Concentric ring superlens based on two-dimensional unit structure assembly and preparation method thereof

Abstract

The application provides a concentric ring superlens based on assembly of two-dimensional unit structures and a preparation method thereof. The application obtains a simulation region of two-dimensional unit structures, obtains processable structures in the simulation region, constructs a unit structure library containing complete optical information according to the processable structures, obtains a two-dimensional structure section according to the unit structure library, rotates the two-dimensional structure section around an optical axis, and obtains the overall three-dimensional structure of the concentric ring superlens. The preparation method of the concentric ring superlens of the application makes the calculation power requirement for designing the concentric ring superlens no longer increase with the increase of the aperture, and the design time of the superlens with an aperture of the order of thousands of wavelengths is reduced from the order of weeks to the order of minutes, which has obvious speed advantages in overall structure assembly, layout generation, sample processing and the like. The focusing efficiency of the concentric ring superlens prepared by the application is obviously higher than that of a Fresnel lens of the same order.

Description

Technical Field

[0001] This application relates to the field of micro-nano structure fabrication technology, and in particular to a concentric ring metalens based on two-dimensional unit structure assembly and its fabrication method. Background Technology

[0002] Modern optical imaging systems show a clear trend towards lightweighting and integration, with increasingly stringent constraints on the size and weight of optical components. Optical metalenses, through subwavelength nanostructure arrays, modulate the energy and phase distribution of light waves. Compared to traditional optical components, they offer numerous advantages in new imaging technologies such as micro-imaging systems, including low cost, ease of integration, and high imaging resolution, thus greatly adapting to the increasingly widespread demand for lightweight applications.

[0003] Currently, metalenses are mainly classified into concentric ring metalenses and array metalenses based on the arrangement of their micro / nano structures. Concentric ring metalenses consist of a series of concentric ring micro / nano structures with widths on the order of wavelength or subwavelength. Because these lenses have a centrosymmetric structure, the design and simulation process only needs to be performed within a two-dimensional cross-section including the lens diameter and optical axis. Through the overall fine design of the multi-ring structure, these metalenses can achieve near-diffraction-limited monochromatic optical imaging. However, since this approach relies on the global design of the lens structure, designing lenses with apertures on the order of thousands of wavelengths places high demands on the computing platform, consuming weeks or even months of time.

[0004] Array-type metalenses are composed of a series of subwavelength three-dimensional unit structures. Each unit contains one or more dielectric nanopillars, which can be equivalent to miniature truncated waveguides placed along the direction of light propagation. The light wave interacts with the nanopillars, generating different waveguide modes and modulating parameters such as amplitude, phase, and polarization. The dielectric pillars are high-refractive-index materials relative to air, and most of the light energy is concentrated inside the dielectric pillars. The energy density within the air gaps at the unit boundaries is low, resulting in weak electromagnetic coupling between units and minimal interference with their optical properties. Based on this principle, the development process of such metalenses no longer focuses on the overall lens but simplifies to the local design of the unit structures: first, three-dimensional unit structures with different complex amplitude output characteristics are obtained by adjusting the cross-sectional shape of the dielectric pillars; then, appropriate unit structures are placed according to the phase requirements at various points in the metalens to construct the overall phase surface. These lenses can achieve efficient focusing with a wide spectrum and large numerical aperture, but the number of their micro / nano structures often reaches 10. 6 ~10 7 / mm 2 The sheer volume of data, coupled with the complex and varied morphology of the unit structures, presents challenges for layout generation and subsequent processing. Summary of the Invention

[0005] Therefore, it is necessary to provide a concentric ring metalens based on two-dimensional unit structure assembly and its preparation method, which can simultaneously solve the problems of large computational load for concentric ring metalenses and large data volume for array-type metalenses, and address the shortcomings of existing technologies.

[0006] To solve the above problems, this application adopts the following technical solution:

[0007] One of the objectives of this application is to provide a method for fabricating a concentric ring metalens based on a two-dimensional unit structure assembly, comprising the following steps:

[0008] Construct the simulation region of the two-dimensional unit structure;

[0009] Obtain the machinable structures in the simulation region;

[0010] Construct a unit structure library containing complete optical information based on the described machinable structure;

[0011] Obtain the two-dimensional structural cross-section based on the aforementioned unit structure library;

[0012] Rotating the two-dimensional cross-section around the optical axis yields the overall three-dimensional structure of the concentric ring metalens.

[0013] In some embodiments, the step of constructing the simulation region of the two-dimensional unit structure specifically includes the following steps:

[0014] The width L, design domain width Ld, thickness H, and structured mesh size Lmesh of the two-dimensional unit structure are determined based on the working wavelength λ, numerical aperture NA, and refractive index n of the selected material of the concentric ring meta-lens, in order to construct the simulation region of the two-dimensional unit structure.

[0015] For a superlens with NA ≤ 0.5, the value of L is slightly less than λ; for a superlens with NA > 0.5, L < λ / 2NA.

[0016] The mesh size satisfies Lmesh≤λ / 8n; the design domain width satisfies Ld=L-2Lmesh; and the structural thickness H is λ / (n-1).

[0017] In some embodiments, the step of obtaining the machinable structure in the simulation region specifically includes the following steps:

[0018] All element structures in the simulation region are represented by 01 strings. Two-dimensional element structures whose minimum structure does not meet the manufacturing process requirements are filtered out, and machinable structures are retained. Here, 1 and 0 represent that the corresponding mesh nodes have medium material and do not have medium material, respectively. The string length is Ld / Lmesh, and Ld / Lmesh is not greater than 20.

[0019] In some embodiments, the step of screening out two-dimensional unit structures whose minimum structure does not meet the process requirements specifically includes the following steps:

[0020] The cell structures are exhaustively enumerated to determine manufacturability. Assuming that the minimum feature size is limited by the processing technology to N times the grid size, if the cell structure string contains a substring with fewer than N consecutive characters of the same value, the cell structure is determined to be an unmanufacturable structure and is filtered out.

[0021] In some embodiments, the step of constructing a unit structure library containing complete optical information based on the fabricatable structure specifically includes the following steps:

[0022] A scattering field calculation model based on finite element analysis is constructed. For the two basic polarization modes of two-dimensional waves, TE and TM, they are set to be equally strong normal incidence as the background field. The total scattering field of the machinable structure is solved according to the Helmholtz equation, and the average complex amplitude of the near-field exit surface is collected.

[0023] In some embodiments, the step of constructing a unit structure library containing complete optical information based on the fabricatable structure specifically includes the following steps:

[0024] In the simulation region, equal-intensity TE and TM waves along the positive y direction are applied as background fields, and the total field after scattering by the unit structure is solved according to the Helmholtz equation.

[0025] A virtual near-field receiving surface is set up 1 to 2 grids above the simulation area, and the average complex amplitudes of the TM and TE waves on this surface are calculated and denoted as Ex and Ez, respectively, to characterize the optical properties of the corresponding unit structure.

[0026] Based on the optical properties, construct a unit structure library containing complete optical information.

[0027] In some embodiments, the step of obtaining the two-dimensional structural cross-section according to the unit structure library specifically includes the following steps:

[0028] For the overall structure of the assembled lens, if the polarization mode weights are assigned as 0, 1 or 10, the arrangement of the unit structure minimizes the square error between the single polarization mode complex amplitude and the required complex amplitude at each point. If both weights are non-zero, the ideal phase difference between the TE and TM waves is introduced and the values ​​are traversed from 0 to 2π to minimize the sum of the weighted complex amplitude errors, and the overall two-dimensional structure is extracted.

[0029] In some embodiments, the step of obtaining the two-dimensional structural cross-section according to the unit structure library specifically includes the following steps:

[0030] Preset weights W for the two polarization modes TE WTM And satisfy W TE >0、W TM >0、W TE +W TM =1;

[0031] Judgment equation W TE =1 or W TM Is the equation 1 true?

[0032] If so, proceed with the following steps:

[0033] In the case of single-polarization mode TE or TM focusing, the ideal normalized complex amplitude is denoted as: Where x is the radial position coordinate of the lens, λ is the incident light wavelength, i is the imaginary unit, and the focal length F is determined by the lens diameter D and the numerical aperture NA, Ψ x0(z0) To take any value for the phase constant; select the m-th unit structure in the interval (m-1)L~mL in the global coordinate system of the lens, where m ranges from 1 to D / 2L, such that the square of the complex amplitude error γ is... m =|E x(z) -E x0(z0) (mL-L / 2)| 2 Minimize; repeat the above steps until all unit structures in the unit structure library are assembled and output a two-dimensional structural cross section;

[0034] If not, proceed with the following steps:

[0035] Taking into account dual-polarization mode focusing, the ideal normalized complex amplitudes of TM and TE are denoted as follows:

[0036]

[0037] Introduce the phase constant difference between the two, ΔΨ=Ψ z0 -Ψ x0 And perform near-continuous sampling within [0, 2π);

[0038] For any given ΔΨ, select the m-th unit structure within the interval (m-1)L~mL in the global coordinate system of the lens, where m ranges from 1 to D / 2L, such that the weighted complex amplitude error squared is...

[0039] γ m =W TM |E x -E x0 (mL-L / 2)| 2 +W TE |E z -E z0 (mL-L / 2)| 2 Minimize and calculate the overall complex amplitude error under the current ΔΨ.

[0040] When a certain value of ΔΨ makes Γ reach its minimum, the corresponding overall two-dimensional structure is the optimal structure under the current weight allocation, and this two-dimensional structure is output.

[0041] In some embodiments, the step of rotating the two-dimensional structural cross-section about the optical axis to obtain the overall three-dimensional structure of the meta-lens specifically includes the following steps:

[0042] Rotate the obtained two-dimensional structural cross-section around the optical axis to obtain the overall three-dimensional structure of the concentric ring metalens.

[0043] The concentric ring meta-lens provided in this application is prepared by any of the concentric ring meta-lens preparation methods described in this application.

[0044] The present application adopts the above technical solution, and its beneficial effects are as follows:

[0045] The concentric ring metalens based on two-dimensional unit structure assembly and its fabrication method provided in this application involve constructing a simulation region of the two-dimensional unit structure, obtaining the machinable structure in the simulation region, constructing a unit structure library containing complete optical information based on the machinable structure, obtaining a two-dimensional structure cross-section based on the unit structure library, and rotating the two-dimensional structure cross-section around the optical axis to obtain the overall three-dimensional structure of the metalens. The above-mentioned fabrication method of the concentric ring metalens avoids the large computational load problem caused by the global structure design of conventional concentric ring metalenses, so that the computational power requirement for designing concentric ring metalenses no longer increases with the increase of aperture. The design time of a metalens with an aperture on the order of thousands of wavelengths is reduced from the order of weeks to the order of minutes. It has significant speed advantages in overall structure assembly, layout generation, and sample processing. Furthermore, the meta-lens has a similar configuration to the phase-type second-order Fresnel lens, and neither requires huge computing power and time costs for structural optimization. However, the meta-lens has obvious advantages in optical performance. Its subwavelength structure allows local phase values ​​to traverse from 0 to 2π, making the focusing efficiency significantly higher than that of the second-order Fresnel lens. Attached Figure Description

[0046] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 A flowchart illustrating the steps of the method for fabricating a concentric ring metalens based on a two-dimensional unit structure assembly provided in this embodiment;

[0048] Figure 2 This is a schematic diagram of the simulation region for constructing the two-dimensional unit structure provided in this embodiment;

[0049] Figure 3 This embodiment provides a flowchart of the steps for obtaining a two-dimensional structural cross-section based on the unit structure library.

[0050] Figure 4 This is a schematic diagram of a two-dimensional structural cross-section obtained from the unit structure library provided in this embodiment;

[0051] Figure 5 This is a schematic diagram of the overall three-dimensional structure of the metalens obtained in this embodiment;

[0052] Figure 6 The image shows the simulated focusing effect of the meta-lens cross-section and a local image of its focal spot obtained in this embodiment. The lens aperture is 2cm, the focal length is 2cm, and the focusing efficiency is 60% when TE and TM waves of equal intensity are incident.

[0053] Figure 7 The image shows the imaging effect of the meta-lens sample obtained in this embodiment on the grating. The temperatures of the bright and dark fringes are 80℃ and 25℃, respectively. The width of the fringe line pairs is 8mm, the test distance is 80cm, and the equivalent spatial frequency is 0.1 line pairs per milliradian.

[0054] Figure 8 This is an image of a person captured by the meta-lens sample obtained in this embodiment. The person being photographed is wearing a short-sleeved thin top and glasses, and the test distance is approximately 2 meters. Detailed Implementation

[0055] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0056] In the description of this application, it should be understood that the terms "upper", "lower", "horizontal", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application.

[0057] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0058] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments.

[0059] This application provides a concentric ring metalens based on two-dimensional unit assembly and its fabrication method, which can simultaneously solve the problems of large computational load for concentric ring metalenses and large data volume for array-type metalenses. Specifically, it includes the following steps:

[0060] Based on the working wavelength and numerical aperture of the concentric ring meta-lens, the total width and design domain width of the two-dimensional unit structure are determined, and the design domain thickness is determined based on the refractive index of the medium material used in the concentric ring meta-lens. Based on the above geometric parameters, a simulation region including geometric domains such as substrate, design domain, air domain, and perfect matching layer is constructed.

[0061] Based on the operating wavelength of the concentric ring metalens, the structured grid size of the design model is determined, and the structured grid is constructed.

[0062] The material distribution within the two-dimensional unit structure design domain is represented by a finite-length 01 string. Each 0 or 1 character represents whether a small area centered on the corresponding grid point and with a grid size as its width contains a medium material.

[0063] The exhaustive method is used to traverse all the 01 strings corresponding to the two-dimensional unit structure. Based on the minimum feature size requirement of the concentric ring meta-lens processing technology, the two-dimensional unit structures whose minimum structure does not meet the processing technology requirements are screened out, and the remaining processable structures are retained.

[0064] Optical performance simulation was performed on the fabricable structure with TE and TM waves of equal strength in the background electric field. The Helmholtz equation was solved using the finite element method under the existing structured grid framework to obtain the total scattering field of the unit structure. The average complex amplitude information of the near-field TE and TM waves at the output end was collected to establish a unit structure library containing complete optical information.

[0065] The focal length is determined based on the aperture and numerical aperture of the meta-lens. The required phase at each point of the lens is determined based on the focal length and operating wavelength of the meta-lens. The required complex amplitude is constructed using the required phase and the background field amplitude.

[0066] The weights for TE and TM waves are selected, including:

[0067] If the weights are allocated as 0, 1 or 10, that is, focusing only on a single polarization mode, the unit structures are arranged sequentially, and the optimal unit is selected point by point to minimize the square error between the complex amplitude of the polarization mode and the required complex amplitude. The corresponding structure is the meta-lens structure for focusing a single polarization mode.

[0068] If both polarization modes have non-zero weights, then the overall difference of the ideal phase of the two polarization modes is introduced. Under the meaning of minimizing the square of the weighted complex amplitude error of each unit, the optimal value of the ideal phase difference is selected so that the sum of the square of the overall weighted complex amplitude error is minimized. The corresponding structure is the structure of the concentric ring superlens that takes into account the focusing of both polarization modes.

[0069] Rotate the two-dimensional cross-section of the concentric ring meta-lens around the optical axis to obtain the overall three-dimensional structure of the concentric ring meta-lens.

[0070] Specifically, Figures 1 to 5 The specific steps of the fabrication method of the concentric ring metalens based on two-dimensional unit structure assembly provided in Embodiment 1 of this application are illustrated.

[0071] Please see Figure 1 The flowchart below shows the steps of the method for preparing a concentric ring metalens based on a two-dimensional unit structure assembly provided in this embodiment 1, including steps S110 to S150. The implementation of each step is described in detail below.

[0072] Step S110: Construct the simulation region of the two-dimensional unit structure.

[0073] Please see Figure 2 This is a structural diagram of the simulation region for constructing the two-dimensional unit structure provided in this embodiment.

[0074] In this embodiment, the step of constructing the simulation region of the two-dimensional unit structure specifically includes the following steps:

[0075] Based on the working wavelength λ, numerical aperture NA, and refractive index n of the selected material of the concentric ring metalens, the width L, design domain width Ld, thickness H, and structured mesh size Lmesh of the two-dimensional unit structure are determined to construct the simulation region of the two-dimensional unit structure. For metalenses with NA ≤ 0.5, L can be slightly less than λ; for metalenses with NA > 0.5, L < λ / 2NA. The mesh size satisfies Lmesh ≤ λ / 8n; the design domain width satisfies Ld = L - 2Lmesh; and the structural thickness H is assumed to be λ / (n-1).

[0076] It is understandable that a slight increase in thickness can be made to increase the phase modulation range of TE and TM waves, but the thickness limit constrained by the processing technology must be met; the lower layer of the perfect matching layer contains 5 to 10 mesh layers, and the upper layer contains 10 to 15 mesh layers; the two sides of the unit structure are periodic boundary conditions.

[0077] Step S120: Obtain the machinable structure in the simulation area.

[0078] In this embodiment, the step of obtaining the machinable structure in the simulation region specifically includes the following steps:

[0079] All element structures in the simulation region are represented by 01 strings. Two-dimensional element structures whose minimum structure does not meet the manufacturing process requirements are filtered out, and only machinable structures are retained. Here, 1 and 0 represent the presence and absence of dielectric material in the corresponding mesh nodes, respectively. The string length is Ld / Lmesh, where Ld / Lmesh is no greater than 20. Therefore, the maximum number of element structures is approximately 2. 20 That is, 10 6 Magnitude;

[0080] The above-described unit structures are exhaustively enumerated to determine manufacturability. If the minimum feature size is limited to N times the grid size by the processing technology, and if the unit structure string contains substrings with fewer than N consecutive characters of the same value, then the unit structure is determined to be an unmanufacturable structure and is filtered out.

[0081] For example, in this embodiment, if N=2, the unit structures containing the substrings "010" and "101" are filtered out, and the remaining processable structures are retained. The above process takes only about 10 seconds. The exhaustive method is the most convenient and fastest method for searching unit structures.

[0082] Step S130: Construct a unit structure library containing complete optical information based on the fabricatable structure.

[0083] Specifically, in step S130, a scattering field calculation model based on finite element analysis is constructed, and TE and TM waves of equal intensity are set as background fields. The total scattering field of the machinable unit structure is solved according to the Helmholtz equation, and the average complex amplitude of the near-field exit surface is collected. Among them, TE and TM waves are two basic polarization modes of two-dimensional waves whose propagation direction is constrained in the simulation plane. TE wave is a transverse electric wave, which means that the direction of the electric field in the electromagnetic wave is perpendicular to the simulation plane; TM wave is a transverse magnetic wave, which means that the direction of the magnetic field in the electromagnetic wave is perpendicular to the simulation plane.

[0084] In some embodiments, the step of constructing a unit structure library containing complete optical information based on the fabricatable structure specifically includes the following steps:

[0085] In the simulation region, equal-intensity TE and TM waves along the positive y-direction are applied as background fields, and the total field after scattering by the unit structure is solved according to the Helmholtz equation. A virtual near-field receiving surface is set up 1 to 2 grids above the simulation region, and the average complex amplitudes of the TM and TE waves on this surface are calculated and denoted as Ex and Ez, respectively, to characterize the optical properties of the corresponding unit structures. Based on the optical properties, a unit structure library containing complete optical information is constructed.

[0086] It is understood that this embodiment constructs a scattering field calculation model based on finite element analysis, sets TE and TM waves of equal intensity as background fields, solves the total scattering field of the machinable unit structure according to the Helmholtz equation, and collects the average complex amplitude of the near-field exit surface.

[0087] Step S140: Obtain the two-dimensional structural cross section according to the unit structure library.

[0088] Specifically, in step S140, the overall lens structure is assembled. If the polarization mode weight is assigned as 0 or 10 (single polarization mode focusing), the unit structure is arranged to minimize the square error between the single polarization mode complex amplitude and the required complex amplitude at each point. If both weights are non-zero, the ideal phase difference between the two polarization modes is introduced and the values ​​from 0 to 2π are traversed to minimize the sum of the weighted complex amplitude errors, and the overall two-dimensional structure is extracted.

[0089] Please see Figure 3 The flowchart for the step of obtaining a two-dimensional structural cross-section based on the unit structure library provided in this embodiment specifically includes the following steps:

[0090] Step S141: Preset the weights W of the two polarization modes TE W TM And satisfy W TE >0、W TM >0、W TE +W TM =1;

[0091] Step S142: Determine equation W TE =1 or W TM Is the equation 1 true?

[0092] If so, proceed with the following steps:

[0093] Step S143: For W TE W TM The values ​​are 1 and 0, or 0 and 1, respectively. That is, in the case of single-polarization mode TE or TM focusing, the ideal normalized complex amplitude is denoted as . The focal length F is determined by the lens diameter D and the numerical aperture NA, Ψ x0(z0) It is a phase constant that can take any value;

[0094] Step S144: Select the m-th unit structure within the interval (m-1)L to mL in the overall coordinate system of the lens, where m ranges from 1 to D / 2L, and make the squared complex amplitude error γ at this point... m =|E x(z) -E x0(z0) (mL-L / 2)| 2 minimize;

[0095] Step S145: Repeat the above steps to output a two-dimensional structural cross-section after all the unit structures in the unit structure library are assembled;

[0096] If not, proceed with the following steps:

[0097] Step S143': Introduce the overall difference ΔΨ=Ψ of the ideal phase z0 -Ψ x0 ;

[0098] Step S144': For W TE W TM Neither of them is 0, meaning that when focusing in both polarization modes is taken into account, the ideal normalized complex amplitudes of TM and TE are denoted as follows:

[0099] Step S145': Perform near-continuous sampling within [0, 2π). For any ΔΨ, select the m-th unit structure within the interval (m-1)L to mL in the overall lens coordinate system, where m ranges from 1 to D / 2L.

[0100] Step S146': Square the weighted complex amplitude error at this point.

[0101] γ m =W TM |E x -E x0 (mL-L / 2)| 2 +W TE |E z -E z0 (mL-L / 2)| 2 Minimize and calculate the overall complex amplitude error under the current ΔΨ.

[0102] Step S146': When a certain value of ΔΨ makes Γ reach its minimum, the corresponding overall two-dimensional structure is the optimal structure under the current weight allocation, and the cross section of this two-dimensional structure is output.

[0103] It is understandable that if the polarization mode weights are assigned as 0, 1 or 10 (single polarization mode focusing), the arrangement of unit structures minimizes the square error between the single polarization mode complex amplitude and the required complex amplitude at each point. If both weights are non-zero, the ideal phase difference between the two polarization modes is introduced and the values ​​are traversed from 0 to 2π to minimize the sum of the weighted complex amplitude errors and extract the overall two-dimensional structure.

[0104] Please see Figure 4 This is a schematic diagram of a two-dimensional structural cross-section obtained from the unit structure library in this embodiment.

[0105] Step S150: Rotate the two-dimensional structure section around the optical axis to obtain the overall three-dimensional structure of the concentric ring meta-lens.

[0106] In this embodiment, the step of rotating the two-dimensional structural cross section around the optical axis to obtain the overall three-dimensional structure of the concentric ring metalens specifically includes the following steps: rotating the obtained two-dimensional structural cross section around the optical axis once to obtain the concentric ring metalens.

[0107] Please see Figure 5 This is a schematic diagram of the overall three-dimensional structure of the metalens obtained in this embodiment.

[0108] In this embodiment, a silicon-based metalens is designed for focusing normally incident monochromatic plane waves with a wavelength of 10 μm. The focusing efficiency for unpolarized light is greater than 60%, and for single-polarization mode focusing, a focusing efficiency of up to 80% can be achieved. See the simulation results for details. Figure 6 Furthermore, simulation verification shows that the lens has good imaging performance in the 9–11 μm band and within a ±30° field of view. (Imaging performance details can be found in the documentation.) Figure 7 , Figure 8 .

[0109] In this embodiment, the design domain thickness is assumed to be the full-wave modulation thickness, i.e., λ / (n-1). However, within the subwavelength scale where the two sides of the unit are limited to air, the optimal thickness that can effectively cover all modulation phases of the two polarization modes may be slightly larger than this value. This application does not make a specific limitation on this.

[0110] In this embodiment, the width of the unit structure should be no less than 12 grid sizes to ensure that the number of processable unit structures is on the order of hundreds, thereby achieving high transmittance modulation of any phase; in addition, the width is no greater than the smaller value between λ and λ / 2NA to ensure that the unit structure has no high diffraction order and that the lens edge satisfies the Nyquist sampling condition to ensure focusing efficiency; this application does not specifically limit the numerical aperture of the metalens and the width of the unit structure.

[0111] In this embodiment, the weight of the polarization mode represents the priority given to its focusing efficiency. The larger the weight of a certain polarization mode, the higher the focusing efficiency of the resulting metalens for that polarization mode. The three-dimensional concentric ring metalens exhibits polarization insensitivity to incident light with spatially consistent polarization characteristics, and its focusing efficiency is approximately the average of the focusing efficiencies of TE and TM waves. For transversely polarized and radially polarized vector beams, their focusing efficiencies correspond to the focusing efficiencies of the overall two-dimensional structure for TE and TM waves, respectively. In this embodiment, for the problem of simultaneously focusing two polarization modes, the weights of both are set to 0.5, that is, the focusing efficiencies of the two polarization modes are considered with equal priority, further eliminating the sensitivity of the three-dimensional metalens structure to vector polarized light, and maximizing the overall focusing efficiency for unpolarized light. This embodiment does not impose specific limitations on the focusing weights.

[0112] This application provides a concentric ring metalens based on two-dimensional unit assembly and its fabrication method. This application constructs a simulation region of the two-dimensional unit structure, obtains the machinable structures within the simulation region, constructs a unit structure library containing complete optical information based on the machinable structures, and then constructs the overall cross-sectional structure of the concentric ring metalens according to the focusing requirements of different polarization modes. The two-dimensional structure cross-section is rotated around the optical axis to obtain the overall three-dimensional structure of the concentric ring metalens. The metalens obtained in the above embodiments of this application possesses the common advantages of metalenses, such as thinness, ease of integration, and the ability to achieve aberration-free focusing. It can overcome computational constraints to design metalenses with apertures on the order of thousands of wavelengths and above, with time costs only on the order of minutes or even seconds. It is the most efficient and cost-effective solution among known metalens design methods. In terms of optical performance, the focusing efficiency of the metalens is significantly better than that of a similarly structured second-order Fresnel lens. Therefore, the metalens design method described in this paper balances optical performance with design and fabrication costs, and has practical application value in next-generation optical imaging and microscopy.

[0113] It is understood that the technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0114] The above are merely preferred embodiments of this application, and only specifically describe the technical principles of this application. These descriptions are only for explaining the principles of this application and should not be construed as limiting the scope of protection of this application in any way. Based on this explanation, any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application, as well as other specific embodiments of this application that can be conceived by those skilled in the art without creative effort, should be included within the scope of protection of this application.

Claims

1. A method for fabricating a concentric ring metalens based on a two-dimensional unit structure assembly, characterized in that, Includes the following steps: Construct the simulation region of the two-dimensional unit structure; Obtain the machinable structures in the simulation region; Construct a unit structure library containing complete optical information based on the described machinable structure; Obtain the two-dimensional structural cross-section based on the aforementioned unit structure library; Rotating the two-dimensional cross-section around the optical axis yields the overall three-dimensional structure of the concentric ring meta-lens; The step of obtaining the machinable structure in the simulation region specifically includes the following steps: All unit structures in the simulation area are represented by 01 strings. Two-dimensional unit structures whose minimum structure does not meet the processing requirements are filtered out, and the machinable structures are retained. Here, 1 and 0 represent that the corresponding mesh nodes have medium material and no medium material, respectively. The string length is Ld / Lmesh, and Ld / Lmesh is no greater than 20; The process of eliminating two-dimensional unit structures whose minimum structure does not meet the processing requirements specifically includes the following steps: The cell structures are exhaustively enumerated to determine manufacturability. Assuming that the minimum feature size is limited by the processing technology to N times the grid size, if the cell structure string contains a substring with fewer than N consecutive characters of the same value, the cell structure is determined to be an unmanufacturable structure and is filtered out.

2. The method for fabricating a concentric ring metalens based on a two-dimensional unit structure assembly as described in claim 1, characterized in that, The steps for constructing the simulation region of the two-dimensional unit structure specifically include the following steps: The width L, design domain width Ld, thickness H, and structured mesh size Lmesh of the two-dimensional unit structure are determined based on the working wavelength λ, numerical aperture NA, and refractive index n of the selected material of the concentric ring meta-lens, in order to construct the simulation region of the two-dimensional unit structure. For a superlens with NA ≤ 0.5, the value of L is slightly less than λ; for a superlens with NA > 0.5, L < λ / 2NA. The mesh size satisfies Lmesh≤λ / 8n; the design domain width satisfies Ld=L-2Lmesh; and the structural thickness H is λ / (n-1).

3. The method for fabricating a concentric ring metalens based on a two-dimensional unit structure assembly as described in claim 2, characterized in that, The step of constructing a unit structure library containing complete optical information based on the said fabricable structure specifically includes the following steps: A scattering field calculation model based on finite element analysis is constructed. For the two basic polarization modes TE and TM of two-dimensional waves, the background field is set to be normal incidence of both with equal intensity. The total scattering field of the machinable structure is solved according to the Helmholtz equation, and the average complex amplitude of the near-field exit surface is collected.

4. The method for fabricating a concentric ring metalens based on a two-dimensional unit structure assembly as described in claim 3, characterized in that, The step of constructing a unit structure library containing complete optical information based on the said fabricable structure specifically includes the following steps: In the simulation region, equal-intensity TE and TM waves along the positive y direction are applied as background fields, and the total field after scattering by the unit structure is solved according to the Helmholtz equation. A virtual near-field receiving surface is set up 1 to 2 grids above the simulation area, and the average complex amplitudes of the TM and TE waves on this surface are calculated and denoted as Ex and Ez, respectively, to characterize the optical properties of the corresponding unit structure. Based on the optical properties, construct a unit structure library containing complete optical information.

5. The method for fabricating a concentric ring metalens based on a two-dimensional unit structure assembly as described in claim 4, characterized in that, The step of obtaining a two-dimensional structural cross-section based on the aforementioned unit structure library specifically includes the following steps: For the overall structure of the assembled lens, if the polarization mode weights are assigned as 0, 1 or 10, the arrangement of the unit structure minimizes the square error between the single polarization mode complex amplitude and the required complex amplitude at each point. If both weights are non-zero, the ideal phase difference between the TE and TM waves is introduced and the values ​​are traversed from 0 to 2π to minimize the sum of the weighted complex amplitude errors, and the overall two-dimensional structure is extracted.

6. The method for fabricating a concentric ring metalens based on a two-dimensional unit structure assembly as described in claim 5, characterized in that, The step of obtaining a two-dimensional structural cross-section based on the aforementioned unit structure library specifically includes the following steps: Preset weights for two polarization modes W TE , W TM And satisfy W TE >0、 W TM >0、 W TE + W TM =1; Judgment Equation W TE =1 or W TM Is the value = 1 true? If so, proceed with the following steps: In the case of single-polarization mode TE or TM focusing, the ideal normalized complex amplitude is denoted as: E x0(z0) ( x )=exp[2πi / λ ·( + Ψ x0(z0) ]], where x is the radial position coordinate of the lens, λ is the incident light wavelength, i is the imaginary unit, and the focal length is λ. F Due to the diameter of the lens D Determining the numerical aperture NA Ψ x0(z0) For any value, the phase constant; in the global coordinate system of the lens ( m -1) L ~ mL Select the first interval m Unit structure, m From 1 to D / 2 L This makes the square of the complex amplitude error here. γ m =| E x(z) -E x0(z0) ( mL - L / 2)| 2 Minimize; repeat the above steps until all unit structures in the unit structure library are assembled and output a two-dimensional structural cross section; If not, proceed with the following steps: Taking into account dual-polarization mode focusing, the ideal normalized complex amplitudes of TM and TE are denoted as follows: E x0 ( x )=exp[2πi / λ ·( + Ψ x0 )]、 E z0 ( x )=exp[2πi / λ ·( + Ψ z0 )]; Introducing the phase constant difference between the two Ψ = Ψ z0 - Ψ x0 And perform near-continuous sampling within [0, 2π); For any Ψ In the global coordinate system of the lens ( m -1) L ~ mL Select the first interval m Unit structure, m From 1 to D / 2 L This makes the weighted complex amplitude error squared here. γ m = W TM | E x -E x0 ( mL - L / 2)| 2 + W TE | E z -E z0 ( mL - L / 2)| 2 Minimize and compute the current Ψ Overall complex amplitude error ; when Ψ A certain value of makes Γ When the minimum value is reached, the corresponding overall two-dimensional structure is the optimal structure under the current weight allocation, and this two-dimensional structure is output.

7. The method for fabricating a concentric ring metalens based on a two-dimensional unit structure assembly as described in claim 6, characterized in that, The step of rotating the two-dimensional structural cross-section around the optical axis to obtain the overall three-dimensional structure of the meta-lens specifically includes the following steps: Rotate the obtained two-dimensional structural cross-section around the optical axis to obtain the overall three-dimensional structure of the concentric ring metalens.

8. A concentric ring meta-lens, characterized in that, It is prepared by the method for preparing concentric ring metalenses according to any one of claims 1 to 7.

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