniformity of the holographic image, a phase smoothing term (total variation loss term) was introduced into the objective function used to update the rotation angle, and its weights were optimized. The phase smoothing term can effectively suppress phase jumps and Gibbs oscillations, thereby improving image quality. By optimizing the weights of the phase smoothing term, a balance can be achieved between image quality and computational complexity, resulting in optimal optimization. This strategy of introducing a phase smoothing term and optimizing its weights provides an effective technical means for generating high-quality holographic images.

[0121] Furthermore, embodiments of this application also provide a computer-readable storage medium storing a computer program, which, when run by a processor, executes the steps of the metasurface structure design method described in the above method embodiments.

[0122] The computer program product of the metasurface structure design method provided in this application includes a computer-readable storage medium storing program code. The instructions included in the program code can be used to execute the steps of the metasurface structure design method described in the above method embodiments. For details, please refer to the above method embodiments, which will not be repeated here.

[0123] In the several embodiments provided in this application, it should be understood that the disclosed methods can also be implemented in other ways. The method embodiments described above are merely illustrative. For example, the flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of methods and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram and / or flowchart, and combinations of blocks in block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0124] In addition, the method steps in the various embodiments of this application can be integrated together to form an independent part for execution, or each method step can be executed by a separate module, or two or more steps can be formed into an independent part for execution.

[0125] If the aforementioned functions are implemented as software functional modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks. It should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element. The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application. It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0126] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A metasurface structure design method, characterized in that, include: Initialize the rotation angle of the metasurface structure; First light field construction step: Construct the transmission light relationship of the current metasurface structure based on the rotation angle; The second light field construction step is to construct the diffraction light relationship of the current metasurface structure based on the transmitted light relationship, so as to determine the light intensity distribution of the image plane. Error construction steps: Calculate the iterative constraint value based on the image plane light intensity distribution and the target light intensity; wherein, the target light intensity is a pre-parameter, the target light intensity is the light intensity corresponding to the target metasurface structure, and the target metasurface structure is the design target; If the iterative constraint value is determined to be greater than the set value, the rotation angle is updated to obtain the updated rotation angle, and the first light field construction step, the second light field construction step, and the error construction step are repeated until the iterative constraint value is not greater than the set value, and the target metasurface structure is determined based on the current rotation angle.

2. The method according to claim 1, characterized in that, in, The iterative constraint values ​​include: light intensity error and total variation loss; The step of calculating the iterative constraint value based on the image plane light intensity distribution and the target light intensity includes: The light intensity error is determined based on the difference between the light intensity distribution on the image plane and the target light intensity. The total variation loss is determined based on the rotation angles of each nanostructure in the current metasurface structure.

3. The method according to claim 2, characterized in that, The determination of light intensity error based on the difference between the image plane light intensity distribution and the target light intensity includes: For the first coordinate, calculate the current light intensity of the current metasurface structure at the first coordinate and the square of the light intensity difference between it and the target light intensity of the target metasurface structure at the first coordinate; wherein, the first coordinate is the coordinate of any nanostructure in the two-dimensional coordinate of the target metasurface structure; The light intensity error is obtained by summing the squares of the light intensity differences of all nanostructures in the two-dimensional coordinates of the target metasurface structure.

4. The method according to claim 2, characterized in that, The determination of the total variation loss based on the rotation angles of each nanostructure in the current metasurface structure includes: Calculate the squared difference of the rotation angles between adjacent coordinates of each nanostructure of the current metasurface structure; The total variation loss of the current metasurface structure is determined based on the squared difference of the rotation angles at each adjacent coordinate.

5. The method according to claim 2, characterized in that, The step of updating the rotation angle to obtain the updated rotation angle includes: The updated rotation angle is calculated by combining the light intensity error, the total variation loss, and the current rotation angle.

6. The method according to claim 5, characterized in that, The calculation of the updated rotation angle, combining the light intensity error, the total variation loss, and the current rotation angle, includes: The sum of the light intensity error and the total variation loss is differentiated with respect to the rotation angle to obtain the iterative difference value; The rotation angle of the updated nanostructure is calculated based on the iterative difference and the rotation angle of the nanostructure on the current metasurface.

7. The method according to claim 1, characterized in that, The construction of the transmission light relationship of the current metasurface structure based on the rotation angle includes: Based on the rotation angle, the Jones matrix corresponding to each nanostructure of the current metasurface structure is constructed; Based on the Jones matrix, the transmission light relationship of the current metasurface structure is determined.

8. The method according to claim 7, characterized in that, The determination of the transmission light relationship of the current metasurface structure based on the Jones matrix includes: Based on the incident light and the Jones matrix, the transmission light relationship of the current metasurface structure is determined.

9. The method according to claim 1, characterized in that, The step of constructing the diffraction relationship of the current metasurface structure based on the transmitted light relationship, in order to determine the light intensity distribution on the image plane, includes: The Fresnel diffraction relation is obtained by integrating the product of the transmitted light relation and the diffraction transfer function. The light intensity distribution on the image plane is determined based on the Fresnel diffraction relation.

10. A metasurface structure, characterized in that, It is designed using the method described in any one of claims 1-9.

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