Multi-focus vector super lens, design method and optical system

Abstract

The invention discloses a multi-focus vector superlens, a design method and an optical system, and the design method comprises the steps: obtaining the Jones matrix information of a current object plane and the Jones matrix information of a target image plane, and determining a target function according to the difference between the Jones matrix information of the current object plane and the Jones matrix information of the target image plane; optimizing the current object plane Jones matrix information based on an iterative Fourier algorithm until the objective function converges, and fixing final object plane Jones matrix information; and according to the final object plane Jones matrix information, calculating final design information of the multi-focus vector super lens. According to the design method, the physical concept of polarization state regulation and control can be introduced, the requirement for the holographic function of the vector super-lens is met, and the design scheme can be rapidly determined.

Description

Technical Field

[0001] The present invention relates to the field of optical imaging technology, and in particular to a multi-focal vector super lens, a design method and an optical system. Background Art

[0002] Metasurface optical devices are widely used in the field of optical imaging due to their advantages of small size, multiple functions, and easy integration, and 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, and are suitable for vector beam shaping, compact polarization beam splitters, full Stokes parameter measurement, three-dimensional structured light generation, and multi-photon quantum entangled state detection and reconstruction.

[0003] Nanostructures are arranged on the side of the metasurface optical device according to a certain phase distribution; in the field of computational holography, a phase recovery algorithm can be used to determine the object plane phase distribution that meets certain requirements in order to design a corresponding metalens. However, in the scenario of optimization based on different incident polarization responses, the traditional phase recovery algorithm simply superimposes the holographic phases regulated by different polarization states, and cannot truly achieve flexible and dynamic polarization state regulation. Summary of the invention

[0004] One of the purposes of the present invention is to provide a multi-focal point vector metalens design method to solve the technical problem that the metalens design method in the prior art cannot truly achieve polarization state regulation, resulting in poor response effect of the designed metalens to polarized light.

[0005] One of the objectives of the present invention is to provide a multi-focal point vector metalens.

[0006] One of the objects of the present invention is to provide an optical system.

[0007] To achieve one of the above-mentioned purposes of the invention, an embodiment of the present invention provides a multi-focal point vector metalens design method, comprising: obtaining the Jones matrix information of the current object plane and the Jones matrix information of the target image plane, and determining the objective function according to the difference between the two; optimizing the current object plane Jones matrix information based on an iterative Fourier algorithm until the objective function converges and fixing the final object plane Jones matrix information; and calculating the final design information of the multi-focal point vector metalens according to the final object plane Jones matrix information.

[0008] As a further improvement of an embodiment of the present invention, the "optimizing the current object plane Jones matrix information based on the iterative Fourier algorithm" specifically includes: determining the gradient constraint factor based on the total phase factor in the current object plane Jones matrix; optimizing the current object plane Jones matrix information based on the iterative Fourier algorithm, and gradient updating the gradient constraint factor after each iteration.

[0009] As a further improvement of an embodiment of the present invention, the gradient constraint factor is a derivative of the objective function with respect to the total phase factor.

[0010] As a further improvement of an embodiment of the present invention, the objective function is the Euclidean distance between the Jones matrix of the current object plane and the Jones matrix of the target image plane.

[0011] As a further improvement of an embodiment of the present invention, the target image plane Jones matrix information carries at least one of Stokes parameter, Mueller matrix information and scattering matrix information under the target polarization state.

[0012] As a further improvement of an embodiment of the present invention, the target image plane matrix information carries ellipticity information and / or azimuth information under the target polarization state; the "obtaining the current object plane Jones matrix information and the target image plane Jones matrix information, and determining the objective function based on the difference between the two" specifically includes: obtaining the ellipticity information and azimuth information under n kinds of target polarization states, and constructing n groups of global Jones matrices corresponding to the Poincare sphere in the xOy coordinate system based on the n groups of ellipticity information and azimuth information; determining the objective function based on the difference between the current object plane Jones matrix information and the global Jones matrix.

[0013] As a further improvement of an embodiment of the present invention, the n target polarization states are configured to form a regular polyhedron on the Poincare sphere.

[0014] As a further improvement of an embodiment of the present invention, the n target polarization states include a circular polarization state, a first elliptical polarization state, a second elliptical polarization state and a third elliptical polarization state.

[0015] As a further improvement of an embodiment of the present invention, n=4.

[0016] As a further improvement of an embodiment of the present invention, the "obtaining the current object plane Jones matrix information and the target image plane Jones matrix information, and determining the objective function based on the difference between the two" specifically includes: using the Jones matrix of the current superlens corresponding to each diffraction order under the linear polarization basis vector on one side of the object plane as the current object plane Jones matrix information, calculating the difference between it and n groups of target image plane Jones matrices, and determining n groups of objective functions for each diffraction order; wherein the n groups of target image plane Jones matrices correspond to n polarization states; the "optimizing the current object plane Jones matrix information based on the iterative Fourier algorithm until the objective function converges and the final object plane Jones matrix information is fixed" specifically includes: based on the vector iterative Fourier algorithm, forward and backward propagation is performed between the object plane and the image plane, optimizing the current object plane Jones matrix until all objective functions converge, and fixing the final object plane Jones matrix information.

[0017] As a further improvement of an embodiment of the present invention, before the step of "taking the Jones matrix of the current metalens corresponding to each diffraction order under the linear polarization basis vector on one side of the object plane as the Jones matrix information of the current object plane", the multi-focal point vector metalens design method also includes: obtaining the rotation angle of the grating element at the current metalens, and constructing an object plane rotation matrix; obtaining at least the first phase delay of the current metalens in the x-polarization direction and the second phase delay in the y-polarization direction, and constructing an object plane Jones vector; and constructing the current object plane Jones matrix according to the object plane rotation matrix and the object plane Jones vector.

[0018] As a further improvement of one embodiment of the present invention, the "constructing an object plane rotation matrix" specifically includes: constructing a first rotation matrix and a second rotation matrix according to the rotation angle and its inverse; the "constructing the current object plane Jones matrix according to the object plane rotation matrix and the object plane Jones vector" specifically includes: constructing the current object plane Jones matrix according to the dot product of the first rotation matrix, the object plane Jones vector and the second rotation matrix.

[0019] As a further improvement of an embodiment of the present invention, the rotation angle is the angle between the direction of the grating element and the x-polarization direction.

[0020] As a further improvement of an embodiment of the present invention, the "calculating the final design information of the multi-focal point vector metalens according to the final object plane Jones matrix information" specifically includes: linearly superimposing the final object plane Jones matrix with the lens phase distribution to determine the overall Jones matrix; performing matrix decomposition on the overall Jones matrix to obtain a Jones decomposition matrix as an overall phase distribution function; wherein the Jones decomposition matrix includes an updated phase delay; and determining the overall design information of the multi-focal point vector metalens according to the overall phase distribution function.

[0021] As a further improvement of an embodiment of the present invention, the "determining the overall design information of the multi-focal point vector superlens according to the overall phase distribution function" specifically includes: retrieving the multi-focal point vector superlens structure parameter library according to at least the phase delay information and rotation angle information carried by the overall phase distribution function, and obtaining the structural design information corresponding to the grating primitive structure; calculating the final polarization degree and the final polarization angle according to the Stokes parameters corresponding to the Jones decomposition matrix.

[0022] As a further improvement of an embodiment of the present invention, before the step of "retrieving a multi-focal point vector superlens structure parameter library at least according to the phase delay information and rotation angle information carried by the overall phase distribution function to obtain structural design information corresponding to the grating primitive structure", the multi-focal point vector superlens design method also includes: implementing rigorous coupled wave analysis equipped with a full analytical Fourier transform to scan a number of superlenses, constructing a number of standard Jones matrices according to the corresponding complex amplitude information, associating the grating primitive structure of the superlens with the corresponding standard Jones matrix, and constructing a multi-focal point vector superlens structure parameter library; wherein the grating primitive structure is a standard three-dimensional structure.

[0023] As a further improvement of an embodiment of the present invention, the "calculating the final polarization degree and the final polarization angle according to the Stokes parameters corresponding to the Jones decomposition matrix" specifically includes: calculating the final ellipticity information and the final azimuth information corresponding to the Poincare sphere according to the Jones decomposition matrix; calculating the first Stokes parameter, the second Stokes parameter, the third Stokes parameter and the fourth Stokes parameter according to the final ellipticity information and the final azimuth information; wherein the first Stokes parameter is the total incident light intensity, the second Stokes parameter is the intensity difference between the x-polarization component and the y-polarization component, the third Stokes parameter is the intensity difference between the first angle polarization component and the second angle polarization component, and the fourth Stokes parameter is the intensity difference between the left-handed circular polarization component and the right-handed circular polarization component; calculating the linear polarization degree according to the first Stokes parameter, the second Stokes parameter and the third Stokes parameter; calculating the circular polarization degree according to the first Stokes parameter and the fourth Stokes parameter; calculating the polarization angle information according to the second Stokes parameter and the third Stokes parameter.

[0024] To achieve one of the above-mentioned purposes of the invention, an embodiment of the present invention provides a multi-focal point vector metalens, wherein the image side surface and / or the object side surface of the multi-focal point vector metalens is arranged with a grating element structure; the grating element structure is configured according to the final design information fixed by the multi-focal point vector metalens design method described in any of the above-mentioned technical solutions.

[0025] To achieve one of the above-mentioned purposes of the invention, one embodiment of the present invention provides an optical system, comprising: the above-mentioned multi-focal point vector super lens, and an optical sensor for converting the optical signal modulated and outputted from one side of the multi-focal point vector super lens into an electrical signal.

[0026] Compared with the prior art, the multi-focal point vector metalens design method provided by the present invention calculates the metalens design information based on the Jones matrix, and can introduce the physical concept of polarization state regulation into the metalens design process, so that the designed metalens can have better polarization performance; since the image plane Jones matrix is ​​set as the target and the iterative Fourier algorithm is implemented to optimize the object plane Jones matrix, it can adapt to the relatively complex vector metalens holographic function requirements and quickly determine the final design information. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is a schematic diagram of the structure of an optical system in one embodiment of the present invention.

[0028] Figure 2 Schematic diagram of the structure of a multi-focal point vector superlens in one embodiment of the present invention.

[0029] Figure 3 It is a schematic structural diagram of a multi-focal point vector superlens in another embodiment of the present invention.

[0030] Figure 4 Schematic diagram of the steps of a multi-focal point vector metalens design method in one embodiment of the present invention.

[0031] Figure 5 It is a flowchart of an iterative Fourier algorithm in one embodiment of the present invention.

[0032] Figure 6 It is a schematic diagram of the changes in dichroism and focal uniformity during the iteration process of the multi-focal point vector superlens design method in the prior art and one embodiment of the present invention.

[0033] Figure 7 1 is a schematic diagram of the steps of an embodiment of a method for designing a superlens in one embodiment of the present invention.

[0034] Figure 8 It is a schematic diagram of the Poincare sphere involved in constructing the far-field Jones matrix in one embodiment of the present invention.

[0035] Fig. 9 It is a schematic diagram of the Poincare sphere and K-space distribution in other embodiments of the present invention.

[0036] Fig.10 1 is a schematic diagram of the steps of another embodiment of a method for designing a superlens in one embodiment of the present invention.

[0037] Fig.11Schematic diagram of the Poincare sphere when the number of polarization states is 4 in one embodiment of the present invention.

[0038] Fig.12 It is a schematic diagram of imaging when the number of polarization states is 4 in one embodiment of the present invention.

[0039] Fig.13 Schematic diagram of the Poincare sphere when the number of polarization states is 6 in one embodiment of the present invention.

[0040] Fig.14 It is a schematic diagram of imaging when the number of polarization states is 6 in one embodiment of the present invention.

[0041] Fig.15 It is a schematic diagram of some steps of a method for designing a superlens in another embodiment of the present invention.

[0042] Fig.16 It is a schematic diagram of the grating element structure in one embodiment of the present invention.

[0043] Fig.17 Schematic diagram of the relationship between four elements in the Jones matrix according to one embodiment of the present invention.

[0044] Fig.18 1 is a schematic diagram of some steps of another embodiment of a method for designing a superlens in one embodiment of the present invention.

[0045] Fig.19 It is a schematic diagram of the relationship between the overall phase distribution, lens phase distribution and multi-focal point vector metalens in one embodiment of the present invention.

[0046] Fig. 20 It is a schematic diagram of the relationship between the final object plane Jones matrix and the corresponding grating primitive structure in one embodiment of the present invention.

[0047] Fig.21 It is a characteristic diagram of the Bloch boundary scan of the grating element structure in one embodiment of the present invention.

[0048] Fig. 22 1 is a schematic diagram of some steps of another embodiment of a method for designing a metalens in one embodiment of the present invention.

[0049] Fig.23 It is a schematic diagram of imaging of a corresponding multi-focal point vector metalens under incident light in the x-polarization direction or non-polarized light in one embodiment of the present invention.

[0050] Fig.24 It is a schematic diagram of imaging of the optimized multi-focal point vector superlens in the prior art and one embodiment of the present invention.

[0051] Fig.25 It is a schematic diagram of the regional arrangement of the grating element structure in one embodiment of the present invention.

[0052] Fig.26 It is a schematic diagram of the periodic arrangement of the grating element structure in the first embodiment of the present invention.

[0053] Fig. 27 It is a schematic diagram of the periodic arrangement of the grating element structure in the second embodiment of the present invention.

[0054] Fig.28 It is a schematic diagram of the periodic arrangement of the grating element structure in the third embodiment of the present invention.

[0055] Fig.29 It is a schematic diagram of parameter relationships generated by optimizing design information determined by a multi-focal point vector superlens design method in one embodiment of the present invention.

[0056] Fig.30 It is a schematic diagram of the relationship between transmittance and incident angle formed by carrying optimized design information in one embodiment of the present invention. DETAILED DESCRIPTION

[0057] The present invention will be described in detail below in conjunction with the specific embodiments shown in the accompanying drawings. However, these embodiments do not limit the present invention, and any structural, methodological, or functional changes made by a person skilled in the art based on these embodiments are all within the scope of protection of the present invention.

[0058] It should be noted that the term "comprises" or any other variation thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device that includes a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In addition, the terms "first", "second", etc. are used for descriptive purposes only and cannot be understood as indicating or implying relative importance.

[0059] One embodiment of the present invention provides an optical system, such as Figure 1 As shown. The optical system can be used for polarization imaging, and is specifically used to obtain the intensity information of the object light, and to extract and analyze the polarization information carried therein, so as to identify the material, internal stress and defects of the object. The optical system provided by the present invention can at least be adapted to the following application scenarios:

[0060] (1) Clearly image objects in strong interference environments such as the atmosphere, underwater, and foggy weather, eliminating the influence of stray light;

[0061] (2) Applied to radio telescope imaging systems, clearly recording the magnetic field environment outside the black hole image in a complex cosmic environment;

[0062] (3) Applied in face recognition scenarios, it can effectively distinguish between human faces and artificial masks, improving the security performance of consumer electronics.

[0063] Polarization imaging can be divided into time-sharing rotation imaging technology, aperture-sharing polarization imaging technology, amplitude-sharing imaging technology and focal plane-sharing imaging technology according to the technical route. The optical system provided by the present invention preferably adopts amplitude-sharing imaging technology, which has the advantage of high-speed real-time acquisition and processing of target polarization information, and can be widely used in military and industrial fields.

[0064] The optical system includes a multi-focal point vector metal lens 100, which is used to realize at least one of the functions of multi-polarization state beam splitting and polarization analysis and multi-focal point lens focusing. Preferably, through the improved multi-focal point vector metal lens design method, the performance parameters such as diffraction efficiency, field of view, uniformity, polarization extinction ratio, etc. of the multi-focal point vector metal lens 100 can be simultaneously enhanced to construct a lightweight and efficient optical system; in one embodiment, the optical system is a polarization imaging module.

[0065] The image side surface and / or the object side surface of the multi-focal vector metal lens 100 are arranged with nanostructures. When the multi-focal vector metal lens 100 is configured to realize the multi-focal focusing and polarization state beam splitting and polarization analysis functions, such nanostructures can be defined as follows: Figure 2 , Figure 3 The grating cell structure 11 is shown.

[0066] In one embodiment, the image side surface of the multi-focal point vector metalens 100 is arranged with a grating primitive structure; the grating primitive structure is configured according to the final design information fixed by a multi-focal point vector metalens design method. In one embodiment, the object side surface of the multi-focal point vector metalens 100 is arranged with a grating primitive structure; the grating primitive structure is configured according to the final design information fixed by a multi-focal point vector metalens design method. In one embodiment, both the image side surface and the object side surface of the multi-focal point vector metalens 100 are arranged with a grating primitive structure.

[0067] The above-mentioned multi-focal point vector metalens design method can be configured according to any of the technical solutions described below, so as to utilize the multi-focal point vector metalens to replace the separated optical devices in the traditional polarization imaging system, and provide a polarization imaging system with high integration and high efficiency; in the design process, based on the polarization response analysis of multi-degree-of-freedom metasurface devices, it can provide the needs of rapid optimization and physical-driven iteration of large-size metasurface devices, thereby improving the diffraction efficiency.

[0068] The optical system includes a light sensor 200, which is used to convert the light signal modulated and outputted from one side of the multi-focal vector metal lens 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 multi-focal vector metal lens 100, which are modular functional devices, can together form a simple, compact, low-cost, and easy-to-prepare optical system.

[0069] In addition, the multi-focal vector superlens 100 can be packaged with the light sensor 200 in an imaging module, and the imaging module can have a smaller size than the prior art, for example, less than 5 mm, thereby reducing the volume of the polarization imaging system.

[0070] The nanostructures such as the grating element structure 11 provided by the present invention can be prepared by micro-nano technology. The multi-focal vector super lens 100 is designed based on silicon material. Since it has lower absorption loss and higher refractive index in the near-infrared band window, the design of the multi-focal vector super lens 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.

[0071] In addition, the nanostructures can be formed into a columnar shape and have a sub-wavelength size. The basic shape formed by the nanostructure projected onto one side of the substrate can be extended from a circle, a round hole, a square, a square hole, etc. to a free geometric figure. The substrate can be a glass substrate or a silicon substrate, and the structures can include air, glue, silicon oxide, silicon nitride and other materials as filling materials.

[0072] In the process of simulating and designing the optical path, or forming an optical system or an imaging system, a basic light source may be provided on one side of the object side surface of the multi-focal vector metalens 100. The basic light source includes, but is not limited to, LED (Light-Emitting Diode), EEL (Edge-Emitting Laser), VCSEL (Vertical Cavity Surface Emitting Laser), light exciter, etc.; of course, natural light may also be used as the basic light source.

[0073] On the one hand, the multi-focal vector metalens designed according to the method provided below can support various application scenarios such as visible light and mid-infrared, which are not exhaustive in the present invention. On the other hand, in the process of simulating and designing the optical path, or executing the multi-focal vector metalens design method provided below, various existing lighting devices such as visible light and mid-infrared can be used as light sources, which are not exhaustive in the present invention.

[0074] Figure 2 Four structural configurations of multi-focal vector metalens 100 are provided.

[0075] like Figure 2 As shown in (a), in this embodiment, a double-piece multi-focal vector superlens 100 is provided, each of which includes a substrate 10 and a grating element structure 11 (i.e., a nanostructure) for forming a supersurface, and can be aligned and bonded by gluing.

[0076] like Figure 2 As shown in (b), in this embodiment, a monolithic multi-focal vector superlens 100 is provided, having two groups of grating elementary structures 11 (i.e., nanostructures) for forming a supersurface, which are arranged on the same substrate 10 and are respectively located on the object side surface and the image side surface.

[0077] like Figure 2 As shown in (c), in this embodiment, a double-piece multi-focal vector metal lens 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 a filter 12 is arranged at least on the image side surface of the multi-focal vector metal lens 100 close to the light sensor side. The filter 12 can be formed by a nanostructure arranged at the substrate 10, or by coating.

[0078] like Figure 2 As shown in (d), in this embodiment, a monolithic multi-focal 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 at the substrate 10, or can be formed by coating.

[0079] In addition, the optical system and the metasurface formed by the grating element structure 11 in the multi-focal vector metalens 100 are coaxial systems; corresponding to functions such as single-focal convergence or multi-focal convergence, the multi-focal vector metalens 100 can be realized by designing a metasurface or by configuring a traditional lens. Other devices can also be added to the optical system to improve the function, such as by setting a fisheye lens on one side of the object side surface to increase the field of view.

[0080] Figure 3A preferred embodiment of a multi-focal point vector metalens 100 is provided. The multi-focal point vector metalens 100 includes a grating unit cell structure 11, a substrate 10 connected to the grating unit cell structure 11, a filler 13 connecting the grating unit cell 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.

[0081] Specifically, one set of anti-reflection films 14 covers the surface of the filler 13 away from the substrate 10, and the other set of anti-reflection films 14 covers the surface of the substrate 10 away from the grating element structure 11. Figure 1 and Figure 2 As shown in (d), the object side surface (light incident side) and the image side surface (light exiting side) of the multi-focal point vector metalens 100 are both covered with an anti-reflection film 14; in the embodiment in which the filter 12 is provided, the anti-reflection film 14 located on one side of the substrate 10 can be provided between the filter 12 and the substrate 10. By providing the anti-reflection film 14, the reflectivity can be reduced and the transmittance can be increased, thereby improving the diffraction order efficiency, suppressing the zero-order diffraction, and thus improving the efficiency of the multi-focal point vector metalens 100.

[0082] The anti-reflection 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, and the second material layer 142 is preferably made of silicon oxide, so that the high transmittance requirement when the light beam is incident at a large angle can be met.

[0083] Among them, 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 side of the object side surface, the filler 13 can be connected to the first material layer 141 or the second material layer 142; on the side of 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, according to the preparation materials of the substrate 10 and the filler 13, a suitable material layer can be selected to be connected thereto. For example, when the substrate 10 and the filler 13 are both prepared by silicon oxide, the first material layer 141 prepared by silicon nitride can be connected to the substrate 10 and the filler 13, and the second material layer 142 is connected to the outside of the first material layer 141.

[0084] In one embodiment, the antireflection film 14 on both sides of the grating unit 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, so as to obtain the optimal metasurface efficiency.

[0085] In one embodiment, the anti-reflection film 14 on both sides of the grating unit structure 11 is provided with a second material layer 142, a first material layer 141, a second material layer 142 and a first material layer 141 in sequence from the outside to the inside (one 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. Thereby, the optimal metasurface efficiency is obtained.

[0086] like Figure 4 As shown, one embodiment of the present invention provides a multi-focal point vector metalens design method, which specifically includes the following steps.

[0087] Step S1, obtaining Jones matrix information of the current object plane and Jones matrix information of the target image plane, and determining the objective function according to the difference between the two.

[0088] Step S2, optimizing the current object plane Jones matrix information based on the iterative Fourier algorithm until the objective function converges, and fixing the final object plane Jones matrix information.

[0089] Step S3, calculating the final design information of the multi-focal vector superlens according to the final object plane Jones matrix information.

[0090] In this way, compared with the traditional scalar iterative Fourier algorithm for optimizing the phase distribution function of the object plane, which can only be performed by linearly superimposing multiple groups of holographic phases controlled by different polarization states, and cannot truly reflect the current physical concept of polarization state control, the iterative Fourier algorithm provided by the present invention breaks through the technical barriers, takes the Jones matrix of the object plane as the optimization object, and continuously optimizes and iterates according to the relationship between the Jones matrices at the object plane and the image plane, which can fully reflect the physical concept of polarization state control.

[0091] Furthermore, the multi-focal point vector metalens design method provided by the present invention can ultimately optimize the design information corresponding to the multi-focal point vector metalens having high focusing efficiency, high focal uniformity, high extinction ratio, and sufficient suppression of zero-order diffraction and having a large bandwidth by adjusting hyperparameters such as learning rate and learning rate reduction parameters in the iterative Fourier algorithm.

[0092] Combination Figure 5As shown in FIG. 1 , when executing the multi-focal vector metalens design method provided by the present invention, firstly, on the object plane side, the object plane Jones matrix J(x, y) is constructed according to the initialized grating primitive structure (i.e., the metasurface), and on the far field side (i.e., the image plane), the target image plane Jones matrix A(k x ,k y ), first forward propagation and determine the difference between the two according to the objective function, iteratively update the image plane Jones matrix A′(k x ,k y ), and then back-propagation updates the object plane Jones matrix J′(x,y), and repeats this process until the objective function converges and the final object plane Jones matrix is ​​determined.

[0093] In one implementation, the step S2 of "optimizing the Jones matrix information of the current object plane based on an iterative Fourier algorithm" may specifically include the following steps.

[0094] Step S21, determining a gradient constraint factor according to the total phase factor in the Jones matrix of the current object plane.

[0095] Step S22, optimizing the Jones matrix information of the current object plane based on an iterative Fourier algorithm, and performing a gradient update on the gradient constraint factor after each iteration.

[0096] In this way, a gradient descent constraint can be introduced into the iterative Fourier algorithm to improve the convergence stability and avoid falling into a local optimal solution or a non-convergent result. Specifically, the gradient constraint factor can be determined according to the gradient of the objective function during the iteration process, which can further enhance the physical constraint capability of the iterative Fourier algorithm to improve the stability of the optimization solution while ensuring the calculation speed.

[0097] Figure 6 (a) shows the relationship between dichroism and focus uniformity (UE) as the iteration progresses in the prior art. Figure 6 (b) shows the relationship between the dichroism and focal uniformity in the multi-focal point vector metalens design method provided by the present invention as the iterative process develops. It can be seen that the solution provided by the present invention has a faster convergence speed and better convergence characteristics due to the introduction of the gradient descent constraint, and enables the vector iterative Fourier algorithm to have the ability to jump out of the local optimal solution to a certain extent, so as to provide a strong algorithm support for the design of the multi-focal point vector metalens.

[0098] In one embodiment, the gradient constraint factor is the derivative of the objective function with respect to the total phase factor. Specifically, the objective function is defined as FoM, and the total phase factor in the Jones matrix of the current object plane generated during the iteration is Then the gradient constraint factor At least:

[0099]

[0100] After one iteration, the overall phase factor of the current object plane matrix information can be updated as follows:

[0101]

[0102] Among them, α is the gradient learning rate factor.

[0103] In one embodiment, the objective function is the Euclidean distance between the current object plane Jones matrix and the target image plane Jones matrix. In this way, an objective function with good convergence and clear optimization direction can be constructed, which helps to improve the accuracy and speed of iterative operations. The object plane Jones matrix formed in the iterative process on each diffraction order is defined as J(k x ,k y ), then the objective function FoM can at least satisfy:

[0104] FoM=[J(k x ,k y )-A(k x ,k y )] 2 .

[0105] In one embodiment, the configuration of the gradient constraint factor and the objective function can be a combination of the above two embodiments, so as to take into account the advantages of the above two embodiments, have a better phase recovery effect, numerical stability, and can be adapted to polarization state control, and have a wider range of applications. Based on this, the better gradient constraint factor At least:

[0106]

[0107] In one embodiment, the Jones matrix information of the target image plane carries the Stokes parameters under the target polarization state; in one embodiment, the Jones matrix information of the target image plane carries the Mueller matrix information; in one embodiment, the Jones matrix information of the target image plane carries the scattering matrix information.

[0108] Wherein, it is preferred that the target image plane Jones matrix information is constructed based on Stokes parameters. Stokes parameters are used to describe the intensity and polarization state of light waves. Since Stokes parameters are associated with polarization degree and polarization angle, in one embodiment, when constructing the target image plane Jones matrix information, the target polarization degree and target polarization angle can be set first, and the target Stokes parameters corresponding to the target can be reversely derived and solved, and then the target image plane Jones matrix can be reconstructed based on the target Stokes parameters. The relationship described here will be described in detail below and will not be repeated here.

[0109] The Stokes parameter may include a first Stokes parameter S0, a second Stokes parameter S1, a third Stokes parameter S2 and a fourth Stokes parameter S3. The first Stokes parameter S0 is used to describe the total incident light intensity; the second Stokes parameter S1 is used to describe the light intensity difference between the x polarization component and the y polarization component; the third Stokes parameter S2 is used to describe the light intensity difference between the first angle polarization component and the second angle polarization component; the fourth Stokes parameter S3 is used to describe the light intensity difference between the left circular polarization component and the right circular polarization component. The first angle is +45°; the second angle is -45°.

[0110] Before participating in the calculation, the first Stokes parameter S0, the second Stokes parameter S1, the third Stokes parameter S2 and the fourth Stokes parameter S3 can be normalized respectively; the value range of the normalized first Stokes parameter S0 is between 0 and 1; the value range of the normalized second Stokes parameter S1, the third Stokes parameter S2 and the fourth Stokes parameter S3 is between -1 and +1. For the natural non-polarized scene, the light intensity I in the x-polarization direction x The light intensity I in the y-polarization direction y Equal; +45° polarization component light intensity I +45° , with the polarization component light intensity I at an angle of -45° -45° Equal; left-handed circularly polarized component light intensity I l The right circular polarization component light intensity I r In other words, if the values ​​of the first Stokes parameter S0, the second Stokes parameter S1, the third Stokes parameter S2 and the fourth Stokes parameter S3 are not 0, it proves that polarized light exists.

[0111] The mechanism of action of Stokes parameters is to realize calculation by measuring the intensity of light in different polarization components, including total intensity, linear polarization components in horizontal and vertical directions, and circular polarization components. The mechanism of action of Mueller matrix is ​​to assist in light path simulation and design by describing the change of polarization state of light passing through optical elements. The mechanism of action of scattering matrix is ​​to assist in optical design by describing the scattering process when electromagnetic waves interact with particles or interfaces, providing the relationship between incident waves and scattered waves. You can choose according to your needs in actual operation.

[0112] The Stokes parameter is reflected on the Poincare sphere side and can be described and fixed using ellipticity and azimuth. Therefore, the ellipticity information and azimuth information referred to in the following text can be interpreted as a kind of Stokes parameter.

[0113] In one embodiment, the Jones matrix of the target image plane carries the ellipticity information of the target polarization state; in one embodiment, the Jones matrix of the target image plane carries the azimuth information of the target polarization state; in one embodiment, the Jones matrix of the target image plane carries both the ellipticity information and the azimuth information of the target polarization state. In this way, the complete characteristics of polarized light can be better described, and the key information of the target polarization state on the wavefront shape and polarization state of polarized light can be provided.

[0114] In one embodiment, Figure 7 As shown, the multi-focal point vector super lens design method specifically includes the following steps.

[0115] Step S11, obtaining ellipticity information and azimuth information under n target polarization states, and constructing n groups of global Jones matrices corresponding to the Poincare sphere in the xOy coordinate system according to the n groups of ellipticity information and azimuth information.

[0116] Step S12, determining the objective function according to the difference between the current object plane Jones matrix information and the global Jones matrix.

[0117] Step S2, optimizing the current object plane Jones matrix information based on the iterative Fourier algorithm until the objective function converges, and fixing the final object plane Jones matrix information.

[0118] Step S3, calculating the final design information of the multi-focal vector superlens according to the final object plane Jones matrix information.

[0119] In this way, the polarization state can be expressed more intuitively and comprehensively based on the Poincare sphere, and according to the correlation of the characteristic points on the surface of the Poincare sphere corresponding to different polarization states, the multi-focal vector superlens can be more conveniently designed and optimized to achieve the desired polarization state regulation or analysis.

[0120] Figure 8For the simulated Poincare sphere, different polarization states correspond to different characteristic points on the Poincare sphere. In the scenario of drawing the polarization state, the ellipticity χ and the azimuth ψ can be used to describe the coordinates of the points on the Poincare sphere surface and inside the sphere, and then describe the polarization state.

[0121] The radius of the Poincare sphere is determined by the polarization degree of the incident light, and its maximum value is 1, corresponding to completely polarized light. The azimuth angle ψ, also known as the orientation angle, is between ±90° and can be measured from the S1 axis. The ellipticity χ is between ±45° and can be measured from the equator of the Poincare sphere. Points at the equator of the Poincare sphere represent linear polarization states, points at the two poles of the Poincare sphere represent circularly polarized light, and points at other positions on the spherical surface of the Poincare sphere represent other elliptically polarized light.

[0122] The ellipticity information of each diffraction order is defined as χ(k x ,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:

[0123] A(k x ,k y )=|α * (k x ,k y )><α(k x ,k y )|.

[0124] 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 )> is the conjugate transpose vector of .

[0125] Among them, the Jones matrix vector |α(k x ,k y )>At least:

[0126]

[0127] Among them, the rotation matrix R(ψ(k x ,ky ))At least:

[0128]

[0129] 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:

[0130]

[0131] J xOy (x,y)=F -1 (A(k x ,k y )).

[0132] In this way, the vector iterative inverse Fourier transform is performed on the target image plane Jones matrix to obtain the global Jones matrix J xOy (x, y), based on the ellipticity information χ, the azimuth information ψ and its own matrix decomposition form, it is possible to establish a corresponding relationship with the current object plane Jones matrix information to achieve iterative optimization and update. In one embodiment, the current object plane Jones matrix is ​​a description form based on the electric field under the linear polarization basis vector, carrying a phase delay or a combination of phase delay and transmittance, so the corresponding parameters can be iteratively updated to continuously optimize the current object plane Jones matrix.

[0133] On the one hand, the object optimized by the 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] On the other hand, the number of target polarization states n can be adaptively adjusted according to the requirements of accuracy, lens focusing, etc. Fig. 9 As shown, the upper row is the Poincare sphere corresponding to several target polarization state configuration schemes, and the lower row is a schematic diagram of the corresponding K space distribution. 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.

[0135] When n=4, the four target polarization states may include one circular polarization state and three elliptical polarization states. Specifically, the characteristic point pointed by the circular polarization state and the characteristic points pointed by the three elliptical polarization states (the first elliptical polarization state, the second elliptical polarization state and the third elliptical polarization state) are located on both sides of the equator. Preferably, the corresponding characteristic points are connected to form a regular tetrahedron.

[0136] When n=6, the six target polarization states may include two circular polarization states and four linear polarization states. Specifically, the characteristic points pointed to by the two circular polarization states are located at the two poles of the Poincare sphere, and the characteristic points pointed to by the four linear polarization states are located at the equator of the Poincare sphere, and are evenly spaced. Preferably, the corresponding characteristic points are connected and surrounded to form a regular octahedron.

[0137] When n=8, the eight target polarization states can all be elliptical polarization states. Specifically, the characteristic points pointed to by four of the elliptical polarization states correspond to the characteristic points pointed to by the other four elliptical polarization states on both sides of the equator. Preferably, the corresponding characteristic points are connected to form a regular hexahedron.

[0138] When n=12, the 12 target polarization states may include eight elliptical polarization states and four linear polarization states. Specifically, the characteristic points pointed to by the four elliptical polarization states correspond to the characteristic points pointed to by the other four elliptical polarization states on both sides of the equator; the characteristic points pointed to by the four linear polarization states are located at the equator of the Poincare sphere and are evenly spaced. Preferably, the corresponding characteristic points are connected to form a regular icosahedron.

[0139] When n=20, the 20 target polarization states may include 16 elliptical polarization states and four linear polarization states. Specifically, the characteristic points pointed to by eight of the elliptical polarization states and the characteristic points pointed to by the other eight elliptical polarization states are located on both sides of the equator and correspond to each other; the characteristic points pointed to by the four linear polarization states are located at the equator of the Poincare sphere and are evenly spaced. Preferably, the corresponding characteristic points are connected and arranged to form a regular dodecahedron.

[0140] In the technical solution provided by the present invention, preferably n = 4. In this way, higher reconstruction accuracy can be achieved and the computational burden is smaller.

[0141] In one embodiment, the (0, 1) diffraction order can be set to a right-handed polarization state |α(ψ0=0°, χ0=45°)>; the (-1, 0) diffraction order can be set to an elliptical polarization state |α(ψ0=60°, χ0=-9.73°)>; the (0, -1) diffraction order can be set to an elliptical polarization state |α(ψ0=0°, χ0=-9.73°)>; the (1, 0) diffraction order can be set to an elliptical polarization state |α(ψ0=120°, χ0=-9.73°)>.

[0142] In one embodiment, if Fig.10 As shown, the multi-focal point vector super lens design method provided by the present invention specifically includes the following steps.

[0143] Step S10, using the Jones matrix of the current metalens corresponding to each diffraction order under the linear polarization basis vector on one side of the object plane as the current object plane Jones matrix information, calculating the difference between it and n groups of target image plane Jones matrices, and determining n groups of target functions corresponding to each diffraction order.

[0144] Step S20, based on the vector iterative Fourier algorithm, forward and backward propagation is performed between the object plane and the image plane to optimize the current object plane Jones matrix until all objective functions converge and the final object plane Jones matrix information is fixed.

[0145] Step S3, calculating the final design information of the multi-focal vector superlens according to the final object plane Jones matrix information.

[0146] Among them, n groups of target image plane Jones matrices correspond to n polarization states.

[0147] In this way, the fixed final object plane Jones matrix information can be regarded as being able to simultaneously meet the control requirements of n polarization states to support the multi-polarization beam splitting and polarization analysis function, and further applied to extended scenarios of multi-focus vector polarization modules such as super polarization beam splitters.

[0148] Based on this, in one embodiment, when n=4, Fig.11 The distribution of characteristic points of four polarization states corresponding to the Poincare sphere is shown, including a circular polarization state Port10, a first elliptical polarization state Port11, a second elliptical polarization state Port12 and a third elliptical polarization state Port13.

[0149] Fig.12 (a) shows the pseudo-color image of the first Stokes parameter S0, Fig.12 (b) shows the pseudo-color image of the second Stokes parameter S1, Fig.12 (c) shows a pseudo-color image of the third Stokes parameter S2, Fig.12 (d) shows the pseudo-color image of the fourth Stokes parameter S3. After iterative optimization, when n=4, at least the performance configuration of the average extinction ratio of each diffraction order is 12dB, the focus uniformity is 0.08, the average focusing efficiency of each focus is 90%, and the diffraction angle of each diffraction order is 9.83° can be achieved.

[0150] In another embodiment, n=6, Fig.13 The distribution of characteristic points of four polarization states corresponding to the Poincare sphere is shown, including circular polarization states Port21 and Port26, and elliptical polarization states Port22, Port23, Port24 and Port25.

[0151] Fig.14 (a) shows the pseudo-color image of the first Stokes parameter S0, Fig.14(b) shows the pseudo-color image of the second Stokes parameter S1, Fig.14 (c) shows a pseudo-color image of the third Stokes parameter S2, Fig.14 (d) shows the pseudo-color image of the fourth Stokes parameter S3. After iterative optimization, when n=6, at least the performance configuration of an average extinction ratio of 13 dB for each diffraction order, a focus uniformity of 0.1, and an average focusing efficiency of 90% for each focus can be achieved.

[0152] Specifically, the average extinction ratio is defined as ER, which at least satisfies:

[0153]

[0154] in, is the transmitted light intensity at the mth diffraction order when the mth diffraction order polarization state light is incident; is the transmitted light intensity at the mth diffraction order when the orthogonal polarized light of the mth diffraction order polarization state is incident.

[0155] Specifically, focus uniformity is defined as UE, which at least satisfies:

[0156]

[0157] Among them, Imax is the light intensity value with the maximum light intensity among n focuses (that is, multi-focus focusing; preferably n=4) under the condition of natural light incidence; Imin is the light intensity value with the minimum light intensity among the four focuses under the condition of natural light incidence.

[0158] Specifically, the diffraction angle is defined as θ0, which at least satisfies:

[0159]

[0160] Where λ is the wavelength of the incident light, and p is the period of the grating part in the grating element structure at the metasurface.

[0161] In one embodiment, if Fig.15 As shown, before step S1, especially before step S10, the multi-focal vector superlens design method also includes the following steps.

[0162] Step P1, obtain the rotation angle of the grating element at the current super lens and construct the object plane rotation matrix.

[0163] Step P2, at least obtaining the first phase delay of the current metalens in the x polarization direction and the second phase delay in the y polarization direction, and constructing the Jones vector of the object plane.

[0164] Step P3, constructing the current object plane Jones matrix according to the object plane rotation matrix and the object plane Jones vector.

[0165] In this embodiment, by constructing a Jones matrix in the form of a decomposed matrix under the linear polarization basis vector as the Jones matrix of the current object plane, on the one hand, it is possible to establish a close connection with the phase delay, grating rotation angle or primitive rotation angle, and accurately describe the polarization characteristics of the current grating primitive structure; on the other hand, it is possible to construct an architecture similar to the global Jones matrix, which is convenient for comparison operations and rapid determination and updating of the elements in the Jones matrix of the current object plane.

[0166] Fig.16 Four square columnar nanostructures with different size configurations are shown, which can be used as the grating unit structure; specifically, the four nanostructures have different aspect ratios in the mutually perpendicular x-direction and y-direction. For example, Fig.16 The length and width of the leftmost nanostructure are equal and may both be 150 nm; Fig.16 The width of the nanostructure on the left in the middle in the x direction is smaller than the length in the y direction and may have a length of 250 nm and a width of 150 nm; Fig.16 The middle right nanostructure has a length in the x direction that is greater than its width in the y direction and may have a length of 250 nm and a width of 75 nm; Fig.16 The rightmost nanostructure has a length in the x-direction that is greater than its width in the y-direction and may have a length of 350 nm and a width of 150 nm.

[0167] Fig.16 The rotation angle θ of the grating element structure is also shown. In this embodiment, the angle between the direction of the nanostructure (ie, the grating element) and the x-polarization direction (especially the positive direction thereof) is defined as the rotation angle θ.

[0168] In the figure, the nanostructure (ie, grating element structure) is made of silicon material and the substrate is made of silicon oxide material as an example, but this does not mean that the present invention is limited to this material combination.

[0169] In the process of scanning the grating element structure, the element rotation angle θ is introduced to define the Jones matrix of the current object plane in the linear polarization basis vector based on the electric field as J(x,y), then the phase delay in the x direction is (i.e., the first phase delay) and the y-direction phase delay The object plane Jones vector constructed by the second phase delay is:

[0170]

[0171] The object plane rotation matrix R(θ) constructed according to the rotation angle θ is:

[0172]

[0173] Therefore, the current object plane Jones matrix having a dispersed matrix form and corresponding to the linear polarization basis vector can be fixed based on the Jones vector and the rotation matrix R(θ).

[0174] In one embodiment, the "construction plane rotation matrix" in step P1 may specifically include the steps of: constructing a first rotation matrix and a second rotation matrix according to the rotation angle and its inverse.

[0175] That is, the first rotation matrix can be constructed separately:

[0176] And, the second rotation matrix:

[0177]

[0178] Step P3 specifically includes the steps of: constructing the current object plane Jones matrix according to the dot product of the first rotation matrix, the object plane Jones vector and the second rotation matrix.

[0179] That is, the current object plane Jones matrix J(x,y) in the form of a decomposition matrix under the linear polarization basis vector at least satisfies:

[0180]

[0181] Among them, J xx (x,y),J xy (x,y),J yx (x,y),J yy (x,y) are the four elements in the Jones matrix. The relationship between the elements can be found in Fig.17 Specifically, 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 obtained after the y polarization component of the input light 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 obtained after the y-polarization component of the input light passes through the metalens.

[0182] In one embodiment, if Fig.18 As shown, step S3 specifically includes the following steps.

[0183] Step S31, linearly superimpose the final object plane Jones matrix and the lens phase distribution to determine the overall Jones matrix.

[0184] Step S32, performing matrix decomposition on the overall Jones matrix to obtain a Jones decomposition matrix as the overall phase distribution function.

[0185] Step S33, determining overall design information of the multi-focal point vector metalens according to the overall phase distribution function.

[0186] The Jones decomposition matrix includes updated phase delay and rotation angle.

[0187] In this way, the phase distribution of the vector metagrating carried by the Jones matrix in the final object plane can be superimposed on the phase distribution of the lens to realize the design of a multi-focal vector superlens with multi-polarization state beam splitting and polarization analysis functions and multi-focal lens focusing functions, and the designed multi-focal vector superlens has the advantages of high focusing efficiency, high focal uniformity, high extinction ratio, perfect suppression of zero-order diffraction, and large bandwidth.

[0188] like Fig.19 As shown, the final object plane Jones matrix is ​​defined by J xx (x,y),J xy (x,y),J yx (x,y),J yy If the vector metagrating is composed of (x, y) elements, the linear phase superposition of the lens phase distribution and the final object plane Jones matrix can be performed first, and then the phase distribution of the vector metagrating can be naturally updated and fused. Then, the matrix decomposition can be performed to determine the updated phase delay, so as to further evaluate its difference with the target image plane Jones matrix, so as to finally determine the design information.

[0189] On the one hand, the lens phase distribution It is used to realize the lens focusing function of the metalens itself, especially to realize the multi-focal focusing function. In one embodiment, the lens phase distribution The following steps can be performed to determine: taking the resolution of the optical sensor as a constraint, performing iterative optimization in the optical path optimization platform until the imaging performance and / or resolution of the optical system composed of the optical sensor and the current metalens reaches the set target, and fixing the basic phase distribution information of the current metalens. Wherein, the optical path optimization platform is Zemax; the way to evaluate the imaging performance is to calculate the degree of point convergence in the focusing diagram; the way to evaluate the resolution is to calculate the value of the modulation transfer function.

[0190] where the Jones decomposition matrix corresponding to the overall Jones matrix has the following form:

[0191]

[0192] in, is the first overall phase delay, is the second overall phase delay.

[0193] On the other hand, the means for linear phase superposition of the lens phase distribution and the final object plane Jones matrix can be to perform array element multiplication of the two.

[0194] In one embodiment, the step S33 may further specifically include the following steps.

[0195] Step S331, searching a multi-focal point vector superlens structure parameter library at least according to the phase delay information and rotation angle information carried by the overall phase distribution function, to obtain structural design information corresponding to the grating primitive structure.

[0196] Step S332, calculating the final polarization degree and the final polarization angle according to the Stokes parameters corresponding to the Jones decomposition matrix.

[0197] Of course, the above two steps are not limited to being implemented on the basis of step S33. In other words, even if the linear superposition of the final object plane Jones matrix and the lens phase distribution is not performed, the structural design information can be retrieved and determined, and the final polarization degree and final polarization angle can be calculated based on the final object plane Jones matrix or its decomposition matrix.

[0198] For step S331, combined Figures 19 to 21 , whether based on the phase delay information of the final object plane Jones matrix (e.g., the first phase delay Second phase delay ) and rotation angle information (for example, rotation angle θ) for retrieval, or based on the phase delay information and rotation angle information carried by the overall phase distribution function for retrieval, the fixed structure design information can be matched according to the multi-focus vector superlens structure parameter library.

[0199] In one embodiment, the multi-focal vector super lens structure parameter library is used to construct the relationship between the phase delay or its combination with the rotation angle information and the grating element structure design. In one embodiment, the multi-focal vector super lens structure parameter library is used to construct the relationship between the phase delay or its combination with the transmittance (for example, the first transmittance Tx, the second transmittance Ty) and the grating element structure design.

[0200] In one embodiment, the multi-focal vector metalens structure parameter library is used to construct the relationship between the final object plane Jones matrix or its decomposition matrix and the grating element structure design (especially, the relationship between the grating part structure design). In one embodiment, the multi-focal vector metalens structure parameter library is used to construct the relationship between the overall Jones matrix or its decomposition matrix (that is, the overall phase distribution function) and the grating element structure design.

[0201] In one embodiment, before calling the multi-focal point vector super-lens structure parameter library, especially before the above step S331, the multi-focal point vector super-lens design method may further include:

[0202] Step P0, implement rigorous coupled wave analysis equipped with full analytical Fourier transform to scan several metalenses, construct several standard Jones matrices according to 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.

[0203] Wherein, the grating primitive structure is a standard three-dimensional structure. The standard three-dimensional structure is an elliptical column, a rectangular column, a polygonal column, etc. In the case where the grating primitive structure is a standard three-dimensional structure, its periodic distribution function has a fixed and clear Fourier domain expression, which can not only avoid the discretization of the structure in the Fourier expansion stage, but also further improve the speed of data acquisition and calculation, reduce the calculation pressure, and speed up the preparation time. Specifically, its Fourier domain expression can be obtained by searching an information optics library constructed based on prior information such as information optics textbooks.

[0204] The full-analysis Fourier transform is used to analyze the frequency domain characteristics of complex signals. The full-analysis Fourier transform is used to expand the first periodic distribution function, which can overcome the technical barriers of the traditional discrete Fourier transform (DFT) and fast Fourier transform (FFT) that require discretization processing. It can adapt to the periodic distribution function and the structural characteristics of the grating primitive, implement continuous signal processing, provide the complete amplitude and phase information of the signal in the frequency domain, support the processing of band-limited signals and avoid the processing of negative frequency components.

[0205] Due to the use of rigorous coupled wave analysis (RCWA, Rigorous Coupled-Wave Analysis), 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 in the spatial frequency, which can perform full-wave simulation of periodic structures more accurately and efficiently.

[0206] Fig.21 (a) shows the relationship between the x-direction size Dx of the nanostructure, the y-direction size Dy of the nanostructure and the x-direction transmittance Tx when the x-polarization direction is the incident direction after performing Bloch boundary scanning on the nanostructure; Fig.21(b) shows the relationship between the x-direction size Dx of the nanostructure, the y-direction size Dy of the nanostructure, and the y-direction transmittance Ty when the y-polarization direction is 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 numerical values ​​can be determined by referring to the color depth of the base map at the hexagonal star point in the figure.

[0207] Fig.21 (c) shows the x-direction size Dx, y-direction size Dy and x-direction phase delay of the nanostructure obtained after Bloch boundary scanning when the x-polarization direction is the incident direction. The relationship diagram between Fig.21 (d) shows 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.

[0208] In this way, the first phase delay can be fixed during scanning. Second phase delay After the first transmittance Tx and the second transmittance Ty are determined, the standard Jones matrix is ​​fixed. A single standard Jones matrix corresponds to a single standard superlens, and multiple groups of superlenses are provided as samples for constructing a structural parameter library.

[0209] The function of step S332 can be defined as generating relevant parameters for evaluating the performance of the structural design information while determining the structural design information, so as to facilitate selection and calling.

[0210] In one embodiment, if Fig. 22 As shown, step S332 may specifically include the following steps.

[0211] Step M1, calculating the final ellipticity information and the final azimuth information corresponding to the Poincare sphere according to the Jones decomposition matrix.

[0212] Step M2, calculating the first Stokes parameter, the second Stokes parameter, the third Stokes parameter and the fourth Stokes parameter according to the final ellipticity information and the final azimuth information.

[0213] Step M3, calculating the linear polarization degree of polarization according to the first Stokes parameter, the second Stokes parameter and the third Stokes parameter.

[0214] Step M4, calculating the circular polarization degree according to the first Stokes parameter and the fourth Stokes parameter.

[0215] Step M5, calculating polarization angle information according to the second Stokes parameter and the third Stokes parameter.

[0216] Among them, the first Stokes parameter is the total incident light intensity, the second Stokes parameter is the light intensity difference between the x-polarization component and the y-polarization component, the third Stokes parameter is the light intensity difference between the first angle polarization component and the second angle polarization component, and the fourth Stokes parameter is the light intensity difference between the left-handed circular polarization component and the right-handed circular polarization component.

[0217] In one implementation, the first Stokes parameter S0, the second Stokes parameter S1, the third Stokes parameter S2 and the fourth Stokes parameter S3 may respectively satisfy:

[0218]

[0219] The linear polarization degree of polarization DOLP can at least meet the following requirements:

[0220]

[0221] The circular polarization degree of polarization DOCP can at least meet the following requirements:

[0222]

[0223] Polarization angle information AOP can at least meet the following requirements:

[0224]

[0225] The total degree of polarization information DOP can at least meet the following requirements:

[0226]

[0227] At this point, according to the multi-focal point vector metalens design method provided above, the designed multi-focal point vector metalens can take into account both the functions of multi-polarization state beam splitting and polarization analysis and multi-focal point lens focusing.

[0228] Fig.23 (a) shows the imaging of incident light in the x-polarization direction by the multi-focal vector metalens provided by the present invention in combination with a light sensor; Fig.23 (b) shows the imaging of non-polarized light incident on the multi-focal vector superlens in combination with an optical sensor. The multi-focal vector superlens designed by the present invention can achieve high-precision full Stokes parameter reconstruction, has a larger field of view, less distortion, and can complete multi-focal focusing and real-time polarization imaging.

[0229] Fig.24 (a) shows the imaging situation on one side of the optical sensor when four focal points or multiple focal points thereof are realized in the prior art, corresponding to Fig. 9 The K-space distribution when n=4 is provided. 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 since the light sensors are arranged in the horizontal and vertical directions, this multi-focal spot arrangement will cause a large area waste on one side of the light sensor. However, expanding the number of focal points to 6 or 8 will increase the design difficulty, process complexity and cost.

[0230] Based on this, the multi-focal point vector superlens provided by the present invention, after the step S331, further includes the step of rotating the supersurface defined by the structural design information by 45 degrees about its geometric center, and fixing the rotated structural design information as the lens design information.

[0231] Thus, when the metalens equipped with the lens design information is implemented, it can produce the following Fig.24 In the imaging situation shown in (b), the light spot images can be arranged in a matrix in the horizontal and vertical directions consistent with the light sensor, so that the area of ​​the light sensor can be maximized and the field of view can be expanded. Combined with the design method provided by the present invention, there is almost no zero-order diffraction technology effect, and a pairwise tangent structure can be constructed to further expand the field of view.

[0232] In order to further increase the field of view, the following technical solutions may be used to optimize the design information determined above.

[0233] In one embodiment, the diffraction angle can be increased by reducing the period and using high-order diffraction, thereby increasing the field of view. For example, before optimization, the period of the grating element structure at the multi-focal vector super lens is 11*500nm, with a first-order diffraction angle of 9.84°; after the first optimization, the period can be reduced to 7*500nm, so that the first-order diffraction angle is 15.57°; after the second optimization, high-order diffraction can be introduced, and on the basis of maintaining the period of 7*500nm, it has a second-order diffraction angle of 32.48°.

[0234] In another embodiment, nanostructures such as grating element structures can be configured into a variable period arrangement to improve the edge efficiency of the superlens and increase the transmittance and efficiency under a large field of view.

[0235] Fig.25Three regional arrangement schemes of grating element structures are provided. The distribution of the grating element structures on the object side or image side radiates outward in a fixed shape with a certain point as the center, dividing the side into a number of concentric areas. Preferably, the center is the geometric center of the side. The fixed shape can be as follows: Fig.25 (a) as shown in the rectangular shape, Fig.25 (b) The hexagonal shape or Fig.25 (c) as shown in the circular ring; when the variable period arrangement is implemented, it is preferred to use Fig.25 (c) The circular ring-shaped area arrangement scheme.

[0236] Figure 26 to Figure 28 Three periodic arrangement schemes of grating element structures are provided.

[0237] in, Fig.26 The fixed period arrangement is disclosed. The distances between the grating element structures located in different regions and the radiation center O are different, and the radial period L1 and the circumferential period L2 of the grating element structures located in different regions are the same.

[0238] Fig. 27 The invention discloses a double variable period arrangement. The distances between the grating element structures located in different regions and the radiation center O are different, and the radial period L1 and the circumferential period L2 of the grating element structures located in different regions are different; preferably, the ratios of the radial period L1 and the circumferential period L2 of the grating element structures located in different regions are the same. 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.

[0239] Fig.28 The invention discloses a single variable period arrangement mode, wherein the distances between the grating element structures in different regions and the radiation center O are different, and the circumferential period L2 of the grating element structures in different regions are the same, and the radial period L1 is different. 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.

[0240] In this way, a multi-focal vector metalens with high efficiency and large field of view can be configured to improve the efficiency of the structure at the edge while ensuring the phase and optimize the overall efficiency.

[0241] Specifically, the following steps may be performed to specifically determine the period of the grating element structure.

[0242] Step R1, obtain and determine the relationship between the grating element structure period (Period) and the transmittance (Transmission) according to several preset incident angles, and fix the optimal structure period corresponding to each preset incident angle. Fig.29As shown in (a), the optimal structural period is 420nm at 0° incidence, 390nm at 15° incidence, 350nm at 30° incidence, and 320nm at 45° incidence.

[0243] 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; Fig.29 (b) and Fig.29 (c).

[0244] Step R3, according to the above relationship, determine the variation curve of focusing efficiency (or transmittance) with the incident angle, and set the periodic arrangement of the grating element structure accordingly; Fig.29 (d), where 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 425nm fixed periodic arrangement.

[0245] In another embodiment, the reflection can be greatly reduced and the tolerance can be increased by coating an anti-reflection film. The specific solution can be found in the above text and will not be described here.

[0246] Of course, the above implementations can be combined to form the best optimization solution. Fig.30 The graph shows the relationship between the transmittance and the incident angle when the two implementation methods of the anti-reflection film 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 (Best result with variable period) provided by the present invention has more beneficial transmittance and focusing efficiency performance under a large field of view.

[0247] In summary, the multi-focal vector superlens, design method and optical system provided by the present invention calculate the superlens design information based on the Jones matrix, and can introduce the physical concept of polarization state regulation into the superlens design process, so that the designed superlens can have better polarization performance; because the image plane Jones matrix is ​​set as the target and the iterative Fourier algorithm is implemented to optimize the object plane Jones matrix, it can adapt to the relatively complex vector superlens holographic function requirements and quickly determine the final design information.

[0248] It should be understood that although this specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description 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 mode may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

[0249] The series of detailed descriptions listed above are only specific descriptions of feasible implementation methods of the present invention. They are not intended to limit the scope of protection of the present invention. Any equivalent implementation methods or changes that do not deviate from the technical spirit of the present invention should be included in the scope of protection of the present invention.

Claims

1. A multi-focal vector metalens design method, characterized in that: include: Obtain the Jones matrix information of the current object plane and the Jones matrix information of the target image plane, and determine the objective function according to the difference between the two; Optimizing the current object plane Jones matrix information based on an iterative Fourier algorithm until the objective function converges, and fixing the final object plane Jones matrix information; According to the final object plane Jones matrix information, the final design information of the multi-focal vector super lens is calculated.

2. The multi-focal point vector metalens design method according to claim 1, characterized in that: The “optimizing the Jones matrix information of the current object plane based on the iterative Fourier algorithm” specifically includes: Determining a gradient constraint factor according to a total phase factor in the Jones matrix of the current object plane; The Jones matrix information of the current object plane is optimized based on an iterative Fourier algorithm, and the gradient constraint factor is gradient updated after each iteration.

3. The multi-focal point vector superlens design method according to claim 2, characterized in that: The gradient constraint factor is a derivative of the objective function with respect to the total phase factor.

4. The multi-focal point vector metalens design method according to claim 1, characterized in that: The objective function is the Euclidean distance between the Jones matrix of the current object plane and the Jones matrix of the target image plane.

5. The multi-focal point vector metalens design method according to claim 1, characterized in that: The target image plane Jones matrix information carries at least one of the Stokes parameter, Mueller matrix information and scattering matrix information under the target polarization state.

6. The multi-focal point vector metalens design method according to claim 1, characterized in that: The target image plane matrix information carries the ellipticity information and / or azimuth information under the target polarization state; the "obtaining the current object plane Jones matrix information and the target image plane Jones matrix information, and determining the objective function according to the difference between the two" specifically includes: Obtaining ellipticity information and azimuth information under n target polarization states, and constructing n sets of global Jones matrices corresponding to the Poincare sphere in the xOy coordinate system according to the n sets of ellipticity information and azimuth information; The objective function is determined according to the difference between the current object plane Jones matrix information and the global Jones matrix.

7. The multi-focal point vector metalens design method according to claim 6, characterized in that: The n target polarization states are configured to form a regular polyhedron on the Poincare sphere.

8. The multi-focal point vector metalens design method according to claim 6, characterized in that: The n target polarization states include a circular polarization state, a first elliptical polarization state, a second elliptical polarization state and a third elliptical polarization state.

9. The multi-focal point vector metalens design method according to claim 6, characterized in that: n＝4。 10. The multi-focal point vector metalens design method according to claim 1, characterized in that: The "obtaining Jones matrix information of the current object plane and Jones matrix information of the target image plane, and determining the objective function according to the difference between the two" specifically includes: The Jones matrix of the current metalens corresponding to each diffraction order under the linear polarization basis vector on one side of the object plane is used as the Jones matrix information of the current object plane, and the difference between the Jones matrix and n groups of target image plane Jones matrices is calculated, and n groups of target functions are determined for each diffraction order; wherein the n groups of target image plane Jones matrices correspond to n polarization states; The “optimizing the current object plane Jones matrix information based on an iterative Fourier algorithm until the objective function converges and fixing the final object plane Jones matrix information” specifically includes: Based on the vector iterative Fourier algorithm, forward and backward propagation is performed between the object plane and the image plane to optimize the current object plane Jones matrix until all objective functions converge and the final object plane Jones matrix information is fixed.

11. The multi-focal point vector metalens design method according to claim 10, characterized in that: Before the step of "taking the Jones matrix of each diffraction order of the current metalens under the linear polarization basis vector on one side of the object plane as the Jones matrix information of the current object plane", the multi-focal vector metalens design method further includes: Get the rotation angle of the grating element at the current superlens and construct the object plane rotation matrix; At least obtaining a first phase delay of the current metalens in the x-polarization direction and a second phase delay in the y-polarization direction, and constructing an object plane Jones vector; The current object plane Jones matrix is ​​constructed according to the object plane rotation matrix and the object plane Jones vector.

12. The multi-focal point vector metalens design method according to claim 11, characterized in that: The "structure plane rotation matrix" specifically includes: Constructing a first rotation matrix and a second rotation matrix according to the rotation angle and its inverse; The “constructing the current object plane Jones matrix according to the object plane rotation matrix and the object plane Jones vector” specifically includes: The current object plane Jones matrix is ​​constructed according to the dot product of the first rotation matrix, the object plane Jones vector and the second rotation matrix.

13. The multi-focal point vector metalens design method according to claim 11, characterized in that: The rotation angle is the angle between the direction of the grating element and the x-polarization direction.

14. The multi-focal point vector metalens design method according to claim 1, characterized in that: The “calculating the final design information of the multi-focal vector super-lens according to the final object plane Jones matrix information” specifically includes: Performing linear phase superposition on the final object plane Jones matrix and the lens phase distribution to determine an overall Jones matrix; Performing matrix decomposition on the overall Jones matrix to obtain a Jones decomposition matrix as an overall phase distribution function; wherein the Jones decomposition matrix includes an updated phase delay; According to the overall phase distribution function, the overall design information of the multi-focal point vector metalens is determined.

15. The multi-focal point vector metalens design method according to claim 14, characterized in that: The “determining the overall design information of the multi-focal point vector metalens according to the overall phase distribution function” specifically includes: At least according to the phase delay information and the rotation angle information carried by the overall phase distribution function, a multi-focus vector super lens structure parameter library is retrieved to obtain the structural design information corresponding to the grating primitive structure; The final polarization degree and the final polarization angle are calculated according to the Stokes parameters corresponding to the Jones decomposition matrix.

16. The multi-focal point vector metalens design method according to claim 15, characterized in that: Before the step of “searching a multi-focal point vector metalens structure parameter library at least according to the phase delay information and the rotation angle information carried by the overall phase distribution function to obtain the structure design information corresponding to the grating primitive structure”, the multi-focal point vector metalens design method further 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 structure parameter library; wherein the grating primitive structure is a standard three-dimensional structure.

17. The multi-focal point vector metalens design method according to claim 15, characterized in that: The “calculating the final polarization degree and the final polarization angle according to the Stokes parameters corresponding to the Jones decomposition matrix” specifically includes: Calculate the final ellipticity information and final azimuth information corresponding to the Poincare sphere according to the Jones decomposition matrix; Calculate a first Stokes parameter, a second Stokes parameter, a third Stokes parameter and a fourth Stokes parameter according to the final ellipticity information and the final azimuth information; wherein the first Stokes parameter is the total incident light intensity, the second Stokes parameter is the light intensity difference between the x-polarization component and the y-polarization component, the third Stokes parameter is the light intensity difference between the first angle polarization component and the second angle polarization component, and the fourth Stokes parameter is the light intensity difference between the left-handed circular polarization component and the right-handed circular polarization component; Calculating a linear polarization degree of polarization according to the first Stokes parameter, the second Stokes parameter and the third Stokes parameter; Calculate the circular polarization degree according to the first Stokes parameter and the fourth Stokes parameter; Polarization angle information is calculated according to the second Stokes parameter and the third Stokes parameter.

18. A multi-focal vector metalens, characterized in that: The image side surface and / or object side surface of the multi-focal point vector superlens is arranged with a grating element structure; the grating element structure is configured according to the final design information fixed by the multi-focal point vector superlens design method according to any one of claims 1-17.

19. An optical system, characterized in that: include: The multi-focal point vector superlens of claim 18, and a light sensor for converting a light signal modulated and outputted from one side of the multi-focal point vector superlens into an electrical signal.

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