Multifocal vector metalens, design method, and optical system

Abstract

Disclosed in the present application are a multifocal vector metalens, a design method, and an optical system. The design method for a multifocal vector metalens comprises: by using the resolution of an optical sensor as a constraint condition, determining primitive phase distribution information of a metalens; under the guidance of a target polarization state, optimizing and determining an object-plane Jones matrix that carries vector grating phase distribution information; and linearly superimposing the primitive phase distribution information and the vector grating phase distribution information, so as to generate overall phase distribution design information. The design method for a multifocal vector metalens provided in the present application can organically integrate a focusing performance and a polarization control performance, thus assisting in the construction of a metalens structure that accommodates both functions.

Description

Multifocal vector metalens, design method and optical system

[0001] This application claims priority to Chinese patent application filed on September 5, 2023, with application number 202311139940.4, entitled “Multifocal vector superlens, design method and optical system”, the entire contents of which are incorporated herein by reference. Technical Field

[0002] The present invention relates to the field of optical imaging technology, and in particular to a multi-focal vector metalens, a design method and an optical system. Background Art

[0003] Metasurface optical devices are widely used in optical imaging due to their small size, multifunctionality, and ease of integration. They are expected to become the development platform for the next generation of highly integrated polarization imaging systems. When configured as multi-degree-of-freedom metasurface optical devices, they can also achieve efficient control of parameters such as the amplitude, phase, and polarization state of the incident light. They are suitable for applications such as vector beam shaping, compact polarization beam splitters, full-Stokes parameter measurement, three-dimensional structured light generation, and detection and reconstruction of multi-photon quantum entangled states.

[0004] Nanostructures are arranged on the sides of the metasurface optical device according to a certain phase distribution. Existing techniques typically construct a focusing metalens and a polarization control grating separately and then simply combine them at the macroscopic level. This results in poor flexibility and low degrees of freedom in the resulting optical device, and the focusing and polarization control performance of the resulting optical device cannot be effectively integrated.

[0005] Summary of the Invention

[0006] One of the purposes of this application is to provide a multi-focal vector metalens design method to solve the technical problem in the prior art that it is impossible to uniformly construct an optical device that takes into account both focusing performance and polarization detection performance.

[0007] One of the objectives of this application is to provide a multi-focal vector metalens.

[0008] One of the objectives of the present application is to provide an optical system.

[0009] To achieve one of the above-mentioned purposes, an embodiment of the present application provides a multi-focal vector metalens design method, comprising: determining the elementary phase distribution information of the metalens with the resolution of the optical sensor as a constraint condition; optimizing and determining the object plane Jones matrix carrying the vector grating phase distribution information under the guidance of the target polarization state; linearly superimposing the elementary phase distribution information and the vector grating phase distribution information to generate overall phase distribution design information.

[0010] As a further improvement of one embodiment of the present application, the “determining the elementary phase distribution information of the metalens with the resolution of the light sensor as a constraint condition” specifically includes: performing iterative optimization within the optical path design platform with the resolution of the light sensor as a constraint condition until the imaging performance of the optical system composed of the light sensor and the current metalens, or the resolution capability of the optical system, or both the imaging performance and the resolution capability of the optical system reach the set target, thereby determining the elementary phase distribution information of the current metalens.

[0011] As a further improvement of an embodiment of the present application, the optical path design platform is Zemax; the "iterative optimization within the optical path design platform" specifically includes: performing iterative optimization within the optical path design platform based on the degree of point convergence in the focusing diagram and the value of the modulation transfer function.

[0012] As a further improvement of an embodiment of the present application, the "linearly superimposing the primitive phase distribution information and the vector grating phase distribution information to generate overall phase distribution design information" specifically includes: updating each matrix element in the object plane Jones matrix according to the primitive phase distribution information to obtain a superimposed Jones matrix; performing matrix decomposition on the superimposed Jones matrix to obtain a vector rotation decomposition matrix as the overall phase distribution design information.

[0013] As a further improvement of an embodiment of the present application, the object plane Jones matrix includes a first matrix element, a second matrix element, a third matrix element and a fourth matrix element; the first matrix element represents the ratio of the amplitude and phase of the x-polarization component of the input light after the x-polarization component passes through the superlens; the second matrix element represents the ratio of the amplitude and phase of the y-polarization component of the input light after the y-polarization component passes through the superlens; the third matrix element represents the ratio of the amplitude and phase of the y-polarization component of the input light after the x-polarization component passes through the superlens; the fourth matrix element represents the ratio of the amplitude and phase of the x-polarization component of the input light after the y-polarization component passes through the superlens; the "updating each matrix element in the object plane Jones matrix according to the primitive phase distribution information to obtain a superimposed Jones matrix" specifically includes: performing array element multiplication on the primitive phase distribution matrix and the object plane Jones matrix to obtain the superimposed Jones matrix.

[0014] As a further improvement of an embodiment of the present application, the vector rotation decomposition matrix includes a Jones vector and a rotation matrix; the Jones vector includes at least a first overall phase delay information of the metalens in the x-polarization direction and a second overall phase delay information in the y-polarization direction; the rotation matrix includes at least the rotation angle information of the metalens grating element.

[0015] As a further improvement of an embodiment of the present application, after "linearly superimposing the primitive phase distribution information and the vector grating phase distribution information to generate overall phase distribution design information", the multi-focal vector superlens design method also includes: searching the multi-focal vector superlens parameter library according to the overall phase distribution design information to obtain structural design information corresponding to the grating primitive structure; and optimizing the structural design information according to the grating primitive arrangement rules.

[0016] As a further improvement to an embodiment of the present application, before the step of "searching a multi-focal vector superlens parameter library based on the overall phase distribution design information to obtain structural design information corresponding to the grating elemental structure", the multi-focal vector superlens design method specifically includes: implementing rigorous coupled wave analysis equipped with a full-analytic Fourier transform to scan a number of superlenses, constructing a number of standard Jones matrices based on the corresponding complex amplitude information, associating the grating elemental structure of the superlens with the corresponding standard Jones matrix, and constructing a multi-focal vector superlens parameter library; wherein, the grating elemental structure is a standard three-dimensional structure.

[0017] As a further improvement of an embodiment of the present application, the grating element arrangement rule is set as follows: the grating elements are arranged radially from the center of the metasurface to the surrounding areas, the distance between all grating elements located in the first area and the center of the metasurface has a first average distance, and the total number of grating elements located in the first area is positively correlated with the first average distance.

[0018] As a further improvement of an embodiment of the present application, the grating element arrangement rule is set as follows: the grating elements are arranged radiating from the center of the metasurface in a first shape to the surrounding areas; wherein the first shape is a polygon or a ring.

[0019] As a further improvement of an embodiment of the present application, the grating element arrangement rule is set as follows: the grating elements are arranged radiatingly in a ring shape from the center of the metasurface, and all grating elements located in the second region have a second average distance from the center of the metasurface, and the second average distance is greater than the first average distance; the grating element arrangement rule is further set as follows: the radial period of the grating elements in the first region is greater than the radial period of the grating elements in the second region, or the circumferential period of the grating elements in the first region is greater than the circumferential period of the grating elements in the second region, or the radial period of the grating elements in the first region is greater than the radial period of the grating elements in the second region, and the circumferential period of the grating elements in the first region is greater than the circumferential period of the grating elements in the second region.

[0020] As a further improvement to an embodiment of the present application, after "optimizing the structural design information according to the grating element arrangement rules", the multi-focal vector superlens design method further includes: rotating the supersurface defined by the optimized structural design information by 45 degrees about its geometric center, and generating the corresponding final design information.

[0021] As a further improvement of an embodiment of the present application, the "optimizing and determining the object plane Jones matrix carrying the vector grating phase distribution information under the guidance of the target polarization state" specifically includes: determining the target image plane Jones matrix information according to the target polarization state, and determining the objective function according to the difference between it and the target image plane Jones matrix information; optimizing the current object plane Jones matrix information based on the vector iterative Fourier algorithm until the objective function converges, and determining the final object plane Jones matrix information.

[0022] To achieve one of the above-mentioned purposes, an embodiment of the present application provides a multi-focal vector metalens, which is configured to set a grating element structure according to the overall phase distribution design information generated by the multi-focal vector metalens design method described in any of the above technical solutions; the metalens also includes a substrate connected to the grating element structure, a filler connected to the grating element structure, and an anti-reflection film arranged at the substrate or at the filler or at both the substrate and the filler, wherein the anti-reflection film includes a first material layer and a second material layer.

[0023] To achieve one of the above-mentioned purposes, one embodiment of the present application provides an optical system, comprising: the above-mentioned multi-focal vector metalens, and an optical sensor for converting the optical signal modulated output from one side of the multi-focal vector metalens into an electrical signal.

[0024] Compared with the existing technology, the multi-focus vector metalens design method provided in this application determines the corresponding phase distribution information for metalens focusing and polarization control at the phase distribution level, and updates the overall phase distribution design with the phase information after linear superposition. It can organically integrate focusing performance and polarization control performance, and assist in constructing a metalens structure that takes both functions into account. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] FIG1 is a schematic structural diagram of an optical system in one embodiment of the present application.

[0026] FIG2 is a schematic structural diagram of a multi-focal vector metalens in one embodiment of the present application.

[0027] FIG3 is a schematic structural diagram of a multi-focal vector metalens in another embodiment of the present application.

[0028] FIG4 is a schematic diagram of the steps of a method for designing a multi-focal vector metalens in one embodiment of the present application.

[0029] FIG5 is a schematic diagram of an optical path simulation of a module equipped with a monolithic metalens in one embodiment of the present application.

[0030] FIG6 is a schematic diagram of an optical path simulation of a module equipped with a double-chip metalens in one embodiment of the present application.

[0031] FIG7 is a schematic diagram of the relationship between four elements in the Jones matrix in one embodiment of the present application.

[0032] FIG8 is a schematic diagram showing the relationship between the overall phase distribution, the lens phase distribution, and the multi-focal vector metalens in one embodiment of the present application.

[0033] FIG9 is a schematic diagram of a grating element structure in one embodiment of the present application.

[0034] FIG10 is a characteristic diagram of the Bloch boundary scan of the grating element structure in one embodiment of the present application.

[0035] FIG11 is a flow chart of a vector iterative Fourier algorithm in one embodiment of the present application.

[0036] FIG12 is a schematic diagram showing the changes in dichroism and focal uniformity during the iteration process of the multi-focal vector metalens design method in the prior art and one embodiment of the present application.

[0037] FIG13 is a schematic diagram of a Poincare sphere used to construct a far-field Jones matrix in one embodiment of the present application.

[0038] FIG14 is a schematic diagram of the Poincare sphere and K-space distribution in other embodiments of the present application.

[0039] FIG15 is a schematic diagram showing some steps of a method for designing a metalens in another embodiment of the present application.

[0040] FIG16 is a schematic diagram showing the relationship between the final object plane Jones matrix and the corresponding grating element structure in one embodiment of the present application.

[0041] FIG17 is a schematic diagram of the regional arrangement of the grating element structure in one embodiment of the present application.

[0042] FIG18 is a schematic diagram of the periodic arrangement of the grating element structure in the first embodiment of the present application.

[0043] FIG19 is a schematic diagram of the periodic arrangement of the grating element structure in the second embodiment of the present application.

[0044] FIG20 is a schematic diagram of the periodic arrangement of the grating element structure in the third embodiment of the present application.

[0045] FIG21 is a schematic diagram of parameter relationships generated by optimizing the design information determined by the multi-focal vector metalens design method in one embodiment of the present application.

[0046] FIG22 is a schematic diagram showing the relationship between transmittance and incident angle formed by carrying optimized design information in one embodiment of the present application.

[0047] FIG23 is a schematic diagram of imaging of the prior art and the optimized multi-focal vector metalens in one embodiment of the present application.

[0048] FIG24 is a schematic diagram of imaging of a corresponding multi-focal vector metalens under x-polarized incident light or unpolarized light in one embodiment of the present application. DETAILED DESCRIPTION

[0049] The present application will be described in detail below with reference to the specific embodiments shown in the accompanying drawings. However, these embodiments do not limit the present application, and any structural, methodological, or functional changes made by a person skilled in the art based on these embodiments are included within the scope of protection of the present application.

[0050] It should be noted that the term "comprises" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article, or apparatus that includes a list of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In addition, the terms "first," "second," etc. are used for descriptive purposes only and should not be understood as indicating or implying relative importance.

[0051] One embodiment of the present application provides an optical system, as shown in Figure 1. The optical system can be used for polarization imaging, and is specifically used to obtain intensity information of light at an object, and to extract and analyze the polarization information carried therein, thereby identifying the material, internal stress, and defects of the object. The optical system provided by the present application can be adapted to at least the following application scenarios:

[0052] (1) In strong interference environments such as the atmosphere, underwater, and foggy weather, the optical system is used to clearly image the object and eliminate the influence of stray light;

[0053] (2) Applying optical systems to radio telescope imaging systems to clearly record the magnetic field environment outside the black hole image in a complex cosmic environment;

[0054] (3) Apply the optical system to face recognition scenarios to effectively distinguish between human faces and artificial masks, thereby improving the security performance of consumer electronics.

[0055] Polarization imaging can be categorized by technology, including time-sharing rotation imaging, aperture-sharing polarization imaging, amplitude-sharing imaging, and focal plane-sharing imaging. The optical system provided herein preferably employs amplitude-sharing imaging, which offers the advantage of high-speed, real-time acquisition and processing of target polarization information, and is therefore widely applicable in military and industrial fields.

[0056] The optical system includes a multi-focal vector metalens 100, configured to implement at least one of the following functions: multi-polarization state beam splitting and polarization analysis; and multi-focal lens focusing. Preferably, an improved multi-focal vector metalens design method can simultaneously enhance the performance parameters of the multi-focal vector metalens 100, such as diffraction efficiency, field of view, uniformity, and polarization extinction ratio, to construct a lightweight, highly efficient optical system. In one embodiment, the optical system is a polarization imaging module.

[0057] Nanostructures are arranged on the image-side surface and / or the object-side surface of the multi-focal vector metalens 100. When the multi-focal vector metalens 100 is configured to implement multi-focal focusing and polarization-state beam splitting and analysis functions, such nanostructures can be configured as the grating element structure 11 shown in Figures 2 and 3.

[0058] In one embodiment, the image-side surface of the multi-focal vector metalens 100 is arranged with a grating elemental structure; the grating elemental structure is configured according to the overall phase distribution design information determined by a multi-focal vector metalens design method. In one embodiment, the object-side surface of the multi-focal vector metalens 100 is arranged with a grating elemental structure; the grating elemental structure is configured according to the overall phase distribution design information determined by a multi-focal vector metalens design method. In one embodiment, both the image-side and object-side surfaces of the multi-focal vector metalens 100 are arranged with grating elemental structures.

[0059] The multifocal vector metalens design method described above can be configured according to any of the technical solutions described below, replacing the separate optical components in traditional polarization imaging systems with the multifocal vector metalens to provide a highly integrated and efficient polarization imaging system. During the design process, based on the analysis of the polarization response of multi-degree-of-freedom metasurface devices, the multifocal vector metalens design method can meet the needs of rapid optimization and physically driven iteration of large-scale metasurface devices, thereby improving diffraction efficiency.

[0060] The optical system includes a light sensor 200 for converting the modulated optical signal output from one side of the multifocal vector metalens 100 into an electrical signal. The light sensor 200 may include a CCD (Charge-Coupled Device) sensor or a CMOS (Complementary Metal Oxide Semiconductor) sensor. The light sensor 200 and the multifocal vector metalens 100 are modular devices with specific functions, and together they form a simple, compact, low-cost, and easily fabricated optical system.

[0061] In addition, the multi-focal vector metalens 100 can be packaged with the light sensor 200 in an imaging module. The imaging module can have a smaller size than the existing technology, for example, less than 5 mm, thereby reducing the volume of the polarization imaging system.

[0062] The nanostructures such as the grating element structure 11 provided in the present application can be prepared using micro-nano processes. The multi-focal vector superlens 100 is designed based on silicon materials. Due to its low absorption loss and high refractive index in the near-infrared band window, the design of the multi-focal vector superlens 100 can be based on 940nm as the central wavelength. Among them, the micro-nano process of silicon-based materials includes but is not limited to coating, ultraviolet lithography, electron beam lithography (EBL, Electron Beam Lithography) and RIE (Reaction Ion Etching, reactive ion etching). The nanostructure prepared based on the above process can achieve a minimum line width of 30nm and a maximum aspect ratio of 10:1, so as to achieve high-precision vector diffraction.

[0063] Furthermore, the nanostructures can be formed into columns with subwavelength dimensions. The basic shapes formed by the nanostructures projected onto one side of the substrate can be expanded from circles, round holes, squares, and square holes to free-form geometric shapes. The substrate can be a glass or silicon substrate, and the spaces between the structures can be filled with materials such as air, glue, silicon oxide, and silicon nitride.

[0064] During optical path simulation and design, or during the formation of an optical system or imaging system, a basic light source may be provided on the object-side surface of the multi-focal vector metalens 100. The basic light source includes, but is not limited to, an LED (Light-Emitting Diode), an EEL (Edge-Emitting Laser), a VCSEL (Vertical Cavity Surface Emitting Laser), a light exciter, and the like; of course, natural light may also be used as the basic light source.

[0065] On the one hand, the multifocal vector metalens designed according to the method provided below can support various application scenarios such as visible light and mid-infrared, and this application does not provide an exhaustive list. On the other hand, when performing optical path simulation and design, or executing the multifocal vector metalens design method provided below, various existing lighting devices that can emit light such as visible light and mid-infrared bands can be used as light sources, and this application does not provide an exhaustive list.

[0066] FIG2 provides four structural configurations of the multi-focal vector metalens 100 .

[0067] As shown in FIG2(a), in this embodiment, a double-piece multi-focal vector metalens 100 is provided, each of which includes a substrate 10 and a grating element structure 11 (i.e., a nanostructure) for forming a metasurface, and can be aligned and bonded by gluing.

[0068] As shown in FIG2( b ), in this embodiment, a monolithic multi-focal vector metalens 100 is provided, having two groups of grating element structures 11 (i.e., nanostructures) for forming a metasurface, which are arranged on the same substrate 10 and located on the object-side surface and the image-side surface, respectively.

[0069] As shown in FIG2(c), in this embodiment, a dual-piece multifocal vector metalens 100 is provided. Each multifocal vector metalens 100 includes a substrate 10 and a grating element structure 11 (i.e., a nanostructure) for forming a metasurface. A filter 12 is disposed on at least the image-side surface of the multifocal vector metalens 100 near the optical sensor. The filter 12 can be formed by a nanostructure disposed on the substrate 10 or by coating.

[0070] As shown in FIG2(d), in this embodiment, a monolithic multifocal vector metalens 100 is provided, and a filter 12 is arranged on at least one side of its image-side surface. The filter 12 can be formed by a nanostructure arranged on the substrate 10 or by coating.

[0071] Furthermore, the optical system and the metasurface formed by the grating elemental structure 11 in the multifocal vector metalens 100 are both coaxial systems. The multifocal vector metalens 100 can achieve functions such as single-focus convergence or multi-focus convergence by designing a metasurface or configuring a traditional lens. Other components can also be added to the optical system to enhance functionality. For example, a fisheye lens can be provided on the object-side surface to increase the field of view.

[0072] FIG3 provides a preferred embodiment of a multi-focal vector metalens 100. The multi-focal vector metalens 100 includes a grating elemental structure 11, a substrate 10 connected to the grating elemental structure 11, a filler 13 connecting the grating elemental structure 11 and the substrate 10, and an anti-reflection film 14 disposed on one side of the substrate 10 and / or the filler 13. In this embodiment, the anti-reflection film 14 is preferably disposed on one side of both the substrate 10 and the filler 13.

[0073] Specifically, one set of antireflection films 14 covers the surface of the filler 13 facing away from the substrate 10, and the other set of antireflection films 14 covers the surface of the substrate 10 facing away from the grating element structure 11. As shown in FIG1 and FIG2(d), both the object-side surface (light-entering side) and the image-side surface (light-exiting side) of the multifocal vector metalens 100 are covered with antireflection films 14. In an embodiment in which a filter 12 is provided, the antireflection film 14 located on the side of the substrate 10 can be provided between the filter 12 and the substrate 10. By providing the antireflection film 14, the reflectivity can be reduced and the transmittance can be increased, thereby improving the diffraction order efficiency and suppressing the zero-order diffraction, thereby improving the efficiency of the multifocal vector metalens 100.

[0074] The antireflection film 14 includes a first material layer 141 and a second material layer 142. The first material layer 141 is preferably made of silicon nitride, while the second material layer 142 is preferably made of silicon oxide. This ensures high transmittance even at high incident angles.

[0075] The first material layer 141 or the second material layer 142 can be connected to the substrate 10 or the filler 13. Specifically, on the object-side surface, the filler 13 can be connected to the first material layer 141 or the second material layer 142; on the image-side surface, the substrate 10 can be connected to the first material layer 141 or the second material layer 142. In this embodiment, the appropriate material layer can be selected based on the materials used to make the substrate 10 and the filler 13. For example, when both the substrate 10 and the filler 13 are made of silicon oxide, the first material layer 141 made of silicon nitride can be connected to the substrate 10 and the filler 13, and the second material layer 142 can be connected to the outside of the first material layer 141.

[0076] In one embodiment, the antireflection film 14 on both sides of the grating element structure 11 is composed of a single first material layer 141 and a single second material layer 142. When the wavelength of the incident light is 940 nm, the thickness of the first material layer 141 is preferably 50 nm ± 5 nm, and the thickness of the second material layer 142 is preferably 215 nm ± 5 nm, to achieve optimal metasurface efficiency.

[0077] In one embodiment, the anti-reflection film 14 on both sides of the grating unit structure 11 is sequentially provided with a second material layer 142, a first material layer 141, a second material layer 142, and a first material layer 141 from the outside to the inside (the side of the grating unit structure 11), to form a double-layer anti-reflection film structure. When the wavelength of the incident light is 940nm, the thickness of the outer second material layer 142 is preferably 165nm±5nm, the thickness of the outer first material layer 141 is preferably 385nm±5nm, the thickness of the inner second material layer 142 is preferably 55nm±5nm, and the thickness of the inner first material layer is preferably 40nm±5nm. This achieves optimal metasurface efficiency.

[0078] As shown in FIG4 , an embodiment of the present application provides a multi-focal vector metalens design method, which specifically includes the following steps.

[0079] Step S1, determining the elementary phase distribution information of the metalens with the resolution of the light sensor as a constraint condition.

[0080] Step S2: Under the guidance of the target polarization state, optimize and determine the object plane Jones matrix carrying the vector grating phase distribution information.

[0081] Step S3: linearly superimpose the element phase distribution information and the vector grating phase distribution information to generate overall phase distribution design information.

[0082] In this way, the vector grating phase distribution information carried by the optimized object plane Jones matrix can be and the element phase distribution information used to realize the lens function The multi-focal vector metalens is designed by superposition, so that it has multi-polarization state beam splitting and polarization analysis functions and multi-focal lens focusing functions, and the designed multi-focal vector metalens has the advantages of high focusing efficiency, high focus uniformity, high extinction ratio, perfect suppression of zero-order diffraction, and large bandwidth.

[0083] The performance of the metalens depends on precise control of the phase. The accuracy of the light sensor may be lower than the accuracy requirement of the metasurface. Taking into account factors such as error accumulation, the resolution of the light sensor is used as a constraint to determine the elementary phase distribution information, which can make the constructed multi-focal vector metalens more operable.

[0084] While this application proposes constructing a metasurface using primitives to achieve lens focusing and other functions, this application does not exclude the use of traditional lenses to achieve focusing functions. For solutions using traditional lenses to achieve focusing functions, the primitive phase information in step S1 refers to the overall phase distribution of the metalens.

[0085] In one embodiment, step S1 specifically includes:

[0086] In step S10, iterative optimization is performed within the optical path design platform using the light sensor resolution as a constraint until the imaging performance of the optical system formed by the light sensor and the current metalens, or the resolution of the optical system, or both the imaging performance and the resolution of the optical system, reach the set target, and the elementary phase distribution information of the current metalens is determined.

[0087] Figure 5 shows the optical path obtained by simulating a module containing a single multi-focal vector metalens, and Figure 6 shows the optical path obtained by simulating a module containing two multi-focal vector metalens. Based on this, the focusing performance of the metalens can be optimized by adjusting the optical path, so that at least the imaging performance and resolution meet the requirements. In addition, in the implementation method that relies on the metalens configuration to achieve multi-focal focusing, it is also necessary to optimize the number of convergent focal points of the metalens to reach the set target; for example, the number of convergent focal points n = 4; in other implementations, n can also be 6 or other values.

[0088] The quality of an optical system's imaging can be assessed by calculating indicators such as the modulation transfer function (MTF), aberrations (e.g., spherical aberration, chromatic aberration, astigmatism, and field curvature), wavefront distortion (Wavefront Aberration), point spread function (PSF), blur, chromatic aberration, transmittance and reflectance, and distortion correction. In one embodiment, the assessment can be based on the degree of point convergence in a condenser diagram.

[0089] The resolution of an optical system can be assessed by calculating indicators such as the optical transfer function (OTF), point spread function (PSF), cut-off frequency, differential amplitude transfer function (DATF), amplitude and phase errors, Moiré and interference patterns, and Airy disks. In one embodiment, the evaluation can be performed based on the value of the modulation transfer function.

[0090] In one embodiment, the optical path design platform is Zemax. The "performing iterative optimization in the optical path design platform" in step S10 specifically includes the following steps:

[0091] S100, in the optical path design platform, performs iterative optimization based on the degree of point convergence in the spotlight diagram and the value of the modulation transfer function.

[0092] In one embodiment, the polychromatic diffusion modulation transfer function (MTF) can be determined by fitting the relationship between the spatial modulus of the optical transfer function (OTF) and the spatial frequency in cycles per (Spatial Frequency in Cycles Per) to evaluate and optimize the optical system, thereby determining the elementary phase distribution information of the metalens.

[0093] The spatial modulus of the optical transfer function (OTF) represents the system's transmission efficiency at different spatial frequencies. Spatial frequency is a measure of the frequency or periodicity of changes in an image. The polychromatic scattering modulation transfer function (MTF) is used to evaluate an optical system's imaging capabilities for polychromatic light sources (i.e., light containing multiple wavelengths).

[0094] In one embodiment, image modulation analysis (IMA) can be performed on the metasurface to determine a spot diagram for optical system evaluation and optimization, thereby determining the elementary phase distribution information of the metalens.

[0095] Among them, image modulation analysis mainly projects a specific test pattern into the optical system and measures the characteristics of the pattern obtained on the image plane to evaluate the modulation transfer function and other performance indicators, and identify possible aberrations, distortions or other problems in the system; the spotlight can be used to analyze the imaging of a single point or object, and evaluate the imaging performance of the optical system based on the quality of the spot (good, or blurred, distorted).

[0096] In one embodiment, the polychromatic diffusion through focus (MTF) can be determined by fitting the relationship between the spatial modulus of the optical transfer function (OTF) and the focus shift in millimeters to evaluate and optimize the optical system, thereby determining the elementary phase distribution information of the metalens.

[0097] Here, focus shift refers to the distance by which the focus of an optical system is moved from its standard or original position.

[0098] In one implementation, step S3 specifically includes the following steps.

[0099] Step S31 , updating each matrix element in the object plane Jones matrix according to the primitive phase distribution information to obtain a superimposed Jones matrix.

[0100] Step S32: performing matrix decomposition on the superimposed Jones matrix to obtain a vector rotation decomposition matrix as the overall phase distribution design information.

[0101] On the one hand, compared to traditional approaches that optimize and determine the phase distribution function, this application uses the Jones matrix to describe the modulation behavior of at least the grating portion of a multi-focal vector lens. This allows the physical concept of polarization state control to be incorporated into the algorithm, assisting in the construction of a flexible polarization state adjustment strategy. On the other hand, the Jones matrix is ​​also used as an overlay object during the subsequent superposition of phase distribution information, fully integrating the lens focusing function of the metalens element with the polarization response function of the vector grating, forming an organic whole.

[0102] Of course, this does not mean that the elemental part of the superlens and the grating part of the superlens must be arranged on the same substrate. The technical solution of the aforementioned double-piece superlens can also be adopted. After unified superposition and optimization, the elemental part is configured on one of the superlenses and the grating part is configured on the other superlens.

[0103] In one embodiment, the vector rotation decomposition matrix carries phase delay information. In one embodiment, the vector rotation decomposition matrix carries transmittance information and phase delay information. In one embodiment, the vector rotation decomposition matrix carries phase delay information and rotation angle information. In one embodiment, the vector rotation decomposition matrix carries phase delay information, rotation angle information, and transmittance information. Therefore, the design and configuration of the grating element structure at the metalens can be formed based on this.

[0104] In one embodiment, the object plane Jones matrix includes a first matrix element J xx (x,y), the second matrix element J yy (x,y), the third matrix element J xy (x,y) and the fourth matrix element J yx (x,y). The relationship between the four matrix elements is shown in Figure 7. The object plane Jones matrix is ​​constructed under the linear polarization basis vector; the optimized object plane Jones matrix J constructed by the above four matrix elements is * (x,y) can at least satisfy:

[0105] Among them, the first matrix element J xx (x, y) represents the ratio of the amplitude and phase of the x polarization component obtained after the x polarization component of the input light passes through the metalens; the second matrix element J yy (x, y) represents the ratio of the amplitude and phase of the y polarization component of the input light after the y polarization component passes through the metalens; the third matrix element J xy(x, y) represents the ratio of the amplitude and phase of the y polarization component obtained after the x polarization component of the input light passes through the metalens; the fourth matrix element J yx (x,y) represents the ratio of the amplitude and phase of the x-polarization component of the input light's y-polarization component after passing through the metalens. This allows for comprehensive analysis of polarization transformations, facilitating calculations of optical system transfer functions, analysis of non-ideal polarization effects, and optimization of optical systems through parameter adjustments.

[0106] Based on this, step S32 specifically includes the step of performing an element-wise multiplication of the primitive phase distribution matrix and the object plane Jones matrix to obtain the superimposed Jones matrix. In this manner, linear phase superposition is first performed on the lens phase distribution and the final object plane Jones matrix, naturally resulting in an update and fusion of the vector metagrating phase distribution. Matrix decomposition is then performed to determine the updated phase delay, further determining the final design information. This fully linearly superimposes the primitive phase distribution and the vector grating phase distribution, facilitating unified optimization and metalens configuration.

[0107] In conjunction with FIG8 , in one embodiment, the vector rotation decomposition matrix includes the Jones vector. Corresponding to the overall phase delay information carried by the vector rotation decomposition matrix The Jones vector at least includes the first overall phase delay information of the metalens in the x-polarization direction And the second total phase delay information in the y polarization direction First overall phase delay information and the second overall phase delay information Determined based on the metalens after phase superposition. In one embodiment, the vector rotation decomposition matrix includes a rotation matrix. The rotation matrix includes at least the rotation angle information θ of the metalens grating element. In one embodiment, the vector rotation decomposition matrix is ​​configured as a combination of the above two embodiments.

[0108] In this way, a close connection with the phase delay, grating rotation angle or element rotation angle can be established to accurately describe the polarization characteristics of the current grating element structure.

[0109] The following will specifically introduce the physical meaning of the phase delay information in the x-polarization direction and the phase delay information in the y-polarization direction corresponding to the structure. It can be used to explain how to construct the design information with data such as phase delay information, as well as to explain the acquisition method and connotation of the above-mentioned primitive phase distribution information, vector grating phase distribution information, and overall phase delay information.

[0110] Figure 9 shows four square-pillar nanostructures of different sizes, which can serve as the grating element structure. Specifically, the four nanostructures have different aspect ratios in the mutually perpendicular x and y directions. For example, the length and width of the nanostructure shown on the far left of Figure 9 are equal, and can both be 150 nm. The nanostructure shown on the middle left of Figure 9 has a width in the x direction that is less than its length in the y direction, and can have a length of 250 nm and a width of 150 nm. The nanostructure shown on the middle right of Figure 9 has a length in the x direction that is greater than its width in the y direction, and can have a length of 250 nm and a width of 75 nm. The nanostructure shown on the far right of Figure 9 has a length in the x direction that is greater than its width in the y direction, and can have a length of 350 nm and a width of 150 nm.

[0111] FIG9 also shows a rotation angle θ of the grating element structure. In this embodiment, the angle between the direction of the nanostructure (ie, the grating element) and the x-polarization direction (particularly its positive direction) is defined as the rotation angle θ.

[0112] The embodiment shown in FIG9 is based on an example in which the nanostructure (ie, the grating element structure) is made of silicon material and the substrate is made of silicon oxide material. This does not mean that the present application is limited to this material combination.

[0113] Phase distribution information can be obtained by scanning the grating element structure. Specifically, it can be scanned by implementing rigorous coupled wave analysis equipped with full analytical Fourier transform. Phase distribution information includes phase delay information in the x-polarization direction. Phase delay information in the y-polarization direction and the rotation angle θ.

[0114] Figure 10(a) shows the relationship between the x-direction dimension Dx and the y-direction dimension Dy of the nanostructure, as obtained by performing a Bloch boundary scan on the nanostructure with the x-polarization direction as the incident direction, and the x-direction transmittance Tx. Figure 10(b) shows the relationship between the x-direction dimension Dx and the y-direction dimension Dy of the nanostructure, as well as the y-direction transmittance Ty, as obtained with the y-polarization direction as the incident direction. The x-direction transmittance Tx and the y-direction transmittance Ty can be used as anisotropic response parameters of the nanostructure, and their values ​​can be determined by referring to the color depth of the base image at the hexagonal star point in the figure.

[0115] Figure 10(c) shows the x-direction size Dx, y-direction size Dy of the nanostructure and the x-direction phase delay obtained after Bloch boundary scanning of the nanostructure with the x-polarization direction as the incident direction. Figure 10 (d) shows the relationship between the x-direction size Dx of the nanostructure, the y-direction size Dy of the nanostructure and the y-direction phase delay when the y-polarization direction is the incident direction. Phase delay in the x-direction and y-direction phase delay It can be used as an anisotropic response parameter of the nanostructure, and its value can be determined by referring to the color depth of the base map at the hexagonal star point in the figure.

[0116] In this way, the phase distribution information may correspond to the phase delay in the x-polarization direction having the above-mentioned physical meaning. Phase delay in the y-polarization direction and / or the first transmittance Tx, the second transmittance Ty, and / or the rotation angle θ.

[0117] Specifically, the element phase distribution information can be determined by scanning; preferably, scanning is performed by rigorous coupled wave analysis equipped with a full analytical Fourier transform. The vector grating phase distribution is determined by an iterative optimization algorithm; preferably, it is determined by optimizing the vector iterative Fourier algorithm integrated with gradient descent. The overall phase distribution information (for example, the first overall phase delay information) Second overall phase delay information ) is obtained through linear superposition.

[0118] In one embodiment, the vector rotation decomposition matrix obtained after the matrix decomposition operation contains the first overall phase delay information Second overall phase delay information The Jones vector can be:

[0119] The first rotation matrix R(θ) containing the rotation angle θ is:

[0120] The second rotation matrix R(-θ) containing the rotation angle (-θ) is:

[0121] Based on this, the vector rotation decomposition matrix in the form of a decomposition matrix under the linear polarization basis vector at least satisfies:

[0122] In one embodiment, step S2 further includes the following steps.

[0123] Step S21, determining target image plane Jones matrix information according to the target polarization state, and determining an objective function according to the difference between the target image plane Jones matrix information and the target image plane Jones matrix information;

[0124] Step S22: Optimize the current object plane Jones matrix information based on a vector iterative Fourier algorithm until the objective function converges, and determine the final object plane Jones matrix information.

[0125] Since forward and backward propagation optimization is performed at the Jones matrix level, the physical concept of polarization state control can be fully reflected, a vector iterative Fourier algorithm can be constructed, and by adjusting hyperparameters such as the learning rate and the learning rate reduction parameter, the design information corresponding to a multi-focal vector superlens with high focusing efficiency, high focal uniformity, high extinction ratio, sufficient suppression of zero-order diffraction and large bandwidth can be finally optimized.

[0126] As shown in FIG11 , when executing the multi-focal vector metalens design method provided by the present application, the object plane Jones matrix J(x, y) is first constructed on the object plane side according to the initialized grating primitive structure (i.e., metasurface), and the target image plane Jones matrix A(k) is determined on the far field (i.e., image plane) side according to the design goal. x ,k y ), first forward propagation and determine the difference between the two according to the objective function, iteratively update the target image plane Jones matrix A′(k x ,k y ), and then back-propagate to update the object plane Jones matrix J′(x,y), and repeat the iteration until the objective function converges to determine the final object plane Jones matrix J * (x,y).

[0127] On the one hand, the Jones matrix of the object plane formed in the iterative process of each diffraction order is defined as J(k x ,k y ), the Euclidean distance between it and the Jones matrix of the target image plane can be set as the objective function. The objective function is defined as FoM, which can at least satisfy: FoM=[J(k x ,k y )-A(k x ,k y )] 2 .

[0128] On the one hand, gradient descent constraints can be introduced into the vector iterative Fourier algorithm to improve convergence. Specifically, the gradient of the objective function can be calculated during the iteration process to further enhance the physical constraint capability of the vector iterative Fourier algorithm, thereby improving the stability of the optimization solution while ensuring computational speed. In one embodiment, the gradient constraint factor can be determined based on the derivative of the objective function with respect to the overall phase factor in the current object plane matrix information generated during the iteration process.

[0129] The overall phase factor of the current object plane matrix information generated during the iteration process is defined as Then the gradient constraint factor can at least satisfy:

[0130] After one iteration, the overall phase factor of the current object plane matrix information can be updated as follows:

[0131] Among them, α is the gradient learning rate factor.

[0132] Figure 12(a) shows the relationship between dichroism and focal uniformity (UE) as the iteration progresses in the prior art. Figure 12(b) shows the relationship between dichroism and focal uniformity as the iteration progresses in the multifocal vector metalens design method provided by the present application. It can be seen that the solution provided by the present application has a faster convergence speed and better convergence characteristics, and enables the vector iterative Fourier algorithm to escape local optimal solutions to a certain extent, thereby providing powerful algorithmic support for the design of multifocal vector metalens.

[0133] On the one hand, the object optimized by the vector iterative Fourier algorithm can be the grating part in the grating element structure, and the target image plane Jones matrix can be set based on the goal of realizing a multi-diffraction order arbitrary polarization vector diffraction grating.

[0134] In one embodiment, a target image plane Jones matrix can be constructed in a global xOy coordinate system based on the Poincare sphere. For example, n sets of target image plane Jones matrices can be constructed based on the ellipticity and azimuth information corresponding to each diffraction order under n target polarization states. Furthermore, by constructing the corresponding n sets of global Jones matrices in the xOy coordinate system, a correlation is established with the object plane Jones matrix to iteratively determine the final object plane Jones matrix.

[0135] Figure 13 shows the constructed Poincare sphere. When plotting polarization states, the ellipticity χ and azimuth ψ can be used to describe the coordinates of points on the Poincare sphere and within it. The radius of the Poincare sphere is determined by the polarization degree of the incident light, with a maximum value of 1, corresponding to fully polarized light. The azimuth ψ, also known as the orientation angle, ranges from ±90° and can be measured from the S1 axis. The ellipticity χ ranges from ±45° and can be measured from the equator of the Poincare sphere. Points at the equator represent linearly polarized light, points at the poles of the Poincare sphere represent circularly polarized light, and points elsewhere on the Poincare sphere represent other elliptically polarized light.

[0136] The ellipticity information of each diffraction order is defined as χ(kx ,k y ), the azimuth information of each diffraction order is ψ(k x ,k y ), then the target image plane Jones matrix A(k x ,k y ) at least satisfies: A(k x ,k y )=|α * (k x ,k y )><α(k x ,k y )|.

[0137] Among them, |α(k x ,k y )> is the Jones matrix vector, |α * (k x ,k y )> is the Jones matrix vector |α(k x ,k y )>, <α(k x ,k y )| is the Jones matrix vector|α(k x ,k y )>'s conjugate transpose vector.

[0138] Among them, the Jones matrix vector |α(k x ,k y )>At least:

[0139] Among them, the rotation matrix R(ψ(k x ,k y ))At least:

[0140] Based on this, the global Jones matrix J in the xOy coordinate system can be determined according to the ellipticity information χ and the azimuth information ψ xOy (x,y) satisfies at least: J xOy (x,y)=F -1 (A(k x ,k y )).

[0141] The Jones matrix A(k x ,k y ) performs vector iterative inverse Fourier transform to obtain the global Jones matrix J xOy(x, y), based on the ellipticity information χ, azimuth information ψ and its own matrix decomposition form, it is possible to establish a corresponding relationship with the electric field-based description J(x, y) of the Jones matrix in the linear polarization basis vector provided above, and then the phase delay, or the phase delay and transmittance can be updated to redetermine the Jones matrix of the current object plane and achieve iterative optimization.

[0142] On the other hand, the number of target polarization states, n, can be adaptively adjusted based on accuracy and other requirements. As shown in Figure 14, the top row shows the Poincare spheres corresponding to several target polarization state configurations, and the bottom row shows the corresponding K-space distributions. In one embodiment, the convex polyhedron formed by sequentially connecting the characteristic points corresponding to the n target polarization states on the Poincare sphere is a regular polyhedron.

[0143] When n=4, the four target polarization states may include one circular polarization state and three elliptical polarization states, and the corresponding characteristic points are connected to form a regular tetrahedron.

[0144] When n=6, the six target polarization states may include two circular polarization states and four linear polarization states, and the corresponding characteristic points are connected to form a regular octahedron.

[0145] When n=8, the eight target polarization states may all be elliptical polarization states, and the corresponding characteristic points are connected to form a regular hexahedron.

[0146] When n=12, the 12 target polarization states may include eight elliptical polarization states and four linear polarization states, and the corresponding characteristic points are connected to form a regular icosahedron.

[0147] When n=20, the 20 target polarization states may include 16 elliptical polarization states and 4 linear polarization states, and the corresponding characteristic points are connected to form a regular dodecahedron.

[0148] In the technical solution provided in this application, preferably n=4.

[0149] In one embodiment, as shown in FIG15 , after step S3 , the multi-focal vector superlens design method further includes the following steps.

[0150] Step S4: searching a multi-focal vector superlens parameter library according to the overall phase distribution design information to obtain structural design information corresponding to the grating element structure.

[0151] Step S5: Optimizing the structural design information according to the grating element arrangement rule.

[0152] For step S4, in combination with FIG8 and FIG16, the search can be performed based on the vector rotation decomposition matrix as the overall phase distribution design information, or based on the determined first overall phase delay information And the second overall phase delay information A search is performed to match and determine the structural design information based on the multi-focal vector super lens structure parameter library.

[0153] In one embodiment, the multi-focal vector metalens structure parameter library is used to construct the relationship between phase delay or its combination with rotation angle information and the grating element structure design. In one embodiment, the multi-focal vector metalens structure parameter library is used to construct the relationship between phase delay or its combination with transmittance (e.g., first transmittance Tx, second transmittance Ty) and the grating element structure design.

[0154] In one embodiment, the multi-focal vector metalens structure parameter library is used to construct a relationship between overall phase distribution design information, such as a rotational decomposition matrix, and the grating element structure design. In one embodiment, the multi-focal vector metalens structure parameter library is used to construct a relationship between a Jones matrix, such as one constructed from four matrix elements, and the grating element structure design.

[0155] In one embodiment, as shown in FIG15 , before calling the multi-focal vector metalens structure parameter library, especially before the above step S4, the multi-focal vector metalens design method may further include:

[0156] Step S0: Implement rigorous coupled wave analysis equipped with a fully analytical Fourier transform to scan several metalenses, construct several standard Jones matrices based on the corresponding complex amplitude information, associate the grating element structure of the metalens with the corresponding standard Jones matrix, and construct a multi-focus vector metalens structure parameter library.

[0157] The grating elemental structure is a standard three-dimensional structure. Examples of standard three-dimensional structures include elliptical cylinders, rectangular prisms, and polygonal prisms. When the grating elemental structure is a standard three-dimensional structure, its periodic distribution function has a fixed and well-defined Fourier domain expression. This not only avoids discretization of the structure during the Fourier expansion phase, but also further improves data acquisition and computation speed, reduces computational burden, and speeds up preparation. Specifically, the Fourier domain expression corresponding to this grating elemental structure can be obtained by searching an information optics library constructed based on prior information, such as information optics textbooks.

[0158] The full-analytic Fourier transform (FFT) is used to analyze the frequency domain characteristics of complex signals. Expanding the first periodic distribution function using the FFT overcomes the technical barriers of discretization required by traditional discrete Fourier transforms (DFT) and fast Fourier transforms (FFT). It adapts to the characteristics of periodic distribution functions and grating element structures, performs continuous signal processing, provides complete amplitude and phase information in the frequency domain, supports the processing of band-limited signals, and avoids the processing of negative frequency components.

[0159] Due to the use of Rigorous Coupled-Wave Analysis (RCWA), compared with the traditional finite-difference time-domain method and finite element method, the electromagnetic wave problem that can be solved in the spatial domain is converted into a problem of solving Maxwell's equations at spatial frequency, which can perform full-wave simulation of periodic structures more accurately and efficiently.

[0160] In one embodiment, as shown in FIG17 , the grating element arrangement rule is set as follows: the grating elements are arranged radially from the center O of the metasurface, all grating elements located in a first region Z1 have a first average distance from the metasurface center O, and the total number of grating elements located in the first region Z1 is positively correlated with the first average distance. Of course, in other embodiments, the metasurface center O can be set to any point on the metasurface, not limited to the geometric center of the region where the metasurface is located.

[0161] Figure 17 specifically provides three regional arrangement schemes for grating element structures. The distribution of the grating element structure on the object side or image side, the grating element arrangement rule is set as follows: the metasurface center O is arranged in a first shape radiating outward in all directions, dividing the side into a number of concentric regions. The shape can be a rectangle (polygon) as shown in Figure 17 (a), a hexagon (polygon) as shown in Figure 17 (b), or a ring (annular) as shown in Figure 17 (c). When implementing a variable period arrangement, the ring-shaped regional arrangement scheme in Figure 17 (c) is preferably adopted.

[0162] In one embodiment, as shown in Figures 18 to 20, the grating element arrangement rule is set as follows: the grating elements are arranged in a circular shape radiating from the center O of the metasurface to the surrounding areas, and the distance between all grating elements located in the second area Z2 and the center of the metasurface has a second average distance, and the second average distance is greater than the first average distance.

[0163] In the first embodiment, as shown in FIG18 , the grating element arrangement rule can be further set: the distances between the grating element structures located in different regions and the radiation center O are different, and the radial period L1 and circumferential period L2 of the grating element structures located in different regions are the same.

[0164] In combination with the second embodiment and the third embodiment, as shown in Figures 19 and 20, the grating element arrangement rule can be further set as follows: the radial period of the grating elements in the first region Z1 is greater than the radial period of the grating elements in the second region, or the circumferential period of the grating elements in the first region Z1 is greater than the circumferential period of the grating elements in the second region, or the radial period of the grating elements in the first region Z1 is greater than the radial period of the grating elements in the second region, and the circumferential period of the grating elements in the first region Z1 is greater than the circumferential period of the grating elements in the second region.

[0165] According to the second embodiment (double variable period arrangement) provided in FIG19 , the grating element arrangement rule can be further set as follows: the radial period L1 of the grating elements in the first region Z1 is greater than the radial period L1 of the grating elements in the second region Z2, and the circumferential period L2 of the grating elements in the first region Z1 is greater than the circumferential period L2 of the grating elements in the second region Z2.

[0166] Furthermore, the grating element arrangement rule can be set such that the distances between the grating element structures in different regions and the radiation center O are different, and the radial period L1 and circumferential period L2 of the grating element structures in different regions are different. Preferably, the ratio of the radial period L1 to the circumferential period L2 of the grating element structures in different regions is the same. In a preferred embodiment, the greater the distance between the grating element structures and the radiation center O, the smaller the radial period L1 and the smaller the circumferential period L2.

[0167] According to the third embodiment (single variable period arrangement method) provided in FIG20 , the grating element arrangement rule can be further set as follows: the radial period L1 of the grating elements in the first region Z1 is greater than the radial period L1 of the grating elements in the second region Z2, and the circumferential period L2 of the grating elements in the first region Z1 is equal to the circumferential period L2 of the grating elements in the second region Z2.

[0168] Furthermore, the grating element arrangement rule can be set such that the distances between the grating element structures in different regions and the radiation center O are different, and the grating element structures in different regions have the same circumferential period L2 and different radial period L1. In a preferred embodiment, the greater the distance between the grating element structures and the radiation center O, the smaller the radial period L1, and the circumferential period L2 remains unchanged.

[0169] In this way, a multi-focal vector metalens with high efficiency and large field of view can be configured to improve the focusing efficiency of the edge structure while ensuring the phase and optimize the overall focusing efficiency.

[0170] Specifically, the following steps may be performed to specifically determine the period of the grating element structure.

[0171] Step R1: Obtain and fit the relationship between the grating element period and transmittance based on several preset incident angles, and determine the optimal period for each preset incident angle. As shown in Figure 21(a), the optimal period is 420nm at 0° incident angle, 390nm at 15° incident angle, 350nm at 30° incident angle, and 320nm at 45° incident angle.

[0172] Step R2, according to the above relationship, sequentially fit the relationship between the angle (angle) and the structural period, and the relationship between the radius length (um) and the structural period; as shown in Figure 21 (b) and Figure 21 (c).

[0173] In step R3, based on the above relationship, the focusing efficiency (or transmittance) variation curve with the incident angle is determined, and the periodic arrangement of the grating element structure is set accordingly; as shown in Figure 21 (d), ModeA refers to the double-variable periodic arrangement mentioned above, ModeB refers to the single-variable periodic arrangement mentioned above, and P452nm refers to the fixed periodic arrangement of 425nm.

[0174] In another embodiment, an anti-reflection coating can be applied to significantly reduce reflection and increase tolerance. The specific solution can be found in the previous section and will not be repeated here.

[0175] Of course, the above-mentioned embodiments can be combined to form the best optimization solution. Figure 22 shows the relationship between transmittance and incident angle when both the anti-reflection coating solution and the variable period arrangement solution are implemented simultaneously. It can be seen that compared with the P425nm fixed period arrangement, the composite optimization solution provided by this application (Best result with variable period) has more beneficial transmittance and focusing efficiency performance at a large field of view angle.

[0176] Figure 23(a) shows the imaging situation on one side of the optical sensor when achieving four focal points or multiples thereof in the prior art, corresponding to the K-space distribution when n=4 provided in Figure 14. It can be seen that the spot images are located at four positions: (0, 1), (-1, 0), (1, 0), and (0, -1). This multi-focal focusing scheme is conducive to structural configuration, but because the optical sensors are arranged horizontally and vertically, this multi-focal spot arrangement results in a large area of ​​waste on one side of the optical sensor. However, expanding the number of focal points to 6 or 8 increases design difficulty, process complexity, and cost.

[0177] Based on this, the multi-focal vector metalens provided in the present application further includes, after step S5, the step of rotating the metasurface defined by the optimized structural design information by 45 degrees about the geometric center of the metasurface, and generating the corresponding final design information; that is, determining the rotated structural design information as the final design information.

[0178] In this way, when the metalens equipped with the lens design information is implemented, it can produce an imaging situation as shown in (b) of Figure 23. The light spot images can be arranged in a matrix in the horizontal and vertical directions consistent with the light sensor, thereby maximizing the utilization of the area of ​​the light sensor and expanding the field of view. Combined with the design method provided in this application, there is almost no zero-order diffraction technology effect, and a two-way tangent structure can be constructed to further expand the field of view.

[0179] Figure 24 (a) shows the imaging of x-polarized light incident on the multi-focal vector metalens provided by this application in conjunction with an optical sensor; Figure 24 (b) shows the imaging of unpolarized light incident on the multi-focal vector metalens in conjunction with an optical sensor. The multi-focal vector metalens designed in this application can achieve high-precision full-Stokes parameter reconstruction, have a larger field of view, and minimize distortion. It can also perform multi-focal focusing and real-time polarization imaging, and avoid zero-order diffraction.

[0180] In summary, the multi-focal vector metalens, design method, and optical system provided in this application determine the corresponding phase distribution information for metalens focusing and polarization control at the phase distribution level, and update the overall phase distribution design with the phase information after linear superposition. It can organically integrate focusing performance and polarization control performance, and assist in constructing a metalens structure that takes both functions into account.

[0181] It should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each implementation method can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

[0182] The series of detailed descriptions listed above are only specific descriptions of feasible implementation methods of this application. They are not intended to limit the scope of protection of this application. Any equivalent implementation methods or changes that do not deviate from the technical spirit of this application should be included in the scope of protection of this application.

Claims

1. A multi-focal vector metalens design method, characterized in that: include: Taking the resolution of the optical sensor as a constraint, the elementary phase distribution information of the metalens is determined; Under the guidance of the target polarization state, the Jones matrix of the object plane carrying the phase distribution information of the vector grating is optimized and determined; The primitive phase distribution information and the vector grating phase distribution information are linearly superimposed to generate overall phase distribution design information.

2. The multi-focal point vector metalens design method according to claim 1, characterized in that: The “determining the elementary phase distribution information of the metalens with the resolution of the optical sensor as a constraint condition” specifically includes: Taking the resolution of the light sensor as a constraint, iterative optimization is performed within the optical path design platform until the imaging performance of the optical system composed of the light sensor and the current superlens, or the resolution capability of the optical system, or both the imaging performance and the resolution capability of the optical system reach the set target, and the primitive phase distribution information of the current superlens is determined.

3. The multi-focal point vector superlens design method according to claim 2, characterized in that: The optical path design platform is Zemax; the “iterative optimization in the optical path design platform” specifically includes: In the optical path design platform, iterative optimization is performed based on the degree of point convergence in the spotlight diagram and the value of the modulation transfer function.

4. The multi-focal point vector metalens design method according to claim 1, characterized in that: The “linearly superimposing the element phase distribution information and the vector grating phase distribution information to generate overall phase distribution design information” specifically includes: Update each matrix element in the object plane Jones matrix according to the primitive phase distribution information to obtain a superposition Jones matrix; Matrix decomposition is performed on the superposition Jones matrix to obtain a vector rotation decomposition matrix as the overall phase distribution design information.

5. The multi-focal point vector metalens design method according to claim 4, characterized in that: The object plane Jones matrix includes a first matrix element, a second matrix element, a third matrix element and a fourth matrix element; the first matrix element represents the ratio of the amplitude and phase of the x polarization component obtained after the x polarization component of the input light passes through the super lens; the second matrix element represents the ratio of the amplitude and phase of the y polarization component obtained after the y polarization component of the input light passes through the super lens; The third matrix element represents the ratio of the amplitude and phase of the y polarization component obtained after the x polarization component of the input light passes through the metalens; the fourth matrix element represents the ratio of the amplitude and phase of the x polarization component obtained after the y polarization component of the input light passes through the metalens; The “updating each matrix element in the object plane Jones matrix according to the primitive phase distribution information to obtain a superposition Jones matrix” specifically includes: The element-by-element Jones matrix is ​​obtained by performing element multiplication on the primitive phase distribution matrix and the object plane Jones matrix.

6. The multi-focal point vector superlens design method according to claim 4, characterized in that: The vector rotation decomposition matrix includes a Jones vector and a rotation matrix; the Jones vector includes at least first overall phase delay information of the metalens in the x-polarization direction and second overall phase delay information in the y-polarization direction; the rotation matrix includes at least rotation angle information of the metalens grating element.

7. The multi-focal point vector superlens design method according to claim 1, characterized in that: After "linearly superimposing the element phase distribution information and the vector grating phase distribution information to generate overall phase distribution design information", the multi-focal vector metalens design method further includes: According to the overall phase distribution design information, a multi-focal vector superlens parameter library is retrieved to obtain structural design information corresponding to the grating primitive structure; The structural design information is optimized according to the grating element arrangement rule.

8. The multi-focal point vector metalens design method according to claim 7, characterized in that: Before the step of "searching a multi-focal point vector super lens parameter library according to the overall phase distribution design information to obtain structural design information corresponding to the grating primitive structure", the multi-focal point vector super lens design method specifically includes: A rigorous coupled wave analysis equipped with a fully analytical Fourier transform is implemented to scan a number of superlenses, and a number of standard Jones matrices are constructed according to the corresponding complex amplitude information. The grating primitive structure of the superlens is associated with the corresponding standard Jones matrix to construct a multi-focus vector superlens parameter library; wherein the grating primitive structure is a standard three-dimensional structure.

9. The multi-focal point vector metalens design method according to claim 7, characterized in that: The grating element arrangement rule is set as follows: the grating elements are arranged radially from the center of the metasurface to the surrounding areas, the distance between all grating elements located in the first area and the center of the metasurface has a first average distance, and the total number of grating elements located in the first area is positively correlated with the first average distance.

10. The multi-focal point vector metalens design method according to claim 9, characterized in that: The grating element arrangement rule is set as follows: the grating elements are arranged radiating from the center of the metasurface in a first shape to the surrounding areas; wherein the first shape is a polygon or a ring.

11. The multi-focal point vector metalens design method according to claim 9, characterized in that: The grating element arrangement rule is set as follows: the grating elements are arranged in a ring-shaped manner from the center of the metasurface to the surrounding areas, and the distance between all grating elements located in the second area and the center of the metasurface has a second average distance, and the second average distance is greater than the first average distance; The grating element arrangement rule further sets: the radial period of the grating elements in the first region is greater than the radial period of the grating elements in the second region, or the circumferential period of the grating elements in the first region is greater than the circumferential period of the grating elements in the second region, or the radial period of the grating elements in the first region is greater than the radial period of the grating elements in the second region, and the circumferential period of the grating elements in the first region is greater than the circumferential period of the grating elements in the second region.

12. The multi-focal point vector metalens design method according to claim 7, characterized in that: After the step of "optimizing the structural design information according to the grating element arrangement rule", the multi-focal vector superlens design method further includes: The hypersurface defined by the optimized structural design information is rotated 45 degrees at its geometric center to generate the final design information.

13. The multi-focal point vector metalens design method according to claim 1, characterized in that: The “optimizing and determining the object plane Jones matrix carrying the vector grating phase distribution information under the guidance of the target polarization state” specifically includes: Determine Jones matrix information of a target image plane according to the target polarization state, and determine a target function according to a difference between the Jones matrix information of the target image plane and the target polarization state; The current object plane Jones matrix information is optimized based on a vector iterative Fourier algorithm until the objective function converges, and the final object plane Jones matrix information is determined.

14. A multi-focal vector metalens, characterized in that: A grating element structure is configured to be set according to the overall phase distribution design information generated by the multi-focal point vector metalens design method according to any one of claims 1 to 13; the metalens also includes a substrate connected to the grating element structure, a filler connected to the grating element structure, and an anti-reflection film arranged on the substrate or at the filler or at both the substrate and the filler, the anti-reflection film comprising a first material layer and a second material layer.

15. An optical system, characterized in that: include: The multi-focal point vector metal lens of claim 14, and a light sensor for converting a light signal modulated and outputted from one side of the multi-focal point vector metal lens into an electrical signal.

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