Single-layer wide-view-field broadband achromatic metamaterial lens and design method

Abstract

The invention provides a single-layer large-view-field broadband achromatic metamaterial lens and a design method thereof. The super-structure lens comprises a unit structure array and a substrate from top to bottom, and the shape of a unit structure is related to the polarization characteristic of the super-structure lens. A large-view-field broadband super-structure lens design is realized by using a principle of combining a secondary phase with achromatism, a phase-wavelength-incident angle database and an amplitude-wavelength-incident angle database of a scanning unit structure are obtained by changing the geometric size and the incident angle of the unit structure, the unit structure with large angle tolerance is screened out by using an optimization algorithm, and a super-structure with a wide angle tolerance is obtained. Therefore, the super-structure lens has the performance of a large view field, the actual phase provided by the unit structure in the database can be matched with the target phase, and the broadband achromatic performance is achieved. The device is ingenious in design and simple in structure, the large-view-field broadband achromatic focusing function can be achieved through the single-layer super-structure lens, and the device can be used in functional devices for polarization detection, light field imaging, wavefront detection and the like.

Description

Technical Field

[0001] The present invention relates to the field of electromagnetic wavefront regulation technology and large field of view, broadband achromatic imaging, and particularly relates to a design method for a single-layer large field of view broadband achromatic metasurface lens. Background Art

[0002] Optical focusing lenses have a wide range of applications in fields such as imaging and detection. Two key indicators characterizing the performance of lenses are the spectral bandwidth and the field of view. In practical applications, the existence of off-axis aberration and chromatic aberration severely limits the field of view and bandwidth of a single lens. According to aberration theory, to achieve wide-field broadband achromatic performance, it is necessary to increase the number of optical elements or increase the surface curvature, which will inevitably lead to an increase in the system volume. Therefore, it is imperative to study highly integrated optical lenses with large fields of view and achromatic properties.

[0003] As a wavefront regulation platform, a metasurface can arbitrarily regulate the light field at the sub-wavelength scale, overcoming the bulkiness and complexity of traditional lenses, and has been widely applied in fields such as imaging, holography, and polarization detection. In addition, metasurfaces also exhibit excellent performance in dispersion and field of view regulation. However, there is relatively little work on simultaneously overcoming chromatic aberration and field of view limitations. The dual-lens with a 60° field of view proposed by Kim et al. can only work at multiple discrete wavelengths. Although the imaging metasurface lens proposed by Huang et al. can work within a 60° field of view from 470 nm to 650 nm, the lens is a double-layer lens facing complex manufacturing and alignment problems. Although Luo et al. proposed that a single-layer metasurface has a 40° field of view, it is only applicable to three discrete wavelengths of 473 nm, 532 nm, and 632.8 nm. Therefore, it is still a huge challenge to realize a single-layer metasurface lens with broadband achromatism and a wide field of view. Summary of the Invention

[0004] To solve the above problems, the present invention proposes a single-layer large field of view broadband achromatic metasurface lens and a design method, which can achieve a metasurface lens with achromatic focusing within a large field of view and broadband on a single metasurface, and the design method is applicable to both polarization-dependent and polarization-independent metasurface lenses.

[0005] The technical solution adopted by the present invention to solve its technical problems is as follows:

[0006] A single-layer large field of view broadband achromatic metasurface lens, the metasurface lens is a single-layer structure, and includes a unit structure array 1 and a substrate 2 from top to bottom. The unit structure array is composed of a plurality of unit structures, and the unit structure is a nanorod. The metasurface lens can achieve broadband achromatism under a 100° field of view, and the relative bandwidth can reach 0.4.

[0007] Furthermore, the metasurface lens satisfies f < D < 4f, where f is the preset focal length of the metasurface lens, and D is the aperture of the metasurface lens.

[0008] Furthermore, the metasurface lens can be designed to be polarization-dependent or polarization-independent.

[0009] Furthermore, the polarization characteristics of the metasurface lens are related to the shape of the unit structure. When the designed metasurface lens has polarization-independent performance, the unit structure array is composed of isotropic unit structures, such as cylinders and regular polygonal columns; when the designed metasurface lens has polarization-dependent performance, the unit structure array is composed of anisotropic unit structures, such as rectangular columns and elliptical cylinders, etc., or is jointly composed of anisotropic and isotropic unit structures, but cannot be composed only of isotropic unit structures.

[0010] Furthermore, the period of the unit structure is P, and its value range is 0.2λ0 < P < 0.5λ0, and the column height is h, and its value range is 0.5λ0 < h < 2λ0, where λ0 is the central wavelength. The geometric size range of the nanocolumns is limited by the processing conditions.

[0011] Furthermore, the determination of the period P and column height h parameters needs to ensure the following conditions:

[0012] 1) The phase responses of all unit structures that meet the processing conditions can cover 2π;

[0013] 2) The unit structure has good angular tolerance: at different angles, the phase shifts generated by most unit structures are constants, that is, the phase difference between unit structures does not change significantly with the incident angle.

[0014] Furthermore, the phase distribution of the metasurface lens is:

[0015]

[0016] where λ is any wavelength within the working bandwidth, θ is the incident angle, f is the preset focal length, r is the radial distance from any position to the center of the metasurface lens, and φ shift (λ,θ) is the phase shift related to the wavelength and incident angle, which is the optimization quantity in the design.

[0017] On another aspect of the present invention, a design method for a single-layer large-field-of-view broadband achromatic metasurface lens is provided. The method is applied to the metasurface lens, and the method includes:

[0018] Step 1: Determine the design wavelength band [λ min , λ max of the metasurface lens, the lens aperture D and the focal length f; go to Step 2.

[0019] Step 2: Select the materials of the unit structure and the substrate according to the design wavelength band to ensure high transmittance. Determine the period P and height h of the unit structure; go to Step 3.

[0020] Step 3: Establish a phase - wavelength - incident angle and amplitude - wavelength - incident angle database.

[0021] Based on the parameters and materials determined in Step 2, change the geometric dimensions of the nanocolumns, perform wavelength and angle scans, and obtain the phase - wavelength - incident angle and amplitude - wavelength - incident angle databases of the scanned unit structure.

[0022] When the metasurface lens is polarization - independent, scan the isotropic unit structure to obtain the phase and amplitude data of unit structures with different sizes at different incident angles and wavelengths.

[0023] When the metasurface lens is linearly - polarization - dependent, scan the hybrid structure of the anisotropic unit structure and the isotropic unit structure to obtain the co - polarization phase and amplitude data of unit structures with different sizes at different incident angles and wavelengths.

[0024] When the metasurface lens is circularly - polarization - dependent, scan the anisotropic unit structure to obtain the cross - polarization phase and amplitude data of unit structures with different sizes at different incident angles and wavelengths;

[0025] Proceed to Step 4.

[0026] Step 4: Determine the target phase and the optimization quantity according to the design requirements.

[0027] 1) When the large - field - of - view broadband achromatic metasurface lens is a polarization - independent lens:

[0028] The target phase of the metasurface lens in Claim 7 can be written as:

[0029]

[0030] The target phase is completely provided by the transmission phase, and the optimization quantity is φ shift (λ,θ).

[0031] 2) When the large - field - of - view broadband achromatic metasurface lens is a linearly - polarization - dependent lens:

[0032] The target phase of the metasurface lens in Claim 7 can be written as:

[0033]

[0034] The target phase is completely provided by the transmission phase, || represents the phase of the co - polarization part mainly considered when horizontally polarized light is incident on the unit structure and exits, and the optimization quantity is φ ||,shift (λ,θ).

[0035] For linearly - polarization - dependent lenses at other angles, just rotate the horizontally - polarized - light - related lens by the corresponding angle.

[0036] 3) When the large field of view broadband achromatic metasurface lens is a circular polarization-related lens:

[0037] The target phase of the metasurface lens in claim 7 can be decomposed into the following form:

[0038]

[0039] The target phase is provided by the transmission phase and the geometric phase together, where is provided by the geometric phase, is provided by the transmission phase, cross represents that the phase of the cross-polarization part is mainly considered in the optimization, and the optimization quantity is φ cross,shift (λ,θ).

[0040] Proceed to step five.

[0041] Step five: Determine the evaluation function and optimize to obtain the phase distribution of the metasurface lens.

[0042] The purpose of the optimization is to make the optimized phase distribution match the preset ideal phase distribution as perfectly as possible, that is, to minimize the difference (wavefront aberration) between the optimized wavefront and the ideal wavefront. Therefore, the evaluation function can be expressed as:

[0043]

[0044] represents the total wavefront aberration, which is the sum of the wavefront aberrations of the metasurface lens at each radial distance r under all incident wavelengths and angles, represents the actual phase. Specifically, represents at the incident wavelength λ i and the angle θ j when, the actual phase of the metasurface lens at the radial distance r(x k ,y l ), and the initial value of the actual phase is randomly generated from the data in the database, represents the target phase in step four or or w ij represents the weight factor, which is used to balance the optimization effect, and its magnitude is reasonably adjusted according to the designed function, optimization results, and database. The optimization algorithm is used for continuous iteration to reduce the total wavefront aberration. During the iteration process, the actual wavefront gradually approaches the target wavefront, and thus the optimal unit structure arrangement phase and the optimization quantity in step four are obtained.

[0045] The metasurface lens has central symmetry. In the optimization, the evaluation function can be simplified into the following form, reducing the two-dimensional optimization of the metasurface lens to one-dimensional, which reduces the calculation amount and optimization time.

[0046]

[0047] Transfer to Step Six.

[0048] Step Six: Conduct numerical simulation based on the optimized phase distribution in Step Five. End the design if the expected effect is met; if the effect is not good, adjust the weight factor of the evaluation function according to the simulation effect, and return to Step Five.

[0049] Furthermore, before optimization, the difficult-to-fabricate and low-transmittance unit structures are removed in the design method to ensure the high efficiency of the metasurface lens.

[0050] Furthermore, the metasurface lens designed by the method has a simple structure, is easy to fabricate, and can achieve the large-field-of-view broadband achromatic aberration function with a single piece.

[0051] The beneficial effects of the present invention are as follows:

[0052] First, compared with the large-field-of-view broadband achromatic aberration lens realized by traditional optical elements, the metasurface lens proposed by the present invention avoids the problems of large volume and complex structure. Compared with the currently proposed double-layer large-field-of-view broadband achromatic aberration metasurface lens and single-layer large-field-of-view multi-wavelength metasurface lens, the metasurface lens proposed by the present invention avoids the problems of difficult processing and alignment faced by the former, and expands the bandwidth of the metasurface lens compared with the latter.

[0053] Second, in the design process, not only the dispersion of the structure but also the angular response of the structure are considered. Therefore, compared with the previous large-field-of-view broadband metasurface lens, the metasurface lens proposed by the present invention has a larger working field of view and a wider relative bandwidth. The metasurface lens proposed by the present invention can not only achieve a large field of view of 100° and a relative bandwidth of 0.4, but also is a single-layer structure, with the characteristics of being thin, light, and easy to fabricate.

[0054] Finally, the design method proposed by the present invention is not only applicable to the design of polarization-independent single-layer large-field-of-view broadband achromatic aberration metasurface lenses, but also applicable to the design of polarization-dependent single-layer large-field-of-view broadband achromatic aberration metasurface lenses. Therefore, it can be applied to various application scenarios such as light field imaging and polarization detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is a schematic diagram of the single-layer large-field-of-view broadband achromatic aberration metasurface lens of the present invention.

[0056] Figure 2 (a) is a schematic diagram of the unit structure in the embodiment of the present invention.

[0057] Figure 2 (b) is the phase-wavelength-incident angle and amplitude-wavelength-incident angle database established in the embodiment of the present invention.

[0058] Figure 2(c) shows the amplitude response and phase response of the unit structure (l1, w1, l2, w2) in the embodiment of the present invention at 0° and 30° incidence.

[0059] Figure 2 (d) shows the normalized magnetic energy density distribution diagrams of the unit structure (l1, w1) in the embodiment of the present invention at different wavelengths and incident angles.

[0060] Figure 3 (a)- Figure 3 (d) are respectively the comparison diagrams of the optimized phase and the ideal phase in the embodiment of the present invention at 0°, 10°, 20°, and 30° incidence.

[0061] Figure 4 (a)- Figure 4 (f) are respectively the simulation results of the focal depth and the focal plane intensity distribution at different wavelengths in the embodiment of the present invention for the designed metasurface lens at 0°, 10°, 20°, 30°, 40°, and 50° incidence.

[0062] Figure 5 (a) shows the comparison between the electromagnetic simulation results and the theoretical values of the focal length of the designed metasurface lens in the embodiment of the present invention under different incidence conditions.

[0063] Figure 5 (b) shows the comparison between the electromagnetic simulation results and the actual values of the incident angle of the designed metasurface lens in the embodiment of the present invention under different incidence conditions.

[0064] Figure 5 (c) shows the full width at half maximum calculated by simulation of the designed metasurface lens in the embodiment of the present invention under different incidence conditions.

[0065] Figure 5 (d) shows the focusing efficiency calculated by simulation of the designed metasurface lens in the embodiment of the present invention under different incidence conditions.

[0066] Explanation of reference numerals:

[0067] 1 is the unit structure array, and 2 is the substrate. Detailed implementation manners

[0068] The present invention will be described in detail below in conjunction with the accompanying drawings and specific implementation manners. However, the protection scope of the present invention is not limited to the following embodiments, and should include all the contents in the claims. Moreover, those skilled in the art can implement all the contents in the claims from the following one embodiment.

[0069] The present invention provides a single-layer large-field-of-view broadband achromatic metasurface lens. The large-field-of-view broadband achromatic metasurface lens is a single-layer structure, including a unit structure array 1 and a substrate 2 from top to bottom. The unit structure array is composed of multiple unit structures, and the unit structures are nano-columns, which can achieve broadband achromatism under a 100° field of view, and the relative bandwidth can reach 0.4.

[0070] The metasurface lens satisfies f < D < 4f, where f is the preset focal length of the metasurface lens, and D is the aperture of the metasurface lens.

[0071] The metasurface lens can be designed to be polarization-dependent or polarization-independent.

[0072] The polarization characteristics of the metasurface lens are related to the shape of the unit structure; when the designed metasurface lens has polarization-independent performance, the unit structure array is composed of isotropic unit structures; when the designed metasurface lens has polarization-dependent performance, the unit structure array is composed of anisotropic unit structures, or jointly composed of anisotropic and isotropic unit structures, but cannot have only isotropic unit structures.

[0073] The period of the unit structure is P, and its value range is 0.2λ0 < P < 0.5λ0. The column height is h, and its value range is 0.5λ0 < h < 2λ0, where λ0 is the central wavelength. The determination of the parameters of the period P and the column height h needs to ensure the following conditions:

[0074] 1) The phase responses of all unit structures that meet the processing conditions can cover 2π;

[0075] 2) The unit structure has good angular tolerance: at different angles, the phase shifts generated by most unit structures are constants, that is, the phase differences between unit structures do not change significantly with the incident angle.

[0076] The phase distribution of the metasurface lens is:

[0077]

[0078] where λ is any wavelength within the working bandwidth, θ is the incident angle, f is the preset focal length, r is the radial distance from any position to the center of the metasurface lens, and φ shift (λ,θ) is the phase shift related to the wavelength and the incident angle, which is the optimization quantity in the design.

[0079] The present invention also provides a design method for a single-layer large-field-of-view broadband achromatic metasurface lens. The method includes:

[0080] Step 1: Determine the design wavelength band [λ min , λ max of the metasurface lens, the lens aperture D and the focal length f; then go to Step 2;

[0081] Step 2: Select the material of the unit structure and the substrate according to the designed wavelength band to ensure high transmittance. Determine the period P and height h of the unit structure; go to Step 3;

[0082] Step 3: Establish a database of phase-wavelength-incident angle and amplitude-wavelength-incident angle;

[0083] Based on the parameters and materials determined in Step 2, change the geometric dimensions of the nanocolumns, perform wavelength and angle scanning, and obtain the phase-wavelength-incident angle and amplitude-wavelength-incident angle databases of the scanned unit structure;

[0084] When the metasurface lens is polarization-independent, only the isotropic unit structure needs to be scanned to obtain the phase and amplitude data of the unit structures with different sizes at different incident angles and wavelengths;

[0085] When the metasurface lens is linearly polarization-dependent, scan the hybrid structure of the anisotropic unit structure and the isotropic unit structure to obtain the co-polarization phase and amplitude data of the unit structures with different sizes at different incident angles and wavelengths;

[0086] When the metasurface lens is circularly polarization-dependent, scan the anisotropic unit structure to obtain the cross-polarization phase and amplitude data of the unit structures with different sizes at different incident angles and wavelengths;

[0087] Go to Step 4;

[0088] Step 4: Determine the target phase and the optimization quantity according to the design requirements;

[0089] 1) When the large field-of-view broadband achromatic metasurface lens is a polarization-independent lens:

[0090] The target phase of the metasurface lens is:

[0091]

[0092] The target phase is completely provided by the transmission phase, and the optimization quantity is φ shift (λ,θ);

[0093] 2) When the large field-of-view broadband achromatic metasurface lens is a linearly polarization-dependent lens:

[0094] The target phase of the metasurface lens is:

[0095]

[0096] The target phase is completely provided by the transmission phase, || indicates that the phase of the co-polarization part of the horizontally polarized light incident on the unit structure and then exiting is mainly considered in the optimization, and the optimization quantity is φ ||,shift (λ,θ);

[0097] 3) When the large field-of-view broadband achromatic metasurface lens is a circular polarization-related lens:

[0098] The target phase of the metasurface lens can be decomposed into the following form:

[0099]

[0100] The target phase is provided by the transmission phase and the geometric phase together, where is provided by the geometric phase, is provided by the transmission phase, and cross represents that the phase of the cross-polarization part is mainly considered in the optimization, and the optimization quantity is φ cross,shift (λ,θ);

[0101] Go to Step Five;

[0102] Step Five: Determine the evaluation function and optimize to obtain the phase distribution of the metasurface lens;

[0103] The evaluation function can be expressed as:

[0104]

[0105] represents the total wavefront aberration, which is the sum of the wavefront aberrations of the metasurface lens at each radial distance r for all incident wavelengths and angles, represents the actual phase. Specifically, represents at the incident wavelength λ i and the angle θ j when, the actual phase of the metasurface lens at the radial distance r(x k ,y l ), and the initial value of the actual phase is randomly generated from the data in the database, represents the target phase in Step Four or or w ij represents the weight factor; it is used to balance the optimization effect, and its magnitude is reasonably adjusted according to the designed function, optimization results, and database.

[0106] Use the optimization algorithm to continuously iterate to reduce the total wavefront aberration. During the iteration process, the actual wavefront gradually approaches the target wavefront, and then the optimal unit structure arrangement phase and the optimization quantity in Step Four are obtained;

[0107] The metasurface lens has central symmetry, and the evaluation function in the optimization is simplified to the following form:

[0108]

[0109] Go to Step Six;

[0110] Step 6: Conduct numerical simulation based on the optimized phase distribution in Step 5. If the expected effect is achieved, end the design; if the effect is not good, adjust the weight factor of the evaluation function according to the simulation effect, and return to Step 5.

[0111] Before optimization, unit structures that are difficult to process and have low transmittance are removed to ensure the high efficiency of the metasurface lens.

[0112] The metasurface lens structure designed by the method has a simple structure, is easy to process, and can achieve large-field broadband achromatic aberration function with a single piece.

[0113] The specific implementation process is as follows:

[0114] The design method of the single-layer large-field broadband achromatic metasurface lens is applicable not only to polarization-related designs but also to polarization-independent designs. In the design, there are only slight differences in the decomposition of the target phase, but the essential target phase and optimization method are the same. In this embodiment, a single-layer large-field broadband achromatic metasurface lens related to horizontal polarization is taken as an example.

[0115] In this embodiment, the preset wavelength band is 1μm - 1.4μm, and the field of view is 60°. The designed metasurface lens has an aperture of 16.4μm and a focal length of 8μm, satisfying f < D < 4f, where f is the preset focal length of the metasurface lens and D is the aperture of the metasurface lens. As Figure 1 Shown is a schematic diagram of a single-layer large-field broadband achromatic metasurface lens related to horizontal polarization. The metasurface lens is a single-layer structure, including a unit structure array 1 and a substrate 2 from top to bottom.

[0116] The unit structure array is composed of unit structures. The unit structure is a nanorod, and its shape is related to the polarization characteristics of the metasurface lens. When the designed metasurface lens has polarization-independent performance, the unit structure array is composed of isotropic unit structures, such as cylinders, regular polygon columns; when the designed metasurface lens has polarization-related performance, the unit structure array is composed of anisotropic unit structures, such as rectangular columns, elliptical cylinders, etc., or composed of both anisotropic and isotropic unit structures, but cannot be composed of only isotropic unit structures. In this embodiment, the metasurface lens is related to horizontal polarization, so the unit structure is a rectangular nanorod including a rectangular column and a square column.

[0117] In this embodiment, the design wavelength band is near-infrared, so aluminum oxide (Al2O3) and silicon (Si) with high transmittance in the near-infrared are selected. Among them, the substrate material is Al2O3, the rectangular nanorod material is Si, and the nanorod array is arranged on the substrate. The following conditions are comprehensively considered:

[0118] 1) The phase responses of all unit structures that meet the processing conditions can cover 2π;

[0119] 2) The unit structure has good angular tolerance: at different angles, the phase shifts generated by most unit structures are constant, that is, the phase difference between unit structures does not change significantly with the incident angle.

[0120] Finally, the period of the unit structure is determined as P = 0.4 μm, the column height is h = 1 μm, and the central wavelength is λ0 = 1.2 μm, satisfying the value range of 0.2λ0 < P < 0.5λ0, and the column height is h, with its value range of 0.5λ0 < h < 2λ0

[0121] The phase distribution of the metasurface lens in the design is as follows:

[0122]

[0123] where λ is any wavelength within the working bandwidth, θ is the incident angle, f is the preset focal length, r is the radial distance from any position to the center of the metasurface lens, and φ shift (λ,θ) is the phase shift related to the wavelength and incident angle, which is the optimization quantity in the design. The specific optimization process is as follows:

[0124] After clarifying the design band, lens aperture, focal length, unit structure material, and the period P and height h of the unit structure, a phase-wavelength-incident angle and amplitude-wavelength-incident angle database is established. As Figure 2 shown is the established database and the response characteristics of some unit structures. Figure 2 (a) is the schematic diagram of the unit structure of this embodiment. In this embodiment, the scanning ranges of the major axis and minor axis of the unit structure are both 80 nm - 320 nm, and the scanning is performed with a step of 10 nm. The scanning band range is 0.9 μm - 1.7 μm. Figure 2 (b) only shows the phase-wavelength-incident angle and amplitude-wavelength-incident angle databases at wavelengths of 1 μm, 1.1 μm, 1.2 μm, 1.3 μm, and 1.4 μm when the incident angles are 0° and 30°. It can be seen from the database that the phase of the scanned unit structure covers the 2π phase space, and the amplitude response is relatively high. This is mainly because the absorption loss of the unit structure material in the near-infrared band is small and the refractive index difference is large, and the phase and amplitude distribution diagrams of the database show good performance. For clarity, two unit structures (l1 = 80 nm, w1 = 80 nm, l2 = 100 nm, w2 = 320 nm) are selected for analysis. Figure 2(c) shows the amplitude and phase responses of these two cells at incident angles of 0° and 30°, respectively. The phase compensations of the two cells are 332.86° and 558.50° at 0° incidence, and 292.57° and 541.52° at 30° incidence. Within the designed bandwidth, different incident angles affect the phase responses of the cells, but the phase shift between the cells remains basically unchanged. The phase distribution is approximately linearly related to the wavelength. These two characteristics ensure the successful realization of achromatic large-field focusing. Figure 2 (d) shows the normalized magnetic energy density distribution map of the unit structure (l1, w1) at different wavelengths and incident angles. The black line is the contour of the unit structure. It can be seen that the magnetic field energy is highly concentrated within the nanocolumns, while the optical coupling between adjacent nanocolumns is very weak. In summary, the databases established for horizontal polarization all have rich phase compensations and high amplitude responses, laying a good foundation for the design of high-performance large-field broadband achromatic metasurfaces.

[0125] The large-field broadband achromatic metasurface is a linearly polarized light-related lens. Therefore, the target phase of the metasurface is:

[0126]

[0127] For linearly polarized light-related lenses at other angles, the horizontally polarized light-related lens only needs to be rotated by the corresponding angle.

[0128] The target phase is completely provided by the transmission phase. || represents that in the optimization, the phase of the co-polarized part of the horizontally polarized light incident on the unit structure and then exiting is mainly considered. The optimization quantity is φ ||,shift (λ, θ), whose function is to make the phase response in the database match the target phase.

[0129] The first term in the formula is the quadratic phase, which has the characteristic of converting the rotational symmetry in the object space into the translational symmetry in the image space and can be used in the design of wide-angle lenses. The second term φ ||,shift (λ, θ) is only related to λ and θ and has no effect on the focusing effect. Therefore, the target phase can be used to achieve a large-field design.

[0130] In the formula, the focal length f is a fixed value, making the lens have a stable focal length in the large-field broadband incident angle. Therefore, in the optimization, the phase of the lens needs to be close to the target phase. The optimization quantity is φ ||,shift (λ, θ) is only related to λ and θ and has nothing to do with the radial distance r. Therefore, for any radial distance r, the phase of the metasurface is related to the wavelength and has a linear relationship with 1 / λ. The unit structure is to compensate for the dispersion caused by the light transmission in the air. Therefore, the phase response of the unit structure should also have a linear relationship with 1 / λ. In addition, the target phase is related to the radial distance r. Therefore, the unit structure should also be able to provide a rich phase coverage.

[0131] The purpose of optimization is to make the actual phase distribution of the metasurface lens as perfectly matched as possible with the preset phase distribution, that is, to minimize the difference (wave aberration) between the optimized wavefront and the ideal wavefront. Therefore, the evaluation function can be expressed as:

[0132]

[0133] represents the total wave aberration, which is the sum of the wave aberrations at each position for each wavelength and angle. represents the actual phase, and its initial value is randomly generated from the data in the database. represents the target phase in step four ( or or ). The optimization algorithm is used to continuously iterate to reduce the total wave aberration. During the iteration process, the actual wavefront gradually approaches the target wavefront, and then the optimal phase of the unit structure arrangement and the optimization amount in step four are obtained.

[0134] The designed metasurface lens has central symmetry. In the optimization, the evaluation function can be simplified into the following form:

[0135]

[0136] The simplified evaluation function reduces the two-dimensional optimization of the metasurface lens to one-dimensional, reducing the computational amount and optimization time.

[0137] In this embodiment, the particle swarm optimization algorithm is used to continuously iterate to reduce the wave aberration, and then the optimal arrangement of the unit structure is obtained. During the optimization process, as long as φ ||,shift (λ,θ) is determined, the optimized wavefront with the minimum wave phase difference can be uniquely determined from the database. Therefore, the optimization process can be understood as a process of finding the optimal optimization amount φ ||,shift (λ,θ) with the wave aberration as the evaluation function. In this process, to ensure that the finally optimized metasurface lens has high efficiency, the unit structures with low transmittance in the database are excluded before optimization. In this embodiment, the weight factor w is 1. The setting of the weight factor is mainly determined by comprehensively considering the optimization results, the database, and the objective function. The initial optimization amount φ ||,shift (λ,θ) is randomly generated. The initial wavefront is obtained through the generated initial reference phase, and then the best wavefront corresponding to the current database is obtained through 1200 iterations of the particle swarm optimization algorithm.

[0138] Figure 3 is the phase distribution in the radial direction of the horizontally polarized related single-layer large field-of-view broadband achromatic metasurface lens optimized. The discrete points represent the actual optimized phase, and the solid line represents the ideal phase. Figure 3 (a)- Figure 3(d) Comparison diagrams of the optimized phase and the ideal phase at wavelengths of 1μm, 1.1μm, 1.2μm, 1.3μm, and 1.4μm under the incident angles of 0°, 10°, 20°, and 30° respectively. The actual optimized phase is close to the ideal phase, thus achieving the expected design requirements.

[0139] The obtained optimized phase is used for the metasurface design and simulated by an electromagnetic simulation software. Only the incident angles of 0° - 30° and wavelengths of 1μm - 1.4μm are considered in the optimization. In fact, the optimized metasurface lens is still effective at larger incident angles and wavelengths, mainly because the phase response of the optimized structure maintains a linear relationship between the phase and the wavelength at longer wavelengths under the incidence of a larger field of view. Figure 4 (a)- Figure 4 (f) Simulation results of the focal depth and focal plane intensity distribution of the metasurface lens designed in the embodiment of the present invention at 1μm, 1.1μm, 1.2μm, 1.3μm, 1.4μm, and 1.5μm under the incident angles of 0°, 10°, 20°, 30°, 40°, and 50° respectively. The simulation results show that plane waves with different incident angles and wavelengths are incident on the metasurface, and the focal length remains at 5.4μm, proving that the device achieves achromatism for a large field of view. This embodiment is only for reference of the present invention. In actual optimization, the optimization range of the wavelength can be extended to 1.5μm, and the incident angle can be extended to 50°, and better optimization effects can be obtained.

[0140] In addition, according to the spot distribution results simulated by the electromagnetic simulation software, the focal length, full width at half maximum, incident angle, and focusing efficiency of the metasurface lens are calculated. Figure 5 (a) Comparison between the electromagnetic simulation results and the theoretical values of the focal length of the metasurface lens designed in the embodiment of the present invention under different incident conditions. The focal length calculated by the electromagnetic simulation is basically consistent with the focal length calculated by the numerical simulation, further proving that the optimized metasurface lens achieves dispersion control and field of view regulation. Figure 5 (b) Comparison between the electromagnetic simulation results and the actual values of the incident angle of the metasurface lens designed in the embodiment of the present invention under different incident conditions. The actual incident angle is known, and the incident angle calculated by the simulation is obtained according to the lateral offset of the focused spot, which is the ability inherent in the quadratic phase itself. The simulation results show that only when the incident angle is 50°, there is a slight deviation between the calculated result and the theoretical value, and the maximum calculation error is 3.7°. Figure 5 (c) The full width at half maximum calculated by the simulation of the metasurface lens designed in the embodiment of the present invention under different incident conditions. As the incident angle increases, the value of the full width at half maximum gradually increases. Figure 5 (d) The focusing efficiency calculated by the simulation of the metasurface lens designed in the embodiment of the present invention under different incident conditions.

[0141] In this embodiment, although only the case of normal incidence is simulated, the designed metasurface lens is centrosymmetric. Therefore, for the corresponding negative incidence angle, except that the translation direction of the light spot on the focal plane is opposite to that of the positive incidence angle, the others are the same. So the designed metasurface lens can effectively achieve focusing on the same focal plane at the incidence angles from -50° to 50°.

[0142] In summary, the simulation proves that the designed horizontally polarized light-related metasurface lens achieves achromatic focusing within the range of 1μm - 1.5μm (relative bandwidth 0.4) and the field of view can reach 100° (±50°).

[0143] In this embodiment, due to considerations of computer performance, only some wavelengths and incidence angles are optimized. In actual optimization, the number of optimized wavelengths and angles can be increased to fully cover the designed wavelength band and angles, and better optimization results can be obtained.

[0144] Taking the design in the near-infrared band as an example in this embodiment, without loss of generality, the present invention is also applicable to other bands.

[0145] The above design process, embodiments and simulation results well verify the present invention.

[0146] Therefore, the embodiments of the present invention have been described above in conjunction with the accompanying drawings. However, the present invention is not limited to the above specific embodiments. The above embodiments are merely illustrative and not restrictive. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included within the protection scope of the present application. The parts not elaborated in detail in the present invention belong to the well-known technologies in the art.

Claims

1. A single-layer large field-of-view broadband achromatic metasurface lens, characterized in that, The large field-of-view broadband achromatic metasurface lens is a single-layer structure, including a unit structure array 1 and a substrate 2 from top to bottom. The unit structure array consists of multiple unit structures, and the unit structure is a nanocolumn, which can achieve broadband achromatism under a 100° field of view, and the relative bandwidth can reach 0.

4.

2. The single-layer large-field-of-view broadband achromatic metasurface lens according to claim 1, wherein The metasurface lens satisfies f < D < 4f, where f is the preset focal length of the metasurface lens and D is the aperture of the metasurface lens.

3. A single-layer large field of view broadband achromatic metasurface lens according to claim 1, characterized in that, The metasurface lens can be designed to be polarization-dependent or polarization-independent.

4. A single-layer large field-of-view broadband achromatic metasurface lens according to claim 1, characterized in that, The polarization characteristics of the metasurface lens are related to the shape of the unit structure; When the designed metasurface lens has polarization-independent performance, the unit structure array consists of isotropic unit structures; when the designed metasurface lens has polarization-dependent performance, the unit structure array consists of anisotropic unit structures, or is composed of a combination of anisotropic and isotropic unit structures, but cannot consist of only isotropic unit structures.

5. The unit structure according to claim 4, characterized in that, The period of the unit structure is P, and its value range is 0.2λ0 < P < 0.5λ0, and the column height is h, and its value range is 0.5λ0 < h < 2λ0, where λ0 is the central wavelength.

6. The unit structure according to claim 5, characterized in that, The determination of the period P and column height h parameters needs to ensure the following conditions: 1) The phase responses of all unit structures that meet the processing conditions can cover 2π; 2) The unit structure has good angular tolerance: at different angles, the phase shifts generated by most unit structures are constant, that is, the phase difference between unit structures does not change significantly with the incident angle.

7. A single-layer large-field-of-view broadband achromatic metasurface lens according to claim 1, characterized in that, The phase distribution of the metasurface lens is: Among them, λ is any wavelength within the working bandwidth, θ is the incident angle, f is the preset focal length, r is the radial distance from any position to the center of the metasurface lens, and φ shift (λ,θ) is the phase shift related to the wavelength and the incident angle, which is the optimization quantity in the design.

8. A design method for a single-layer large-field-of-view broadband achromatic metasurface lens as described in any one of claims 1-7, characterized in that, The method includes: Step 1: Determine the design wavelength band [λ min , λ max of the metasurface lens, the lens aperture D, and the focal length f; proceed to Step 2; Step 2: Select the materials of the unit structure and the substrate according to the designed wavelength band to ensure high transmittance. Determine the period P and height h of the unit structure; go to Step 3; Step 3: Establish a phase-wavelength-incident angle, amplitude-wavelength-incident angle database; Based on the parameters and materials determined in Step 2, change the geometric dimensions of the nanocolumns, perform wavelength and angle scans, and obtain the phase-wavelength-incident angle and amplitude-wavelength-incident angle databases of the scanned unit structures; When the metasurface lens is polarization-independent, only the isotropic unit structures need to be scanned to obtain the phase and amplitude data of unit structures with different sizes at different incident angles and wavelengths; When the metasurface lens is linearly polarization-dependent, scan the hybrid structure of anisotropic unit structures and isotropic unit structures to obtain the co-polarization phase and amplitude data of unit structures with different sizes at different incident angles and wavelengths; When the metasurface lens is circularly polarization-dependent, scan the anisotropic unit structures to obtain the cross-polarization phase and amplitude data of unit structures with different sizes at different incident angles and wavelengths; Go to Step 4; Step 4: Determine the target phase and optimization amount according to the design requirements; 1) When the large field-of-view broadband achromatic metasurface lens is a polarization-independent lens: The target phase of the metasurface lens is: The target phase is completely provided by the transmission phase, and the optimization amount is φ shift (λ,θ); 2) When the large field-of-view broadband achromatic metasurface lens is a linearly polarization-dependent lens: The target phase of the metasurface lens is: The target phase is completely provided by the transmission phase, || indicating that the phase of the co-polarized part of the horizontally polarized light incident on the unit structure and then exiting is mainly considered in the optimization, and the optimization amount is φ ||,shift (λ,θ); 3) When the large field-of-view broadband achromatic metasurface lens is a circularly polarization-dependent lens: The target phase of the metasurface lens can be decomposed into the following form: The target phase is jointly provided by the transmission phase and the geometric phase, where is provided by the geometric phase, is provided by the transmission phase, and "cross" indicates that the phase of the cross-polarization part is mainly considered in the optimization, and the optimization amount is φ cross,shift (λ,θ); Go to Step 5; Step 5: Determine the evaluation function and optimize to obtain the phase distribution of the metasurface lens; The evaluation function can be expressed as: represents the total wave aberration, which is the sum of the wave aberrations of the metasurface lens at each radial distance r for all incident wavelengths and angles. represents the actual phase. represents at the incident wavelength λ i and the angle θ j , the actual phase of the metasurface lens at the radial distance r(x k ,y l ). The initial value of the actual phase is randomly generated from the data in the database. represents the target phase in step four ( or or ), and w ij represents the weight factor. An optimization algorithm is used for continuous iteration to reduce the total wavefront aberration. During the iteration process, the actual wavefront gradually approaches the target wavefront, thereby obtaining the optimal unit structure arrangement phase and the optimization amount in Step 4. The metasurface lens has central symmetry, and the evaluation function in the optimization is simplified to the following form: Proceed to Step 6; Step 6: Perform numerical simulation according to the optimized phase distribution in Step 5. End the design if the expected effect is satisfied; if the effect is not good, adjust the weight factor of the evaluation function according to the simulation effect, and return to Step 5.

9. The design method of a single-layer large field of view broadband achromatic metalens according to claim 8, characterized in that, Before optimization, unit structures that are difficult to process and have low transmittance are removed to ensure the high efficiency of the metasurface lens.

10. The design method of a single-layer large-field-of-view broadband achromatic metasurface lens according to claim 8, characterized in that, A single piece can achieve the function of large field of view broadband achromatism.

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