CN113642197B - A Spectral Analysis-Based Metasurface Construction Method - Google Patents

Abstract

The invention discloses a metasurface construction method based on spectral analysis. By acquiring incident beam information, the incident surface electromagnetic field distribution data is determined according to the incident beam information; the target beam information is acquired, and the exit surface electromagnetic field distribution data is determined according to the target beam information; The electromagnetic field distribution data of the surface and the electromagnetic field distribution data of the exit surface are used to construct a metasurface. The invention determines the respective electromagnetic field distributions of the incident surface and the outgoing surface of the metasurface by analyzing the incident beam and the target beam. Since the electromagnetic field distribution is closely related to the structural characteristics of the metasurface, the structural characteristics of the metasurface can be determined based on the respective electromagnetic field distributions of the incident surface and the exit surface, and then the construction of the metasurface can be realized. The invention does not need to carry out simulation optimization, and solves the problem of consuming a large amount of calculation cost and time cost by using commercial software to carry out simulation optimization on each structural unit on the metasurface when constructing the metasurface in the prior art.

Description

A Spectral Analysis-Based Metasurface Construction Method

technical field

The invention relates to the technical field of optical devices, in particular to a method for constructing a metasurface based on spectral analysis.

Background technique

In recent years, new metasurfaces composed of artificial materials have received extensive attention from academia and industry in the past 20 years due to their low profile, thinness, and ease of installation, and have made great progress and development. Metasurface/metalens can realize multi-feed multi-beam, single feed multi-beam and other functions by modulating the surface phase. Because the function of each structural unit on the metasurface is different, the physical parameters of each structural unit are also different, so the construction of non-uniform metasurfaces is a difficult problem in the scientific research and technology community. In the prior art, commercial software is usually used to simulate and optimize each structural unit on the metasurface, so as to complete the construction of the metasurface, resulting in the construction process that consumes a lot of computational cost and time cost.

Therefore, the existing technology still needs to be improved and developed.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide a method for constructing a metasurface based on spectral analysis, aiming at the above-mentioned defects of the prior art. The simulation optimization of each structural unit leads to the problem of consuming a lot of computational cost and time cost.

The technical scheme adopted by the present invention to solve the problem is as follows:

In a first aspect, an embodiment of the present invention provides a method for constructing a metasurface based on spectral analysis, wherein the method includes:

acquiring incident beam information, and determining the electromagnetic field distribution data on the incident surface according to the incident beam information;

acquiring target beam information, and determining the electromagnetic field distribution data on the exit surface according to the target beam information;

A metasurface is constructed according to the electromagnetic field distribution data on the incident surface and the electromagnetic field distribution data on the exit surface.

In an embodiment, the determining the electromagnetic field distribution data on the incident surface according to the incident beam information includes:

According to the incident beam information, determine the angular spectral domain electromagnetic field distribution data of the incident beam;

According to the electromagnetic field distribution data in the angular spectrum domain, the electromagnetic field distribution data on the incident surface is determined.

In an embodiment, the determining, according to the incident beam information, the angular spectral domain electromagnetic field distribution data of the incident beam includes:

determining, according to the incident beam information, first spatial domain electromagnetic field distribution data corresponding to a source field, where the source field is used to transmit the incident beam;

Through Fourier transform, the electromagnetic field distribution data in the first spatial domain is converted into the angular spectral domain to obtain the electromagnetic field distribution data in the angular spectral domain.

In an embodiment, the determining the electromagnetic field distribution data on the incident surface according to the electromagnetic field distribution data in the angular spectrum domain includes:

Phase accumulation is performed on the electromagnetic field distribution data in the angular spectrum domain to obtain the electromagnetic field distribution data on the incident surface.

In an embodiment, the determining the electromagnetic field distribution data on the exit surface according to the target beam information includes:

According to the target beam information, determine the electromagnetic field distribution data in the second spatial domain corresponding to the target far field, wherein the target far field is the space where the target beam is located;

Inverse Fourier transform is performed on the electromagnetic field distribution data in the second spatial domain to obtain the electromagnetic field distribution data on the exit surface.

In an embodiment, performing inverse Fourier transform on the electromagnetic field distribution data in the second spatial domain to obtain the electromagnetic field distribution data on the exit surface includes:

Converting the electromagnetic field distribution data in the second space domain to a Cartesian coordinate system to obtain Cartesian electromagnetic field distribution data;

performing inverse Fourier transform on the Cartesian electromagnetic field distribution data to obtain initial electromagnetic field distribution data;

Iterative calculation is performed on the initial electromagnetic field distribution data to obtain the electromagnetic field distribution data on the exit surface.

In an embodiment, the iterative calculation of the initial electromagnetic field distribution data to obtain the electromagnetic field distribution data of the exit surface includes:

The amplitude of the initial electromagnetic field distribution data is fixed to a preset amplitude, and the phase of the initial electromagnetic field distribution data is iteratively calculated to obtain the electromagnetic field distribution data of the exit surface.

In one embodiment, the metasurface includes several structural units, and the construction of the metasurface according to the electromagnetic field distribution data on the incident surface and the electromagnetic field distribution data on the exit surface includes:

According to the electromagnetic field distribution data on the incident surface and the electromagnetic field distribution data on the exit surface, determine the target physical parameter corresponding to each of the structural units;

According to the target physical parameters corresponding to each of the structural units, determine the target structural parameters corresponding to each of the structural units;

The metasurface is constructed according to target structural parameters corresponding to several structural units respectively.

In an embodiment, the determining the target physical parameter corresponding to each of the structural units according to the electromagnetic field distribution data on the incident surface and the electromagnetic field distribution data on the exit surface includes:

According to the electromagnetic field distribution data on the incident surface and the electromagnetic field distribution data on the exit surface, determine the initial physical parameters corresponding to each of the structural units;

An optimization objective is determined, and initial physical parameters corresponding to each of the structural units are iteratively calculated according to the optimization objective to obtain target physical parameters corresponding to each of the structural units.

In an embodiment, the determining the initial physical parameter corresponding to each of the structural units according to the electromagnetic field distribution data on the incident surface and the electromagnetic field distribution data on the exit surface includes:

determining a transmission matrix according to the electromagnetic field distribution data on the incident surface and the electromagnetic field distribution data on the exit surface;

According to the transmission matrix, an initial physical parameter corresponding to each of the structural units is determined.

In one embodiment, the optimization objectives include several optimization objectives, and the iterative calculation of the initial physical parameters corresponding to each of the structural units according to the optimization objectives includes:

Inputting the initial physical parameters corresponding to each of the structural units into a multi-objective optimization algorithm corresponding to several of the optimization objectives;

The initial physical parameters corresponding to each of the structural units are iteratively calculated by the multi-objective optimization algorithm.

In an embodiment, the determining the target structural parameter corresponding to each structural unit according to the target physical parameter corresponding to each structural unit includes:

Input the target physical parameters corresponding to each of the structural units into the parameter extraction optimization algorithm;

The target structural parameter corresponding to each structural unit is output through the parameter extraction optimization algorithm.

In a second aspect, an embodiment of the present invention further provides a metasurface construction system based on spectral analysis, wherein the system includes:

an incident surface calculation module, configured to acquire incident beam information, and determine the incident surface electromagnetic field distribution data according to the incident beam information;

an exit surface calculation module, configured to acquire target beam information, and determine the electromagnetic field distribution data of the exit surface according to the target beam information;

A metasurface building module, configured to construct a metasurface according to the electromagnetic field distribution data on the incident surface and the electromagnetic field distribution data on the exit surface.

In a third aspect, an embodiment of the present invention further provides a metasurface, wherein the metasurface is constructed using the method for constructing a metasurface based on spectral analysis as described above.

In a fourth aspect, an embodiment of the present invention further provides a computer-readable storage medium on which a plurality of instructions are stored, wherein the instructions are suitable for being loaded and executed by a processor to implement any of the above-mentioned spectrum-based Analysis of the steps of the metasurface construction method.

Beneficial effects of the present invention: In the embodiment of the present invention, by acquiring incident beam information, the incident surface electromagnetic field distribution data is determined according to the incident beam information; the target beam information is acquired, and the emission surface electromagnetic field distribution data is determined according to the target beam information; according to the incident surface electromagnetic field distribution data and The electromagnetic field distribution data of the exit surface is used to construct a metasurface. The invention determines the respective electromagnetic field distributions of the incident surface and the outgoing surface of the metasurface by analyzing the incident beam and the target beam. Since the electromagnetic field distribution is closely related to the structural characteristics of the metasurface, the structural characteristics of the metasurface can be determined based on the respective electromagnetic field distributions of the incident surface and the exit surface, and then the construction of the metasurface can be realized. The present invention does not need to perform simulation optimization, and solves the problem of consuming a large amount of calculation cost and time cost by using commercial software to perform simulation optimization on each structural unit on the metasurface when constructing the metasurface in the prior art.

Description of drawings

In order to explain the embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments described in the present invention. For those of ordinary skill in the art, other drawings can also be obtained based on these drawings without any creative effort.

FIG. 1 is a schematic flowchart of a method for constructing a metasurface based on spectral analysis provided by an embodiment of the present invention.

FIG. 2 is a schematic diagram of the relationship among the source field, the metasurface, and the far field provided by an embodiment of the present invention.

FIG. 3 is a schematic diagram of Fourier optics provided by an embodiment of the present invention.

FIG. 4 is a schematic diagram of obtaining the phase distribution of the ideal exit surface of the metasurface/metalens by using the limiting amplitude G-S algorithm according to an embodiment of the present invention.

FIG. 5 is a schematic diagram of a complete flow of a metasurface construction method based on spectral analysis provided by an embodiment of the present invention.

FIG. 6 is a schematic diagram of a working principle of a metasurface provided by an embodiment of the present invention.

FIG. 7 is a schematic diagram of a result of a multi-objective optimization algorithm provided by an embodiment of the present invention.

FIG. 8 is a schematic diagram of a Pareto improvement edge provided by an embodiment of the present invention.

FIG. 9 is a schematic diagram of modules inside a metasurface construction system based on spectral analysis provided by an embodiment of the present invention.

FIG. 10 is a functional block diagram of a terminal provided by an embodiment of the present invention.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer and clearer, the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

It should be noted that if there are directional indications (such as up, down, left, right, front, back, etc.) involved in the embodiments of the present invention, the directional indications are only used to explain a certain posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication also changes accordingly.

In recent years, new metasurfaces composed of artificial materials have received extensive attention from academia and industry in the past 20 years due to their low profile, thinness, and ease of installation, and have made great progress and development. Metasurface/metalens can realize multi-feed multi-beam, single feed multi-beam and other functions by modulating the surface phase. Because the function of each structural unit on the metasurface is different, the physical parameters of each structural unit are also different, so the construction of non-uniform metasurfaces is a difficult problem in the scientific research and technology community. In the prior art, commercial software is usually used to simulate and optimize each structural unit on the metasurface, so as to complete the construction of the metasurface, resulting in the construction process that consumes a lot of computational cost and time cost.

In view of the above-mentioned defects of the prior art, the present invention provides a metasurface construction method based on spectral analysis. The method obtains incident beam information and determines incident surface electromagnetic field distribution data according to the incident beam information; The target beam information determines the electromagnetic field distribution data on the exit surface; the metasurface is constructed according to the electromagnetic field distribution data on the entrance surface and the electromagnetic field distribution data on the exit surface. Since the main function of the meta-lens is to modulate electromagnetic waves, the present invention determines the respective electromagnetic field distributions of the incident surface and the outgoing surface of the meta-surface by analyzing the incident beam and the target beam. Since the electromagnetic field distribution is closely related to the structural characteristics of the metasurface, the structural characteristics of the metasurface can be determined based on the respective electromagnetic field distributions of the incident surface and the exit surface, and then the construction of the metasurface can be realized. The present invention does not need to perform simulation optimization, and solves the problem of consuming a large amount of calculation cost and time cost by using commercial software to perform simulation optimization on each structural unit on the metasurface when constructing the metasurface in the prior art.

As shown in Figure 1, the method includes the following steps:

Step S100 , acquiring incident beam information, and determining the electromagnetic field distribution data on the incident surface according to the incident beam information.

Specifically, the incident beam refers to the beam emitted from the source field, and since the properties of the source field are known, the incident beam is also determined. The goal of this embodiment is to construct a metasurface, through which the incoming beam emitted from the source field is modulated, so that the modulated outgoing beam meets the preset condition when reaching the target far field. Since the information of the incident beam can reflect the relevant characteristics of the incident beam, the state of the incident beam when it reaches the incident surface of the metasurface can be calculated based on the information of the incident beam, and then the electromagnetic field distribution of the incident surface can be determined, that is, the electromagnetic field distribution data of the incident surface can be obtained.

In an implementation manner, the step S100 specifically includes the following steps:

Step S101, according to the incident beam information, determine the angular spectral domain electromagnetic field distribution data of the incident beam;

Step S102: Determine the electromagnetic field distribution data on the incident surface according to the electromagnetic field distribution data in the angular spectrum domain.

Because there is usually a certain spatial distance between the source field and the metasurface, that is, the incident beam will reach the incident surface of the metasurface after a certain transmission distance after being emitted from the source field. Therefore, in this embodiment, it is necessary to first determine the initial state of the incident beam when it emerges from the source field, and then calculate the state of the incident beam when it reaches the incident surface of the metasurface after this transmission distance, so as to determine the electromagnetic field distribution on the incident surface. Since the electromagnetic field distribution data in the angular spectrum domain can reflect the energy distribution of the incident beam in all directions after exiting the source field, the electromagnetic field distribution data in the angular spectrum domain can intuitively decompose the incident beam into plane waves propagating in all directions (as shown in Figure 3). Therefore, in this embodiment, it is necessary to first determine the electromagnetic field distribution data in the angular spectral domain according to the incident beam information, and then calculate the state of the plane waves in all directions when they reach the incident surface of the metasurface based on the electromagnetic field distribution data in the angular spectral domain, so as to determine the incident surface. The electromagnetic field distribution data of the incident surface can be obtained.

In an implementation manner, the step S101 specifically includes the following steps:

Step S1011: Determine the electromagnetic field distribution data in the first spatial domain corresponding to the source field according to the incident beam information, wherein the source field is used to transmit the incident beam;

Step S1012 , converting the electromagnetic field distribution data in the first spatial domain into an angular spectral domain through Fourier transform to obtain the electromagnetic field distribution data in the angular spectral domain.

Specifically, as shown in FIG. 2 , since both the source field and the incident beam are known and determined, the relevant characteristic information of the incident beam, that is, the incident beam information, is also determined. Therefore, the electromagnetic field distribution corresponding to the spatial domain where the source field is located may be determined based on the incident beam information, that is, the electromagnetic field distribution data in the first spatial domain can be obtained. Since the Fourier components of the incident beam at different spatial frequencies can be regarded as plane waves propagating in different directions, the electromagnetic field distribution in the spatial domain can be converted into the electromagnetic field distribution in the angular spectral domain through Fourier transform, that is, the angular spectral domain can be obtained. Electromagnetic field distribution data.

For example, as shown in Figure 3, it is known that the electromagnetic field distribution in the spatial domain of the origin plane (z = 0) is E(x, y, 0), and the electromagnetic field distribution in the spatial domain can be converted to the angular spectral domain through spectral transformation to obtain the origin The electromagnetic field distribution in the angular spectral domain corresponding to the surface E(kx,ky,0), the conversion formula is as follows:

In an implementation manner, the step S102 specifically includes the following steps:

Step S1021: Perform phase accumulation on the electromagnetic field distribution data in the angular spectrum domain to obtain the electromagnetic field distribution data on the incident surface.

Specifically, since there is a certain transmission distance between the source field of the emitted beam and the metasurface, the phase of the incident beam will change to a certain extent when it reaches the metasurface incident surface through this transmission distance after exiting from the source field. Therefore, in this embodiment, the electromagnetic field distribution data on the incident surface is obtained by performing phase accumulation on the plane waves in each propagation direction based on the decomposition of the incident beam.

For example, as shown in Figure 3, the plane z' is the incident surface of the metasurface. When the electromagnetic field distribution in the space where the plane z = z' is required (ie, the electromagnetic field distribution of the incident surface) needs to be obtained, the phase accumulation is realized by the following formula, and the solution The electromagnetic field distribution of the incident surface:

、

分别为电磁波沿着x-方向和y-方向的波数，

为限制函数，确保

。位移项

表征了电磁波在传播过程中的相位累积。in,

,

are the wave numbers of the electromagnetic wave along the x-direction and y-direction, respectively,

To limit the function, make sure

. displacement term

The phase accumulation of electromagnetic waves during propagation is characterized.

As shown in Figure 1, the method further includes the following steps:

Step S200: Obtain target beam information, and determine the electromagnetic field distribution data on the exit surface according to the target beam information.

Specifically, the target beam information is determined based on the modulation task, which can reflect the state that the outgoing beam modulated by the metasurface needs to present when it reaches the far field of the target. The state of the beam is obtained to obtain the electromagnetic field distribution of the exit surface, that is, to obtain the electromagnetic field distribution data of the exit surface.

In an implementation manner, the step S200 specifically includes the following steps:

Step S201: Determine electromagnetic field distribution data in the second spatial domain corresponding to the target far field according to the target beam information, wherein the target far field is the space where the target beam is located;

Step S202: Perform inverse Fourier transform on the electromagnetic field distribution data in the second spatial domain to obtain the electromagnetic field distribution data on the exit surface.

Specifically, since the target beam information can reflect the state of the beam existing in the target far field, the electromagnetic field distribution in the space where the target far field is located can be determined based on the target beam information, that is, the electromagnetic field distribution data in the second spatial domain can be determined. In order to infer the state of the beam exiting from the exit surface of the metasurface inversely from the far field of the target, in this embodiment, it is necessary to perform inverse Fourier transform on the electromagnetic field distribution data in the second spatial domain, so as to obtain the beam exiting from the exit surface of the metasurface. The initial state, and the electromagnetic field distribution of the exit surface is determined based on this, that is, the electromagnetic field distribution data of the exit surface is obtained.

In an implementation manner, the step S202 specifically includes the following steps:

Step S2021, converting the electromagnetic field distribution data in the second spatial domain into a Cartesian coordinate system to obtain Cartesian electromagnetic field distribution data;

Step S2022, performing inverse Fourier transform on the Cartesian electromagnetic field distribution data to obtain initial electromagnetic field distribution data;

Step S2023: Perform iterative calculation on the initial electromagnetic field distribution data to obtain the electromagnetic field distribution data on the exit surface.

Specifically, in order to solve the initial state when the beam exits from the exit surface of the metasurface, in this embodiment, it is first necessary to convert the electromagnetic field distribution in the space of the target far field into the electromagnetic field distribution in the Cartesian coordinate system to obtain the Cartesian electromagnetic field distribution data , thereby transforming the problem to be solved into a function solving problem. Then, the inverse Fourier transform is performed on the Cartesian electromagnetic field distribution data to obtain the initial electromagnetic field distribution data, and the initial electromagnetic field distribution data is iteratively optimized until it meets the electromagnetic field distribution of the exit surface corresponding to the target far field. The electromagnetic field distribution data on the exit surface can be obtained.

In an implementation manner, the step S2023 specifically includes the following steps:

Step S20231: Fix the amplitude of the initial electromagnetic field distribution data to a preset amplitude, and perform an iterative calculation on the phase of the initial electromagnetic field distribution data to obtain the electromagnetic field distribution data of the exit surface.

For the front surface design of the metasurface exit surface, it is too complicated to control the changes of the amplitude and phase at the same time. In order to reduce the calculation cost, this embodiment adopts an iterative algorithm for limiting the amplitude, that is, the amplitude of the initial electromagnetic field distribution data. Fixed, only iteratively calculates its phase until it converges to the ideal phase, and obtains the electromagnetic field distribution data on the exit surface. The preset amplitude value may be set according to the modulation task, for example, the preset amplitude value may be set according to the amplitude distribution from the source field to the incident surface in a lossless condition.

Specifically, the iterative algorithm for limiting the amplitude used in this embodiment is the amplitude limiting optimization scheme of the Gerchberg-Saxton algorithm. For ease of understanding, this embodiment provides a step flow of the algorithm:

1. Transform the desired far-field pattern to a Cartesian coordinate system.

2. Inverse Fourier transform the pattern in the Cartesian coordinate system to the near field.

3. Replace the amplitude distribution of the near field with the amplitude distribution of the feed propagating to the incident surface without loss.

4. The far field resulting from the near field distribution after the Fourier transform is replaced. and replace the magnitude of the far field with the magnitude of the desired far field.

5. Repeat steps 2-4 until convergence.

For example, as shown in Figure 4, first determine the target to obtain an elliptical far-field distribution, and then force the electromagnetic field amplitude distribution of the exit surface of the metasurface to be a Gaussian distribution, and through iterative calculation, finally obtain the target far-field distribution. Radiation, phase distribution at the exit surface of the field.

In an implementation manner, for the processing of the inverse Fourier transform from the far field to the exit surface, in addition to the optimized iterative algorithm, a non-iterative algorithm such as direct amplitude encoding (Direct Amplitude Encoding) may also be used.

As shown in Figure 1, the method further includes the following steps:

Step S300 , constructing a metasurface according to the electromagnetic field distribution data on the incident surface and the electromagnetic field distribution data on the exit surface.

Specifically, the goal of this embodiment is to calculate the electromagnetic field distribution data of the incident surface by forward analyzing the propagation process of the incident beam from the known source field to the incident surface of the metasurface, and then determine the front surface of the metasurface incident surface. Design: By reversely analyzing the back-propagation process of the target beam from the target far field to the exit surface of the metasurface, the electromagnetic field distribution data of the exit surface is calculated, and the front design of the exit surface of the metasurface is determined. Finally, a metasurface that can complete the modulation task is constructed according to the calculated front surface design of the incident surface and the output surface. After the construction is completed, the incident beam propagates from the source field to the metasurface, and after the modulation of the metasurface, it exits and propagates to the target far field, and the target beam can be obtained.

In an implementation manner, the metasurface includes several structural units, and the step S300 specifically includes the following steps:

Step S301, according to the electromagnetic field distribution data on the incident surface and the electromagnetic field distribution data on the exit surface, determine the target physical parameter corresponding to each of the structural units;

Step S302, according to the target physical parameter corresponding to each described structural unit, determine the target structural parameter corresponding to each described structural unit;

Step S303 , constructing the metasurface according to target structural parameters corresponding to a plurality of the structural units respectively.

A metasurface is an ultra-thin two-dimensional array plane composed of multiple structural units, and the scattering properties of each unit are the superposition of the responses to all incident waves. the convolution. In order to reduce the computational overhead, this embodiment divides the construction task of the metasurface into the construction task of each structural unit, and the construction task of each structural unit mainly includes determining its corresponding physical parameters and structural parameters. Wherein, for each structural unit, first determine the corresponding target physical parameters, and then solve the corresponding target structural parameters based on the target physical parameters. Finally, according to the corresponding target structural parameters of all structural units, a metasurface that can complete the modulation task can be constructed.

In an implementation manner, the step S301 specifically includes the following steps:

Step S3011, according to the electromagnetic field distribution data on the incident surface and the electromagnetic field distribution data on the exit surface, determine the initial physical parameters corresponding to each of the structural units;

Step S3012: Determine an optimization target, perform iterative calculation on the initial physical parameters corresponding to each of the structural units according to the optimization target, and obtain target physical parameters corresponding to each of the structural units.

Specifically, this embodiment mainly adopts an iterative optimization method to determine the target physical parameters of each structural unit. However, before the iterative calculation, it is necessary to use the calculated electromagnetic field distribution data on the incident surface and the electromagnetic field distribution data on the exit surface to set initial physical parameters for each structural unit, and then perform iterative optimization based on the initial physical parameters. And because blind optimization will be very time-consuming, and different optimization objectives iteratively produce different results, it is also necessary to determine the optimization objective. For example, the optimization objective can be loss, or fit, or efficiency, etc., and then determine based on Iteratively calculates the initial physical parameters of each structural unit until the ideal physical parameters of each structural unit, that is, the target physical parameters, are iterated.

In an implementation manner, the step S3011 specifically includes the following steps:

Step S30111: Determine a transmission matrix according to the electromagnetic field distribution data on the incident surface and the electromagnetic field distribution data on the exit surface;

Step S30112: Determine initial physical parameters corresponding to each of the structural units according to the transmission matrix.

This embodiment mainly adopts the transmission matrix method to determine the initial physical parameters of each structural unit. Specifically, the metasurface is equivalent to a transmission medium. According to the calculated electromagnetic field distribution data on the incident surface and the electromagnetic field distribution data on the exit surface, a transmission matrix that reflects the mapping relationship of the electromagnetic fields in the space before and after the metasurface can be determined. Based on the transmission matrix, the projection/reflection responses of each structural unit to all angular spectral components of the incident beam in a periodic environment can be calculated, thereby setting initial physical parameters for each structural unit.

、

、

与

）。其中，

为介电张量，

为介磁张量，

为电磁互耦导率张量，

为磁电互耦导率张量。The transfer matrix method needs to treat each structural unit as a discrete volume tensor (

,

,

and

). in,

is the dielectric tensor,

is the dielectric tensor,

is the electromagnetic mutual coupling conductivity tensor,

is the magnetoelectric mutual coupling conductivity tensor.

Knowing the volume tensor and the plane waves incident in all directions, the total response of each artificial unit to the incident field can be efficiently calculated by using the transfer matrix method. The specific implementation process of the transfer matrix method is as follows:

1. Analytically calculate the transmission/reflection response of each structural unit to all angular spectral components of the incident wave in a periodic environment using the transmission matrix method.

2. Perform inverse Fourier transform on the field in the angular spectral domain, and convert it into the electromagnetic field distribution in the spatial domain.

3. Extract the corresponding spatial field strength and phase of each structural unit in the aperiodic array environment.

4. Combine these discrete electromagnetic field distributions according to the aperiodic front distribution to generate the final transmitted/reflected spatial field.

In an implementation manner, the optimization objective includes several optimization objectives, and the step S3012 specifically includes the following steps:

Step S30121, inputting the initial physical parameters corresponding to each of the structural units into a multi-objective optimization algorithm corresponding to several of the optimization objectives;

Step S30122, iteratively calculate the initial physical parameters corresponding to each of the structural units through the multi-objective optimization algorithm.

Specifically, when the size of the metasurface is large, the number of corresponding structural units is large, and blind optimization will be very time-consuming. These optimization objectives define a multi-objective optimization algorithm through which the initial physical parameters of each structural unit are iteratively optimized.

In an implementation manner, the incident beam is regarded as a direct incident beam, and the initial physical parameter corresponding to each structural unit is iteratively calculated by the multi-objective optimization algorithm to obtain the target corresponding to each structural unit Physical parameters, specifically:

1. According to the incident beam information and the outgoing beam information corresponding to the direct incident beam, determine the initial volume tensor parameter distribution data (ie, initial physical parameters) corresponding to each structural unit;

2. Input the initial volume tensor parameter distribution data corresponding to each structural unit into the Multi-Objective Optimization Algorithm;

3. Determine the Pareto Improvement Edge (Pareto Front) corresponding to a number of the optimization objectives through the multi-objective optimization algorithm;

4. According to the Pareto improvement edge, determine the target volume tensor parameter distribution data (ie, target physical parameters) corresponding to each of the structural units.

Specifically, the multi-objective optimization algorithm will eventually converge to the vicinity of the preset threshold before the iteration is completed. Figure 7 shows the iterative results of the multi-objective optimization algorithm. In addition, the multi-objective optimization algorithm has multiple optimization objectives, that is, there are multiple costfunctions:

为第i个结构单元的计算出射电磁场幅相，

为第i个结构单元的理想电磁场幅相。图8展示了基于多个优化目标所形成的帕累托改进沿，设计人员可以根据设计需要从中确定一个择优点。in

is the calculated outgoing electromagnetic field amplitude of the i-th structural unit,

is the ideal electromagnetic field amplitude phase of the i-th structural unit. Figure 8 shows the Pareto improvement edge formed based on multiple optimization objectives, from which the designer can determine a preferred advantage according to the design needs.

In an implementation manner, the step S302 specifically includes the following steps:

Step S3021, inputting the target physical parameter corresponding to each of the structural units into the parameter extraction optimization algorithm;

Step S3022 , output the target structural parameter corresponding to each structural unit through the parameter extraction optimization algorithm.

Specifically, the parameter raising optimization algorithm in this embodiment is a comprehensive algorithm, which includes a parameter raising algorithm and an optimization algorithm. After the target physical parameters of each structural unit are determined, the structural parameters corresponding to the target physical parameters of each structural unit can be calculated through the parameter extraction optimization algorithm, that is, the target structural parameters of each structural unit can be obtained (as shown in Figure 5). shown). Then, from the existing mature structures, the man-made structural units that meet the requirements are determined for the construction of metasurfaces. Since the change of the physical equivalent parameter corresponding to the change of the artificial structure parameter generally has a trend correspondence, the above process does not consume too much computing resources.

For example, taking the three-layer structure shown in Figure 6 as an example, by changing the structural parameters of each layer of the patch, such as the size of the patch, the size of the slit, etc., a high transmission efficiency and a wide range of phase for incident electromagnetic waves can be achieved. changes, ie changes in physical parameters, so this structure can be identified as a realization of non-uniform fronts, ie metasurfaces. Since the changes of the structural parameters and physical parameters of each layer of patches have a trend, when designing a metasurface, once the physical parameters of each layer of patches are determined, the corresponding structural parameters can be deduced.

The advantages of the present invention are:

1. The present invention proposes a comprehensive algorithm based on Fourier optics method, equivalent parameter distribution, parameter extraction method, transmission matrix method and multi-objective optimization algorithm, from the feed source to the far field, the metasurface transmission array/ The reflection array is optimized for modeling, so as to achieve the purpose of intelligent design.

2. The methods adopted in the present invention are all analytical methods or semi-analytical methods, which greatly speed up the operation speed when designing the array, thereby realizing the purpose of efficient design.

3. The present invention is a systematic approach and is therefore general. It can be applied to the design of metasurface transmission array/reflection array systems with different feed sources, different feed positions, different front surface positions, and different far-field forms, and the limitations are greatly reduced compared to the previous methods.

4. During the modeling of the present invention, the super-unit is equivalent to the body parameters, and the transmission matrix method is used to analyze its full-angle spectral characteristics (transmission and reflection of incident electromagnetic waves at different angles and different polarizations), so as to fully consider the interaction between the unit and the electromagnetic field. characteristics, which in turn reduces errors during the design phase.

5. The present invention adopts a multi-objective optimization algorithm during the fitting optimization, so that the trade-off relationship between each index of the metasurface reflection array/transmission array can be quantitatively analyzed.

6. The present invention adopts an iterative algorithm limiting the amplitude when performing the Fourier transformation from the far field to the near field, thereby more accurately evaluating the amplitude and phase distribution of the required surface on the exit surface.

Based on the above embodiments, the present invention also provides a metasurface construction system based on spectral analysis, as shown in FIG. 9 , the system includes:

Incident surface calculation module 01, configured to acquire incident beam information, and determine incident surface electromagnetic field distribution data according to the incident beam information;

The exit surface calculation module 02 is used for acquiring target beam information, and determining the electromagnetic field distribution data of the exit surface according to the target beam information;

A metasurface construction module 03, configured to construct a metasurface according to the electromagnetic field distribution data on the incident surface and the electromagnetic field distribution data on the exit surface.

Based on the above embodiments, the present invention further provides a metasurface, wherein the metasurface is constructed using the method for constructing a metasurface based on spectral analysis described in any of the above embodiments.

Based on the above embodiments, the present invention also provides a terminal, the principle block diagram of which may be shown in FIG. 10 . The terminal includes a processor, a memory, a network interface, and a display screen connected through a system bus. Among them, the processor of the terminal is used to provide computing and control capabilities. The memory of the terminal includes a non-volatile storage medium and an internal memory. The nonvolatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the execution of the operating system and computer programs in the non-volatile storage medium. The network interface of the terminal is used to communicate with external terminals through a network connection. The computer program, when executed by the processor, implements a spectral analysis-based metasurface construction method. The display screen of the terminal may be a liquid crystal display screen or an electronic ink display screen.

Those skilled in the art can understand that the principle block diagram shown in FIG. 10 is only a block diagram of a partial structure related to the solution of the present invention, and does not constitute a limitation on the terminal to which the solution of the present invention is applied. The specific terminal may include There are more or fewer components than shown in the figures, or some components are combined, or have a different arrangement of components.

In one implementation, one or more programs are stored in a memory of the terminal, and are configured to be executed by one or more processors, including for performing spectral analysis-based hyperprocessing Instructions for surface construction methods.

Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be implemented by instructing relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage In the medium, when the computer program is executed, it may include the processes of the above-mentioned method embodiments. Wherein, any reference to memory, storage, database or other medium used in the various embodiments provided by the present invention may include non-volatile and/or volatile memory. Nonvolatile memory may include read only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous chain Road (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM) and so on.

In summary, the present invention discloses a metasurface construction method, system, metasurface, beam modulation method and storage medium based on spectral analysis. The method obtains incident beam information and determines the incident surface according to the incident beam information. Electromagnetic field distribution data; obtain target beam information, and determine exit surface electromagnetic field distribution data according to the target beam information; construct a metasurface according to the incident surface electromagnetic field distribution data and the exit surface electromagnetic field distribution data. Since the main function of the meta-lens is to modulate electromagnetic waves, the present invention determines the respective electromagnetic field distributions of the incident surface and the outgoing surface of the meta-surface by analyzing the incident beam and the target beam. Since the electromagnetic field distribution is closely related to the structural characteristics of the metasurface, the structural characteristics of the metasurface can be determined based on the respective electromagnetic field distributions of the incident surface and the exit surface, and then the construction of the metasurface can be realized. The present invention does not need to perform simulation optimization, and solves the problem of consuming a large amount of calculation cost and time cost by using commercial software to perform simulation optimization on each structural unit on the metasurface when constructing the metasurface in the prior art.

It should be understood that the application of the present invention is not limited to the above examples. For those of ordinary skill in the art, improvements or transformations can be made according to the above descriptions, and all these improvements and transformations should belong to the protection scope of the appended claims of the present invention.

Claims (4)

1. a metasurface construction method based on spectral analysis, is characterized in that, described method comprises: Obtain incident beam information; determining, according to the incident beam information, first spatial domain electromagnetic field distribution data corresponding to a source field, where the source field is used to transmit the incident beam; Transforming the electromagnetic field distribution data in the first spatial domain into an angular spectral domain through Fourier transform to obtain the electromagnetic field distribution data in the angular spectral domain; Phase accumulation is performed on the electromagnetic field distribution data in the angular spectrum domain to obtain the electromagnetic field distribution data on the incident surface; Obtain target beam information; According to the target beam information, determine the electromagnetic field distribution data in the second spatial domain corresponding to the target far field, wherein the target far field is the space where the target beam is located; Converting the electromagnetic field distribution data in the second space domain to a Cartesian coordinate system to obtain Cartesian electromagnetic field distribution data; performing inverse Fourier transform on the Cartesian electromagnetic field distribution data to obtain initial electromagnetic field distribution data; Fixing the amplitude of the initial electromagnetic field distribution data as a preset amplitude, and performing iterative calculation on the phase of the initial electromagnetic field distribution data to obtain electromagnetic field distribution data on the exit surface; determining a transmission matrix according to the electromagnetic field distribution data on the incident surface and the electromagnetic field distribution data on the exit surface; According to the transmission matrix, determine the initial physical parameter corresponding to each structural unit; determining an optimization objective, the optimization objective includes several optimization objectives; The initial physical parameters corresponding to each of the structural units are input into a multi-objective optimization algorithm corresponding to several of the optimization objectives; the initial physical parameters corresponding to each of the structural units are iteratively calculated by the multi-objective optimization algorithm to obtain target physical parameters corresponding to each of the structural units; Input the target physical parameters corresponding to each of the structural units into the parameter extraction optimization algorithm; Outputting target structural parameters corresponding to each of the structural units through the parameter extraction optimization algorithm; constructing a metasurface according to target structural parameters corresponding to each of the structural units, wherein the metasurface includes a plurality of the structural units; The step of fixing the amplitude of the initial electromagnetic field distribution data to a preset amplitude, and iteratively calculating the phase of the initial electromagnetic field distribution data, includes: Using the improved Gerchberg-Saxton algorithm, the amplitude of the initial electromagnetic field distribution data is fixed, and its phase is iteratively calculated until it converges to the ideal phase; The execution process of the improved Gerchberg-Saxton algorithm is as follows: transform the required far-field pattern into a Cartesian coordinate system; transform the pattern in the Cartesian coordinate system into the near field through inverse Fourier; The value distribution is replaced by the amplitude distribution of the feed propagating to the incident surface without loss; the far field generated by the near-field distribution after the Fourier transform is replaced; and the amplitude of the far field is replaced by the desired far field. Amplitude; The transfer matrix method treats each structural unit as a discrete volume tensor

,

,

and

,in,

is the dielectric tensor,

is the dielectric tensor,

is the electromagnetic mutual coupling conductivity tensor,

is the magnetoelectric mutual coupling conductivity tensor; the volume tensor and the plane waves incident in all directions are known, and the total response of each structural unit to the incident field is calculated by the transmission matrix method; wherein, the implementation process of the transmission matrix method As follows: The transmission/reflection response of each structural unit to all angular spectral components of the incident wave in a periodic environment is analytically calculated using the transmission matrix method; distribution; extract the corresponding spatial field strength and phase of each structural unit in the aperiodic front environment; combine these discrete electromagnetic field distributions according to the aperiodic front distribution to generate the final transmission/reflection space field. 2. a metasurface construction system based on spectral analysis, is characterized in that, described system comprises: an incident surface calculation module, configured to acquire incident beam information, and determine first spatial domain electromagnetic field distribution data corresponding to a source field according to the incident beam information, wherein the source field is used to transmit the incident beam; Transforming the electromagnetic field distribution data in the first spatial domain into an angular spectral domain through Fourier transform to obtain the electromagnetic field distribution data in the angular spectral domain; Phase accumulation is performed on the electromagnetic field distribution data in the angular spectrum domain to obtain the electromagnetic field distribution data on the incident surface; an exit surface calculation module, configured to acquire target beam information, and determine electromagnetic field distribution data in the second spatial domain corresponding to the target far field according to the target beam information, wherein the target far field is the space where the target beam is located; Converting the electromagnetic field distribution data in the second space domain to a Cartesian coordinate system to obtain Cartesian electromagnetic field distribution data; performing inverse Fourier transform on the Cartesian electromagnetic field distribution data to obtain initial electromagnetic field distribution data; Fixing the amplitude of the initial electromagnetic field distribution data as a preset amplitude, and performing iterative calculation on the phase of the initial electromagnetic field distribution data to obtain electromagnetic field distribution data on the exit surface; a metasurface building module, configured to determine a transmission matrix according to the electromagnetic field distribution data on the incident surface and the electromagnetic field distribution data on the exit surface; According to the transmission matrix, determine the initial physical parameter corresponding to each structural unit; determining an optimization objective, the optimization objective includes several optimization objectives; The initial physical parameters corresponding to each of the structural units are input into a multi-objective optimization algorithm corresponding to several of the optimization objectives; the initial physical parameters corresponding to each of the structural units are iteratively calculated by the multi-objective optimization algorithm to obtain target physical parameters corresponding to each of the structural units; Input the target physical parameters corresponding to each of the structural units into the parameter extraction optimization algorithm; Outputting target structural parameters corresponding to each of the structural units through the parameter extraction optimization algorithm; constructing a metasurface according to target structural parameters corresponding to each of the structural units, wherein the metasurface includes a plurality of the structural units; The step of fixing the amplitude of the initial electromagnetic field distribution data to a preset amplitude, and iteratively calculating the phase of the initial electromagnetic field distribution data, includes: Using the improved Gerchberg-Saxton algorithm, the amplitude of the initial electromagnetic field distribution data is fixed, and its phase is iteratively calculated until it converges to the ideal phase; The execution process of the improved Gerchberg-Saxton algorithm is as follows: transform the required far-field pattern into a Cartesian coordinate system; transform the pattern in the Cartesian coordinate system into the near field through inverse Fourier; The value distribution is replaced by the amplitude distribution of the feed propagating to the incident surface without loss; the far field generated by the near-field distribution after the Fourier transform is replaced; and the amplitude of the far field is replaced by the desired far field. Amplitude; The transfer matrix method treats each structural unit as a discrete volume tensor

,

,

and

,in,

is the dielectric tensor,

is the dielectric tensor,

is the electromagnetic mutual coupling conductivity tensor,

is the magnetoelectric mutual coupling conductivity tensor; the volume tensor and the plane waves incident in all directions are known, and the total response of each structural unit to the incident field is calculated by the transmission matrix method; wherein, the implementation process of the transmission matrix method As follows: The transmission/reflection response of each structural unit to all angular spectral components of the incident wave in a periodic environment is analytically calculated using the transmission matrix method; distribution; extract the corresponding spatial field strength and phase of each structural unit in the aperiodic front environment; combine these discrete electromagnetic field distributions according to the aperiodic front distribution to generate the final transmission/reflection space field. 3. A metasurface, characterized in that, the metasurface is constructed using the method for constructing a metasurface based on spectral analysis as claimed in claim 1. 4. A computer-readable storage medium having a plurality of instructions stored thereon, wherein the instructions are adapted to be loaded and executed by a processor to realize the spectral analysis-based metasurface construction of claim 1 steps of the method.

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