Intermediate infrared large-aperture all-silicon super-structure lens and design method thereof

Abstract

The invention discloses a mid-infrared large-aperture all-silicon super-structure lens and a design method thereof, and belongs to the field of silicon-based super-lenses, the mid-infrared large-aperture all-silicon super-structure lens comprises a super-unit array composed of a plurality of super-units, the plurality of super-units comprise the same silicon substrate and a silicon nano-column vertically grown at the center of the silicon substrate, and the change range of the diameter D of the silicon nanorods of the plurality of super units is 440-1350nm, and the step length is 10nm, so that the full coverage of the phase delay # imgabs0 # of incident mid-infrared light is realized by adjusting the diameter D of the silicon nanorods, and the transmission coefficient txx of a single super unit is greater than 0.7. By adopting the mid-infrared large-aperture all-silicon metamaterial lens and the design method thereof, high-precision phase regulation and control are realized by constructing a dense phase sampling unit library of 40 super units, the mid-infrared all-silicon metamaterial lens with the aperture of about 10mm is formed by combining a large-scale array design, and the mid-infrared large-aperture all-silicon metamaterial lens has the advantages of high focusing precision, large numerical aperture and good broadband adaptability; the problems that a traditional metamaterial lens is large in phase fitting error and small in caliber are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of silicon-based superlenses, and particularly to a mid-infrared large-aperture all-silicon metasurface lens and a design method thereof. Background Art

[0002] In the field of optical metamaterials, dielectric superlenses have the advantages of low optical loss, wide working bandwidth, good compatibility, high production efficiency, and flexible material selection and design compared with traditional plasmonic metasurfaces, and thus are widely used. At the same time, as a high-refractive-index material, silicon is widely used in the construction of all-dielectric superlenses due to its mature processing technology.

[0003] However, the existing research on silicon-based superlenses mainly focuses on visible light (400 - 700 nm) and near-infrared (800 - 1550 nm). The technological development for the mid-infrared band (3 - 5 μm) faces the following challenges:

[0004] 1. The contradiction between phase modulation accuracy and unit design: The mid-infrared wavelength is relatively long (e.g., 3.75 μm is 5 times that of visible light), which requires the corresponding increase of the supercell period. However, traditional phase sampling methods (such as π / 2 or π / 4 gradients) can only provide 8 - 16 discrete phase states, resulting in a significant deviation between the discrete phase distribution and the theoretical focusing phase (continuous spherical wavefront). For example, in 2015, the Manuel Decker team used a 16-element library in a near-infrared Huygens metasurface, and its phase error was amplified to more than 1 / 10 of the wavelength in the mid-infrared band, leading to the energy leakage of the focal spot sidelobe and the focal length shift.

[0005] 2. The simulation and processing bottlenecks in large-aperture design: Mid-infrared optical systems often require a 10-mm-level aperture to achieve a high numerical aperture (e.g., NA = 0.724), corresponding to tens of millions of supercells (such as a 5500×5500 array). Traditional electromagnetic simulation software (such as FDTD, CST) is limited by computing resources and cannot directly process large-scale structures. Only the full-wave simulation of a single unit takes about several hours, and the full-array simulation requires more than one million core-hours, resulting in extremely high engineering design costs. In addition, the processing accuracy requirements for silicon-based supercells are extremely strict, and the dense phase sampling leads to a large span of structural parameters (such as diameters from 440 - 1350 nm). The resolution of existing lithography processes (usually at the 100-nm level) is difficult to ensure the consistency of structures of different sizes.

[0006] 3. The lack of broadband characteristics and dispersion compensation: The 3 - 5 μm atmospheric window covers multiple application wavelengths (e.g., 3 μm for combustion diagnosis, 5 μm for night vision imaging), but most existing silicon-based supercells are optimized for a single wavelength and do not consider the influence of refractive index dispersion on phase delay. For example, when the wavelength shifts from 3.75 μm to 3 μm or 5 μm, the phase response of traditional units drifts by more than π / 2, resulting in the dispersion of the focused spot and making it difficult to meet the requirements of broadband scenarios.

[0007] In summary, although the silicon-based dielectric metasurface lens shows the potential for mid-infrared applications, there are still gaps in its core technologies: the high-density phase sampling method and the large-aperture efficient design technology. The existing technologies have not solved the key problems of "insufficient focusing accuracy caused by sparse phase sampling" and "infeasibility of large-scale array simulation". Summary of the Invention

[0008] The purpose of the present invention is to provide a mid-infrared large-aperture all-silicon metasurface lens and its design method to solve the above technical problems.

[0009] To achieve the above object, the present invention provides a mid-infrared large-aperture all-silicon metasurface lens, including a metasurface unit array composed of multiple metasurface units. The multiple metasurface units include the same silicon substrate and silicon nanocolumns vertically grown at the center of the silicon substrate. The diameter D of the silicon nanocolumns of the multiple metasurface units varies in the range of 440 nm - 1350 nm with a step of 10 nm to achieve full coverage of the phase delay of the incident mid-infrared light by adjusting the diameter D of the silicon nanocolumns. The transmission coefficient t of a single metasurface unit > 0.7; xx

[0010] The diameter of the silicon nanocolumns is smaller than the arrangement period of the metasurface units, and the refractive index of the silicon nanocolumns is the same as that of the silicon substrate.

[0011] Preferably, the phase regulation of the metasurface unit array satisfies:

[0012]

[0013] In the formula, represents the focusing phase, λ represents the working wavelength, X and Y represent the position coordinates of the metasurface units, and f represents the focal length;

[0014] The continuous phase obtained from formula (1) is discretized according to 40 gradients, and then according to the law that the phase changes with a period of 2π, the discretized phase is normalized to 0 - 2π to form a dense phase sampling unit library.

[0015] Preferably, the number of single-sided metasurface units of the metasurface unit array is 5500, forming a 5500×5500 metasurface unit array with an overall aperture of less than 10 mm.

[0016] Preferably, the height h1 of the silicon nanocolumns = 2000 nm;

[0017] The height h2 of the silicon substrate = 2000 nm, and the arrangement period P = 1750 nm.

[0018] ​Preferably, both the silicon nanocolumns and the silicon substrate are silicon dielectrics, and the operating wavelength of the silicon dielectric is 3.75 μm, the relative permittivity ε = 11.7649, and the permeability μ = 1.

[0019] Preferably, for the mid-infrared large-aperture all-silicon metasurface lens, the lens diameter D fo = 1750 nm * 5500 nm, the focal length d = 15 mm, and the numerical aperture N A ≈ 0.724;

[0020] At a wavelength of 3.75 μm, the full width at half maximum of the focal plane ≤ 2362.5 nm.

[0021] A design method for a mid-infrared large-aperture all-silicon metasurface lens includes the following steps:

[0022] S1. Based on formula (1), use simulation software to call the dense phase sampling unit library to generate a 5500×5500 supercell array;

[0023] S2. Encode the 40 normalized phase values in the dense phase sampling unit library in sequence, and establish a correspondence table of phase value - unit number - silicon nanocolumn diameter;

[0024] S3. Design the silicon nanocolumn diameter: read the theoretical phase of each coordinate, match the unit number of the phase value closest to it in the unit library, and assign the corresponding silicon nanocolumn diameter according to the correspondence table of phase value - unit number - silicon nanocolumn diameter to form a global phase distribution matrix;

[0025] S4. Equivalent each supercell in the global phase distribution matrix to a phase delay point, and construct a simplified diffraction integral model;

[0026] S5. Perform simulation verification in batches: use electromagnetic simulation software to generate a small-aperture array of 60*60 supercells, and obtain the focal plane light intensity distribution and the full width at half maximum

[0027] S6. Based on the verification results of the small-aperture array, use the simplified diffraction integral model to deduce the focal plane light intensity of the 5500×5500 supercell array, and verify the improvement effect of dense phase sampling on the focus energy concentration;

[0028] S7. Fix the silicon nanocolumn diameter that has passed the verification.

[0029] Preferably, the expression of the simplified diffraction integral model described in step S4 is as follows:

[0030]

[0031] Wherein, U represents the focal plane optical field, t(X,Y) represents the initial optical field at the coordinates (X,Y), k is the wave number and k = 2π / λ, R represents the three-dimensional Euclidean distance related to the coordinates, and i represents the imaginary unit.

[0032] Preferably, after step S7, there is also step S8: Substitute D fo = 1750nm * 60nm, d = 50000nm into the following formula to solve for the numerical aperture N A :

[0033] N A = n × sinθ (3);

[0034] Wherein, n represents the refractive index of the silicon medium; θ represents half of the maximum field of view angle, and θ = tan(D fo / 2d);

[0035] Obtain N A ≈0.724.

[0036] Therefore, the present invention adopts the above-mentioned mid-infrared large-aperture all-silicon metasurface lens and its design method, and the beneficial effects are as follows:

[0037] 1. Adopt an extremely small phase gradient of π / 20 (traditional metasurfaces are mostly π / 2 or π / 4), construct a dense phase unit library containing 40 supercells, and discretize the focusing phase distribution function into 40 gradients to achieve high-precision control of the optical field phase, significantly improving the focusing accuracy and energy concentration of the metasurface lens;

[0038] 2. Aiming at the problem that the mid-infrared large-aperture metasurface lens with tens of millions of supercells cannot run in conventional electromagnetic simulation software, a method combining diffraction integral and small-aperture simulation is proposed. Approximate the supercells as phase delay points, and replace the full-scale electromagnetic simulation through the accumulation calculation of the focal plane optical field, effectively solving the design and verification problem of large-aperture metasurface lenses.

[0039] The technical solution of the present invention will be further described in detail below through the accompanying drawings and embodiments. Description of the Drawings

[0040] Figure 1 It is a model structure diagram of the supercell of a mid-infrared large-aperture all-silicon metasurface lens of the present invention;

[0041] Figure 2 It is the transmission parameter diagram of the mid-infrared large-aperture all-silicon metasurface lens in the simulation experiment, where (a) is the transmission parameter diagram when D = 690nm, and (b) is the transmission parameter diagram when D varies in the range of 440nm - 1350nm;

[0042] Figure 3Schematic diagram of the transmission parameters of the unit library and lens parameters for the simulation experiment, where (a) is the transmission parameter diagram of the π / 5 phase gradient, (b) is the transmission parameter diagram of the π / 20 phase gradient, and (c) is the schematic diagram of the lens parameters;

[0043] Figure 4 For the 5500 of the simulation experiment 2 Phase diagram of the dense sampling design of the supercell;

[0044] Figure 5 For the 1000 of the simulation experiment 2 Reference diagram of the 1000 supercells, where (a) is the diffraction integral focal plane diagram of the 1000 supercells 2 and (b) is the phase diagram of the dense sampling design of the 1000 supercells; 2 Phase diagram of the dense sampling design of the 1000 supercells;

[0045] Figure 6 Diagrams of the light intensity distribution of the transmission field when the phase gradients are π / 20 and π / 5 respectively for the simulation experiment. Among them, (a) is the light intensity distribution diagram of the focal plane when the phase gradient is π / 20, (b) is the light intensity distribution diagram of the focal plane when the phase gradient is π / 5, (c) is the result diagram of the transverse envelope and full width at half maximum of the focal plane when the phase gradient is π / 20, (d) is the result diagram of the transverse envelope and full width at half maximum of the focal plane when the phase gradient is π / 5, (e) is the light intensity distribution diagram of the xoz plane when the phase gradient is π / 20, (f) is the light intensity distribution diagram of the xoz plane when the phase gradient is π / 5, (g) is the comparison diagram of the light intensity envelope on the z-axis and the actual focal length when the phase gradient is π / 20, and (h) is the comparison diagram of the light intensity envelope on the z-axis and the actual focal length when the phase gradient is π / 5;

[0046] Figure 7 Diagrams of the full width at half maximum results when the incident wavelengths are 3μm, 4.5μm, and 5 respectively for the simulation experiment. Among them, (a) is the full width at half maximum result diagram when the incident wavelength is 3μm, (b) is the full width at half maximum result diagram when the incident wavelength is 4.5μm, and (c) is the full width at half maximum result diagram when the incident wavelength is 5μm.

[0047] Reference numerals

[0048] 1. Silicon base; 2. Silicon nanocolumn. Detailed implementation manners

[0049] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer and more understandable, the embodiments of the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the embodiments of the present invention and are not used to limit the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of this application. The examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals represent the same or similar elements or elements with the same or similar functions throughout.

[0050] It should be noted that the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or server that includes a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or are inherent to these processes, methods, products, or devices.

[0051] The embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings.

[0052] As Figure 1 shown, a mid-infrared large-aperture all-silicon metasurface lens includes a metasurface unit array composed of multiple meta-units. The multiple meta-units include the same silicon substrate 1 and silicon nanocolumns 2 vertically grown at the center of the silicon substrate 1. The diameter D of the silicon nanocolumns 2 of the multiple meta-units varies in the range of 440 nm - 1350 nm with a step size of 10 nm to achieve full coverage of the phase delay of the incident mid-infrared light by adjusting the diameter D of the silicon nanocolumns 2. The transmission coefficient t of a single meta-unit > 0.7; the diameter of the silicon nanocolumns 2 is smaller than the arrangement period of the meta-units, and the refractive index of the silicon nanocolumns 2 is the same as that of the silicon substrate 1. xx The phase regulation of the metasurface unit array satisfies:

[0053] The phase regulation of the metasurface unit array satisfies:

[0054]

[0055] In the formula, represents the focusing phase, λ represents the working wavelength, X and Y represent the position coordinates of the meta-units, and f represents the focal length;

[0056] The continuous phase obtained from formula (1) is discretized according to 40 gradients, and then according to the law that the phase changes in a 2π period, the discretized phase is normalized to 0 - 2π to form a dense phase sampling unit library.

[0057] The number of single-sided supercells in the metasurface unit array is 5,500, forming a 5,500×5,500 metasurface unit array, and the overall aperture is less than 10 mm.

[0058] The height h1 of the silicon nanocolumn 2 is 2,000 nm; the height h2 of the silicon substrate 1 is 2,000 nm, and the arrangement period P is 1,750 nm.

[0059] Both the silicon nanocolumn 2 and the silicon substrate 1 are silicon dielectrics, and the operating wavelength of the silicon dielectric is 3.75 μm, the relative permittivity ε = 11.7649, and the magnetic permeability μ = 1.

[0060] The lens diameter D of the mid-infrared large-aperture all-silicon metasurface lens fo = 1,750 nm * 5,500 nm, the focal length d = 15 mm, and the numerical aperture N A ≈ 0.724; at a wavelength of 3.75 μm, the full width at half maximum of the focal plane ≤ 2,362.5 nm.

[0061] A design method of a mid-infrared large-aperture all-silicon metasurface lens includes the following steps:

[0062] S1. Based on formula (1), use simulation software to call the dense phase sampling unit library to generate a 5,500×5,500 metasurface unit array;

[0063] S2. Encode the 40 normalized phase values in the dense phase sampling unit library in sequence, and establish a correspondence table of phase value - unit number - silicon nanocolumn diameter;

[0064] S3. Design the silicon nanocolumn diameter: read the theoretical phase of each coordinate, match the unit number of the phase value closest to it in the unit library, and allocate the corresponding silicon nanocolumn diameter according to the correspondence table of phase value - unit number - silicon nanocolumn diameter to form a global phase distribution matrix;

[0065] S4. Equivalent each metasurface unit in the global phase distribution matrix to a phase delay point, and construct a simplified diffraction integral model;

[0066] The expression of the simplified diffraction integral model described in step S4 is as follows:

[0067]

[0068] In the formula, U represents the light field on the focal plane, t(X,Y) represents the initial light field at the coordinate (X,Y), k is the wave number and k = 2π / λ, R represents the three-dimensional Euclidean distance related to the coordinate, and i represents the imaginary unit.

[0069] S5. Sub-scale simulation verification: Use electromagnetic simulation software to generate a small-aperture array of 60*60 metasurface units, and obtain the light intensity distribution and full width at half maximum of its focal plane

[0070] S6. Based on the verification results of the small-aperture array, use the simplified diffraction integral model to deduce the focal plane light intensity of the 5500×5500 supercell array, and verify the improvement effect of dense phase sampling on the focus energy concentration;

[0071] S7. Solidify the diameter of the verified silicon nanocolumns.

[0072] Preferably, after step S7, there is further step S8. Substitute D fo = 1750nm*60nm and d = 50000nm into the following formula to solve for the numerical aperture N A :

[0073] N A = n×sinθ (3);

[0074] In the formula, n represents the refractive index of the silicon medium; θ represents half of the maximum field of view angle, and θ = tan(D fo / 2d);

[0075] Obtain N A ≈0.724.

[0076] It should be noted that the design of the numerical aperture needs to follow the requirements of the optical system. When N A is too large, due to the diffraction effect of light, the energy of the focal spot will decrease and the focal spot size will become larger, which is suitable for applications that require a larger focal spot or a lower energy density, such as certain imaging systems or scenarios that require uniform illumination. When N A is too small, the focal spot is smaller and the energy is concentrated, which is suitable for applications that require high resolution and high energy density, such as laser processing, microscopy imaging or lithography technology.

[0077] Simulation experiment

[0078] As Figure 2 shown, use the electromagnetic simulation software to scan the supercell with a silicon nanocolumn diameter D = 690nm from 60THz to 100THz. The results are as Figure 2 (a) shown, and its transmission coefficient remains above 0.7 and the phase change is obvious. Keeping other parameters unchanged, further change the size of the silicon nanocolumn diameter D for scanning. The change range of D is 440 - 1350nm, with a step size of 10nm. Incident 3.75μm mid-infrared waves on all supercells. The results are as Figure 2 (b) shown, and its transmission coefficient t xx is above 0.7, and the phase delay covers the change from -π to +π, proving that this supercell has good mid-infrared transparency and the potential of a screening structure. Based on the above structure design, as Figure 4 shown, the dense phase distribution of 5500×5500 supercells, and asFigure 5 From the phase distribution of the 1000×1000 supercells shown, it can be seen that its focal spot is clear, the energy is concentrated without speckles.

[0079] As Figure 3 shown, further screening is carried out by adding phase gradients of π / 5 and π / 20, and the transmission coefficient is required to be higher than 0.7. Unit libraries with quantities of 10 and 40 are respectively established for reference and comparison. Then, based on formula (1), the unit libraries with phase gradients of π / 5 and π / 20 are called for automatic arraying, and two small-aperture metasurfaces composed of 60*60 supercells are generated to compare the influence of phase gradients on the focusing effect. In this simulation experiment, an antireflection layer of SiO2 with a thickness of 650 nm is set on the back of the metasurface lens composed of the small-aperture metasurface to improve the transmittance, and the relative permittivity of SiO2 is 2.1025 and the permeability is 1. Plane waves of 3.75 μm are respectively incident on the two metasurface lenses, and a probe is set at a height of 65000 nm from the surface of the metasurface lens. Using an 80 THz field monitor, the light intensity distributions in the focal plane and the xoz plane are obtained, the envelope when y = 0 in the focal plane is intercepted, and then it is normalized to calculate the full width at half maximum (FWHM) to compare the focusing effect. At the same time, the envelope when x = 0 in the xoz plane is intercepted to calculate the actual focal length f sim . As Figure 6 shown, when the phase gradient is π / 5, FWHM = 2231.25 nm, f sim = 57100 nm, and the offset reaches 7100 nm. While when the phase gradient is π / 20, FWHM = 2362.5 nm, f sim = 48300 nm, with only an offset of 1700 nm.

[0080] Mid-infrared waves at 3 μm, 4.5 μm, and 5 μm within the atmospheric window range are respectively incident on the metasurface lens composed of the dense phase sampling unit library of the present invention, and the frequency range covers 60 THz - 100 THz to verify its focusing effect. The normalized envelope when y = 0 in the focal plane is as Figure 7 shown. When mid-infrared waves of 3 μm, 4.5 μm, and 5 μm are incident, the offset of the actual focal length from the preset focal length is relatively large, but the FWHM is still small, being 4200 nm, 2100 nm, and 2363 nm respectively, and the sidelobes are small and the energy is concentrated. It is proved that in the 3 - 5 μm band, the all-silicon dielectric metasurface lens with a phase gradient of π / 20 still has a certain focusing ability, thus verifying the effectiveness of the present invention.

[0081] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions of the present invention or make equivalent replacements, and these modifications or equivalent replacements do not enable the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A mid-infrared large-aperture all-silicon metasurface lens, comprising a metasurface unit array composed of multiple metasurface units, characterized in that: Multiple supercells include the same silicon substrate and silicon nanocolumns vertically grown at the center of the silicon substrate, and the diameter D of the silicon nanocolumns in the multiple supercells varies in the range of 440 nm - 1350 nm with a step size of 10 nm, so as to realize the phase delay of incident mid-infrared light by adjusting the diameter D of the silicon nanocolumns for full coverage, and the transmission coefficient t of a single supercell xx > 0.7; The diameter of the silicon nanocolumns is less than the arrangement period of the meta-units, and the refractive index of the silicon nanocolumns is the same as that of the silicon substrate.

2. The mid-infrared large-aperture all-silicon metasurface lens according to claim 1, characterized in that: The phase regulation of the meta-unit array satisfies: In the formula, represents the focusing phase, λ represents the working wavelength, X and Y represent the position coordinates of the supercell, and f represents the focal length; The continuous phase obtained from formula (1) is discretized into 40 gradients, and then according to the law that the phase varies with a period of 2π, the discretized phase is normalized to 0 - 2π to form a dense phase sampling unit library.

3. The mid-infrared large-aperture all-silicon metasurface lens according to claim 2, wherein: The number of unilateral meta-units in the metasurface unit array is 5500, forming a 5500×5500 meta-unit array with an overall aperture less than 10 mm.

4. The mid-infrared large-aperture all-silicon metasurface lens according to claim 3, wherein: The height h1 of the silicon nanocolumns is 2000 nm; The height h2 of the silicon substrate is 2000 nm, and the arrangement period P is 1750 nm.

5. The mid-infrared large-aperture all-silicon metasurface lens according to claim 3, characterized in that: Both the silicon nanocolumns and the silicon substrate are silicon dielectrics, and the working wavelength of the silicon dielectric is 3.75 μm, the relative permittivity ε = 11.7649, and the magnetic permeability μ = 1.

6. The mid-infrared large-aperture all-silicon metasurface lens according to claim 3, wherein: Lens diameter D of the mid-infrared large-aperture all-silicon metasurface lens fo = 1750 nm * 5500 nm, focal length d = 15 mm, numerical aperture N A ≈ 0.724; At a wavelength of 3.75 μm, the full width at half maximum of the focal plane ≤ 2362.5 nm.

7. A design method for a mid-infrared large-aperture all-silicon metasurface lens according to any one of the above-mentioned claims 2-6, characterized in that: It includes the following steps: S1. Based on formula (1), use simulation software to call the dense phase sampling unit library to generate a 5500×5500 meta-unit array; S2. Encode the 40 normalized phase values in the dense phase sampling unit library in sequence, and establish a correspondence table of phase value - unit number - silicon nanocolumn diameter; S3. Design the silicon nanocolumn diameter: read the theoretical phase of each coordinate, match the unit number of the phase value closest to it in the unit library, and allocate the corresponding silicon nanocolumn diameter according to the correspondence table of phase value - unit number - silicon nanocolumn diameter to form a global phase distribution matrix; S4. Equivalent each meta-unit in the global phase distribution matrix to a phase delay point, and construct a simplified diffraction integral model; S5. Verify in different scales: use electromagnetic simulation software to generate a small-aperture array of 60*60 meta-units, and obtain its focal plane light intensity distribution and full width at half maximum S6. Based on the verification results of the small-aperture array, use the simplified diffraction integral model to deduce the focal plane light intensity of the 5500×5500 meta-unit array, and verify the improvement effect of dense phase sampling on the focus energy concentration; S7. Solidify the silicon nanocolumn diameter that passes the verification.

8. The design method according to claim 7, characterized in that: The expression of the simplified diffraction integral model described in step S4 is as follows: In the formula, U represents the light field at the focal plane, t(X,Y) represents the initial light field at the coordinate (X,Y), k is the wave number and k = 2π / λ, R represents the three-dimensional Euclidean distance related to the coordinate, and i represents the imaginary unit.

9. The design method according to claim 7, characterized in that: After step S7, there is also step S8, substituting D fo = 1750 nm * 60 nm, d = 50000 nm into the following formula to solve for the numerical aperture N A : N A = n × sinθ (3); Wherein, n represents the refractive index of the silicon medium; θ represents half of the maximum viewing angle, and θ = tan(D fo / 2d); Obtain N A ≈0.724

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