Phase optimization of metasurface, design method, device, equipment and storage medium

Abstract

The application provides a metasurface phase optimization method, a design method, a device, equipment and a storage medium, wherein the phase optimization method comprises the following steps: determining a first parameter required at a plurality of positions of a metasurface and a second parameter required according to a candidate phase distribution of the metasurface; selecting a plurality of candidate nano structures corresponding to the plurality of positions from a preset database to form a candidate metasurface; determining a parameter difference value of the candidate metasurface; determining that the candidate phase distribution meets the requirements in the case that the imaging quality of the candidate metasurface meets a required target imaging quality and the parameter difference value is less than a preset threshold; otherwise, updating the candidate phase distribution. Through the technical scheme provided by the embodiment of the application, the metasurface produced has a better modulation effect on wide-spectrum incident light in a working waveband, has smaller chromatic aberration, and can ensure the manufacturability of the metasurface.

Description

Technical Field

[0001] This invention relates to the field of metasurface technology, and more specifically, to a metasurface phase optimization, design method, apparatus, device, and storage medium. Background Technology

[0002] When designing metasurfaces using optical design software, a multi-round phase optimization approach is typically employed. In each round of phase optimization, an evaluation function for the metasurface's imaging quality is used to optimize the phase distribution. After multiple rounds of phase optimization, a phase distribution that satisfies the design requirements for imaging quality can be obtained. Optical design software generally uses polynomials to characterize the phase distribution, which can accurately represent the desired phase distribution. Furthermore, simulations demonstrate that the optimized phase distribution achieves good imaging results.

[0003] However, in practice, the following problem often occurs: when a metasurface is fabricated using the optimized phase distribution, the imaging effect of the fabricated metasurface is not as good as the simulated imaging effect, and there is an inconsistency between the two. Summary of the Invention

[0004] To address the existing technical problems, embodiments of the present invention provide a phase optimization, design method, apparatus, device, and storage medium for metasurfaces.

[0005] In a first aspect, embodiments of the present invention provide a phase optimization method for a metasurface, comprising:

[0006] Based on the candidate phase distribution of the metasurface, a first parameter and a second parameter required at multiple locations on the metasurface are determined respectively; one of the first parameter and the second parameter is the phase, and the other is the group delay or group delay dispersion;

[0007] Multiple candidate nanostructures corresponding to the multiple locations are selected from a preset database to form candidate metasurfaces;

[0008] Determine the parameter difference value of the candidate metasurface; the parameter difference value represents the difference between a first parameter of the candidate nanostructure and a first parameter required at the corresponding location, and the difference between a second parameter of the candidate nanostructure and a second parameter required at the corresponding location;

[0009] If the imaging quality of the candidate metasurface meets the required target imaging quality and the parameter difference value is less than a preset threshold, the candidate phase distribution is determined to meet the requirements; otherwise, the candidate phase distribution is updated.

[0010] Secondly, embodiments of the present invention also provide a method for designing metasurfaces, including:

[0011] Determine the target imaging quality required for the metasurface;

[0012] The phase optimization method as described in the first aspect is repeatedly performed on the candidate phase distribution of the metasurface until the candidate phase distribution meets the requirements;

[0013] The candidate phase distribution that meets the requirements is taken as the target phase distribution, and the metasurface is designed based on the target phase distribution and the selected nanostructure.

[0014] Thirdly, embodiments of the present invention also provide a phase optimization device for a metasurface, comprising:

[0015] The parameter determination unit is used to determine, based on the candidate phase distribution of the metasurface, a first parameter and a second parameter required at multiple locations on the metasurface, respectively; one of the first parameter and the second parameter is phase, and the other is group delay or group delay dispersion;

[0016] The selection unit is used to select multiple candidate nanostructures corresponding to the multiple positions from a preset database to form candidate metasurfaces;

[0017] A difference determination unit is used to determine the parameter difference value of the candidate metasurface; the parameter difference value represents the difference between the first parameter of the candidate nanostructure and the first parameter required at the corresponding position, and the difference between the second parameter of the candidate nanostructure and the second parameter required at the corresponding position;

[0018] The processing unit is configured to determine that the candidate phase distribution meets the requirements if the imaging quality of the candidate metasurface meets the required target imaging quality and the parameter difference value is less than a preset threshold; otherwise, the candidate phase distribution is updated.

[0019] Fourthly, embodiments of the present invention also provide a design apparatus for metasurfaces, comprising:

[0020] A determination module is used to determine the target imaging quality required for the metasurface;

[0021] An optimization module is used to iteratively execute the phase optimization method as described in the first aspect on the candidate phase distribution of the metasurface until the candidate phase distribution meets the requirements;

[0022] The design module is used to select a candidate phase distribution that meets the requirements as the target phase distribution, and design a metasurface based on the target phase distribution and the selected nanostructure.

[0023] Fifthly, embodiments of the present invention provide a metasurface design apparatus, including a processor and a memory, wherein the memory stores a computer program, the processor executes the computer program stored in the memory, and the computer program, when executed by the processor, implements the metasurface phase optimization method described in the first aspect or the metasurface design method described in the second aspect.

[0024] In a sixth aspect, embodiments of the present invention also provide a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the metasurface phase optimization method described in the first aspect or the metasurface design method described in the second aspect.

[0025] The phase optimization, design method, apparatus, device, and storage medium for metasurfaces provided in this invention, in the phase optimization process, in addition to determining the phase, also determine the group delay or group delay dispersion; the parameter difference value represents the difference between the actual parameters and the required parameters of the candidate nanostructure, and candidate nanostructures that meet the requirements in terms of wavelength, group delay, or group delay dispersion are determined, thereby ensuring that the candidate nanostructures have a relatively good modulation effect on incident light of any wavelength within the working band; the metasurfaces fabricated based on these candidate nanostructures have a relatively good modulation effect on broadband incident light within the working band with small color difference. Furthermore, the candidate nanostructures are nanostructures selected from a database, which are fabricable, ensuring that the designed target phase distribution is basically consistent with the actual phase distribution of the fabricated metasurface, effectively guaranteeing the fabricability of the metasurface, and the fabricated metasurface has small color difference. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of the present invention or the background art, the accompanying drawings used in the embodiments of the present invention or the background art will be described below.

[0027] Figure 1 A flowchart of a metasurface phase optimization method provided by an embodiment of the present invention is shown;

[0028] Figure 2 The diffused spots formed on the metasurface in Comparative Example 1 are shown;

[0029] Figure 3 A full-wave simulation diagram of the metasurface in Comparative Example 1 is shown;

[0030] Figure 4 A comparison diagram is shown between the required phase distribution and the actual phase distribution of the metasurface in Comparative Example 1.

[0031] Figure 5 A comparison diagram is shown in Comparative Example 1, showing the group delay required for the metasurface and the actual group delay.

[0032] Figure 6 This diagram illustrates the required phase distribution of the metasurface in Embodiment 1 provided by the present invention.

[0033] Figure 7 This diagram illustrates the group delay required for the metasurface in Embodiment 1 provided by the present invention.

[0034] Figure 8 This diagram shows a comparison between the required phase distribution and the actual phase distribution of the metasurface in Embodiment 1 provided by the present invention.

[0035] Figure 9 This diagram shows a comparison between the required group delay and the actual group delay of the metasurface in Embodiment 1 provided by the present invention.

[0036] Figure 10 This diagram illustrates a full-wave simulation of the metasurface in Embodiment 1 provided by the present invention.

[0037] Figure 11 This diagram illustrates the required phase distribution of the metasurface in Embodiment 2 provided by the present invention.

[0038] Figure 12 This diagram illustrates the group delay required for the metasurface in Embodiment 2 provided by the present invention.

[0039] Figure 13 This diagram shows a comparison between the required phase distribution and the actual phase distribution of the metasurface in Embodiment 2 provided by the present invention.

[0040] Figure 14 This diagram shows a comparison between the required group delay and the actual group delay of the metasurface in Embodiment 2 provided by the present invention.

[0041] Figure 15 This shows a full-wave simulation diagram of the metasurface in Embodiment 2 provided by the present invention;

[0042] Figure 16 A schematic diagram of the full-band dispersion spot is shown in Embodiment 3 provided by the present invention;

[0043] Figure 17 This diagram shows a comparison between the required phase distribution and the actual phase distribution of the metasurface in Embodiment 3 provided by the present invention.

[0044] Figure 18 This shows a full-wave simulation diagram of the metasurface in Embodiment 3 provided by the present invention;

[0045] Figure 19 A schematic diagram of the full-band dispersion spot is shown in Embodiment 4 provided by the present invention;

[0046] Figure 20 This diagram shows a comparison between the required phase distribution and the actual phase distribution of the metasurface in Embodiment 4 provided by the present invention.

[0047] Figure 21 This shows a full-wave simulation diagram of the metasurface in Embodiment 4 provided by the present invention;

[0048] Figure 22 A schematic diagram of the structure of a metasurface phase optimization device provided in an embodiment of the present invention is shown;

[0049] Figure 23 A schematic diagram of a metasurface design apparatus provided in an embodiment of the present invention is shown;

[0050] Figure 24 A schematic diagram of the structure of an electronic device provided in an embodiment of the present invention is shown. Detailed Implementation

[0051] In the process of realizing this invention, the inventors discovered that the imaging effect of the fabricated metasurface is not as good as the simulated imaging effect, mainly due to the following reasons: the incident light that the metasurface needs to modulate is generally light within a single wavelength band, that is, the working wavelength band of the metasurface includes multiple wavelengths; the phase distribution of the metasurface is a continuous function expressed by a polynomial, and the actual phase distribution of the metasurface is slightly different for different wavelengths of incident light. This means that the nanostructure at a certain location on the metasurface needs to have corresponding and different modulation phases for different wavelengths of incident light; however, phase optimization generally only focuses on the phase distribution corresponding to one or more key wavelengths, and the nanostructures in the database have specific modulation phases for different wavelengths of incident light. This results in the nanostructure selected when fabricating the metasurface having a better modulation effect for key wavelengths of incident light, but a poorer modulation effect for other wavelengths of incident light, thus leading to a generally poor imaging effect of the metasurface and easily causing problems such as large color differences.

[0052] In this embodiment of the invention, group delay (GD) or group delay dispersion (GDD) is used to select a more suitable nanostructure from the database, so that the nanostructure has a better modulation effect on incident light of multiple wavelengths.

[0053] Figure 1 A flowchart illustrating a phase optimization method for a metasurface provided by an embodiment of the present invention is shown. Figure 1As shown, the method includes steps 101 to 103.

[0054] Step 101: Based on the candidate phase distribution of the metasurface, determine the required first parameter and the required second parameter at multiple locations on the metasurface; one of the first parameter and the second parameter is the phase, and the other is the group delay or group delay dispersion.

[0055] In this embodiment of the invention, a multi-round phase optimization method is adopted for the phase distribution of the metasurface, that is, the phase optimization method provided in this embodiment of the invention is executed multiple times to obtain a suitable phase distribution; for ease of description, "candidate phase distribution" is used to represent the current phase distribution of the metasurface in each round of phase optimization.

[0056] For example, the phase distribution of a metasurface is a continuous function that can be expressed as a polynomial, and the phase distribution of a metasurface can be defined by any of the following formulas:

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063] Where ω is the angular frequency of light, c is the speed of light, r represents the position at a distance r from the center of the metasurface, and x and y are the positions on the metasurface with the center of the metasurface as the origin of the coordinate system. This is a preset phase, which can be 0; This represents the modulation phase of the nanostructure at position r on the metasurface with respect to incident light of angular frequency ω. Correspondingly, This represents the modulation phase of the nanostructure at position (x, y) on the metasurface with respect to incident light of angular frequency ω. i b i a ij b ij All of these are undetermined coefficients that need to be optimized, and N is the order of the undetermined coefficients.

[0064] Phase optimization is essentially the process of determining the required undetermined coefficients. For example, if the phase distribution of the metasurface is represented by formula (1-2), then in each round of phase optimization, the undetermined coefficient 'a' for the current round can be determined. i b iThe magnitude of the phase distribution is used to determine the phase distribution of the current round, i.e., the candidate phase distribution. Through multiple rounds of phase optimization, a candidate phase distribution that meets the requirements can be determined, and the corresponding undetermined coefficients can be determined.

[0065] In each round of phase optimization operation (the phase optimization method is executed once in each round of phase optimization operation), there is a corresponding candidate phase distribution. In the first round of phase optimization operation, the candidate phase distribution can be the initially generated one; in subsequent phase optimization operations, the candidate phase distribution is the phase distribution generated in the previous round.

[0066] A candidate phase distribution can represent the phase at each location on the metasurface. To determine whether the candidate phase distribution meets the requirements, embodiments of the present invention make a judgment based on phase, group delay, group delay dispersion, etc. In embodiments of the present invention, a first parameter and a second parameter represent the parameters required to determine whether the candidate phase distribution meets the requirements, and one of the first parameter and the second parameter is phase, and the other is group delay or group delay dispersion. For example, the first parameter is phase, and the second parameter is group delay or group delay dispersion; or, the first parameter is group delay or group delay dispersion, and the second parameter is phase.

[0067] After determining the candidate phase distribution, the first and second parameters at multiple locations within the metasurface's range can be determined based on this distribution, thus determining the phase, group delay, and group delay dispersion at these multiple locations. To accurately determine whether the candidate phase distribution meets the requirements, the phases at these multiple locations should represent the phases at all locations on the metasurface, ensuring that these multiple locations represent all locations on the metasurface. For example, these multiple locations could represent more than 90% of the locations within the metasurface's range, or all locations. Generally, the phase at a certain location on the metasurface depends only on the distance r from that location to the center of the metasurface, as shown in equations (1-1) to (1-5). In this case, different radial locations can be selected as the aforementioned multiple locations.

[0068] The parameters such as phase, group delay, and group delay dispersion determined based on the candidate phase distribution are theoretical parameters, which are relatively accurate. For ease of description, in this embodiment of the invention, the parameters determined based on the candidate phase distribution are referred to as the required parameters, i.e., the required first parameter and the required second parameter. For example, the phase at a certain position determined based on the candidate phase distribution is called the required phase at that position. It can be understood that in this embodiment of the invention, "required first parameter," "required phase," etc., refer to the parameters that the nanostructure selected from the database (i.e., the candidate nanostructure below) needs to have during the current round of phase optimization operation. However, these parameters are not necessarily the parameters required for the final metasurface, and the parameters may also differ from the actual parameters of the selected nanostructure.

[0069] During phase optimization, the phase distribution of only one wavelength within the operating band can be optimized. This candidate phase distribution can be the phase distribution corresponding to a specific wavelength within the metasurface's operating band, such as the phase distribution corresponding to the center wavelength. Correspondingly, the phase can be the phase corresponding to a specific wavelength within the metasurface's operating band, such as the phase corresponding to the center wavelength. Based on the candidate phase distribution corresponding to a single wavelength, the required first and second parameters at each location can be determined.

[0070] For example, the candidate phase distribution corresponding to the angular frequency ω can be represented by any of the forms in equations (1-1) to (1-6) above. Correspondingly, let ω ± Δω represent the neighborhood frequency domain of the angular frequency ω. In the neighborhood frequency domain of the angular frequency ω, the corresponding phase distribution can be represented as follows:

[0071]

[0072]

[0073]

[0074]

[0075]

[0076]

[0077] Here, Δω represents the difference in angular frequency, which is generally a relatively small value.

[0078] Based on equations (2-1) to (2-6) above, the group delay and group delay dispersion corresponding to the angular frequency ω at a certain location on the metasurface can be determined. For example, the group delay GD(r,ω) corresponding to the angular frequency ω at location r is:

[0079]

[0080] The group delay dispersion GDD(r,ω) at position r corresponding to the angular frequency ω is:

[0081]

[0082] In cases where group delay dispersion does not need to be calculated, for example, where one of the first and second parameters is the phase and the other is the group delay, the group delay within the working band can be taken as a constant value. That is, for a certain position, only one group delay can be determined. For example, in the above equation (3), ω represents the angular frequency of the center, and Δω represents the difference between the range of angular frequencies and the angular frequency of the center. That is, the range of angular frequencies corresponding to the working band is (ω-Δω, ω+Δω). Then, the group delay GD(r,ω) determined by the above equation (3) can be taken as the group delay within the working band at position r. The working band corresponds to only one group delay, which can simplify the subsequent processing complexity and facilitate rapid optimization.

[0083] Step 102: Select multiple candidate nanostructures corresponding to multiple locations from the preset database to form candidate metasurfaces.

[0084] In this embodiment of the invention, the database is a database containing multiple nanostructures. Different nanostructures in the database generally have different sizes, resulting in specific phases and group delays. For example, by constructing the database, the phase, group delay, and group delay dispersion corresponding to each nanostructure in the database can be determined. For example, the nanostructures in the database have different modulation phases for different wavelengths. Therefore, based on the methods for determining the group delay and group delay dispersion shown in equations (3) and (4) above, the group delay and group delay dispersion of the nanostructure can be determined.

[0085] Suitable nanostructures can be selected from a database based on candidate phase distributions, thereby forming a metasurface whose phase distribution is substantially consistent with the candidate phase distribution. For ease of description, in this embodiment of the invention, the selected nanostructure is referred to as a candidate nanostructure, and the metasurface constructed from the candidate nanostructure is referred to as a candidate metasurface. Since the candidate nanostructure is selected from the database, its phase, group delay, group delay dispersion, etc., can be determined, thereby determining the first parameter and the second parameter of the candidate nanostructure.

[0086] In this embodiment of the invention, since the candidate nanostructure is a nanostructure from the database and is fabricable, the candidate metasurface is also fabricable. The parameters determined based on the candidate phase distribution in step 101 are the desired parameters, which are target values. The candidate nanostructures selected in step 102, however, have their own corresponding parameters, which are actual values. The closer the actual value is to the target value, the more the phase distribution of the candidate metasurface formed from these candidate nanostructures matches the candidate phase distribution; and, candidate superlenses that closely match the candidate phase distribution can be fabricated.

[0087] Step 103: Determine the parameter difference value of the candidate metasurface; the parameter difference value represents the difference between the first parameter of the candidate nanostructure and the first parameter required at the corresponding location, and the difference between the second parameter of the candidate nanostructure and the second parameter required at the corresponding location.

[0088] Because the parameters of the selected candidate nanostructure may differ significantly from the actual required parameters, the actual multi-wavelength phase distribution of the candidate metasurface may differ considerably from the required multi-wavelength phase distribution. For example, at position r, the phase of the candidate nanostructure is relatively close to the required phase, but the group delay of the candidate nanostructure differs significantly from the required group delay. This means that the candidate metasurface cannot accurately represent the candidate phase distribution.

[0089] In this embodiment of the invention, a parameter difference value is used to represent the difference between a candidate metasurface and a candidate phase distribution. Specifically, this parameter difference value can represent the difference between a first parameter of the candidate nanostructure and a first parameter required at the corresponding location, and it can also represent the difference between a second parameter of the candidate nanostructure and a second parameter required at the corresponding location.

[0090] To facilitate subsequent phase optimization using this parameter difference, the difference is represented by a value not less than 0. For example, the absolute value between the first parameter of the candidate nanostructure and the required first parameter at the corresponding location is used as the difference between the two.

[0091] For example, the first parameter is the phase, and the second parameter is the group delay; for position r, the required phase at position r is... The required group delay is GD tar (r), the phase of the candidate nanostructure at position r is The group delay of the candidate nanostructure is GD real (r), then the difference between the first parameter of the candidate nanostructure and the first parameter required at the corresponding location can be The difference between the second parameter of the candidate nanostructure and the second parameter required at the corresponding location can be |GD real (r)-GD tar (r)|. For example, you can use With |GD real (r)-GD tar The weighted sum of (r)| represents the difference value of the parameter.

[0092] Furthermore, the parameter difference value can be determined based on the parameter differences at multiple locations, so that the parameter difference value can represent the magnitude of the difference between the candidate metasurface and the candidate phase distribution more completely and accurately. For example, the mean of the parameter differences at multiple locations can be used as the parameter difference value, or the maximum value of the parameter differences at multiple locations can be used as the parameter difference value.

[0093] Step 104: If the imaging quality of the candidate metasurface meets the required target imaging quality and the parameter difference is less than a preset threshold, determine that the candidate phase distribution meets the requirements; otherwise, update the candidate phase distribution.

[0094] After a certain round of phase optimization, if the candidate phase distribution of the metasurface meets the requirements, it can be considered that the candidate phase distribution is the required phase distribution, and the phase optimization ends; if the candidate phase distribution of the metasurface does not meet the requirements, a new candidate phase distribution needs to be determined and the phase optimization method is re-executed.

[0095] In this embodiment of the invention, when designing a required metasurface, it is necessary to determine the required imaging quality of the metasurface. Imaging quality can be represented by imaging parameters, such as the focal length, dispersion, and aberrations of a superlens, which can be determined based on the actual situation. For ease of description, the required imaging quality of the metasurface is referred to as "target imaging quality".

[0096] In determining whether a candidate phase distribution meets the requirements, it is necessary to determine whether the imaging quality of the candidate metasurface meets the requirements, i.e., whether it meets the target imaging quality. If it meets the target imaging quality, it means that the candidate metasurface basically meets the imaging requirements. Furthermore, if the parameter difference value is also less than a preset threshold, it means that the candidate phase distribution can be accurately represented using the candidate nanostructures selected from the database, i.e., the corresponding metasurface can be fabricated. This allows the fabricated metasurface to be relatively close to the metasurface simulated by the candidate phase distribution, and the fabricated metasurface has a better imaging effect.

[0097] If the imaging quality of the candidate metasurface does not meet the target imaging quality, and / or the parameter difference value is not less than the preset threshold, it indicates that the candidate phase distribution itself is not suitable, or the corresponding metasurface cannot be fabricated using the nanostructures in the database. In this case, the candidate phase distribution needs to be updated to obtain a new candidate phase distribution. Then, the next round of phase optimization operation, i.e., steps 101 to 104, is performed on the new candidate phase distribution to determine whether the new candidate phase distribution meets the requirements, until a candidate phase distribution that meets the requirements is obtained.

[0098] If the parameter difference value is not less than the preset threshold, it will generally cause the imaging quality of the candidate metasurface to fail to meet the target imaging quality. Therefore, when judging whether the candidate phase distribution meets the requirements, it is possible to first judge whether the parameter difference value is less than the preset threshold. If the parameter difference value is less than the preset threshold, then it is judged whether the imaging quality of the candidate metasurface meets the target imaging quality.

[0099] In this embodiment of the invention, the imaging quality of a metasurface can be determined using conventional methods. For example, the imaging quality of a metasurface can be determined based on the phase distribution at one or more discrete wavelengths. If the imaging quality of a candidate metasurface meets the target imaging quality, it indicates that the imaging quality of the candidate metasurface meets the requirements at one or more discrete wavelengths. However, this does not guarantee good imaging quality at other wavelengths. In this embodiment of the invention, in addition to determining whether the imaging quality of a candidate metasurface meets the target imaging quality, it is also necessary to determine whether the parameter difference value is less than a preset threshold in order to select candidate nanostructures whose phase and group delay (or group delay dispersion) are close to the target value. Equations (3) and (4) above can represent the relationship between group delay (or group delay dispersion) and phase. Based on the relationship between group delay (or group delay dispersion) and phase, it can be seen that if the phase at one or more wavelengths meets the requirements within the working band, since the group delay (or group delay dispersion) of the candidate nanostructure is also the same as the target value, the phase at any wavelength within the working band meets the requirements. That is, the finally selected candidate nanostructure has a better modulation effect on incident light of any wavelength within the working band.

[0100] The phase optimization method for metasurfaces provided in this invention determines not only the phase but also the group delay or group delay dispersion during the phase optimization process. The parameter difference value represents the difference between the actual parameters and the required parameters of the candidate nanostructure. Candidate nanostructures that meet the requirements for wavelength, group delay, or group delay dispersion are selected, ensuring that the candidate nanostructures have good modulation effects for incident light of any wavelength within the working band. Metasurfaces fabricated based on these candidate nanostructures exhibit good modulation effects for broadband incident light within the working band, with minimal color difference. Furthermore, the candidate nanostructures are selected from a database and are fabricable, ensuring that the designed target phase distribution is essentially consistent with the actual phase distribution of the fabricated metasurface, effectively guaranteeing the fabricability of the metasurface and resulting in a metasurface with minimal color difference.

[0101] Optionally, the process of "updating candidate phase distribution" in step 104 above may specifically include the following step A1.

[0102] Step A1: Update the candidate phase distribution according to the objective function; the objective function includes an imaging quality difference term and a parameter difference term. The imaging quality difference term represents the difference between the imaging quality of the candidate metasurface and the target imaging quality, while the parameter difference term represents the difference between the parameter difference value and a preset threshold.

[0103] When optimizing the phase distribution to obtain a new phase distribution, an objective function is generally used to achieve phase optimization and obtain an updated candidate phase distribution. In this embodiment of the invention, the objective function includes an imaging quality difference term and a parameter difference term; wherein, the imaging quality difference term is used to represent the difference between the imaging quality of the candidate metasurface and the target imaging quality, so as to evaluate whether the imaging quality of the candidate metasurface meets the requirements; the parameter difference term represents the difference between the parameter difference value and a preset threshold, so as to evaluate whether the first parameter and the second parameter of the candidate metasurface meet the requirements.

[0104] For example, let imaging parameters represent imaging quality; V represents the actual imaging parameters of the candidate metasurface, and T represents the required imaging parameters. Then, the difference between the imaging quality of the candidate metasurface and the target imaging quality can be represented by VT. Similarly, if Δ represents the parameter difference value and th represents a preset threshold, then the difference between the parameter difference value and the preset threshold can be represented by Δ-th. This imaging quality difference term can be expressed as f(VT), the parameter difference term can be expressed as g(Δ-th), and the objective function can be MF. 2 = f(VT) + g(Δ-th), or, MF 2 =W1f(VT)+W2(Δ-th). Where f() and g() are preset corresponding functions, and W1 and W2 are the weighting coefficients of the imaging quality difference term and the parameter difference term, respectively, and their sum can be 1.

[0105] In this embodiment of the invention, the objective function includes an imaging quality difference term and a parameter difference term. The candidate phase distribution is updated based on the objective function, which not only enables the imaging quality to meet the requirements, but also makes the phase and group delay of the designed candidate metasurface close to the real phase and group delay in the database, thereby obtaining a candidate phase distribution that meets the requirements.

[0106] The imaging quality difference term can be a traditional function used to evaluate imaging quality. For example, the imaging quality difference term f(VT) satisfies the following equation:

[0107]

[0108] Among them, V k T represents the actual value of the aberration corresponding to the k-th operator; k This represents the target value of the aberration corresponding to the k-th operator; w kRepresents the weight factor for the k-th operator; (V l -T l ) 2 Represents a Lagrange multiplier; w l This represents the weight factor for the l-th operator.

[0109] Since the difference between the parameter difference value Δ and the preset threshold th needs to be sufficiently small, and the closer the parameter difference value Δ is to 0, the better. Therefore, the difference between the parameter difference value Δ and the preset threshold th should not be represented as |Δ-th|, etc. In this embodiment of the invention, the parameter difference item is represented by the difference value Δ minus the preset threshold th, Δ-th, and is represented in a segmented form.

[0110] Specifically, when the parameter difference value Δ is greater than the preset threshold th, there is a positive correlation between the parameter difference term and the difference between the parameter difference value Δ and the preset threshold th; that is, the larger Δ-th is, the larger the parameter difference term is. When the parameter difference value Δ is less than the preset threshold th, the parameter difference term is zero. If the parameter difference value Δ is equal to the preset threshold th, any of the above processing methods can be used; for example, if Δ = th, then the parameter difference term is zero.

[0111] In this embodiment of the invention, the desired candidate phase distribution can be obtained by minimizing the objective function. Generally, in the initial stage of phase optimization, the parameter difference value Δ is greater than the preset threshold th. Let Δ-th represent the parameter difference term of the objective function, and optimization can be performed in the direction of reducing the parameter difference value Δ. In the later stage of phase optimization, if the parameter difference value Δ is less than the preset threshold th, the parameter difference term is zero, that is, the objective function is equivalent to only containing the imaging quality difference term. At this time, it is only necessary to ensure that the imaging quality of the candidate metasurface meets the requirements.

[0112] For example, the parameter difference term satisfies: S1 = (Δ - th) × H(Δ - th). Where S1 represents the parameter difference term, Δ represents the parameter difference value, th represents the preset threshold, and H() is the Heaviside function.

[0113] That is, the difference term of this parameter satisfies:

[0114]

[0115] For example, the objective function could be:

[0116] MF 2 =W1f(TV)+W2(Δ-th)×H(Δ-th) (7)

[0117] The numerical value MF determined by the objective function can be used directly. 2This is used to determine whether the candidate phase distribution meets the requirements. To avoid mistakenly assuming the current candidate phase distribution meets the requirements when the parameter difference value Δ is greater than the preset threshold th, the weight coefficient W2 of the parameter difference term can be set to a larger value.

[0118] The preset threshold th can be set based on actual conditions. For example, if the parameter difference value Δ is only related to the phase, then the preset threshold th can be a preset phase value; for example, if the phase is expressed in radians (rad), the preset threshold th can satisfy: th < 1; for example, th is 0.9, 0.8, etc. Or, for example, if the parameter difference value Δ is only related to the group delay, then the preset threshold th can be a preset group delay difference value; for example, if the unit of group delay is femtoseconds (fs), the preset threshold th can satisfy: th < 20; for example, th is 15, 10, etc.

[0119] Optionally, step 102, “selecting multiple candidate nanostructures corresponding to multiple locations from a preset database”, may specifically include step B1, and step 103, “determining the parameter difference values ​​of the candidate metasurfaces”, may specifically include step C1.

[0120] Step B1: Select the nanostructure in the preset database whose first parameter is closest to the first parameter required at the target location as the candidate nanostructure at the target location; the target location is one of multiple locations.

[0121] Step C1: Determine the difference between the second parameter of each candidate nanostructure and the required second parameter at the corresponding location; determine the parameter difference value based on the difference between the second parameter of all candidate nanostructures and the required second parameter at the corresponding location.

[0122] In this embodiment of the invention, for ease of description, one of the aforementioned multiple locations is referred to as the target location. When selecting a candidate nanostructure at the target location from the database, a first parameter required at the target location is determined. The nanostructure closest to the required first parameter is selected from the database and designated as a candidate nanostructure; that is, the first parameter of the candidate nanostructure is closest to the first parameter required at the target location, for example, the difference between the two is the smallest. Other locations among the multiple locations can also be used as target locations, and a similar processing procedure to step B1 above is performed to determine the candidate nanostructure at the corresponding location.

[0123] When selecting candidate nanostructures using the method described in step B1 above, it can be guaranteed that the difference between the first parameter of the selected candidate nanostructure and the required first parameter is minimized. Although the difference between the two first parameters can be determined at this point, and the parameter difference value can be further determined based on this, since the difference between these two first parameters is already minimized, it can be considered that the first parameter of the candidate nanostructure meets the requirements. Therefore, it is not necessary to further determine whether the first parameter meets the requirements. Thus, when determining the parameter difference value at this point, the difference between the first parameter of the candidate nanostructure and the required first parameter at the corresponding position can be ignored. It is only necessary to determine the difference based on the difference between the second parameter of the candidate nanostructure and the required second parameter at the corresponding position. In other words, when selecting candidate nanostructures using the method described in step B1 above, even if the parameter difference value is determined only based on the difference between the two second parameters, this parameter difference value can still represent the difference between the two first parameters; it's just that the difference between the two first parameters is very small at this point, and it meets the requirements.

[0124] Optionally, when selecting different radial positions r as the aforementioned multiple positions, the average of the differences between the parameters at the multiple positions r can be used as the parameter difference value. Specifically, this parameter difference value can satisfy:

[0125]

[0126] Where Δ represents the parameter difference value, p real (r) represents the second parameter of the candidate nanostructure at position r, p tar (r) represents the second parameter required at position r, R represents the distance from the center to the edge of the metasurface, and m represents the number of nanostructures in the radial direction of the metasurface.

[0127] In this embodiment of the invention, for a metasurface with a distance R from the center to the edge, such as a circular metasurface with radius R, let r represent the distance from the candidate nanostructure to the center of the metasurface, and the value range of this distance r is [0, R]. If the number of nanostructures in the radial direction of the metasurface is m, that is, m candidate nanostructures are needed from the center to the edge of the metasurface, then the sum of the parameter differences of these m candidate nanostructures is... Accordingly, the parameter difference value Δ can be expressed as shown in equation (8) above. For example, if T is the arrangement period of the candidate nanostructures in the metasurface, then the quantity m can be expressed as m = R / T, or m = R / T+1, etc.

[0128] For example, the first parameter is the group delay, and the second parameter is the phase. When selecting candidate nanostructures, for any required group delay at position r, the candidate nanostructure with the closest group delay is determined by traversing the database, thus forming a candidate metasurface. Then, the phase difference Δphi(r) between the phase of the candidate nanostructure at any position r and the required phase at that position r is determined. This parameter difference value Δ can be expressed as:

[0129]

[0130] For example, the first parameter is the phase, and the second parameter is the group delay. When selecting candidate nanostructures, for any desired phase at position r, the candidate nanostructure with the closest phase is determined by traversing the database, thus forming a candidate metasurface. Then, the group delay difference ΔGD(r) between the group delay of the candidate nanostructure and the desired group delay at any position r is determined. This parameter difference Δ can be expressed as:

[0131]

[0132] Optionally, when group delay dispersion needs to be used for judgment, i.e., when one of the first and second parameters is phase and the other is group delay dispersion, the method further includes: determining the required group delay at multiple locations. The difference in this parameter also represents the difference between the group delay of the candidate nanostructure and the required group delay at the corresponding location.

[0133] In this embodiment of the invention, when the first parameter is phase and the second parameter is group delay dispersion, or when the first parameter is group delay dispersion and the second parameter is phase, in addition to using the first parameter and the second parameter, that is, in addition to using the phase and group delay dispersion, the parameter difference value Δ is also determined based on the group delay to ensure that the candidate nanostructure has the required modulation effect for incident light of any wavelength in the working band.

[0134] For example, if candidate nanostructures are selected in the manner described in step B1 above, the parameter difference value Δ needs to be determined based on the second parameter and the group delay. For example, if the first parameter is phase and the second parameter is group delay dispersion, then when determining the parameter difference value Δ, it is necessary to determine: the difference between the group delay of the candidate nanostructure and the required group delay at the corresponding position, and the difference between the group delay dispersion of the candidate nanostructure and the required group delay dispersion at the corresponding position.

[0135] It should be noted that when using group delay dispersion (GDD) for judgment, it is necessary to determine the group delay GD corresponding to multiple wavelengths. That is, the group delay GD within the working band cannot be taken as a constant value. Alternatively, the group delay dispersion GDD within the working band can be taken as a constant value. In this case, when determining the parameter difference value Δ, only the phase and group delay GD corresponding to the center wavelength can be considered.

[0136] The metasurface phase optimization method provided in this invention can obtain a more suitable phase distribution by comprehensively judging whether the candidate phase distribution meets the requirements through phase, group delay, and group delay dispersion.

[0137] Optionally, parameter difference values ​​can be determined based on a wider range of parameters. Specifically, the "phase optimization operation" step described above further includes determining a third parameter required at multiple locations; this third parameter includes the equivalent refractive index and / or the radius of the metasurface. In this case, the parameter difference value also represents the difference between the third parameter of the candidate nanostructure and the third parameter required at the corresponding location.

[0138] In this embodiment of the invention, in addition to determining the parameter difference value based on the first and second parameters, the parameter difference value can also be determined based on a third parameter such as the equivalent refractive index and / or the radius of the metasurface, so as to more accurately indicate whether the selected candidate nanostructure meets the requirements. Wherein, after determining the required phase at a certain location, the required equivalent refractive index at that location can be determined based on existing formulas, which will not be detailed here. The radius of the metasurface is the radius of the overall metasurface structure; if the third parameter includes the radius of the metasurface, the corresponding difference refers to the difference between the radius of the designed metasurface and the radius of the required metasurface, and this difference is unrelated to the nanostructure itself; or, for candidate nanostructures at different locations, the difference corresponding to the radius of the metasurface can be a constant value.

[0139] Specifically, if one of the first and second parameters is phase and the other is group delay, then the third parameter may also include group delay dispersion; if one of the first and second parameters is phase and the other is group delay dispersion, then the third parameter may also include group delay. In this case, the parameter difference value at least includes the differences corresponding to phase, group delay, and group delay dispersion, ensuring that the phase, group delay, and group delay dispersion of the finally determined nanostructure all meet the requirements.

[0140] Optionally, the nanostructure can be selected according to step B1 above, or it can be selected according to steps B2 and B3 below. Specifically, step 102, "selecting multiple candidate nanostructures corresponding to multiple locations from a preset database", includes the following steps B2 and B3.

[0141] Step B2: For a given location, determine the overall difference between the parameters of each nanostructure in the preset database and the parameters required at that location.

[0142] Step B3: Select the nanostructure with the smallest overall difference value as the candidate nanostructure corresponding to that location.

[0143] In this embodiment of the invention, for any position r, when selecting a candidate nanostructure at position r from a preset database, the overall difference value between the parameters of each nanostructure in the preset database and the parameters required at the position is determined; if the preset database contains n nanostructures, then n overall difference values ​​need to be determined, and the smallest one is found among these n overall difference values. The nanostructure corresponding to the smallest overall difference value can be used as the candidate nanostructure selected at position r.

[0144] In this embodiment of the invention, the overall difference value represents the degree of matching between the nanostructure in the preset database and the nanostructure required at position r. The smaller the overall difference value, the higher the degree of matching. Specifically, this embodiment of the invention determines the overall difference value in a weighted manner. The overall difference value diff between a certain nanostructure in the preset database and the nanostructure required at position r satisfies:

[0145] diff=ω phase Δphase+ω GD ΔGD+ω GDD ΔGDD+ω neff Δn eff +ω R ΔR (10)

[0146] Where Δphase represents the difference between the phase of the nanostructure and the phase required at that location, ΔGD represents the difference between the group delay of the nanostructure and the group delay required at that location, ΔGDD represents the difference between the group delay dispersion of the nanostructure and the group delay dispersion required at that location, and Δn eff ΔR represents the difference between the equivalent refractive index of the nanostructure and the required equivalent refractive index at that location; ω represents the difference between the designed metasurface radius and the required metasurface radius. phase ω GD ω GDD ω neff ω R These represent the weights of the corresponding differences. For example, ω phase The weight ω represents the difference between the phase of the nanostructure and the phase required at that location. GD The weights represent the difference between the group delay of the nanostructure and the required group delay at that location, and so on.

[0147] Among them, Δphase, ΔGD, ΔGDD, and Δn in equation (10) above eff Differences such as ΔR can all be differences obtained after normalization; for example, the range of normalized values ​​is (0, a), where a is a positive number, such as a = 1. Furthermore, the sum of all weights can be 1, i.e., ω. phase ω GD ω GDD ω neff ω R The sum of is 1.

[0148] If the phase at a certain location on the metasurface depends only on the distance r from that location to the center of the metasurface, as shown in equations (1-1) to (1-5), the metasurface can be divided into multiple concentric discrete rings according to the arrangement period of the nanostructures, with each discrete ring corresponding to a location r. Based on this method, suitable candidate nanostructures at each location r can be determined, thereby enabling the determination of candidate metasurfaces.

[0149] Alternatively, the overall difference value of the selected candidate metasurface can also be determined according to the above formula (10), that is, the parameter difference value of the candidate nanostructure is the overall difference value; after the candidate metasurface is selected, its overall difference value can be directly used as the parameter difference value.

[0150] In this embodiment of the invention, by comprehensively utilizing parameters such as phase, group delay, and group delay dispersion of the nanostructure, suitable candidate nanostructures can be selected. This allows the optical structure and optical performance parameters of the metasurface to approach the diffraction limit, which is beneficial for eliminating higher-order chromatic aberrations and improving imaging quality. Furthermore, by using the overall difference value to select nanostructures, the matching effect of multiple parameters can be taken into account simultaneously, and suitable candidate nanostructures can be selected more quickly.

[0151] This invention also provides a method for designing metasurfaces, which specifically includes the following steps D1 to D3.

[0152] Step D1: Determine the target imaging quality required for the metasurface.

[0153] Step D2: Repeatedly apply the phase optimization method provided in the above embodiments to the candidate phase distribution of the metasurface until the candidate phase distribution meets the requirements.

[0154] Step D3: Select the candidate phase distribution that meets the requirements as the target phase distribution, and design the metasurface based on the target phase distribution and the selected nanostructure.

[0155] After multiple rounds of phase optimization, if a suitable candidate phase distribution is obtained, a metasurface can be designed and fabricated based on this distribution. For ease of description, the suitable candidate phase distribution is referred to as the "target phase distribution." This target phase distribution corresponds to nanostructures selected from a database, i.e., candidate nanostructures at multiple locations corresponding to the suitable candidate phase distribution. The metasurface designed based on this target phase distribution and the selected nanostructures not only possesses good imaging quality but can also be fabricated using a database.

[0156] The effects of the method will be further illustrated below through an existing comparative example 1, and examples 1, 2, 3, and 4 of applying the method provided in the embodiments of the present invention.

[0157] Comparative Example 1

[0158] In Comparative Example 1, a metasurface capable of correcting advanced chromatic aberrations was obtained using a traditional phase optimization method. Theoretically, the simulation performance of this metasurface can be found in [reference needed]. Figure 2 As shown. Figure 2 The image shows the Airy disks formed on the metasurface when red, green, and blue (RGB) wavelengths of light are transmitted through it. The size of the diffused disk for green (G) light is 13 μm. The diffused disks of this metasurface are all within the diffraction limit, indicating good correction of various aberrations.

[0159] Based on the optimized phase distribution, a suitable nanostructure was selected from the database and a metasurface was formed. Simulations were performed on the entire operating wavelength range based on this metasurface; the full-wavelength simulation results are available in [reference needed]. Figure 3 As shown. The plane containing the metasurface is the xy plane, with the principal optical axis along the z-axis. Figure 3 In the figure (a), the relative light intensity is shown on the z-axis. The focal length of the metasurface is 6.5322 mm. Figure 3 (b) represents the relative light intensity on the x-axis at the focal point of the metasurface, with a diffuse spot size of 86.9543 μm; Figure 3 (c) represents a partial light intensity diagram of the xz plane, where different shades of gray represent different light intensities.

[0160] based on Figure 2 and Figure 3 It can be seen that although traditional optimization methods can theoretically produce metasurfaces with better performance, the actual performance of the metasurfaces decreases significantly after selecting nanostructures from the database, with the size of the diffuse spot increasing from 13 μm to 86.9543 μm.

[0161] This is because, when selecting nanostructures from a database, traditional methods can only determine whether the phase of the nanostructure meets the requirements at one or some discrete wavelengths. In Comparative Example 1, taking the center wavelength as an example, the optimized phase distribution and the actual phase of the metasurface formed by the nanostructure selected from the database can be seen in [reference needed]. Figure 4 As shown; Figure 4 This represents the phase at different positions r, where the curve represents the optimized phase distribution, and each discrete point represents the actual phase of the metasurface. Based on Figure 4 It can be seen that, for the center wavelength, the phase of the selected nanostructure is quite close to the optimized phase distribution.

[0162] However, the group delay corresponding to the optimized phase distribution is comparable to the actual group delay of the metasurface formed by the nanostructures selected from the database. Figure 5 As shown; Figure 5 The group delay (GD) at different locations r is represented, where the curve represents the optimized group delay, and each discrete point represents the actual group delay of the metasurface. Based on Figure 5 It can be seen that the group delay provided by the nanostructure differs significantly from the group delay required by the design.

[0163] Example 1

[0164] Based on the method provided in this embodiment of the invention, the determined target phase distribution and corresponding group delay can be found in [reference needed]. Figure 6 and Figure 7 As shown; Figure 6 This represents the phase required at position r. Figure 7 This represents the required group delay (GD) at position r. Based on the method provided in this embodiment of the invention, the phase and group delay of the nanostructures selected from the database can be found in [reference needed]. Figure 8 and Figure 9 As shown; Figure 8 The curve in the figure represents the phase required at position r, and the discrete points represent the actual phase of the selected nanostructure. Figure 9 The curve in the figure represents the required group delay at point r, and the discrete points represent the actual group delay of the selected nanostructure. Based on Figure 8 and Figure 9 It can be seen that the phase and group delay of the selected nanostructure are well matched with the required phase and group delay.

[0165] A metasurface was formed based on the selected nanostructure, and simulations were performed on the entire wavelength range within the working band based on this metasurface. The full-wavelength simulation results are shown in [link to full-wavelength simulation results]. Figure 10 As shown. The plane containing the metasurface is the xy plane, with the principal optical axis along the z-axis. Figure 10In the figure (a), the relative light intensity is shown on the z-axis. The focal length of the metasurface is 6.5325 mm. Figure 10 In the middle (b), the relative light intensity on the x-axis at the focal point of the metasurface is 9.2283 μm. Figure 10 (c) represents a partial light intensity diagram of the xz plane, where different shades of gray represent different light intensities.

[0166] In Example 1, the required phase and group delay show good matching in the database, and the nanostructure required for optimization also shows good matching in the database, exhibiting good consistency and ensuring the fabrication feasibility of the metasurface. Furthermore, by Figure 10 It can be seen that the metasurface designed based on the design method provided in the embodiments of the present invention has a diffuse spot size of approximately 9.2 μm, and the spot size for beam convergence is within the diffraction limit, resulting in good actual imaging performance of the system.

[0167] Example 2

[0168] Based on the method provided in this embodiment of the invention, the determined target phase distribution and corresponding group delay can be found in [reference needed]. Figure 11 and Figure 12 As shown; Figure 11 This represents the phase required at position r. Figure 12 This represents the required group delay (GD) at position r. Based on the method provided in this embodiment of the invention, the phase and group delay of the nanostructures selected from the database can be found in [reference needed]. Figure 13 and Figure 14 As shown; Figure 13 The curve in the figure represents the phase required at position r, and the discrete points represent the actual phase of the selected nanostructure. Figure 14 The curve in the figure represents the required group delay at point r, and the discrete points represent the actual group delay of the selected nanostructure. Based on Figure 13 and Figure 14 It can be seen that the phase and group delay of the selected nanostructure are well matched with the required phase and group delay.

[0169] A metasurface was formed based on the selected nanostructure, and simulations were performed on the entire wavelength range within the working band based on this metasurface. The full-wavelength simulation results are shown in [link to full-wavelength simulation results]. Figure 15 As shown. The plane containing the metasurface is the xy plane, with the principal optical axis along the z-axis. Figure 15 In the figure (a), the relative light intensity is shown on the z-axis. The focal length of the metasurface is 6.93 mm. Figure 15 In the middle (b), the relative light intensity on the x-axis at the focal point of the metasurface is 10.7881 μm. Figure 15 (c) represents a partial light intensity diagram of the xz plane, where different shades of gray represent different light intensities.

[0170] In Example 1, the required phase and group delay show good matching in the database, and the nanostructure required for optimization also shows good matching in the database, exhibiting good consistency and ensuring the fabrication feasibility of the metasurface. Furthermore, by Figure 15 It can be seen that the metasurface designed based on the design method provided in the embodiments of the present invention has a diffuse spot size of approximately 10.8 μm, and the spot size for beam convergence is within the diffraction limit, resulting in good actual imaging performance of the system.

[0171] Example 3

[0172] The method provided in this embodiment of the invention is applied to a superconducting hybrid system, the full-band dispersion spot size of which is as follows: Figure 16 As shown, the size of the diffuse spot is 5.8 μm. The phase at position r of the designed metasurface can be seen in [reference needed]. Figure 17 As shown; Figure 17 In this context, Theoretical represents the phase required at position r, and Rods represents the actual phase of the selected nanostructure, which is the true value of the nanostructure.

[0173] Depend on Figure 17 It is evident that there is some difference between the selected phase of the nanostructure and the required phase. This is understandable, primarily because the embodiments of this invention consider other parameters such as GD and GDD in addition to the phase. However, this difference is within an acceptable error range and is an acceptable result, with good actual performance, which can be found in [reference needed]. Figure 18 As shown.

[0174] Specifically, a metasurface is formed based on the selected nanostructure, and simulations are performed on the entire wavelength range within the working band based on this metasurface. The full-wavelength simulation results are available in [reference needed]. Figure 18 As shown. The plane containing the metasurface is the xy plane, with the principal optical axis along the z-axis. Figure 18 In the figure (a), the relative light intensity is shown on the z-axis. The focal length of the metasurface is 6.682 mm. Figure 18 In the middle (b), the relative light intensity on the x-axis at the focal point of the metasurface is shown, and the size of the diffuse spot is 6.109 μm. Figure 18 (c) represents a partial light intensity diagram of the xz plane, where different shades of gray represent different light intensities.

[0175] Example 4

[0176] The method provided in this embodiment of the invention is applied to another refracto-hyperhybrid system, whose full-band dispersion spot size is as follows: Figure 19 As shown, the size of the dispersion spot is 5.2 μm. The phase at position r of the designed metasurface can be seen in [reference needed]. Figure 20 As shown; Figure 20 In this context, Theoretical represents the phase required at position r, and Rods represents the actual phase of the selected nanostructure, which is the true value of the nanostructure.

[0177] A metasurface was formed based on the selected nanostructure, and simulations were performed on the entire wavelength range within the working band based on this metasurface. The full-wavelength simulation results are shown in [link to full-wavelength simulation results]. Figure 21 As shown. The plane containing the metasurface is the xy plane, with the principal optical axis along the z-axis. Figure 21 In the figure (a), the relative light intensity is shown on the z-axis. The focal length of the metasurface is 6.5715 mm. Figure 21 In Figure (b), the relative light intensity along the x-axis at the focal point of the metasurface is 5.719 μm. Figure 21 (c) represents a partial light intensity diagram of the xz plane, where different shades of gray represent different light intensities.

[0178] The foregoing has described in detail the phase optimization and design method of metasurfaces provided by the embodiments of the present invention. This method can also be implemented by a corresponding device. The following describes in detail the phase optimization device and design device of metasurfaces provided by the embodiments of the present invention.

[0179] Figure 22 A schematic diagram of a phase optimization device for a metasurface provided in an embodiment of the present invention is shown. Figure 22 As shown, the phase optimization device for the metasurface includes: a parameter determination unit 221, a selection unit 222, a difference determination unit 223, and a processing unit 224.

[0180] The parameter determination unit 221 is used to determine a first parameter and a second parameter required at multiple locations on the metasurface based on the candidate phase distribution of the metasurface; one of the first parameter and the second parameter is phase, and the other is group delay or group delay dispersion;

[0181] The selection unit 222 is used to select multiple candidate nanostructures corresponding to the multiple positions from a preset database to form candidate metasurfaces;

[0182] The difference determination unit 223 is used to determine the parameter difference value of the candidate metasurface; the parameter difference value represents the difference between the first parameter of the candidate nanostructure and the first parameter required at the corresponding position, and the difference between the second parameter of the candidate nanostructure and the second parameter required at the corresponding position;

[0183] The processing unit 224 is used to determine that the candidate phase distribution meets the requirements if the imaging quality of the candidate metasurface meets the required target imaging quality and the parameter difference value is less than a preset threshold; otherwise, it updates the candidate phase distribution.

[0184] In one possible implementation, the selection unit 222 selects multiple candidate nanostructures corresponding to the multiple locations from a preset database, including: selecting the nanostructure in the preset database whose first parameter is closest to the first parameter required at the target location as the candidate nanostructure at the target location; the target location is a position among the multiple locations.

[0185] The difference determination unit 223 determines the parameter difference value of the candidate metasurface, including: determining the difference between the second parameter of each candidate nanostructure and the second parameter required at the corresponding position; and determining the parameter difference value based on the difference between the second parameters of all candidate nanostructures and the second parameter required at the corresponding position.

[0186] In one possible implementation, the processing unit 224 updates the candidate phase distribution by:

[0187] The candidate phase distribution is updated according to an objective function; the objective function includes an imaging quality difference term and a parameter difference term.

[0188] The imaging quality difference term is used to represent the difference between the imaging quality of the candidate metasurface and the target imaging quality, and the parameter difference term represents the difference between the parameter difference value and the preset threshold.

[0189] In one possible implementation, where one of the first parameter and the second parameter is phase and the other is group delay dispersion, the parameter determination unit 221 is further configured to: determine the group delay required at the plurality of locations respectively; the parameter difference value further represents the difference between the group delay of the candidate nanostructure and the group delay required at the corresponding location.

[0190] In one possible implementation, the parameter determination unit 221 is further configured to:

[0191] A third parameter is determined for each of the multiple locations; the third parameter includes the equivalent refractive index and / or the radius of the metasurface; the parameter difference value also represents the difference between the third parameter of the candidate nanostructure and the third parameter required at the corresponding location.

[0192] In one possible implementation, the selection unit 222 selects multiple candidate nanostructures corresponding to the multiple positions from a preset database, including:

[0193] For a given location, determine the overall difference between the parameters of each nanostructure in the preset database and the required parameters at that location; the overall difference value diff satisfies:

[0194] diff=ω phase Δphase+ω GD ΔGD+ω GDD ΔGDD+ω neff Δn eff +ω R ΔR;

[0195] Wherein, Δphase represents the difference between the phase of the nanostructure and the phase required at the stated location, ΔGD represents the difference between the group delay of the nanostructure and the group delay required at the stated location, ΔGDD represents the difference between the group delay dispersion of the nanostructure and the group delay dispersion required at the stated location, and Δn eff ΔR represents the difference between the equivalent refractive index of the nanostructure and the required equivalent refractive index at the stated location; ω represents the difference between the designed metasurface radius and the required metasurface radius. phase ω GD ω GDD ω neff ω R These represent the weights of the corresponding differences;

[0196] The nanostructure with the smallest overall difference value is selected as the candidate nanostructure corresponding to the specified location.

[0197] This invention also provides a design apparatus for metasurfaces, see [link to relevant documentation]. Figure 23 As shown, it includes:

[0198] Determining module 21 is used to determine the target imaging quality required for the metasurface;

[0199] Optimization module 22 is used to repeatedly execute the phase optimization method provided in the above embodiments on the candidate phase distribution of the metasurface until the candidate phase distribution meets the requirements;

[0200] Design module 23 is used to take the candidate phase distribution that meets the requirements as the target phase distribution, and design a metasurface based on the target phase distribution and the selected nanostructure.

[0201] It should be noted that the devices provided in the above embodiments are only illustrated by the division of the above functional modules when implementing the corresponding functions. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. In addition, the devices provided in the above embodiments and the phase optimization and design method embodiments of metasurfaces belong to the same concept, and their specific implementation process can be found in the method embodiments, which will not be repeated here.

[0202] According to one aspect of this application, embodiments of the present invention also provide a computer program product comprising a computer program containing program code for performing the methods shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network via a communication component. When the computer program is executed by a processor, it performs the metasurface phase optimization method or design method provided in embodiments of this application.

[0203] Furthermore, embodiments of the present invention also provide an electronic device, which includes a processor and a memory. The memory stores a computer program, and the processor is capable of executing the computer program stored in the memory. When the computer program is executed by the processor, it can implement the phase optimization method or design method of the metasurface provided in any of the above embodiments.

[0204] For example, Figure 24 An electronic device provided by an embodiment of the present invention is shown. The device includes a bus 1110, a processor 1120, a transceiver 1130, a bus interface 1140, a memory 1150, and a user interface 1160.

[0205] In this embodiment of the invention, the device further includes: a computer program stored in a memory 1150 and executable on a processor 1120, which, when executed by the processor 1120, implements the various processes of the above-described metasurface phase optimization and design method embodiments.

[0206] Transceiver 1130 is used to receive and send data under the control of processor 1120.

[0207] In this embodiment of the invention, a bus architecture (represented by bus 1110) is used. Bus 1110 may include any number of interconnected buses and bridges. Bus 1110 connects various circuits, including one or more processors represented by processor 1120 and memory represented by memory 1150.

[0208] Processor 1120 can be an integrated circuit chip with signal processing capabilities. Processors include: general-purpose processors, central processing units, digital signal processors, etc.

[0209] The memory 1150 in this embodiment of the invention can be volatile memory or non-volatile memory, or may include both volatile memory and non-volatile memory.

[0210] Furthermore, embodiments of the present invention also provide a computer-readable storage medium storing a computer program thereon. When the computer program is executed by a processor, it implements the various processes of the above-described metasurface phase optimization method or design method embodiments and can achieve the same technical effect. To avoid repetition, it will not be described again here.

[0211] The above description is merely a specific implementation of the embodiments of the present invention, but the protection scope of the embodiments of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the embodiments of the present invention should be included within the protection scope of the embodiments of the present invention. Therefore, the protection scope of the embodiments of the present invention should be determined by the protection scope of the claims.

Claims

1. A phase optimization method for a metasurface, characterized in that, include: Based on the candidate phase distribution of the metasurface, the required first parameter and the required second parameter at multiple locations on the metasurface are determined respectively; One of the first parameter and the second parameter is the phase, and the other is the group delay or group delay dispersion; Multiple candidate nanostructures corresponding to the multiple locations are selected from a preset database to form candidate metasurfaces; Determine the parameter differences of the candidate metasurfaces; The parameter difference value represents the difference between the first parameter of the candidate nanostructure and the first parameter required at the corresponding position, and the difference between the second parameter of the candidate nanostructure and the second parameter required at the corresponding position; If the imaging quality of the candidate metasurface meets the required target imaging quality and the parameter difference value is less than a preset threshold, the candidate phase distribution is determined to meet the requirements; otherwise, the candidate phase distribution is updated.

2. The method according to claim 1, characterized in that, The step of selecting multiple candidate nanostructures corresponding to the multiple locations from a preset database includes: selecting the nanostructure in the preset database whose first parameter is closest to the first parameter required at the target location as the candidate nanostructure at the target location; the target location is a position among the multiple locations. Determining the parameter difference value of the candidate metasurface includes: determining the difference between a second parameter of each candidate nanostructure and a second parameter required at the corresponding location; and determining the parameter difference value based on the differences between the second parameters of all candidate nanostructures and the second parameter required at the corresponding location.

3. The method according to claim 1 or 2, characterized in that, Updating the candidate phase distribution includes: The candidate phase distribution is updated according to an objective function; the objective function includes an imaging quality difference term and a parameter difference term. The imaging quality difference term is used to represent the difference between the imaging quality of the candidate metasurface and the target imaging quality, and the parameter difference term represents the difference between the parameter difference value and the preset threshold.

4. The method according to claim 3, characterized in that, When the parameter difference value is greater than the preset threshold, there is a positive correlation between the parameter difference item and the difference between the parameter difference value and the preset threshold. If the parameter difference value is less than the preset threshold, the parameter difference item is zero.

5. The method according to claim 1, characterized in that, When one of the first parameter and the second parameter is phase and the other is group delay dispersion, the method further includes: determining the required group delay at each of the plurality of locations; The parameter difference value also represents the difference between the group delay of the candidate nanostructure and the required group delay at the corresponding location.

6. The method according to claim 1, characterized in that, Also includes: Determine the third parameter required at multiple locations; the third parameter includes the equivalent refractive index and / or the radius of the metasurface; The parameter difference value also represents the difference between the third parameter of the candidate nanostructure and the third parameter required at the corresponding location.

7. The method according to claim 6, characterized in that, The step of selecting multiple candidate nanostructures corresponding to the multiple locations from a preset database includes: For a given location, determine the overall difference between the parameters of each nanostructure in the preset database and the required parameters at that location; the overall difference value diff satisfies: diff=ω phase Δphase+ω GD ΔGD+ω GDD ΔGDD+ω neff Δn eff +oh R ΔR; Wherein, Δphase represents the difference between the phase of the nanostructure and the phase required at the stated location, ΔGD represents the difference between the group delay of the nanostructure and the group delay required at the stated location, ΔGDD represents the difference between the group delay dispersion of the nanostructure and the group delay dispersion required at the stated location, and Δn eff ΔR represents the difference between the equivalent refractive index of the nanostructure and the required equivalent refractive index at the stated location; ω represents the difference between the designed metasurface radius and the required metasurface radius. phase ω GD ω GDD ω neff ω R These represent the weights of the corresponding differences; The nanostructure with the smallest overall difference value is selected as the candidate nanostructure corresponding to the specified location.

8. A method for designing metasurfaces, characterized in that, include: Determine the target imaging quality required for the metasurface; The phase optimization method as described in any one of claims 1 to 7 is repeatedly applied to the candidate phase distribution of the metasurface until the candidate phase distribution meets the requirements; The candidate phase distribution that meets the requirements is taken as the target phase distribution, and the metasurface is designed based on the target phase distribution and the selected nanostructure.

9. A phase optimization device for a metasurface, characterized in that, include: The parameter determination unit is used to determine the first parameter and the second parameter required at multiple locations on the metasurface, respectively, based on the candidate phase distribution of the metasurface. One of the first parameter and the second parameter is the phase, and the other is the group delay or group delay dispersion; The selection unit is used to select multiple candidate nanostructures corresponding to the multiple positions from a preset database to form candidate metasurfaces; A difference determination unit is used to determine the parameter difference values ​​of the candidate metasurface; The parameter difference value represents the difference between the first parameter of the candidate nanostructure and the first parameter required at the corresponding position, and the difference between the second parameter of the candidate nanostructure and the second parameter required at the corresponding position; The processing unit is configured to determine that the candidate phase distribution meets the requirements if the imaging quality of the candidate metasurface meets the required target imaging quality and the parameter difference value is less than a preset threshold; otherwise, the candidate phase distribution is updated.

10. A design apparatus for metasurfaces, characterized in that, include: A determination module is used to determine the target imaging quality required for the metasurface; An optimization module is configured to iteratively execute the phase optimization method as described in any one of claims 1 to 7 on the candidate phase distribution of the metasurface until the candidate phase distribution meets the requirements; The design module is used to select a candidate phase distribution that meets the requirements as the target phase distribution, and design a metasurface based on the target phase distribution and the selected nanostructure.

11. An electronic device comprising a processor and a memory, the memory storing a computer program, characterized in that, The processor executes a computer program stored in the memory to implement the metasurface phase optimization method as described in any one of claims 1 to 7 or the design method as described in claim 8.

12. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the metasurface phase optimization method as described in any one of claims 1 to 7 or the design method as described in claim 8.

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