Design method of long-wave infrared achromatic beam splitting focusing type super-structure lens

Abstract

The invention relates to the technical field of optical device design, in particular to a design method of a long-wave infrared achromatic beam splitting focusing type super-structure lens. The method comprises the following steps: determining a substrate material, a nanostructure material, a radius R, a focal length f and four polarization channel focus coordinates; constructing a linear polarization unit phase parameter library and a transmissivity parameter library through FDTD (Frequency Division Time Division) parameter scanning; performing achromatic phase optimization on the four polarization states in the characteristic wavelength set based on a PSO algorithm to generate structural parameter distribution data of a linear polarization part and a circular polarization part; constructing a super-structure lens in a row staggered arrangement manner; and verifying the focusing performance of the super-structure lens array through an angular spectrum propagation algorithm. Nanometer units for regulating and controlling linearly polarized light and circularly polarized light are integrated through row staggered arrangement, the PSO algorithm is combined for achromatic phase collaborative optimization, multi-polarization-state beam splitting and focusing integration is achieved, the working wave band is widened, the broadband focusing consistency is improved, and the design and calculation cost of the super-structure lens array is reduced.

Description

Technical Field

[0001] This invention relates to the field of optical device design technology, and more specifically to a design method for a long-wave infrared achromatic beam-splitting metalens. Background Technology

[0002] In the long-wave infrared band (e.g., 8.4–11.6 μm), polarization imaging can be used for applications such as target detection and material identification. Existing polarization imaging systems typically employ a combination of discrete optical components, such as polarization beam splitters and imaging lenses (or array lenses), to achieve multi-polarization channel detection. However, discrete component solutions may suffer from issues such as large size and weight during system integration, which limits their application in airborne and spaceborne scenarios where miniaturization and high integration are critical.

[0003] To achieve system miniaturization, some studies have proposed integrating beam splitting and focusing functions into a single-layer device using metasurfaces, thus forming an integrated beam splitting and focusing device. Common methods for implementing existing beam-splitting and focusing metalenses include achieving beam splitting and focusing of different polarization states through sub-pixel division, functional region stitching, or multi-layer cascading. However, as device size shrinks further or the number of polarization channels increases, these methods may lead to reduced effective aperture utilization and decreased focusing efficiency, thus hindering further miniaturization and highly integrated applications.

[0004] Furthermore, metasurface phase responses typically exhibit certain dispersion characteristics, potentially leading to focus drift in the long-wave infrared broadband range. This results in devices achieving better performance under single-wavelength or narrow bandwidth conditions, while focusing performance is limited under broadband detection conditions. Therefore, there is a need for a metalens design scheme that is suitable for the long-wave infrared broadband range, capable of multi-polarization state beam splitting and focusing while reducing the impact of chromatic aberration, and also possesses a scalable design and verification process. Summary of the Invention

[0005] In view of this, the present invention provides a design method for a long-wave infrared achromatic differential beam focusing metalens, which aims to improve the existing long-wave infrared polarization imaging devices that have large size, large mass and narrow operating band.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, the present invention provides a design method for a long-wave infrared achromatic differential beam-focusing metalens, comprising the following steps: Determine the substrate material, nanostructure material, and the focal coordinates of the metalens radius R, focal length f, and four polarization channels; The metalens unit was scanned using FDTD software to construct a phase parameter library for the linear polarization unit. and transmittance parameter library ; Based on the Particle Swarm Optimization (PSO) algorithm, achromatic phase optimization is performed on four polarization states within the characteristic wavelength set, and structural parameter distribution data for the linear polarization portion is generated. and the distribution data of structural parameters of the circularly polarized part. ; To integrate units for separately controlling linearly polarized and circularly polarized light within the same device plane, a staggered row arrangement is used to construct the final metalens structure, where the rows with odd numbers adopt the structural parameter distribution data of the linearly polarized portion. Rows with even-numbered row numbers use the circularly polarized partial structural parameter distribution data. .

[0007] In one specific implementation, the focal coordinates of the four polarization channels are respectively (-R / 2, R / 2), (R / 2, R / 2), (-R / 2, -R / 2) and (R / 2, -R / 2) in the focal plane, where R is the radius of the metalens, the focal plane is located at z=f, and f is the focal length.

[0008] In a specific feasible implementation, the focal length f is determined by: establishing a set of candidate focal lengths; for each candidate focal length in the set, calculating the ideal phase distribution corresponding to the focal length based on the Fresnel diffraction integral formula; and using the Strell ratio and focusing efficiency as evaluation indicators, selecting the focal length with the largest Strell ratio and the required focusing efficiency as the final design focal length.

[0009] In one specific implementation scheme, the parameter scanning of the metalens unit using FDTD software includes: The unit shape is determined to be an elliptical cylinder, cuboid, or cross-shaped structure, and the structural parameter vector G is defined, where: For an elliptical cylindrical element, G = (R1, R2); R1 is the major axis radius, and R2 is the minor axis radius; For a cuboid element, G = (L x L y );L x L is the length along the x-direction. y The length along the y-direction; For a cross-shaped rectangular element, G = (L1, W1, L2, W2); L1 and W1 are the length and width of the first rectangular beam, respectively, and L2 and W2 are the length and width of the second rectangular beam, respectively.

[0010] In one specific implementation scheme, the parameters of the particle swarm optimization (PSO) algorithm are set as follows: population size of 100, number of iterations of 150, both learning factors of 1.49445, and particle velocity variation range of [missing information]. The range of particle position variation is .

[0011] In one specific implementation, the achromatic phase optimization includes: For the linearly polarized portion, based on the linearly polarized unit phase parameter library and transmittance parameter library By constructing an objective function consisting of a phase error term and a transmittance penalty term, the optimal additional phase at each characteristic wavelength is obtained, thereby achieving broadband achromatic focusing of the linear polarization channel. For the circularly polarized portion, firstly, based on the linearly polarized unit phase parameter library... and transmittance parameter library Construct a unit phase parameter library corresponding to the circular polarization part and transmittance parameter library Based on the constructed circular polarization unit phase parameter library and transmittance parameter library, the optimal additional phase under each characteristic wavelength is obtained by constructing an objective function of "phase error term + transmittance penalty term", thereby realizing broadband achromatic focusing of the circular polarization channel.

[0012] In one specific feasible implementation, the row staggered arrangement is as follows: With the geometric center of the metalens as the origin of the coordinate system, the plane where the metalens is located is z=0, and the unit array is symmetrically distributed in this plane; The cell rows are numbered sequentially from top to bottom along the positive y-axis. The cell row closest to the edge in the +y direction is numbered as row 1, and the adjacent rows are numbered as row 2, row 3, and so on until row N is numbered. Rows with odd row numbers use preset linear polarization partial structural parameter distribution data. Rows with even-numbered rows use preset circular polarization partial structural parameter distribution data. .

[0013] In one specific implementation scheme, the method further includes: verifying the focusing performance of the metalens using an angular spectrum propagation algorithm, wherein the verification includes constructing the equivalent complex amplitude transmission function of the metalens, performing frequency domain truncation based on the Nyquist sampling theorem, and reconstructing the focal plane light field through two-dimensional Fourier transform and inverse Fourier transform.

[0014] In a specific feasible implementation, the verification steps specifically include: Determine the splicing parameters of the meta-lens array; Construct the complex amplitude transmission function of the metalens array; Free-space focusing simulation and performance evaluation based on angular spectrum propagation algorithm.

[0015] In one specific implementation scheme, determining the stitching parameters of the metalens array includes: assuming the effective aperture of a single beam-splitting focusing metalens is D, and the stitching gap width between adjacent sub-lenses is g, then the array stitching period is: ; Let the effective imaging surface size of the detector be... The number of splices along the x and y directions are respectively: ; This results in a metalens array that covers the effective imaging surface of the detector.

[0016] Compared with existing technologies, the present invention provides a design method for a long-wave infrared achromatic beam-splitting and focusing metalens, used to achieve beam splitting and focusing imaging of 0° and 90° linearly polarized light, as well as LCP and RCP circularly polarized light, in the long-wave infrared band. This invention integrates nano-units that separately control linearly and circularly polarized light onto the same metalens plane using a row-staggered arrangement. It combines a particle swarm optimization (PSO) algorithm for achromatic phase co-optimization design of multiple characteristic wavelengths, and uses an angular spectrum propagation algorithm for rapid verification and performance evaluation in large-aperture devices and array splicing scenarios. Thus, while achieving multi-polarization beam splitting and focusing functionality, it also considers broadband operating performance and the engineering feasibility of large-scale devices, effectively improving the system integration, operating bandwidth, and application flexibility of long-wave infrared polarization imaging devices, and has the following beneficial effects: 1. Achieve integrated multi-polarization beam splitting and focusing: Through a row-staggered arrangement design, nano-units that respond to linearly polarized light and circularly polarized light respectively are integrated into a single metalens plane, realizing the beam splitting and focusing functions of four polarization states within the same device layer. This reduces the reliance of traditional solutions on multi-device combinations, partition splicing, or multi-layer cascade structures, thereby simplifying the system optical structure and improving the feasibility of integrated applications.

[0017] 2. Expanding the operating wavelength range and improving broadband focusing consistency: By introducing the PSO optimization algorithm, achromatic optimization is performed on the focusing phase distribution of the linearly polarized and circularly polarized channels at multiple discrete characteristic wavelength points. High-transmittance elements are also selected, enabling the metalens to exhibit minimal focal length fluctuations at discrete wavelength points in the 8.4–11.6 µm band, with a defocusing coefficient of only 2.45%, thereby reducing the risk of focus drift under multi-wavelength conditions. This alleviates the problem that existing narrowband designs typically only guarantee focusing performance within a narrow wavelength range, while experiencing increased focal length drift and decreased focusing efficiency under wide wavelength conditions.

[0018] 3. Providing a feasible design and low-computational-cost verification method for metalens arrays: For metalens array applications, this method constructs the equivalent complex amplitude transmission function of the metalens array and uses an angular spectrum propagation algorithm to achieve far-field focusing simulation of the stitched array. This avoids directly solving the full-wave electromagnetic problem for large-scale array structures, reducing reliance on computational resources. This enhances the engineering applicability and scalability of this method in the design of polarization beam-splitting and focusing devices for metalens arrays. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0020] Figure 1 This is a schematic diagram illustrating the working principle of a metalens.

[0021] Figure 2 This is an overall flowchart of the design method for a long-wave infrared achromatic differential beam focusing metalens according to the present invention.

[0022] Figure 3 The simulation results are for the meta-lens. (a) is the curve of the meta-lens focal length as a function of the characteristic wavelength, (b) is the curve of the full width at half maximum (FWHM) and diffraction limit as a function of the characteristic wavelength, (c) is the curve of the meta-lens focusing efficiency as a function of the characteristic wavelength, and (d) is the curve of the meta-lens transmittance as a function of the characteristic wavelength.

[0023] Figure 4 Simulation diagram of focal plane light intensity distribution of metalens under incident light with different polarization states; (a) is incident light with 0° linear polarization, (b) is incident light with 90° linear polarization, (c) is incident light with LCP circular polarization, and (d) is incident light with RCP circular polarization. Detailed Implementation

[0024] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0025] The present invention describes a design method for a long-wave infrared achromatic beam-splitting focusing metalens. See [link to relevant documentation]. Figure 2The long-wave infrared refers to the band of 8.4~11.6µm, which is also the operating band of the metalens in this embodiment. The metalens in this embodiment can focus light of four different polarization states—0° and 90° linearly polarized light, and LCP and RCP circularly polarized light—to different focal points. See [link to documentation]. Figure 1 As shown. The focusing phase of the 0° and 90° linearly polarized light is achieved based on the transmission phase principle, while the focusing phase of the LCP and RCP circularly polarized light is achieved jointly by the transmission phase and the geometric phase. Simultaneously, to suppress broadband focus drift caused by metasurface phase dispersion, this embodiment uniformly selects nine discrete wavelength points within the working wavelength range of 8.4~11.6μm to form a characteristic wavelength set. (m=1~9) (that is, 9 wavelength points are selected at 0.4μm intervals), and the metalens is achromatic within the characteristic wavelength set. Subsequent design, optimization and verification are also carried out within the characteristic wavelength set.

[0026] The design method of a long-wave infrared achromatic beam-splitting metalens according to the present invention includes the following steps: S1: Determine the substrate material, nanostructure material, and the focal coordinates of the metalens radius R, focal length f, and four polarization channels.

[0027] (1) Material selection Device materials suitable for the long-wave infrared band include ZnS, Ge, ZnSe, and Si. In this embodiment, the substrate material and nanostructure material can be selected based on the transmittance, refractive index, and manufacturability of the target wavelength band.

[0028] (2) Preset coordinate system and focus coordinates Establish a coordinate system: with the center of the metalens as the origin O, the plane containing the metalens as z=0, the light propagation direction as the +z direction, and the focal plane located at z=f. To achieve spatial separation of the four polarization channels within the focal plane, the focal coordinates must satisfy the following condition: the distance between any two focal points is not less than the diameter of the focused spot under diffraction limit, in order to reduce channel crosstalk; In this embodiment, the coordinates (x, y) of the 0° and 90° linearly polarized light, as well as the LCP and RCP light, on the focal plane are taken as (-R / 2, R / 2), (R / 2, R / 2), (-R / 2, -R / 2) and (R / 2, -R / 2), respectively.

[0029] (3) Selection of focal length of super lens (3.1) Determine the set of candidate focal lengths After determining the radius R, first determine the range of the numerical aperture NA. If NA is too small, it will affect the focusing effect of the meta-lens, while if NA is too large, the difficulty of achromatic correction will increase. It is necessary to determine the range of NA according to the requirements, and then determine the range of the focal length f according to the formula. Then set the scan step size. Generate a discrete set of candidate focal lengths. .

[0030] (3.2) Establish an evaluation index system For sets For each candidate focal length, calculate the ideal phase distribution corresponding to that focal length, and use this ideal phase distribution as the source plane complex amplitude. The phase term (with amplitude set to 1) is substituted into the Fresnel diffraction integral formula to simulate and evaluate the theoretical focusing performance of different candidate focal lengths f. The Fresnel diffraction integral formula is shown below: ; In the formula: This represents the incident complex amplitude distribution at the source plane located at z=0. This represents the complex amplitude distribution at the observation plane at a distance z from the source plane. Let be the horizontal spatial coordinates of the source plane. To observe the horizontal spatial coordinates of the plane. The distance between the source plane and the observation plane. For wavelength, For wave number, The imaginary unit represents the complex amplitude distribution at the observation plane. Then, through the formula The corresponding light intensity distribution was calculated. .

[0031] This invention uses the light intensity distribution results obtained from Fresnel diffraction integrals and employs the following two quantitative indicators to select the final focal length: Streller ratio: defined as the ratio of the actual peak light intensity obtained from simulation to the peak light intensity of an ideal aberration-free diffraction limit under the same aperture.

[0032] Focusing efficiency: defined as the sum of the light intensity of the spot within a radius of 1.5 times the full width at half maximum (FWHM) divided by the total light intensity of the entire focal plane.

[0033] For sets After each value in the simulation calculation is completed, the focal length value with the largest Strell ratio is selected first; if there are multiple candidate values ​​with similar Strell ratios, the one with higher focusing efficiency is selected as the final design focal length f.

[0034] S2: Use FDTD software to perform parameter scanning on the metalens unit and construct a phase parameter library for the linear polarization unit. and transmittance parameter library .

[0035] (1) Determine the unit shape and structural parameters Based on the requirements of polarization-sensitive control, the shape of the nanounit in this embodiment can be selected as an elliptical cylinder, cuboid, or cross-shaped structure, and parameterized modeling is performed within the same unit period P.

[0036] For elliptical cylindrical elements, the structural parameters include the major axis radius R1, the minor axis radius R2, and the element height H; For a cuboid element, the structural parameters include the length L along the x-direction. x Length L along the y-direction y And the unit height H; For a cross-shaped rectangular element, it consists of two intersecting rectangular beams. Its structural parameters include the length L1 and width W1 of the first rectangular beam, the length L2 and width W2 of the second rectangular beam, and the element height H.

[0037] The height H of all elements is known and remains consistent. For ease of subsequent unified description, the unknown geometric parameters of elements with different shapes are uniformly represented as a structural parameter vector G, i.e.: For an elliptical cylindrical element, G = (R1, R2); R1 is the major axis radius, and R2 is the minor axis radius; For a cuboid element, G = (L x L y );L x L is the length along the x-direction. y The length along the y-direction; For a cross-shaped rectangular element, G = (L1, W1, L2, W2); L1 and W1 are the length and width of the first rectangular beam, respectively, and L2 and W2 are the length and width of the second rectangular beam, respectively.

[0038] The range of values ​​for the structural parameters is determined by constraints imposed by the minimum linewidth for processing, the minimum spacing between adjacent units, the processable range of unit height, and the requirement for high transmittance.

[0039] The unit period P is determined based on the subwavelength condition, the Nyquist sampling theorem, and fabrication process constraints, as follows: 1) Subwavelength constraint: To avoid generating higher-order diffraction modes in the operating wavelength band, the unit period P must satisfy the following condition: ; in, The minimum wavelength within the operating band (8.4~11.6μm) This represents the equivalent refractive index corresponding to the unit cell structure.

[0040] 2) Phase sampling accuracy constraint: To ensure the continuity of the phase distribution within the metalens plane and the spatial sampling accuracy, the unit period P must satisfy that the phase change at adjacent units does not exceed π, i.e.: ; in and These represent the phase values ​​of adjacent units.

[0041] 3) Process constraints: The unit period P must be greater than the sum of the minimum feature size allowed by the process and the minimum spacing between adjacent units to ensure the manufacturability and yield of the structure.

[0042] Under the premise of satisfying the above constraints, by comparing different candidate cell periods through numerical simulation, and taking into account indicators such as transmittance, phase coverage range and control sensitivity, the cell period with the best performance is selected as the final cell period value.

[0043] (2) Data acquisition of linear polarization part element parameter sweep. The RCWA solver in FDTD software was used to perform parameter sweep calculations on the element. Under illumination from 0° and 90° linearly polarized light sources, the phase and transmittance responses of the element at different combinations of structural parameters and at various characteristic wavelengths were calculated. Given a fixed polarization state and wavelength of the light source, any given set of element structural parameters corresponds to a uniquely determined phase and transmittance response. The phase and transmittance data corresponding to 0° linearly polarized light are denoted as... and The phase data and transmittance data corresponding to the 90° linearly polarized light are denoted as... and The integrated library of unit phase parameters corresponding to the linearly polarized portion is obtained. With transmittance parameter library .

[0044] S3: Multi-wavelength achromatic optimization and structural parameter distribution generation based on PSO.

[0045] S3 includes: based on the particle swarm optimization (PSO) algorithm, performing achromatic phase optimization on four polarization states within the characteristic wavelength set, and generating structural parameter distribution data for the linear polarization portion. and the distribution data of structural parameters of the circularly polarized part. .

[0046] (1) Set PSO optimization algorithm parameters Since the objective functions for linearly polarized light and circularly polarized light are different, the two parts are optimized separately, with 18 variables optimized for each part individually. Other parameters are set as follows: population size is 100, number of iterations is 150, both learning factors are set to 1.49445, and particle velocity variation range is... The range of particle position variation is .

[0047] (2) Determine the target phase distribution of the metalens corresponding to the four polarization states. To compensate for the dispersion effect of the metalens phase response, at each characteristic wavelength... The following introduces a compensated phase variable for each polarization state: pol represents the polarization state, including {0°, 90°, LCP, RCP}. That is, each polarization state at each characteristic wavelength... Each location corresponds to an independent compensation phase variable. The ideal phase distribution formulas corresponding to the four polarization states are shown in the following equations: In the formula: , , and These represent linearly polarized light at 0°, linearly polarized light at 90°, LCP circularly polarized light, and RCP circularly polarized light at their characteristic wavelengths. The ideal phase distribution is as follows; the focal coordinates of the four ideal phase distribution formulas correspond to ( ), ( ), ( )and ). The radius of the metalens. For the focal length of the meta-lens, , These are the two-dimensional coordinates of the metalens surface. In this step, the PSO algorithm is used to search for the set of compensated phase variables within a defined range. The optimal solution minimizes the overall error between the target phase and the actual phase under multiple wavelengths.

[0048] (3) Constructing the objective function In broadband achromatic design, for each spatial location on the lens, the same geometric parameters need to be found in the parameter library. This specific structure must have a phase response as close as possible to the target compensation phase across all characteristic wavelengths (8.4~11.6µm), achieving broadband integrated dispersion compensation, rather than simply selecting the optimal phase independently for each wavelength. Units with the same shape parameters will have different phase responses at different wavelengths. When the integrated error between the actual phase and the target phase of a unit structure across the nine characteristic wavelengths is minimized, the unit structure can be considered to meet the broadband design requirements.

[0049] Because the design principles of focusing linearly polarized light and circularly polarized light are different, their objective functions are constructed independently. However, the core logic of multi-wavelength matching is the same: for each unit position within the meta-lens, a specific physical structure is searched in the unit parameter library to minimize the overall deviation between its phase response and the target phase at all characteristic wavelengths, while also taking into account high transmittance.

[0050] (3.1) Construction of the objective function for the linearly polarized part For the linearly polarized portion, this invention aims to minimize phase-matching error and maximize transmittance. Specifically, it compares the linearly polarized target phase of each element on the metalens at different characteristic wavelengths with the element phase parameter library. The phase values ​​in the image are matched, and the optimal additional phase under each characteristic wavelength is obtained by constructing an objective function of "phase error term + transmittance penalty term", thereby realizing broadband achromatic focusing of the linear polarization channel.

[0051] Let the coordinates of the center of the i-th unit in the meta-lens be... Then its wavelength The phase of the linearly polarized target is: To measure the deviation between the target phase and the actually achievable phase, a phase error term is introduced. Specifically: Let the linear polarization unit phase parameter library be... and transmittance parameter library It contains n different candidate unit structures, and the geometric parameters of the k-th candidate unit are denoted as . This structure At wavelength The corresponding actual phase and transmittance are denoted as follows: , as well as , .

[0052] For the i-th unit, calculate any candidate structure in the parameter library. Phase matching error at all 9 characteristic wavelengths and transmittance penalty : Where wrap(·) represents mapping the phase difference to Range; m represents the number of wavelengths; This is the transmittance weight, used to balance the effects of phase error and transmittance, and its value ranges from [0,1].

[0053] Given a set of compensated phase variables Next, for each element position i, traverse the n candidate element structures in the parameter library and select the one that makes the parameter position i equal to the position i. The optimal structural parameter with the smallest value The sum of the minimum errors of all N units is the objective function for the linearly polarized part. The compensation phase at each characteristic wavelength is continuously updated using the PSO algorithm. To minimize the overall objective function Finally, the optimal compensation phase for the linearly polarized part is obtained.

[0054] (3.2) Construction of the objective function for the circular polarization part For the circularly polarized portion, a corresponding unit parameter library for the circularly polarized portion must first be constructed based on the unit parameter library for the linearly polarized portion. Then, the optimization objective is to minimize the phase matching error and maximize the transmittance. The circularly polarized target phase of each unit on the metalens at different characteristic wavelengths is matched with the phase values ​​in the unit phase parameter library for the circularly polarized portion. By constructing an objective function consisting of a "phase error term + transmittance penalty term," the optimal additional phase at each characteristic wavelength is obtained, thereby achieving broadband achromatic focusing of the circularly polarized channel.

[0055] Phase modulation of circularly polarized light includes geometric phase and transmission phase. Regarding the geometric phase, according to Berry, MV (1984). "Quantal phase factors accompanying adiabatic changes". Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 392(1802), 45-57, the geometric phase generated by a single element is equal to the element rotation angle. Twice that, when the incident light is left-handed circularly polarized light, the geometric phase is When the incident light is right-handed circularly polarized, the geometric phase is For the transmission phase portion, the parameter library of the linear polarization component can be used. and To construct the element parameter library corresponding to the circularly polarized portion, the specific expression is as follows: in, The unit rotation angle is defined in this invention. The angle between the principal axis of the element in the x-direction and the x-axis is also... Step size is When the incident light is left-handed circularly polarized light, A library of phase parameters for the unit. For the transmission phase portion, This is a library of transmittance parameters for a single unit; when the incident light is right-handed circularly polarized light, A library of phase parameters for the unit. Represents the transmission phase portion, A library of transmittance parameters for each unit; and The phase and transmittance scan data correspond to the 0° linearly polarized light, respectively. and The phase and transmittance scan data correspond to 90° linearly polarized light, respectively. These phase and transmittance data are then integrated to form unit phase parameter libraries for the circularly polarized portion. and unit transmittance parameter library .

[0056] Let the coordinates of the center of the i-th element within the superlens plane be... Then its wavelength The phase of the circularly polarized target is: Simultaneously, a phase error term is introduced. Specifically: assuming a circular polarization unit parameter library... and It contains n different candidate unit structures, and each candidate unit structure also contains 180 rotation angles. The geometric parameters of the k-th candidate unit are denoted as... This structure At wavelength The corresponding actual phase and transmittance are denoted as follows: , as well as , .

[0057] For the i-th unit, calculate any candidate structure in the parameter library. Phase matching error at all 9 characteristic wavelengths and transmittance penalty : Where wrap(·) represents mapping the phase difference to Range; m represents the number of wavelengths; This is the transmittance weight, used to balance the effects of phase error and transmittance, and its value ranges from [0,1].

[0058] In a given set of compensation phases Next, for each unit position i, iterate through the n structures and 180 rotation angles in the parameter library. Select the structure that makes the structure i such that the structure i is the unit ... The optimal structural parameter with the smallest value and rotation angle The sum of the minimum errors of all N units is the objective function for the circularly polarized portion. The compensation phase at each characteristic wavelength is continuously updated using the PSO algorithm. To minimize the overall objective function Finally, the optimal compensation phase for the circularly polarized part is obtained.

[0059] (4) Run the optimization algorithm and generate structural parameter distribution data of the unit and actual phase distribution data of the metalens: After the PSO algorithm finishes its optimization and determines the optimal compensation phase, the optimal compensation phase is substituted into the target phase formula. Subsequently, for the linear polarization part, for each unit position, the optimal geometric structure parameters that minimize the multi-wavelength synthesis error are extracted from the parameter library. Positioning is performed to directly output the distribution data of the linearly polarized structural parameters. For the circularly polarized portion, the same method is used to extract the geometrical parameters that minimize the combined error of the circularly polarized multi-wavelength system. Finally, the distribution data of the structural parameters of the circularly polarized part were obtained. Thus, the mapping from multi-wavelength phase optimization to the spatial structural parameters of the metalens unit has been completed.

[0060] Furthermore, given a fixed polarization state and wavelength of the light source, any given set of unit structure parameters corresponds to a uniquely determined phase and transmittance response. This is based on the physical structure parameter distribution data obtained above. and This allows for the direct extraction and construction of the actual transmittance distribution of the metalens under the corresponding polarization state from the online and circular polarization unit parameter library. , ) and actual phase delay distribution ( , ).

[0061] S4: Verify the focusing performance of the meta-lens using FDTD software.

[0062] To integrate units for separately controlling linearly polarized and circularly polarized light within the same device plane, this embodiment employs a row-alternating arrangement to construct the final metalens structure. Specifically, with the geometric center of the metalens as the origin and the plane containing the metalens at z=0, the unit array is symmetrically distributed within this plane. The unit rows are numbered sequentially from top to bottom along the positive y-axis, with the row closest to the +y edge numbered as row 1, and subsequent adjacent rows numbered as row 2, row 3, and so on, up to row N. The unit structure uses an odd-even alternating layout: rows with odd numbers (1, 3, 5...) use preset linear polarization partial structural parameter distribution data. Rows with even row numbers (2, 4, 6...) use preset circular polarization partial structural parameter distribution data. When the total number of rows N of the metalens is odd, according to the above numbering rules, the Nth row belongs to the odd-numbered row, and the distribution data of the linear polarization structural parameters are automatically adopted. Filling is performed to ensure that each unit row has clear and consistent design rules, thus ensuring the integrity of the structure.

[0063] The staggered row arrangement is used to alternately introduce different functional units in the unit array. The specific arrangement method is not limited to row staggering, but can also be implemented by column staggering, etc. At the same time, the odd-numbered rows and even-numbered rows are used to represent the alternating setting of different functional units in adjacent rows, and the specific correspondence is not limited to the priority setting of a certain type of functional unit.

[0064] Based on the metalens structure, an incident light source and a monitor were set up. Perfectly matched layer boundary conditions were set in the x, y, and z directions of the simulation area to truncate the computational region and absorb the outgoing waves. The finite-difference time-domain (FDTD) method was used to perform full-wave simulation to obtain the far-field focused light intensity distribution, and the focusing efficiency, full width at half maximum (FWHM), and other indicators were calculated to evaluate the focusing performance of the metalens. S5: Construct a metalens array and verify its focusing performance. (1) Determine the splicing parameters of the meta-lens array.

[0065] Let the effective aperture of a single beam-splitting metalens be D, and the seam width between adjacent sub-lenses be g (g>0), then the array stitching period is: Let the effective imaging surface size of the detector be... The number of splices along the x and y directions are respectively: This results in a metalens array that covers the effective imaging surface of the detector.

[0066] (2) Construct the complex amplitude transmission function of the metalens array.

[0067] To perform rapid and feasible performance verification of large-scale metalens arrays, the complex amplitude transmission function of the metalens array in the target operating band is constructed. For any incident polarization state pol∈{0°,90°,LCP,RCP}, the equivalent complex amplitude transmission function corresponding to a single metalens can be expressed as: in, For transmittance distribution, in this embodiment, it is arranged according to the described row-interlacing method. odd rows and It consists of even-numbered rows; For phase delay distribution, in this embodiment, it is distributed according to the row interleaving method. odd rows and Both consist of even-numbered rows and are related to the polarization state. The unit is the imaginary unit. Based on this, the single-lens complex amplitude transmission function is calculated according to the splicing period. By performing translational replication and parallel stitching, the complex amplitude transmission function of the metalens array is obtained. To explicitly represent the effects of splicing seams on diffraction and crosstalk in the model, the transmittance distribution in the seam region can be set according to the transmission characteristics of the shielding material or the actual process material. Preferably, the seam region can satisfy the following: (3) Free space focusing simulation and performance evaluation based on angular spectrum propagation algorithm.

[0068] Due to the large aperture of the metalens array, directly using full-wave electromagnetic calculations would incur extremely high computational costs. Therefore, the angular spectrum propagation algorithm is employed to numerically verify the focusing process of the metalens array in free space. The angular spectrum propagation algorithm mainly consists of the following steps: (3.1) Array emission field construction and initial angular spectrum extraction Under plane wave incidence, the initial complex amplitude field at the exit surface (z=0) of the meta-lens array is determined by the complex amplitude transmission function in step S5(2), i.e.: A two-dimensional Fourier transform is performed on it to extract the initial angular spectrum distribution in the spatial frequency domain: in, and For spatial frequency, This represents the Fourier transform.

[0069] (3.2) Frequency domain truncation and focal plane light field reconstruction based on Nyquist sampling To ensure the accuracy and stability of angular spectrum propagation simulations, the angular spectrum transfer function needs to be truncated in the frequency domain to filter out non-propagating evanescent waves and avoid spectral aliasing caused by discrete sampling. On the one hand, due to the physical limitations of free-space propagation, excessively high spatial frequencies will correspond to exponentially decaying evanescent waves, which can easily lead to divergence in numerical calculations; therefore, the effective frequency needs to be limited. Within the propagation bandwidth. On the other hand, the metalens units are discretely arranged with a period of P, which is equivalent to spatial sampling of the continuous optical field. According to the Nyquist sampling theorem, to prevent aliasing errors caused by high-frequency signal folding, the spatial frequency along each axis must be limited to the cutoff frequency, that is, it must satisfy: Considering the above limitations, the two-dimensional frequency domain truncation window function The expression is as follows: By combining this truncated window function with the free-space transfer function, a modified angular spectrum transfer function can be constructed: Where k is the wave number and the propagation distance z is set to f, the light intensity distribution at the focal plane (z=f) is then reconstructed using a two-dimensional inverse Fourier transform: in This is the inverse Fourier transform.

[0070] (3.3) Evaluation and Calculation of Beam Splitting and Focusing Performance Based on reconstructed focal plane intensity distribution This allows for the acquisition of focusing positions and energy distributions corresponding to different polarization states. Focus position deviation and energy concentration are used as evaluation indicators to verify the beam-splitting and focusing performance of the metalens array in the long-wave infrared broadband range. The energy concentration can be expressed as: In the formula, Ω represents the target focal region window under the current polarization state, and Ω is the region corresponding to the metalens array on the focal plane. This is calculated by individually applying the calculations to each wavelength point within the characteristic wavelength set. and This allows for the verification of the large-scale focusing performance and broadband stability of metalens arrays.

[0071] To verify the feasibility and advantages of this design method, a polarization-sensitive metalens was designed in the 8.4~11.6µm band.

[0072] (1) First, determine the structural parameters of the meta-lens design: Determine the radius R and focal length f of the metalens: the radius R is set to 83µm, and the focal length is determined through step S1(3) above. The initial numerical aperture NA range is set to [0.6, 0.9], corresponding to an initial range of approximately [40.2µm, 110.7µm] for the candidate focal length f. Within this range, the step size is set. 0.5µm is used to generate a set of candidate focal lengths. The simulation was conducted using the evaluation index system of step S1(3) above. The simulation results show that when f=105µm, the Strell ratio reaches its maximum value, and the focusing efficiency meets the requirements. Therefore, in this embodiment, f=105µm is ultimately preferred as the design focal length.

[0073] The parameters of the meta-lens unit are determined as follows: the unit period P is 2.5µm, and the unit shapes are chosen as elliptical cylinders and cuboids. For ease of fabrication, the minimum linewidth between adjacent units is set to 0.5µm. Therefore, the major axis radius R1 and minor axis radius R2 of the elliptical cylinder range from (0.25µm to 1µm), and the scan step size is 0.0075µm. The lengths Lx and Ly along the x and y directions of the cuboid range from (0.5µm to 2µm), and the scan step size is 0.015µm. Transmittance weighting is also specified. Take 0.1.

[0074] The materials for the metalens units were determined: Ge was used as the nanopillar material in the units, and ZnSe was selected as the substrate material.

[0075] (2) Complete the design and simulation of the meta-lens: FDTD simulation results are as follows Figure 3 and Figure 4 As shown. Figure 3 (a) shows the curve of focal length versus characteristic wavelength. To evaluate the achromatic performance of the designed metalens, the defocus coefficient (CV) is introduced as an evaluation index, defined as the ratio of the standard deviation of the focal length corresponding to each discrete characteristic wavelength to the average focal length, expressed as a percentage. It is generally considered that when CV is less than 5%, the device has good achromatic capability within the corresponding wavelength band. Based on the simulated focal length data, the CV is calculated to be 2.45%, which is less than 5%, indicating that the focal length variation is small at different wavelengths. The designed metalens can achieve good achromatic focusing effect in the 8.4~11.6μm wavelength band.

[0076] Figure 3 (b) shows a comparison curve of the full width at half maximum (FWHM) and the diffraction limit as a function of the characteristic wavelength. FWHM is defined as 2.355 times the standard deviation of the fitted curve of the focused spot intensity along the x-axis. The diffraction limit is the minimum theoretical spot width achievable by an ideal imaging system under the same numerical aperture conditions. Figure 3(b) It can be seen that the FWHM at each characteristic wavelength is close to the diffraction limit, indicating that the meta-lens can achieve a focusing effect close to the diffraction limit in the working band and has good focusing quality and imaging performance. Figure 3 (c) is the curve of focusing efficiency as a function of characteristic wavelength. The focusing efficiency is used to characterize the ability of the metalens to focus incident light energy onto the target focal region. It is usually defined as the sum of the light intensity of the spot within 1.5 times the radius of the full width at half maximum (FWHM) divided by the total light intensity of the entire focal plane. Its average focusing efficiency is 38.82%. Figure 3 (d) shows the curve of the transmittance of the meta-lens as a function of the characteristic wavelength, with an average transmittance of 68.03%.

[0077] Figure 4 The figure shows the simulation results of the focal plane light intensity distribution of the metalens under different incident polarization states, which is the "|E|² (xy plane)" distribution. Figure 4 (a) Incident light corresponding to 0° linear polarization Figure 4 (b) Corresponding to 90° linearly polarized light incident. Figure 4 (c) Corresponding to left-handed circularly polarized light (LCP) incident, Figure 4 (d) Corresponding to right-hand circularly polarized light (RCP) incident. As can be seen from the figure, incident light with different polarization states can form spatially separated focused spots with obvious energy concentration, indicating that the designed metalens has good polarization selectivity and beam-splitting focusing ability.

[0078] The various embodiments described in this specification are presented in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A design method for a long-wave infrared achromatic beam-splitting metalens, characterized in that, Includes the following steps: Determine the substrate material, nanostructure material, and the focal coordinates of the metalens radius R, focal length f, and four polarization channels; The metalens unit was scanned using FDTD software to construct a phase parameter library for the linear polarization unit. and transmittance parameter library ; Based on the Particle Swarm Optimization (PSO) algorithm, achromatic phase optimization is performed on four polarization states within the characteristic wavelength set, and structural parameter distribution data for the linear polarization portion is generated. and the distribution data of structural parameters of the circularly polarized part. ; To integrate units for separately controlling linearly polarized and circularly polarized light within the same device plane, a staggered row arrangement is used to construct the final metalens structure, where the rows with odd numbers adopt the structural parameter distribution data of the linearly polarized portion. Rows with even-numbered row numbers use the circularly polarized partial structural parameter distribution data. .

2. The design method of a long-wave infrared achromatic beam-splitting focusing metalens according to claim 1, characterized in that, The focal coordinates of the four polarization channels are (-R / 2, R / 2), (R / 2, R / 2), (-R / 2, -R / 2), and (R / 2, -R / 2) respectively in the focal plane, where R is the radius of the superlens, the focal plane is located at z=f, and f is the focal length.

3. The design method of a long-wave infrared achromatic beam-splitting focusing metalens according to claim 1, characterized in that, The focal length f is determined in the following way: a set of candidate focal lengths is established, and for each candidate focal length in the set, the ideal phase distribution corresponding to the focal length is calculated based on the Fresnel diffraction integral formula. The Strell ratio and focusing efficiency are used as evaluation indicators, and the focal length with the largest Strell ratio and the required focusing efficiency is selected as the final design focal length.

4. The design method of a long-wave infrared achromatic beam-splitting focusing metalens according to claim 1, characterized in that, The parameter scanning of the metalens unit using FDTD software includes: The unit shape is determined to be an elliptical cylinder, cuboid, or cross-shaped structure, and the structural parameter vector G is defined, where: For an elliptical cylindrical element, G = (R1, R2); R1 is the major axis radius, and R2 is the minor axis radius; For a cuboid element, G = (L x L y );L x L is the length along the x-direction. y The length along the y-direction; For a cross-shaped rectangular element, G = (L1, W1, L2, W2); L1 and W1 are the length and width of the first rectangular beam, respectively, and L2 and W2 are the length and width of the second rectangular beam, respectively.

5. The design method of a long-wave infrared achromatic beam-splitting focusing metalens according to claim 1, characterized in that, The parameters of the Particle Swarm Optimization (PSO) algorithm are set as follows: population size of 100, number of iterations of 150, both learning factors of 1.49445, and particle velocity variation range of [missing information]. The range of particle position variation is .

6. The design method of a long-wave infrared achromatic beam-splitting focusing metalens according to claim 1, characterized in that, The achromatic phase optimization includes: For the linearly polarized portion, based on the linearly polarized unit phase parameter library and transmittance parameter library By constructing an objective function consisting of a phase error term and a transmittance penalty term, the optimal additional phase at each characteristic wavelength is obtained, thereby achieving broadband achromatic focusing of the linear polarization channel. For the circularly polarized portion, firstly, based on the linearly polarized unit phase parameter library... and transmittance parameter library Construct a unit phase parameter library corresponding to the circular polarization part and transmittance parameter library Based on the constructed circular polarization unit phase parameter library and transmittance parameter library, the optimal additional phase under each characteristic wavelength is obtained by constructing an objective function of "phase error term + transmittance penalty term", thereby realizing broadband achromatic focusing of the circular polarization channel.

7. The design method of a long-wave infrared achromatic beam-splitting metalens according to claim 1, characterized in that, The row staggered arrangement method is as follows: With the geometric center of the metalens as the origin of the coordinate system, the plane where the metalens is located is z=0, and the unit array is symmetrically distributed in this plane; The cell rows are numbered sequentially from top to bottom along the positive y-axis. The cell row closest to the edge in the +y direction is numbered as row 1, and the adjacent rows are numbered as row 2, row 3, and so on until row N is numbered. Rows with odd row numbers use preset linear polarization partial structural parameter distribution data. Rows with even-numbered rows use preset circular polarization partial structural parameter distribution data. .

8. The design method of a long-wave infrared achromatic beam-splitting focusing metalens according to claim 1, characterized in that, Also includes: The focusing performance of the metalens is verified using an angular spectrum propagation algorithm. The verification includes constructing the equivalent complex amplitude transmission function of the metalens, performing frequency domain truncation based on the Nyquist sampling theorem, and reconstructing the focal plane light field through two-dimensional Fourier transform and inverse Fourier transform.

9. The design method of a long-wave infrared achromatic beam-splitting focusing metalens according to claim 8, characterized in that, The verification steps specifically include: Determine the splicing parameters of the meta-lens array; Construct the complex amplitude transmission function of the metalens array; Free-space focusing simulation and performance evaluation based on angular spectrum propagation algorithm.

10. The design method of a long-wave infrared achromatic beam-splitting metalens according to claim 9, characterized in that, The determination of the stitching parameters for the metalens array includes: assuming the effective aperture of a single beam-splitting focusing metalens is D, and the stitching gap width between adjacent sub-lenses is g, then the array stitching period is: ； Let the effective imaging surface size of the detector be... The number of splices along the x and y directions are respectively: ； This results in a metalens array that covers the effective imaging surface of the detector.

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