A hybrid optical system design method combining superlens and refractive lens

Abstract

The application discloses a hybrid optical system design method combining a super-structured lens and a traditional refractive lens, and comprises the following steps: step 1, ray tracing design and optimization of a refractive lens and a phase plane to obtain an ideal phase profile of the super-structured lens; step 2, designing the super-structured lens according to the ideal phase profile to obtain an actual discrete phase distribution of the super-structured lens; step 3, taking the actual discrete phase of the super-structured lens as an ideal phase plane to perform diffraction propagation simulation suitable for the super-refraction hybrid system to obtain an image quality evaluation index of the optical system; steps 1-3 are sequentially performed, and after completion, the image quality evaluation index of the optical system is evaluated; if the image quality evaluation index meets the technical requirements, the design of the super-refraction hybrid optical system is completed, and the structure parameters of the optical system are obtained; if the technical requirements are not met, the step 1 is returned to repeat the step to perform design optimization.

Description

Technical Field

[0001] This invention relates to a design method for a hybrid optical system that combines metalenses and traditional refractive lenses, belonging to the field of optical metalens technology. Background Technology

[0002] Metasurfaces are a relatively new type of planar optical control element based on the generalized Snell's law. They consist of nanoscale units of subwavelength size and spacing arranged periodically or aperiodically on a two-dimensional plane. By adjusting the shape, size, position, and orientation of these nanoscale units, almost arbitrary control of the phase, amplitude, polarization, and frequency of light can be achieved. Metasurfaces used for imaging are called metalenses. Due to their flexible control mechanism and thinness, applying metalenses to traditional refractive optical imaging systems can overcome existing performance bottlenecks, improve image quality, and reduce system size. Therefore, the development and optimization of optical systems combining metalenses and traditional refractive lenses (referred to as hybrid refractive-meta-lenses systems) has great potential and broad application prospects.

[0003] However, due to the different analytical and computational methods required for traditional refractive lenses and metalenses (e.g., traditional refractive lenses use geometric optics analysis and ray tracing calculations, while metalenses use subwavelength electromagnetic analysis, Maxwell's equations, and diffraction algorithms in diffraction optics), traditional optical system design methods are difficult to apply to the design optimization of hybrid refractive-metalenses. Furthermore, because the combination of metalenses and traditional refractive lenses results in a system aperture at least on the millimeter scale, which is a large area for metalenses with subwavelength characteristic structures, resulting in millions of nanounits. The computational demands for simulation are enormous, even exceeding the memory limits of some computing methods.

[0004] Currently, there are very few design examples and methods for refracto-hybrid optical systems, and existing technologies have certain limitations. Therefore, there is an urgent need for a general design method applicable to millimeter-scale (large area) refracto-hybrid optical systems. Summary of the Invention

[0005] This invention provides a design method for a hybrid optical system that combines metalenses and traditional refractive lenses.

[0006] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0007] A method for designing a hybrid optical system combining metalenses and traditional refractive lenses includes the following steps:

[0008] Step 1: Optimize the ray tracing design of the refractive lens and the phase plane to obtain the ideal phase profile of the metalens;

[0009] Step 2: Design a metalens based on the ideal phase profile and obtain the actual discrete phase distribution of the metalens;

[0010] Step 3: Replace the ideal phase plane with the actual discrete phase of the metalens and perform diffraction propagation simulation applicable to the hybrid system to obtain the image quality evaluation index of the optical system.

[0011] Proceed sequentially through steps 1-3. After completion, evaluate the image quality indicators of the optical system. If the image quality indicators meet the technical requirements, the design of the hybrid optical system is completed, and the structural parameters of the optical system are obtained. If the indicators do not meet the technical requirements, return to step 1 and repeat the steps for design optimization.

[0012] Preferably, step 1 includes the following steps:

[0013] Step 101: Design the initial structure of the optical system according to the technical requirements;

[0014] The initial structure design methods are as follows: PWC decomposition method, which calculates and solves the initial structure parameters, including the diffraction phase surface, using the PWC decomposition method; and reference method, which sets up the initial refractive lens structure by referring to existing lens libraries according to technical requirements and adds the diffraction phase surface at appropriate positions. The diffraction phase surface is the phase surface of the metalens. In order to adapt to the design method of large-area metalenses in subsequent steps, the phase distribution needs to be centrally symmetrical.

[0015] The phase distribution of a metalens that is centrally symmetric can be expressed using any of the following formulas:

[0016]

[0017]

[0018]

[0019] Where λ is the wavelength of light, a i and b i Here, λ is the phase coefficient (used as a variable for ray tracing optimization in subsequent steps), r is the distance from the center of the phase plane of the metalens to any position, and C0(λ) is the phase profile translation parameter, which is a constant for single-band systems and a function of wavelength λ for multi-band systems.

[0020] Step 102: Set the basic parameters required for the optical system and ray tracing according to the technical requirements and simulation needs, including system aperture, field of view, wavelength, environment, and number of tracing rays;

[0021] Step 103: Perform ray tracing simulation for the i-th wavelength and j-th field of view for the set I working wavelengths and J fields of view, where i = 1, ..., I; j = 1, ..., J. Additionally, ray tracing is calculated for the refraction lens and phase plane according to Snell's law and the generalized Snell's law of refraction, respectively. The formulas are as follows:

[0022] Snell's law of refraction: n r sinθ r -n i sinθ i =0

[0023] Generalized Snell's Law of Refraction:

[0024] Where, n r With n i Let θ be the refractive index of the refracting medium and the incident medium, respectively. r and θ i Here, denoted by the angle of refraction and the angle of incidence, respectively; λ is the wavelength of light; and r is the distance from the center of the phase plane of the metalens to any arbitrary position. The phase gradient is the radial direction of the phase plane of the metalens. It is only related to r, therefore it is independent of the phase profile translation parameter C0(λ) in the phase distribution formula;

[0025] Step 104: Establish a comprehensive optical system evaluation system based on first-order technical requirements and multiple imaging performance indicators, and construct an evaluation function;

[0026] Optionally, the formula for the evaluation function is:

[0027]

[0028] Among them, W i As the weight, V i T represents the calculated evaluation value for a single indicator. i The target value for a single indicator;

[0029] Step 105: Optimize the optical system in a direction that makes the evaluation function approach zero. Once the optical system meets the technical requirements, end the optimization and derive the ideal phase distribution of the metalens.

[0030] Preferably, step 2 includes the following steps:

[0031] Step 201: Perform structural parameter scanning on the nanounits constituting the metalens to obtain the phase under different structural parameters and compile them into a phase database. The coverage of the phase database is at least greater than 2π. Additionally, the phase response formula for the nanounits is:

[0032]

[0033] Where λ is the wavelength of light, H is the height of the nanounit, and n eff (λ) is the effective refractive index of the nanounit, which is related to the structural parameters, period, material, and wavelength of light of the nanounit;

[0034] For multi-band optical systems, it is necessary to perform parameter scanning on multiple wavelengths separately to obtain a phase database under multiple wavelengths;

[0035] Step 202: Radially truncate the ideal phase surface of the meta-lens derived in Step 1 to obtain a phase distribution along a radius and discretize the phase profile at intervals smaller than the period of a nanometer unit.

[0036] For an ideal phase profile, when the phase difference between the center and edge points of the phase plane is too large, the phase profile needs to be folded to a range of 2π.

[0037] The interval is smaller than the period of the nanometer unit, and its size is generally one-tenth to one-quarter of the period of the nanometer unit.

[0038] Step 203: Match an ideal discrete phase point on a radius using the phase database to obtain the actual nano-unit matching situation of high-density discrete points on a radius, i.e., the nano-unit matching data pool;

[0039] For multi-band optical systems, nanometer units need to be matched to the ideal phase of multiple wavelengths simultaneously. The quality of multi-wavelength phase matching of nanometer units can be evaluated using the following formula:

[0040]

[0041] Here, since the matching object is a discrete phase point on the radius, the position change is represented by r. and The wavelength λ is at position r = r0, respectively. i The ideal phase and the actual phase of the nanounit are determined by Δ(r0), which is the sum of squares of the errors between the ideal phase and the actual phase of the nanounit at multiple wavelengths. By traversing the database, the minimum Δ(r0) is found, i.e., minΔ(r0) is selected, and the corresponding nanounit is selected, which means minimizing the individual evaluation error of the nanounit.

[0042] Alternatively, the overall error evaluation formula for a radius phase match is as follows:

[0043] Δ total =Σ j minΔ(r j )

[0044] Where, rj Represents r = r j The position of any point after the radius is discretized;

[0045] With Δ total As the evaluation criterion, the phase profile translation parameter C0(λ) from step 101 is used as a variable, and the particle swarm optimization algorithm is used to iteratively optimize Δ. total The minimum phase profile translation parameter C0(λ) is obtained, and then the optimal nano-unit matching situation of high-density discrete points on the radius is obtained, which is the nano-unit matching data pool.

[0046] Step 204: Discretize the ideal phase surface of the metalens into grid-distributed phase points with the nano-unit period as the interval, calculate the distance from each phase point to the center of the phase surface and match it with the discrete point radius value of the nano-unit matching data pool, select a suitable nano-unit, complete the matching design of the metalens, and obtain the actual discrete phase distribution of the metalens.

[0047] The phase of a quarter-pane of the metalens can be matched first, and then the actual discrete phase distribution of the metalens across the entire panorama can be determined by selecting that quarter-pane phase plane.

[0048] Preferably, the nanounits adopt a column structure of the same height, and their cross-sections are selected from centrally symmetrical shapes, i.e., polarization-insensitive structures, including circles, squares, crosses, rings, hollow squares, combinations of multiple circles, combinations of multiple squares, etc.

[0049] Preferably, the material of the nanounit includes TiO2, HfO2, ZrO2, GaN, Si2N3, Si, GaAs, ZnS or AlN.

[0050] Preferably, the height of the nanounit varies from 0 to 1500 nm, the period of the nanounit is generally smaller than the design wavelength, and all nanounits must have the same period.

[0051] Preferably, step 3 includes the following steps:

[0052] Step 301: Interpolate and sample the actual discrete phase distribution of the metalens, and replace the ideal phase surface with the processed phase distribution;

[0053] Step 302: Perform diffraction propagation simulation of the superconducting hybrid system at the i-th wavelength and j-th field of view for I wavelengths and J fields of view, where i = 1, ..., I; j = 1, ..., J; Additionally, the treatment methods for the phase plane of the superconducting lens, the interior of the refractive lens, and the inter-lens relationships differ in the diffraction propagation simulation:

[0054] The diffraction propagation simulation of the superconducting system adopts scalar diffraction algorithms (Fresnel diffraction algorithm and angular spectrum propagation algorithm). The appropriate scalar diffraction algorithm is selected according to the specific situation for the light field diffraction propagation between lenses.

[0055] For the phase plane of the metalens, the angular spectrum propagation algorithm is applied, and the formula is as follows:

[0056]

[0057] Where (x, y) represents the position of any sampling point on the phase plane of the metalens. The phase at the i-th wavelength at this position. The electric field before the incident wave propagates to the phase surface of the metalens. The electric field of the wave emitted from the phase surface of the metalens;

[0058] For the interior of the refractive lens, ray tracing is still used to reconstruct the complex amplitude information after passing through the lens using the path length, position, and angle of each ray.

[0059] Step 303: Based on the diffraction propagation simulation results, obtain the image quality evaluation index of the refractive-hyper-hybrid system;

[0060] Axial chromatic aberration shift can be calculated based on the focusing conditions of different wavelengths;

[0061] Based on the simulation results, the focal intensity distribution of the focal plane can be extracted and normalized, i.e., the point spread function (PSF).

[0062] Based on the point spread function (PSF), the modulation transfer function (MTF) can be further extracted.

[0063] Evaluation of RMS radius and various aberrations based on focal intensity distribution on the focal plane;

[0064] Based on the design method provided by the above technical solution, an exemplary superconducting optical system is designed. The design requirements of the optical system are as follows: the working band is the visible light band (450~633nm), the field of view is 50°, the focal length is 10mm, the F number is 2.5, the total length of the optical system is not greater than 15mm, and the modulation transfer function (MTF) is not less than 0.5 at the cutoff frequency of 30lp / mm.

[0065] Compared with existing technologies, the hybrid optical system design method combining metalenses and traditional refractive lenses of this invention can effectively and quickly complete the design optimization and simulation verification of hybrid refractive-meta-optical systems. Step 1 of the design scheme provides a feasible and convenient design flow for the theoretical structure of the hybrid refractive-meta-optical system. Step 2 provides a fast and efficient design method for large-area metalenses, which greatly simplifies the matching process of metalenses. At the same time, it proposes to introduce a position contour translation parameter C0(λ) and iteratively optimize it through a particle swarm optimization algorithm, which can effectively reduce the overall evaluation error and improve the matching accuracy. The diffraction propagation method proposed in Step 3 can take into account the propagation situation inside the refractive lens. Compared with existing patents that simplify the refractive lens to a phase plane, the error is smaller and the obtained image quality evaluation index is more reliable. Attached Figure Description

[0066] Figure 1 This is the flowchart of the design method for a hybrid optical system combining metalenses and traditional refractive lenses according to the present invention.

[0067] Figure 2 This is an ideal structure for a refracto-hybrid system obtained by ray tracing, which is an optional feature of this invention.

[0068] Figure 3 This is a schematic diagram of an optional nanopillar structure of the present invention.

[0069] Figure 4 This is a database distribution diagram of the relative phase of wavelength 532nm versus 633nm in this invention.

[0070] Figure 5 This illustrates the phase matching of the three wavelengths in the nanounit matching data pool of this invention.

[0071] Figure 6 This is the meridional MTF diagram of the superconducting hybrid optical system of the present invention. Detailed Implementation

[0072] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0073] like Figure 1 As shown, a hybrid optical system design method combining metalenses and traditional refractive lenses includes the following steps:

[0074] Step 1: Optimize the ray tracing design of the refractive lens and the phase plane to obtain the ideal phase profile of the metalens;

[0075] Step 2: Design a metalens based on the ideal phase profile and obtain the actual discrete phase distribution of the metalens;

[0076] Step 3: Replace the ideal phase plane with the actual discrete phase of the meta-lens to perform diffraction propagation simulation applicable to the hybrid system and obtain the image quality evaluation index of the optical system.

[0077] Proceed sequentially through steps 1-3. After completion, evaluate the image quality indicators of the optical system. If the image quality indicators meet the technical requirements, the design of the hybrid optical system is completed, and the structural parameters of the optical system are obtained. If the indicators do not meet the technical requirements, return to step 1 and repeat the steps for design optimization.

[0078] Step 1 includes the following steps:

[0079] Step 101: Design the initial structure of the optical system according to the technical requirements.

[0080] The initial structure design methods include: PWC decomposition, which calculates and solves for the initial structure parameters, including the diffraction phase plane; and a reference method, which sets up the initial refractive lens structure based on existing lens libraries according to technical requirements, and adds the diffraction phase plane at appropriate locations. The diffraction phase plane is the phase plane of the metalens; to accommodate the subsequent design method of large-area metalenses, the phase distribution needs to be centrally symmetrical.

[0081] The phase distribution of a metalens that is centrally symmetric can be expressed using any of the following formulas:

[0082]

[0083]

[0084]

[0085] Where λ is the wavelength of light, a i and b i is the phase coefficient (used as a variable for ray tracing optimization in subsequent steps), r is the distance from the center of the phase plane of the metalens to any position, and C0(λ) is the phase profile translation parameter, which is a constant for single-band systems and a function of wavelength λ for multi-band systems.

[0086] Step 102: Set the basic parameters required for the optical system and ray tracing according to the technical requirements and simulation needs, including system aperture, field of view, wavelength, environment, and the number of tracing rays.

[0087] Step 103: Perform ray tracing simulation for the i-th wavelength and j-th field of view for the set I working wavelengths and J fields of view, where i = 1, ..., I; j = 1, ..., J. Additionally, ray tracing is calculated for the refraction lens and phase plane according to Snell's law and the generalized Snell's law of refraction, respectively. The formulas are as follows:

[0088] Snell's law of refraction: n r sinθ r -n i sinθ i =0

[0089] Generalized Snell's Law of Refraction:

[0090] Where, n r With n i Let θ be the refractive index of the refracting medium and the incident medium, respectively. r and θ i Here, denoted by the angle of refraction and the angle of incidence, respectively; λ is the wavelength of light; and r is the distance from the center of the phase plane of the metalens to any arbitrary position. The phase gradient is the radial direction of the phase plane of the metalens. It is only related to r, therefore it is independent of the phase profile translation parameter C0(λ) in the phase distribution formula.

[0091] Step 104: Establish a comprehensive optical system evaluation system based on first-order technical requirements and multiple imaging performance indicators, and construct an evaluation function.

[0092] Optionally, the formula for the evaluation function is:

[0093]

[0094] Among them, W i As the weight, V i T represents the calculated evaluation value for a single indicator. i This refers to the target value for a single indicator.

[0095] Step 105: Optimize the optical system in a direction that makes the evaluation function approach zero. Once the optical system meets the technical requirements, end the optimization and derive the ideal phase distribution of the metalens.

[0096] Step 2 includes the following steps:

[0097] Step 201: Perform structural parameter scanning on the nanounits constituting the metalens to obtain the phase under different structural parameters and compile it into a phase database. The coverage of the phase database should be at least greater than 2π. Additionally, the phase response formula for the nanounits is:

[0098]

[0099] Where λ is the wavelength of light, H is the height of the nanounit, and n eff (λ) is the effective refractive index of the nanounit, which is related to the structural parameters, period, material, and wavelength of light of the nanounit.

[0100] The nanounits adopt a columnar structure of the same height, and their cross-sections are selected with a centrally symmetrical shape, that is, a polarization-insensitive structure, including circles, squares, crosses, rings, hollow squares, combinations of multiple circles, combinations of multiple squares, etc.

[0101] The materials for nanounits include TiO2, HfO2, ZrO2, GaN, Si2N3, Si, GaAs, ZnS, or AlN.

[0102] The height of the nanounits varies from 0 to 1500 nm. The period of the nanounits is generally smaller than the design wavelength, and all nanounits must have the same period.

[0103] For multi-band optical systems, it is necessary to perform parameter scanning on multiple wavelengths separately to obtain a phase database for multiple wavelengths.

[0104] Step 202: Radially truncate the ideal phase surface of the meta-lens derived in Step 1 to obtain a phase distribution along a radius and discretize the phase profile at intervals smaller than the period of a nanometer unit.

[0105] For an ideal phase profile, when the phase difference between the center and edge points of the phase plane is too large, the phase profile needs to be folded to a range of 2π.

[0106] The interval is smaller than the period of the nanometer unit, and its size is generally one-tenth to one-quarter of the period of the nanometer unit.

[0107] Step 203: Match an ideal discrete phase point on a radius using the phase database to obtain the actual nano-unit matching situation of high-density discrete points on a radius, i.e., the nano-unit matching data pool.

[0108] For multi-band optical systems, nanometer units need to be matched to the ideal phase of multiple wavelengths simultaneously. The quality of multi-wavelength phase matching of nanometer units can be evaluated using the following formula:

[0109]

[0110] Here, since the matching object is a discrete phase point on the radius, the position change is represented by r. and The wavelength λ is at position r = r0, respectively. i The ideal phase and the actual phase of the nanounit are defined, where Δ(r0) is the sum of squared errors between the ideal phase and the actual phase of the nanounit at multiple wavelengths. The database is traversed to minimize Δ(r0), i.e., to find minΔ(r0), and the corresponding nanounit is selected, thus minimizing the individual evaluation error of the nanounit.

[0111] Alternatively, the overall error evaluation formula for a radius phase match is as follows:

[0112] Δ total =Σ j minΔ(r j )

[0113] Where, r j Represents r = r j Let be the position of any point after discretizing the radius.

[0114] With Δ total As the evaluation criterion, the phase profile translation parameter C0(λ) from step 101 is used as a variable, and the particle swarm optimization algorithm is used to iteratively optimize Δ. total The minimum phase profile translation parameter C0(λ) is obtained, and then the optimal nano-unit matching situation of high-density discrete points on the radius is obtained, which is the nano-unit matching data pool.

[0115] Step 204: Discretize the ideal phase surface of the metalens into grid-distributed phase points with the nano-unit period as the interval, calculate the distance from each phase point to the center of the phase surface and match it with the discrete point radius value of the nano-unit matching data pool, select a suitable nano-unit, complete the matching design of the metalens, and obtain the actual discrete phase distribution of the metalens.

[0116] The phase of a quarter-pane of the metalens can be matched first, and then the actual discrete phase distribution of the metalens across the entire panorama can be determined by selecting that quarter-pane phase plane.

[0117] Step 3 includes the following steps:

[0118] Step 301: Interpolate and sample the actual discrete phase distribution of the metalens, and replace the ideal phase surface with the processed phase distribution.

[0119] Step 302: Perform diffraction propagation simulation of the superconducting hybrid system at the i-th wavelength and j-th field of view for I wavelengths and J fields of view, where i = 1, ..., I; j = 1, ..., J. Additionally, the treatment methods for the phase plane of the superconducting lens, the interior of the refractive lens, and the inter-lens relationships differ in the diffraction propagation simulation:

[0120] The diffraction propagation simulation of the superconducting system adopts scalar diffraction algorithms (Fresnel diffraction algorithm and angular spectrum propagation algorithm). The appropriate scalar diffraction algorithm is selected according to the specific situation for the light field diffraction propagation between lenses.

[0121] For the phase plane of the metalens, the angular spectrum propagation algorithm is applied, and the formula is as follows:

[0122]

[0123] Where (x, y) represents the position of any sampling point on the phase plane of the metalens. The phase at the i-th wavelength at this position. The electric field before the incident wave propagates to the phase surface of the metalens. This represents the electric field of the wave emitted from the phase surface of the metalens.

[0124] For the interior of the refractive lens, ray tracing is still used to reconstruct the complex amplitude information after passing through the lens using the path length, position, and angle of each ray.

[0125] Step 303: Based on the diffraction propagation simulation results, obtain the image quality evaluation index of the refractive-hyper-hybrid system.

[0126] Axial chromatic aberration shift can be calculated based on the focusing conditions of different wavelengths;

[0127] Based on the simulation results, the focal intensity distribution of the focal plane can be extracted and normalized, i.e., the point spread function (PSF).

[0128] Based on the point spread function (PSF), the modulation transfer function (MTF) can be further extracted.

[0129] Evaluation of RMS radius and various aberrations based on focal plane intensity distribution.

[0130] Based on the design method provided by the above technical solution, an exemplary hybrid optical system is designed. The design requirements for the optical system are as follows: the operating wavelength is the visible light band (450-633nm), the field of view is 50°, the focal length is 10mm, the F-number is 2.5, the total length of the optical system is no more than 15mm, and the modulation transfer function (MTF) is no less than 0.5 at the cutoff frequency of 30lp / mm.

[0131] The specific design of the superconducting optical system is carried out in three steps according to the technical solution.

[0132] Step 1: Optimize the ray tracing design of the refractive lens and the phase plane to obtain the ideal phase profile of the metalens;

[0133] First, the initial structure of the optical system is designed. Based on the design requirements of the optical system, the Cooke three-element split lens structure is referenced and scaled up according to the reference method, and materials are selected. A metalens is placed in a suitable position. The phase plane formula of the metalens is as follows:

[0134]

[0135] Where λ i -a is the wavelength of light. i1 _a i5 wavelength λ iThe phase coefficient is given by r, which is the distance from the center of the phase plane of the metalens to any position on the plane.

[0136] The design and optimization of the hybrid optical system was carried out in the optical design software Zemax. Basic system parameters were set in the software, including an entrance pupil diameter of 4 mm, three wavelengths (450 nm, 532 nm, and 633 nm), half-field-of-view angles of 0°, 17.5°, and 25°, and the number and distribution of ray tracing samples. Optical tracing simulations were then performed for the three wavelengths and three fields of view. A comprehensive evaluation system was established based on the simulation results. The objective functions used for evaluation included: effective focal length, total system length, wavefront error, RMS radius, various monochromatic aberrations, and MTF index, etc. Appropriate weights were assigned to the objective functions to construct the evaluation function.

[0137] By selecting system structural parameters, including the phase coefficient of the metalens phase plane, the curvature of the refractive lens surface, the thickness of the refractive lens, the distance between the refractive lenses, and the material of the refractive lens, and performing multiple optimization designs, the optical system was ultimately optimized to meet the design requirements, resulting in an optional theoretical structure. The ray tracing diagram of the hybrid refractive-meta-lens system is shown below. Figure 2 As shown. Figure 2 In the middle, the sixth surface (plane) from left to right is the phase surface of the metalens. The contour of the phase surface of the metalens is extracted for the design in step 2.

[0138] Step 2: Design a metalens based on the ideal phase profile to obtain the actual discrete phase distribution of the metalens:

[0139] First, a phase database of nanounits was constructed, and various polarization-insensitive nanopillar structures were selected, such as... Figure 3 As shown, with a period of 400 nm, a nanopillar height of 1000 nm, and TiO2 as the nanopillar material, the phase database of the nanounit at different wavelengths was obtained by scanning the structural parameters and summarizing the wavelengths. For example, the relative phase database distribution of the 532 nm wavelength relative to 633 nm wavelength after 2π folding is shown in the figure. Figure 4 As shown, the horizontal axis represents the phase of the nanounit at a wavelength of 633 nm, and the vertical axis represents the phase difference between the nanounit at wavelengths of 532 nm and 633 nm.

[0140] For the ideal phase plane of the metalens derived in step 1, a phase profile translation parameter C0(λ) that varies with wavelength can be added to it without changing the phase gradient. Therefore, the formula for the phase plane of the meta-lens becomes:

[0141]

[0142] The phase plane of the metalens is folded to a range of 2π and radially truncated to obtain a phase distribution along a radius. The phase profile is then discretized at 100nm intervals. Individual discrete nanounits are matched using the method described for minimizing individual evaluation errors, and the overall evaluation error is minimized through iterative optimization using a particle swarm optimization algorithm with C0(λ) as the variable. The final nanounit matching data pool is obtained, and the matching status of the three wavelength phases in the nanounit matching data pool is as follows: Figure 5 As shown.

[0143] The ideal phase surface of the metalens is discretized into a square grid of phase points with the period of the nanounit as the interval. Based on the nanounit matching data pool, the discrete points on the quarter-circle are matched. Then, the matching situation of the quarter-circle is rotated to obtain the actual discrete phase distribution of the metalens across the entire area.

[0144] Step 3: Based on the actual discrete phase distribution of the metalens, perform diffraction propagation simulation applicable to the hybrid refractive-meta-lens system to obtain the image quality evaluation index of the optical system:

[0145] The simulation of diffraction propagation for hybrid systems requires solving the simulation problems of the phase plane of the metalens and the refractive lens simultaneously. The simulation of the refractive lens and the lens-to-lens simulation can be completed using the Physical Optics Propagation (POP) tool built into Zemax, while the phase plane of the metalens is processed and calculated separately using a scalar diffraction algorithm.

[0146] Using the POP tool in Zemax, the incident light type is set to a "flat-top" beam. Basic parameters, including the number of sampling points and sampling width, are set. Interpolation sampling is performed on the actual discrete phase distribution of the metalens according to the set sampling point distribution. Then, diffraction propagation simulation is performed. For each adjacent surface, Fresnel diffraction algorithm or angular spectrum propagation algorithm is selected according to the actual situation, and whether to use geometric optics propagation calculation (geometric ray propagation is used inside the refractive lens) until the light propagates to the front of the metalens phase using the POP tool. The light field propagating to the front of the metalens is exported. Then, MATLAB is used to calculate the light field of the output metalens according to the angular spectrum diffraction algorithm. Finally, the light field is imported into Zemax and the remaining light field diffraction propagation is completed using the POP tool, realizing the diffraction propagation simulation of the entire refractive-meta-optical hybrid system.

[0147] Irradiance distribution on each surface can be obtained through diffraction propagation simulation. Based on this, image quality evaluation indicators of the system can be extracted. For example, the meridional MTF diagram of the final extracted hyperrefractive hybrid optical system is shown below. Figure 6 As shown, the MTF is greater than 0.5 at the cutoff frequency of 30 lp / mm, which meets the technical requirements.

[0148] Since the image quality evaluation indicators obtained through diffraction propagation all meet the technical requirements, the design of the refractive-hybrid optical system is basically complete.

[0149] This invention combines a hybrid optical system design method using metalenses and traditional refractive lenses. This method can effectively and quickly complete the design optimization and simulation verification of hybrid refractive-meta-optical systems. Step 1 provides a feasible and convenient design process for the theoretical structure of the hybrid refractive-meta-optical system. Step 2 provides a fast and efficient design method for large-area metalenses, greatly simplifying the matching process of metalenses. Furthermore, the introduction of a positional profile translation parameter C0(λ) and iterative optimization using a particle swarm optimization algorithm can effectively reduce overall evaluation errors and improve matching accuracy. Step 3 proposes a diffraction propagation method that takes into account the propagation within the refractive lens. Compared to existing patents that simplify the refractive lens to a phase plane, this method results in smaller phase plane errors and more reliable image quality evaluation indicators.

[0150] Finally, it should be noted that the above embodiments are only illustrative of the technical solutions of the present invention, and not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A design method for a hybrid optical system combining metalenses and refractive lenses, characterized in that, Includes the following steps: Step 1: Optimize the ray tracing design of the refractive lens and the phase plane to obtain the ideal phase profile of the metalens; Step 2: Design a metalens based on the ideal phase profile and obtain the actual discrete phase distribution of the metalens; Step 3: Replace the ideal phase plane with the actual discrete phase of the metalens and perform diffraction propagation simulation applicable to the hybrid system to obtain the image quality evaluation index of the optical system. Proceed sequentially through steps 1-3. After completion, evaluate the image quality indicators of the optical system. If the image quality indicators meet the technical requirements, the design of the hybrid optical system is completed, and the structural parameters of the optical system are obtained. If it does not meet the technical requirements, return to step 1 and repeat the steps to optimize the design; Step 2 includes the following steps: Step 201: Perform structural parameter scanning on the nanounits constituting the metalens to obtain the phase under different structural parameters and compile them into a phase database. The coverage of the phase database is greater than [missing information]. The phase response formula for a nanounit is: in, Where λ is the wavelength of light, and H is the height of the nanometer unit. The effective refractive index of the nanounit is related to the structural parameters, period, material, and wavelength of light of the nanounit. For multi-band optical systems, it is necessary to perform parameter scanning on multiple wavelengths separately to obtain a phase database under multiple wavelengths; Step 202: Radially truncate the ideal phase surface of the meta-lens derived in Step 1 to obtain a phase distribution along a radius and discretize the phase profile at intervals smaller than the period of a nanometer unit. For an ideal phase profile, when the phase difference between the center and edge points of the phase plane is too large, the phase profile needs to be folded. Within the range; The interval is smaller than the nanometer unit period, and its size ranges from one-tenth to one-quarter of the nanometer unit period; Step 203: Match an ideal discrete phase point on a radius using the phase database to obtain the actual nano-unit matching situation of high-density discrete points on a radius, i.e., the nano-unit matching data pool; For multi-band optical systems, nanometer units need to be matched to the ideal phase of multiple wavelengths simultaneously. The multi-wavelength phase matching of nanometer units is evaluated according to the following formula: The matching object is a discrete phase point on the radius, and the position change is represented by r. and They are respectively Location, wavelength The ideal phase and the actual phase of the nanounit are shown below. This represents the sum of squares of the errors between the ideal phase and the actual phase of the nanounit at multiple wavelengths; it is achieved through database traversal. Minimum is the search Selecting appropriate nanounits is to minimize the individual evaluation error of each nanounit. The overall error evaluation formula for a radius-phase matching is shown below: in, Represents r= The position of any point after the radius is discretized; by As the evaluation standard, the phase profile translation parameters in step 101 are used. As variables, iterative optimization is performed using the particle swarm optimization algorithm to make Minimize and obtain the corresponding phase profile translation parameters. This leads to the matching of the optimal nano-unit matching situation for high-density discrete points on the radius, i.e., the nano-unit matching data pool. Step 204: Discretize the ideal phase surface of the metalens into grid-distributed phase points with the nano-unit period as the interval. Calculate the distance from each phase point to the center of the phase surface and match it with the discrete point radius value of the nano-unit matching data pool. Select appropriate nano-units to complete the matching design of the metalens and obtain the actual discrete phase distribution of the metalens. First, match the phase of a quarter of the metalens, and then select the phase of this quarter of the metalens to realize the actual discrete phase distribution of the metalens across the entire area.

2. The design method for a hybrid optical system combining a metalens and a refractive lens according to claim 1, characterized in that, Step 1 includes the following steps: Step 101: Design the initial structure of the optical system according to the technical requirements; The initial structure design methods are as follows: PWC decomposition method, which calculates and solves the initial structure parameters, including the diffraction phase surface, using the PWC decomposition method; and reference method, which sets up the initial refractive lens structure based on the technical requirements and references the existing lens library, and adds the diffraction phase surface; where the diffraction phase surface is the phase surface of the meta-lens, and the phase distribution is centrally symmetrical to adapt to the design method of large-area meta-lens in the subsequent steps. The phase distribution of a metalens that is centrally symmetric can be obtained using any of the following formulas: in, The wavelength of light and The phase coefficient is used as a variable for subsequent ray tracing optimization, where r is the distance from the center of the metalens phase plane to any position. The phase profile translation parameter is a constant for single-band systems and a wavelength for multi-band systems. The function; Step 102: Set the basic parameters required for the optical system and ray tracing according to the technical requirements and simulation needs, including system aperture, field of view, wavelength, environment, and number of tracing rays; Step 103: Perform ray tracing simulation for the i-th wavelength and j-th field of view for the set I working wavelengths and J fields of view, where i=1,,…,I; j=1,…,J; Ray tracing is calculated for the refraction lens and the phase plane according to the refraction law of Snell's law and the generalized Snell's law, respectively. The formulas for the two are as follows: Snell's Law of Refraction: ; Generalized Snell's Law of Refraction: ; in, and These are the refractive indices of the refracting medium and the incident medium, respectively. and These are the angle of refraction and the angle of incidence, respectively. Let λ be the wavelength of light, and r be the distance from the center of the phase plane of the metalens to any position. The phase gradient is the radial direction of the phase plane of the metalens. It is related to r, and therefore to the phase profile translation parameter in the phase distribution formula. Irrelevant; Step 104: Establish a comprehensive optical system evaluation system based on first-order technical requirements and multiple imaging performance indicators, and construct an evaluation function; The formula for the evaluation function is: in, As weight, This refers to the calculated evaluation value for a single indicator. The target value for a single indicator; Step 105: Optimize the optical system in a direction that makes the evaluation function approach zero. Once the optical system meets the technical requirements, end the optimization and derive the ideal phase distribution of the metalens.

3. The design method for a hybrid optical system combining a metalens and a refractive lens according to claim 1, characterized in that, The nanounits adopt a column structure of the same height, and their cross-sections are selected from centrally symmetrical shapes, i.e., polarization-insensitive structures, including circles, squares, crosses, rings, hollow squares, combinations of multiple circles, and combinations of multiple squares.

4. The design method for a hybrid optical system combining a metalens and a refractive lens according to claim 3, characterized in that, The materials of the nanounits include TiO2, HfO2, ZrO2, GaN, Si2N3, Si, GaAs, ZnS, or AlN.

5. The design method for a hybrid optical system combining a metalens and a refractive lens according to claim 4, characterized in that, The height of the nanounits varies from 0 to 1500 nm, the period of the nanounits is smaller than the design wavelength, and all nanounits have the same period.

6. The design method for a hybrid optical system combining a metalens and a refractive lens according to claim 1, characterized in that, Step 3 includes the following steps: Step 301: Interpolate and sample the actual discrete phase distribution of the metalens, and replace the ideal phase surface with the processed phase distribution; Step 302: Perform diffraction propagation simulation of the superconducting hybrid system at the i-th wavelength and j-th field of view for I wavelengths and J fields of view, where i=1,,…,I; j=1,…,J; the treatment methods for the phase plane of the superconducting lens, the interior of the refractive lens, and the inter-lens are different in the diffraction propagation simulation: The diffraction propagation simulation of the superconducting hybrid system adopts the scalar diffraction algorithm, and the scalar diffraction propagation of the light field between lenses is selected according to the specific situation; For the phase plane of the metalens, the angular spectrum propagation algorithm is applied, and the formula is as follows: Where (x,y) represents the position of any sampling point on the phase plane of the metalens. The phase at the i-th wavelength at this position. The electric field before the incident wave propagates to the phase surface of the metalens. The electric field of the wave emitted from the phase surface of the metalens; For the interior of the refractive lens, ray tracing is still used to reconstruct the complex amplitude information after passing through the lens using the path length, position, and angle of each ray. Step 303: Based on the diffraction propagation simulation results, obtain the image quality evaluation index of the refractive-hyper-hybrid system; Calculate the axial chromatic aberration shift based on the focusing conditions of different wavelengths; The focal intensity distribution of the focal plane is extracted based on the simulation results and normalized, i.e., the point spread function (PSF). Based on the point spread function (PSF), the modulation transfer function (MTF) can be further extracted. Evaluation of RMS radius and various aberrations based on focal plane intensity distribution.

7. The design method for a hybrid optical system combining a metalens and a refractive lens according to claim 6, characterized in that, The design requirements for the optical system are as follows: the operating wavelength is the visible light band 450~633nm, the field of view is 50°, the focal length is 10mm, the F number is 2.5, the total length of the optical system is no more than 15mm, and the modulation transfer function (MTF) is no less than 0.5 at the cutoff frequency of 30lp / mm.

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