Surface structure design method of super-structure surface device and super-structure surface device

Abstract

The invention discloses a surface structure design method of a super-structure surface device. The surface structure design method comprises the following steps: (1) obtaining a phase dispersion value corresponding to a super-structure atom; (2) designing a phase function of the device; (3) performing iterative optimization according to the phase function and the phase dispersion value of the super-structure atoms to obtain optimized phase bias terms and super-structure atom arrangement; (4) obtaining corresponding actual physical parameters according to the obtained meta-structure atom arrangement, then comparing the actual physical parameters with design target parameters to analyze errors, and when the errors meet requirements, outputting a current phase bias item and current meta-structure atom arrangement; otherwise, updating the function item, and returning to the step (2). According to the invention, various metasurface dispersion devices can be flexibly designed, and the method provided by the invention can obtain relatively high far-field diffraction efficiency. And secondly, the method is suitable for dispersion design of continuous bandwidth and discrete wavelength. And thirdly, the feasibility of the invention is not limited by the central wavelength of the device, but is suitable for any electromagnetic wave band.

Description

Technical Field

[0001] The present invention belongs to the technical field of metasurface device design, and in particular relates to a metasurface device surface structure design method and device. Background Art

[0002] Metasurface is a new type of diffractive optical device, whose structural feature is that it is composed of a large number of scatterers arranged on a flat substrate. The large number of scatterers on the metasurface can be designed to flexibly control the light field transmission characteristics, making it widely used in imaging devices, spectral analysis devices and other fields. Among them, for imaging devices, it is usually necessary to achieve achromatic dispersion design; for spectral analysis devices, it is usually necessary to achieve uniform dispersion optimization.

[0003] However, as a diffractive optical device, metasurfaces usually have large negative dispersion. Metasurfaces without dispersion design can usually only be applied to single-wavelength scenarios and are difficult to use in wide-band scenarios. A traditional method of regulating the dispersion characteristics of metasurfaces is to combine them with refractive optical elements, using the positive dispersion of the refractive optical elements to compensate for the negative dispersion of the metasurface, thereby obtaining a dispersion value between the two. Devices designed with this method are usually thicker and have a low degree of design freedom. Another commonly used method to regulate the dispersion characteristics of metasurfaces is to arrange metaatoms with different dispersion characteristics in a planar position. Metaatoms with different dispersion characteristics usually have different structural features and sizes.

[0004] The traditional dispersion design method directly matches the dispersion characteristics required by the design target with the meta-atoms one by one, and arranges the meta-atoms in the corresponding positions through a one-time matching to complete the dispersion design. This "one-time" arrangement can often only achieve a rough design of the dispersion characteristics, and the final design result often has a certain deviation from the design target. To obtain more accurate design results, the design still needs to be further optimized. Summary of the invention

[0005] In the present invention, we provide a surface structure design method for metasurface devices. This method is based on the design ideas of phase matching and gradient descent optimization. By optimizing the matching of the target phase and the actual phase, the initial design of the metasurface dispersion control can be realized. By evaluating the far-field energy distribution on the image plane, the design parameters can be reversely adjusted to achieve iterative design. The design method proposed in the present invention can significantly improve the design flexibility and far-field diffraction efficiency of metasurface dispersion devices, and is applicable to the dispersion design of continuous bandwidth and discrete wavelength, and is applicable to any electromagnetic band within the design limit.

[0006] A method for designing a surface structure of a metasurface device, comprising:

[0007] (1) According to the structure of the selected meta-atom, the phase dispersion value corresponding to the meta-atom is obtained;

[0008] (2) designing a phase function of the device according to the functional characteristics of the device to be designed, where the phase function includes a functional term and a phase offset term;

[0009] (3) performing iterative optimization according to the phase function and the phase dispersion value of the meta-atom obtained in step (2) to obtain the optimized phase bias term and the meta-atom arrangement corresponding to the device meta-surface;

[0010] (4) Obtain the corresponding actual physical parameters based on the obtained meta-atomic arrangement, and then compare and analyze the errors with the design target parameters. When the errors meet the requirements, output the current phase bias term and the current meta-atomic arrangement; otherwise, update the function term and return to step (2).

[0011] The meta-atom (or cell) referred to in the present invention is a unit structure of a metasurface device, and its shape feature is a columnar structure with different cross-sectional shapes. According to electromagnetic theory, meta-atoms with different structures have different dispersion characteristics. The structure of the meta-atom can be selected from various existing structures. According to the structural characteristics, the broadband phase characteristics (i.e., phase dispersion) of each meta-atom can be calculated by the numerical simulation method of engineering electromagnetics: ψ k (ω); 1≤k≤N, k is the superstructure atomic number.

[0012] Furthermore, the structure of the superatom is a nano-column structure.

[0013] Furthermore, the nanocolumn structure has a cross-section of a regular hexagon, a ring-shaped regular hexagon, or a snowflake-shaped structure; and the superatom is a combination of one or more of the above-mentioned nanocolumn structures.

[0014] The function of the metasurface dispersion device is determined by the phase design. The phase function of the device function involved in the method of the present invention is composed of the functional items of the device and the broadband phase bias, wherein the functional items are related to the coordinates of the device surface point and the nominal parameters to be optimized, and can be expressed as follows: The phase function φ(x, y, ω) has the following structure:

[0015] φ(x,y,ω)=φ0(x,y,p(ω))+Δφ(ω)

[0016] Among them, φ0(x,y,p(ω)) is the functional item of the device, which is determined by x,y,p(ω). With different dispersion functions, φ0(x,y,p(ω)) is different; Δφ(ω) is the broadband phase bias to be optimized; (x,y) is the coordinate of a point on the surface of the device; p(ω) is the nominal parameter to be optimized. Generally, the nominal parameter p corresponds to the actual physical quantity in a correlation relationship; ω is the angular frequency; in step (4), the functional item is updated by updating the nominal parameter.

[0017] For different devices, the function item φ0(x,y,p(ω)) can be customized. For example, for the dispersion design of the achromatic focusing function, the corresponding function item φ0(x,y,p(ω)) can be designed as follows:

[0018]

[0019] For a device with wavelength-divided focusing function in an equifocal plane, the corresponding function item φ0(x, y, p(ω) can be designed as the following structure:

[0020]

[0021] Among them, in the above two formulas, the nominal parameter p(ω) represents the relationship established with the actual physical quantity. For example, p1(ω) represents the correlation relationship established with the actual focal length, which is the nominal parameter used to adjust the focal length. The actual focal length of the system can be adjusted by optimizing the nominal parameter p1(ω). And p2(ω) is the correlation relationship established with the projection height of different frequencies, which is the nominal parameter used to adjust the projection height, and c is the speed of light.

[0022] The phase offset term Δφ(ω) in the phase function φ(x, y, ω) can be expanded as:

[0023]

[0024] in, is the i-th element in Δφ(ω), that is, at the frequency sampling point ω i The corresponding phase offset φ i , These are variables to be optimized during the design process.

[0025] Furthermore, in step (3), this step is an iterative optimization process, which is logically nested within the iterative process of step (3). The objective function of this step can be expressed as

[0026] arg min Δφ,L(x,y) ‖φ(x,y,ω)-ψ lib (x,y,ω,L(x,y))‖

[0027] Where φ(x, y, ω) is the design target value of broadband phase distribution, ψ lib (x, y, ω, L(x, y)) is the broadband phase distribution that can be provided by the unit structure library (i.e., the set of phase dispersion values ​​of the meta-atoms obtained in step (1)) corresponding to the current atomic arrangement. The variables that can be optimized are the phase shift function Δφ and the meta-atomic arrangement L(x, y). The specific process is as follows.

[0028] 3.1 Calculate the matching error. According to the phase function and the broadband phase distribution, obtain the current matching error ε i , taking the i-th iteration step as an example, the optimization error ε i With the target phase φ i (x,y,ω) and the phase ψ implemented by the unit structure library lib The difference representation of (x,y,ω,L(x,y)) is:

[0029] ε i =‖φ i (x,y,ω)-ψ lib (x,y,ω,L(x,y)‖

[0030] Among them, φ i (x, y, ω) is the current phase function value, φ i,lib (x, y, ω, L(x, y)) is the broadband phase distribution corresponding to the current atomic arrangement, that is, the optimal matching value that can be achieved in the entire unit structure library, which can be calculated by matching position by position;

[0031] 3.2 Use the elements in the phase offset term to differentiate the forward matching error and calculate the error gradient. The error gradient calculation formula is:

[0032] where φ i is the i-th element in the phase offset term Δφ(ω), that is, After the calculation is completed, proceed to step 3.3

[0033] 3.3 Iterative phase offset function. After obtaining the gradient value, the next phase offset function can be iteratively calculated based on the gradient value, that is, the updated phase offset term Δφ i+1 (ω); then use the updated phase offset term to obtain the updated matching error ε i+1 ;

[0034]

[0035] Δφ i (ω) is the phase bias term obtained at the current moment, and η is the learning rate;

[0036] 3.4 Determine whether the iteration should stop. If the updated matching error ε i+1 <ε i ,, then there is still room for optimization, and the updated matching error is used as the current matching error to return to step 3.2; if ε i+1 ≥ε i , it means that the optimization has obtained the minimum value in the previous step, and now it is necessary to output ε i The corresponding phase offset term Δφ i (ω) and the meta-atomic arrangement L(x,y) corresponding to each position on the metasurface.

[0037] Step (4) is an iterative optimization process. Generally, after each execution of step (4) to complete the iterative optimization of the nominal parameters, step (3) needs to be executed to obtain a device layout design with better performance under the new nominal parameter conditions. The optimization goal of this step can be expressed as

[0038] argmin p(ω) ‖t(ω)-d[p(ω)]‖,

[0039] Among them, p(ω) is the nominal parameter, which is the independent variable of iterative optimization; t(ω) is the desired design target parameter, which is a known value; d[p(ω)] is the design result obtained with the nominal parameter as the independent variable. The specific process is described as follows.

[0040] Step (4) specifically includes:

[0041] 4.1 Based on the currently obtained meta-atomic arrangement (the device arrangement design can be obtained from step (3)), the corresponding actual physical parameter d is obtained by electromagnetic field calculation method. j [p(ω)];

[0042] 4.2 Calculation of design error δ j And determine whether to stop iteration, design error δ j The calculation formula is as follows: j <δ min , that is, when the design error is less than the preset acceptable deviation, the iteration is stopped and the current phase bias term Δφ is used i (ω) and the meta-atomic arrangement L(x,y) corresponding to each position of the metasurface are output; if the requirements are not met, proceed to the next step;

[0043] δ j =||t(ω)-d j [p(ω)]||, t(ω) is the desired design target parameter;

[0044] 4.3 Update the nominal parameters and return to step (3); the nominal parameters can be iterated as follows:

[0045] p j+1 (ω)=p j (ω)+η(t(ω)-d j [p(ω)]). Based on this nominal parameter, step 3 should be rerun to obtain a new device design result.

[0046] The present invention provides a metasurface device surface structure obtained by any of the above methods.

[0047] The present invention also provides a metasurface device surface structure, which can be used in the design of other device surface structure design methods and can also be used in the design of the above-mentioned method of the present invention.

[0048] A metasurface device surface structure, wherein the surface is formed by a plurality of nanocolumns arranged in a hexagonal grid. More specifically, each nanocolumn is located as follows: Figure 2 The grid intersection locations are shown.

[0049] Furthermore, the cross section of the nanocolumn is a regular hexagonal structure or a structure formed by removing a portion of a regular hexagonal structure.

[0050] Furthermore, the cross section of the nanocolumn is a regular hexagonal structure, a regular hexagonal ring structure, or a snowflake structure formed by cutting the hexagonal corners.

[0051] More specifically, the meta-atomic structure adopts the following three structures, and the meta-atoms are arranged on the device surface in a specific order according to the design results.

[0052] (i) a columnar shape with a regular hexagonal cross section, i.e., a nanocolumn with a regular hexagonal cross section;

[0053] (ii) A columnar shape having a hollow regular hexagonal cross section, wherein the hollow portion is also a regular hexagonal structure, that is, a hollow nanocolumn having a circular regular hexagonal cross section.

[0054] (iii) The cross section is a regular hexagon after cutting. That is, the cross section of the nanocolumn looks like a snowflake-shaped structure. In actual processing, it can be obtained by cutting the six corners of the regular hexagonal column structure, and the two sides (surfaces) of the cut corners are perpendicular to the original hexagon (the side of the regular hexagonal column), and the six cut corners have the same shape and size.

[0055] The size of the superatom can be freely designed based on the characteristics of the above-mentioned hexagonal grid arrangement and the above-mentioned nanocolumn structure.

[0056] The innovation of the method of the present invention lies in applying the parameter optimization process to the arrangement process of meta-atoms. Each time a temporary meta-atom arrangement is completed, the dispersion characteristics of the device are evaluated once to see if they meet expectations. If they meet expectations, the final design result is determined; if they do not meet expectations, the parameters are adjusted to continue iterative optimization. When arranging meta-atoms, the meta-atom arrangement can achieve the optimal effect through a matching method based on gradient descent. Compared with traditional design methods, the design method proposed in the present invention can significantly improve the design flexibility and far-field diffraction efficiency of metasurface dispersion devices, and is suitable for dispersion design of continuous bandwidth and discrete wavelength, and is applicable to any electromagnetic band within the design limit. The devices designed by the present invention can be widely used in imaging, spectral analysis and other application scenarios.

[0057] The present invention has the following advantages: First, the present invention can flexibly design a variety of metasurface dispersion devices, and the method proposed by the present invention can obtain a higher far-field diffraction efficiency. Second, the present invention is applicable to both continuous bandwidth and discrete wavelength dispersion design. Third, the feasibility of the present invention is not limited to the central wavelength of the device, but is applicable to any electromagnetic band. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 A flow chart of the design method of the present invention;

[0059] Figure 2 Schematic diagram of the placement of atoms in the device metastructure;

[0060] Figure 3 The super-atomic shape used in the present invention;

[0061] Figure 4 Schematic diagram of the function of achromatic meta-lens;

[0062] Figure 5 Achromatic metalens atomic arrangement diagram;

[0063] Figure 6 Schematic diagram of the function of wavelength-divided focusing meta-lens;

[0064] Figure 7 Atomic arrangement diagram of the wavelength-divided focusing metalens. DETAILED DESCRIPTION

[0065] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments:

[0066] Figure 2 This is a schematic diagram of the arrangement of atoms in the superstructure in some devices of the embodiment, where the positions of each atom are arranged according to a hexagonal grid; Figure 3Schematic diagram of the shape of the superstructure atom used in the embodiment section, including three structures: (1) regular hexagonal nanocolumn structure; (2) regular hexagonal ring nanocolumn; (3) snowflake-shaped nanocolumn formed by cutting the corners of regular hexagonal nanocolumns.

[0067] Figure 1 FIG. 1 is a flow chart of a design method of the present invention, a method for designing a surface structure of a metasurface device, comprising the following steps:

[0068] (1) According to the structure of the selected meta-atom, the phase dispersion value corresponding to the meta-atom is obtained;

[0069] The meta-atom (or cell) referred to in the present invention is a unit structure of a meta-surface device, and its shape feature is a columnar structure with different cross-sectional shapes. Specifically, the unit structure selected in this embodiment is as follows: Figure 3 According to electromagnetic theory, meta-atoms with different structures have different dispersion characteristics. The broadband phase characteristics (i.e. phase dispersion) of each meta-atom can be calculated by numerical simulation methods of engineering electromagnetics. k (ω); 1≤k≤N, k is the superstructure atom number, and N is the total number of superstructure atoms.

[0070] (2) determining a phase function of the device according to the functional characteristics of the device to be designed, where the phase function includes a functional term and a phase offset term;

[0071] The phase function φ(x, y, ω) of the present invention has the following structure:

[0072] φ(x,y,ω)=φ0(x,y,p(ω))+Δφ(ω) (1)

[0073] Among them, φ0(x,y,p(ω)) is the functional item of the device, which is determined by x,y,p(ω); Δφ(ω) is the broadband phase bias to be optimized; (x,y) is the coordinate of a point on the surface of the device; p(ω) is the nominal parameter to be optimized. Generally, the nominal parameter p(ω) corresponds to the actual physical quantity in a correlation relationship; ω is the angular frequency.

[0074] For different devices, the functional item φ0(x, y, p(ω) can be customized. For example, for the dispersion design of the achromatic focusing function, the corresponding functional item φ0(x, y, p(ω) can be designed as follows:

[0075]

[0076] For a device with wavelength-divided focusing function in an equifocal plane, the corresponding function item φ0(x, y, p(ω) can be designed as the following structure:

[0077]

[0078] Among them, in the above two formulas, the nominal parameter p(ω) represents the relationship established with the actual physical quantity. For example, p1(ω) represents the correlation relationship established with the actual focal length, which is the nominal parameter used to adjust the focal length. The actual focal length of the system can be adjusted by optimizing the nominal parameter p1(ω). And p2(ω) is the correlation relationship established with the projection height of different frequencies, which is the nominal parameter used to adjust the projection height, and c is the speed of light.

[0079] The phase offset term Δφ(ω) in the phase function φ(x, y, ω) can be expanded as:

[0080]

[0081] in, is the i-th element in Δφ(ω), that is, at the frequency sampling point ω i The corresponding phase offset φ i , These are variables to be optimized during the design process.

[0082] (3) performing iterative optimization based on the obtained phase function and the phase dispersion value of the meta-atoms to obtain the optimized phase bias term and the meta-atomic arrangement corresponding to the device meta-surface;

[0083] This step is an iterative optimization process, which is logically nested within the iterative process of step (3). The objective function of this step can be expressed as

[0084] arg min Δφ,L(x,y) ‖φ(x,y,ω)-ψ lib (x,y,ω,L(x,y))‖

[0085] Where φ(x, y, ω) is the design target value of broadband phase distribution, which is calculated by equation (1), and ψ lib (x, y, ω, L(x, y)) is the broadband phase distribution that can be provided by the unit structure library corresponding to the current atomic arrangement (i.e., the set of phase dispersion values ​​of the meta-atoms obtained in step (1)), which is obtained by the current atomic arrangement and the corresponding phase dispersion values ​​provided by the unit structure library in step (1); the optimizable variables are the phase shift function Δφ (i.e., the phase bias term Δφ(ω)) and the meta-atomic arrangement L(r).

[0086] The specific process is as follows:

[0087] 3.1 Calculate the matching error. According to the phase function and the broadband phase distribution, obtain the current matching error ε i , taking the i-th iteration step as an example, the optimization error ε i With the target phase φ i(x,y,ω) and the phase ψ implemented by the unit structure library i,lib The difference representation of (x,y,ω,L(x,y)) is:

[0088] ε i =‖φ i (x,y,ω)-ψ lib (x,y,ω,L(x,y))‖ (5)

[0089] Among them, φ i (x, y, ω) is the current phase function value, φ i,lib (x, y, ω, L(x, y)) is the broadband phase distribution corresponding to the current atomic arrangement, that is, the optimal matching value that can be achieved in the entire unit structure library, which can be calculated by matching position by position;

[0090] 3.2 Calculate the error gradient. The calculation formula of the error gradient is:

[0091] where φ i is the i-th element in the phase offset term Δφ(ω), that is, Refer to formula (4) and proceed to step 3.3 after calculation is completed;

[0092] 3.3 Iterative Phase Shift Function After obtaining the gradient value, the next phase shift function (Formula (6)) can be iteratively calculated according to the gradient value, that is, the updated phase offset term Δφ i+1 (ω); then according to formula (5), the updated matching error ε is obtained by using the updated phase offset term i+1 ;

[0093]

[0094] Δφ i (ω) is the phase bias term obtained at the current time i, η1 is the learning rate, and the general value is between 0.01-0.1;

[0095] 3.4 Determine whether the iteration should stop. If the updated matching error ε i+1 <ε i , it means there is still room for optimization, and the updated matching error is used as the current matching error to return to step 3.2; if ε i+1 ≥ε i , it means that the optimization has obtained the minimum value in the previous step, and now it is necessary to output ε i The corresponding phase offset term Δφ i (ω) and the corresponding meta-atomic arrangement L at each position of the metasurface i (x,y); After completing this step, proceed to step (4);

[0096] (4) Obtain the corresponding actual physical parameters based on the obtained meta-atomic arrangement, and then perform error analysis with the design target parameters. When the error meets the requirements, output the current phase bias term and the current meta-atomic arrangement; otherwise, update the function term and return to step (2).

[0097] Step (4) is an iterative optimization process. Generally, after each execution of step (4) to complete the iterative optimization of the nominal parameters, step (3) needs to be executed to obtain a device layout design with better performance under the new nominal parameter conditions. The optimization goal of this step can be expressed as:

[0098]

[0099] Where p(ω) is the nominal parameter and the independent variable of iterative optimization; t(ω) is the desired design target parameter and the known value; d[p(ω)] is the design result obtained with the nominal parameter as the independent variable.

[0100] The specific process is as follows:

[0101] 4.1 According to the currently obtained superstructure atomic arrangement L i (x, y) (the device layout design can be obtained from step (3)), and the corresponding actual physical parameters d are obtained by electromagnetic field calculation method j [p(ω)];

[0102] 4.2 Calculate the current design error δ j And determine whether to stop iteration, design error δ j The calculation formula is shown in the following formula (7). j <δ min , that is, when the design error is less than the preset acceptable deviation, the iteration is stopped and the current phase bias term Δφ is used i (ω) and the corresponding meta-atomic arrangement L at each position of the metasurface i (x,y) output; if it does not meet the requirements, go to the next step;

[0103] δ j =||t(ω)-d j [p(ω)]|| (7)

[0104] t(ω) is the desired design target parameter;

[0105] 4.3 Update the nominal parameters and return to step (3); the nominal parameters can be iterated as follows:

[0106] p j+1 (ω)=p j (ω)+η2(t(ω)-d j[p(ω)]). η2 is the learning rate, which is generally between 0.01-0.1;

[0107] Based on this nominal parameter, step 3 should be rerun to obtain a new device design result.

[0108] Through the above steps, the optimal nominal parameters of the device and the meta-atomic arrangement L(x, t) are finally obtained.

[0109] Example 1

[0110] Example 1 is an achromatic meta-lens, and its functionality is shown as follows: Figure 4 As shown, it can focus light of different wavelengths in a broadband range at the same point. According to the design function of achromatism, the function term of its broadband phase is shown in formula (2). According to the design method proposed by the present invention, the atomic arrangement diagram of the achromatic meta-lens meta-structure is as follows: Figure 5 Its specific design parameters are a diameter of 50 microns, a focal length of 160 microns, a working band of 850-1800 nanometers, a center distance of 800 nanometers between adjacent meta-atoms, a height of 0.9 microns, and the material used for the meta-atoms is silicon.

[0111] Example 2

[0112] Example 2 is a wavelength-splitting focusing meta-lens, which is used to focus light of different wavelengths at different plane positions, such as Figure 6 As shown. According to the wavelength-divided focusing design function, the function term of its broadband phase is shown in formula (3). The atomic arrangement diagram of the wavelength-divided focusing meta-lens is shown in Figure 7 The working parameters of design example 2 are: diameter 25 microns, focal length 75 microns, working band 850-1800 nanometers, center distance between adjacent meta-atoms 800 nanometers, height of meta-atoms 0.9 microns, and the material used for meta-atoms is silicon.

Claims

1. A method for designing a surface structure of a metasurface device, characterized in that: include: (1) According to the structure of the selected meta-atom, the phase dispersion value corresponding to the meta-atom is obtained; (2) designing a phase function of the device according to the functional characteristics of the device to be designed, where the phase function includes a functional term and a phase offset term; (3) performing iterative optimization according to the phase function and the phase dispersion value of the meta-atoms obtained in (2) to obtain the optimized phase bias term and the meta-atomic arrangement corresponding to the device meta-surface; (4) Obtain the corresponding actual physical parameters based on the obtained meta-atomic arrangement, and then compare and analyze the errors with the design target parameters. When the errors meet the requirements, output the current phase bias term and the current meta-atomic arrangement; otherwise, update the function term and return to step (2).

2. The method for designing the surface structure of a metasurface device according to claim 1, characterized in that: The structure of the superatom is a nanorod structure.

3. The method for designing the surface structure of a metasurface device according to claim 2, characterized in that: The nanocolumn structure has a cross section of a regular hexagon, a ring-shaped regular hexagon, or a snowflake-shaped structure; the superatom is a combination of one or more of the above-mentioned nanocolumn structures.

4. The method for designing the surface structure of a metasurface device according to claim 1, characterized in that: The phase function is composed of functional items of the device and a broadband phase offset, wherein the functional items are related to the coordinates of the device surface points and the nominal parameters to be optimized.

5. The method for designing the surface structure of a metasurface device according to claim 1, characterized in that: Step (3) specifically includes: 3.1 Obtaining a current matching error according to the phase function and the phase distribution; 3.2 Use the elements in the phase offset term to differentiate the front matching error and obtain the error gradient; 3.3 Obtain an updated phase bias term; and obtain an updated matching error using the updated phase bias term; 3.4 If the updated matching error is smaller than the matching error in the previous step, return to step 3.2 with the updated matching error as the current matching error; otherwise, output the phase bias term corresponding to the current matching error and the meta-atomic arrangement corresponding to each position of the metasurface.

6. The method for designing the surface structure of a metasurface device according to claim 1, characterized in that: Step (4) specifically includes: 4.1 According to the currently obtained superstructure atomic arrangement, the corresponding actual physical parameter d is obtained through electromagnetic field calculation method j [p(ω)]; 4.2 Calculation of design error δ j And determine whether to stop iteration. When the design error is less than the preset acceptable deviation, stop iteration and output the meta-structure atomic arrangement corresponding to the current phase bias term and each position of the metasurface; if it does not meet the requirements, proceed to the next step; 4.3 Update the nominal parameters and return to step (3).

7. The method for designing the surface structure of a metasurface device according to claim 4, characterized in that: For a device with achromatic focusing function, the functional items of the device are: For a device having a wavelength-divided focusing function in an equifocal distance plane, the functional items of the device are: p1(ω) represents a correlation relationship with the actual focal length and is a nominal parameter for adjusting the focal length. p2(ω) represents a correlation relationship with the projection heights of different frequencies and is a nominal parameter for adjusting the projection height.

8. A surface structure of a metasurface device, characterized in that: The surface is formed by arranging a plurality of nano-pillars, and the nano-pillars are arranged in a hexagonal grid.

9. The surface structure of the metasurface device according to claim 8, characterized in that: The cross section of the nanocolumn is a regular hexagonal structure or a structure formed by removing a portion of the regular hexagonal structure.

10. The surface structure of the metasurface device according to claim 9, characterized in that: The cross section of the nanocolumn is a regular hexagonal structure, a regular hexagonal ring structure, or a snowflake structure formed by cutting the hexagonal corners.

Images