Mixed-order Poincare light beam polarization state characterization method based on diffraction metasurface

Abstract

The invention discloses a polarization state characterization method of a mixed-order Poincare light beam based on a diffraction metasurface, and relates to the technical field of mixed-order Poincare light beam detection. Decomposing the mixed-order Poincare light beam into a left-handed circularly polarized light vortex and a right-handed circularly polarized light vortex; the left-hand circularly polarized light vortex and the right-hand circularly polarized light vortex are emitted to a metasurface designed through a diffractive optical neural network, and the left-hand circularly polarized light vortex and the right-hand circularly polarized light vortex are converted into a preset number of focuses through the metasurface; performing linear superposition on a preset number of focuses corresponding to the left-hand circularly polarized light vortex and a preset number of focuses corresponding to the right-hand circularly polarized light vortex to obtain a preset number of complex focuses; and acquiring the intensity of the preset number of complex focuses, and analyzing the intensity of the preset number of complex focuses through the electronic deep neural network model to obtain the polarization information of the mixed-order Poincare beam. According to the method, the polarization state of the mixed-order Poincare light beam can be accurately represented.

Description

Technical Field

[0001] The present invention relates to the technical field of hybrid-order Poincaré beam detection, and particularly relates to a method for characterizing the polarization state of a hybrid-order Poincaré beam based on a diffractive metasurface. Background Art

[0002] Currently, hybrid-order Poincaré beams have become an important focus in the field of high-throughput optical communication. The polarization state of a hybrid-order Poincaré beam is a key resource for optical communication, which helps to achieve high-throughput information multiplexing. Therefore, real-time characterization of the polarization state of a hybrid-order Poincaré beam is a prerequisite for promoting classical optical communication and quantum optical communication.

[0003] In the prior art, the method for characterizing the polarization state of a hybrid-order Poincaré beam relies on the Stokes polarization method, which usually requires at least four independent measurements, and each measurement projects the state onto different polarization components. However, polarization state characterization requires pixel-precise alignment and point-to-point calculation of Stokes parameters, which introduces registration errors and results in inaccurate characterization of the polarization state of a hybrid-order Poincaré beam. Summary of the Invention

[0004] Based on this, it is necessary to provide a method for characterizing the polarization state of a hybrid-order Poincaré beam based on a diffractive metasurface to accurately characterize the polarization state of a hybrid-order Poincaré beam for the above technical problems.

[0005] The present invention adopts the following technical solutions:

[0006] The present invention provides a method for characterizing the polarization state of a hybrid-order Poincaré beam based on a diffractive metasurface, including:

[0007] Decompose the hybrid-order Poincaré beam into a left-handed circularly polarized light vortex and a right-handed circularly polarized light vortex;

[0008] Emit the left-handed circularly polarized light vortex and the right-handed circularly polarized light vortex onto a metasurface designed by a diffractive optical neural network respectively, and convert the left-handed circularly polarized light vortex and the right-handed circularly polarized light vortex into a preset number of focal points through the metasurface;

[0009] Linearly superpose the preset number of focal points corresponding to the left-handed circularly polarized light vortex and the preset number of focal points corresponding to the right-handed circularly polarized light vortex to obtain a preset number of complex focal points;

[0010] Collect the intensities of the preset number of complex focal points, and analyze the intensities of the preset number of complex focal points through an electronic deep neural network model to obtain the polarization information of the hybrid-order Poincaré beam.

[0011] Optionally, the preset number is 3, and the amplitudes and phases of the preset number of focal points corresponding to the left-handed circularly polarized light vortex satisfy: A 1 = A2 = A 3 = 1, The amplitudes and phases of the preset number of foci corresponding to the right-handed circularly polarized light vortex satisfy: A 1 = A 2 = A 3 = 1,

[0012] where A 1 , A 2 , A 3 are the amplitudes of the three foci respectively, are the phases of the three foci respectively.

[0013] Optionally, the metasurface is bilayer and consists of silicon nitride nanorods on a quartz substrate; the size and azimuth angle of the silicon nitride nanorods vary spatially to achieve the required phase of the output foci.

[0014] Optionally, collecting the intensities of the preset number of complex foci includes:

[0015] For any complex focus, integrating the Poynting vector of the preset region centered on the complex focus to obtain the intensity of the complex focus.

[0016] Optionally, the amplitude of the complex focus is expressed as:

[0017]

[0018] where A n represents the amplitude of the complex focus, and represent the initial amplitudes of the right-handed circularly polarized light vortex component and the left-handed circularly polarized light vortex component respectively, σ L represents the initial amplitude of the left-handed circularly polarized light vortex, θ L represents the initial phase of the left-handed circularly polarized light vortex, represents the preset phase of the focus corresponding to the left-handed circularly polarized light vortex, σ R represents the initial amplitude of the right-handed circularly polarized light vortex, θ R represents the initial phase of the focus corresponding to the right-handed circularly polarized light vortex, represents the preset phase of the focus corresponding to the right-handed circularly polarized light vortex, and i represents the position of the i-th focus.

[0019] Optionally, analyzing the intensities of the preset number of complex foci through an electronic deep neural network model to obtain the polarization information of the hybrid-order Poincaré beam, including:

[0020] Determining the intensity ratio of the preset number of complex foci according to the intensities of the preset number of complex foci;

[0021] Input the intensity ratio into an electronic deep neural network model to obtain the polarization information of the hybrid-order Poincaré beam.

[0022] Optionally, the electronic deep neural network model includes an input layer, a non-linear fully connected layer, and an output layer; inputting the intensity ratio into the electronic deep neural network model to obtain the polarization information of the hybrid-order Poincaré beam includes:

[0023] Input the intensity ratio into each neuron of the non-linear fully connected layer through the input layer to obtain the feature data output by each neuron;

[0024] Input the feature data output by each neuron into the output layer to obtain the polarization information of the hybrid-order Poincaré beam.

[0025] The present invention provides a polarization state characterization device for a hybrid-order Poincaré beam based on a diffractive metasurface, including:

[0026] A decomposition module for decomposing the hybrid-order Poincaré beam into a left-handed circularly polarized light vortex and a right-handed circularly polarized light vortex;

[0027] A diffraction module for respectively emitting the left-handed circularly polarized light vortex and the right-handed circularly polarized light vortex onto a metasurface designed by a diffractive optical neural network, and converting the left-handed circularly polarized light vortex and the right-handed circularly polarized light vortex into a preset number of focal points through the metasurface;

[0028] A superposition module for linearly superposing the preset number of focal points corresponding to the left-handed circularly polarized light vortex and the preset number of focal points corresponding to the right-handed circularly polarized light vortex to obtain a preset number of complex focal points;

[0029] An analysis module for collecting the intensities of the preset number of complex focal points and analyzing the intensities of the preset number of complex focal points through an electronic deep neural network model to obtain the polarization information of the hybrid-order Poincaré beam.

[0030] The above at least one technical solution adopted by the present invention can achieve the following beneficial effects:

[0031] Through the metasurface designed by a diffractive optical neural network, the two circularly polarized light vortices of the hybrid-order Poincaré beam are mapped to three focal points on the output plane and linearly superposed. Subsequently, through the electronic deep neural network model, the polarization information of the hybrid-order Poincaré beam is reconstructed from the intensities of the superposed complex focal points. The method of the present invention avoids the dependence on polarization basis projection and is fundamentally different from the traditional method that relies on Stokes parameter measurement. Therefore, it eliminates the errors usually introduced by spatial registration and separation in Stokes parameter evaluation and improves the accuracy of characterizing the polarization state of the hybrid-order Poincaré beam. Description of the Drawings

[0032] The accompanying drawings described herein are used to provide a further understanding of the present invention, and constitute a part of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention, and do not constitute an improper limitation to the present invention. In the drawings:

[0033] Figure 1 It is a schematic flow chart of a method for characterizing the polarization state of a hybrid-order Poincaré beam based on a diffractive metasurface provided by the present invention;

[0034] Figure 2 It is a schematic flow chart of a metasurface designed based on a diffractive optical neural network provided by the present invention;

[0035] Figure 3 It is a schematic flow chart of a method for characterizing the polarization state of a hybrid-order Poincaré beam based on a diffractive metasurface provided by the present invention;

[0036] Figure 4 It is a schematic diagram of the working mechanism of a spin-multiplexed diffractive metasurface for characterizing the polarization information of a hybrid-order Poincaré beam provided by the present invention;

[0037] Figure 5 It is a schematic structural diagram of an electronic deep neural network for reconstructing the polarization information of a hybrid-order Poincaré beam provided by the present invention;

[0038] Figure 6 It is a schematic diagram of characterizing the polarization information of a hybrid-order Poincaré beam driven by an electronic deep neural network model provided by the present invention;

[0039] Figure 7 It is a schematic diagram of a single-shot characterization of the polarization information of a hybrid-order Poincaré beam provided by the present invention;

[0040] Figure 8 It is a schematic verification diagram of characterizing the polarization information of a hybrid-order Poincaré beam provided by the present invention;

[0041] Figure 9 It is a schematic diagram of a device for characterizing the polarization state of a hybrid-order Poincaré beam based on a diffractive metasurface provided by the present invention. Detailed implementation manners

[0042] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the specific embodiments of the present invention and the corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0043] Hybrid-order Poincaré beams (HyOPBs) integrate orbital angular momentum (OAM) and spin angular momentum (SAM) to represent the joint spatial evolution of phase and polarization, playing a crucial role in multiple fields such as optical communication, sensing, and quantum information. Due to their infinite OAM orthogonal states and dynamic polarization capabilities, HyOPBs have become an important focus in the field of high-throughput optical communication. The state of polarization (SOP) of HyOPBs is a key resource for optical communication, which helps to achieve high-throughput information multiplexing. Therefore, single-shot real-time characterization of SOP is a prerequisite for advancing classical and quantum optical communication.

[0044] Traditionally, the characterization method relies on Stokes polarimetry, which usually requires at least four independent measurements, each projecting the state onto different polarization components. This method requires multiple reconfigurable polarization optical elements, resulting in a bulky device and limited time resolution. However, in all these previous experiments, SOP characterization requires pixel-precise alignment and point-by-point calculation of Stokes parameters, which introduces registration errors and complicates the processing. Therefore, these methods are not suitable for accurate, real-time, and tightly integrated HyOPBs detection.

[0045] Metasurfaces composed of subwavelength optical scatterer arrays can customize the amplitude, phase, and polarization characteristics of the light field, providing a versatile platform for compact planar optics. So far, remarkable applications of metasurfaces include superlenses, holography, structured light generation, and optical computing. Recent progress has demonstrated the feasibility of metasurface-supported ellipsometry for single-shot measurement of polarization detection. These devices accurately determine the polarization state by measuring the light intensity in different polarization bases and obtaining Stokes parameters. However, although these devices are compact and efficient, most of them are limited to resolving polarization states on the standard Poincaré sphere. For HyOPBs, especially those with complex vector light fields and large angular quantum numbers, it is difficult for metasurface-based ellipsometers to accurately characterize due to the need for additional spatial multiplexing and separation. Therefore, accurate, fast, and single-shot characterization of HyOPBs using metasurfaces has not been achieved and remains an area to be further explored.

[0046] Based on this, the present invention proposes a method for characterizing the polarization state of a hybrid-order Poincaré beam based on a diffractive metasurface, which is a direct single-shot measurement method for using a spin-multiplexed diffractive metasurface to completely characterize any hybrid-order Poincaré beam. Through the metasurface designed by a diffraction neural network, the two circularly polarized waves of the hybrid-order Poincaré beam are mapped to three specified focal points on the output plane. Subsequently, an electronic deep neural network model reconstructs all relevant polarization information of the hybrid-order Poincaré beam, including amplitude and phase difference, from the intensities of these focal points. This can not only achieve single-shot and real-time characterization, but also eliminate additional measurement errors and minimize the device size by eliminating the need for reconfigurable polarization elements. In particular, the method of the present invention avoids dependence on polarization basis projection and is fundamentally different from traditional methods that rely on Stokes parameter measurement. Therefore, it eliminates the errors usually introduced by spatial registration and separation in Stokes parameter evaluation. The designed diffractive metasurface essentially represents an optical processor that supports arbitrary vector mode transformation, and these diffractive metasurfaces facilitate single-shot, real-time, and accurate characterization of hybrid-order Poincaré beams in a compact and integrated format, paving the way for the progress of high-capacity optical communication, entangled quantum information encoding, and high-dimensional optical encryption.

[0047] The following will, with reference to the accompanying drawings, detail the technical solutions provided by each embodiment of the present invention.

[0048] Figure 1 It is a schematic flowchart of a method for characterizing the polarization state of a hybrid-order Poincaré beam based on a diffractive metasurface in the present invention, specifically including the following steps:

[0049] S101, decompose the hybrid-order Poincaré beam into a left-handed circularly polarized optical vortex and a right-handed circularly polarized optical vortex.

[0050] The state of the hybrid-order Poincaré beam can be represented by a linear superposition of left-handed circularly polarized (LCP) optical vortices and right-handed circularly polarized (RCP) optical vortices with different topological charges, as shown in formula (1).

[0051]

[0052] where, |ψ m,n,σ,θ > is the hybrid-order Poincaré beam, |R,m> represents an RCP optical vortex with a topological charge of m, |L,n> represents an LCP optical vortex with a topological charge of n, σ and θ respectively represent the amplitudes and phase differences of the orthogonal polarization bases, corresponding to the hybrid-order poincar <s:1>Azimuth and polar angles on the sphere (HyOPS). Generally, the conventional strategy for fully characterizing hyopb is to obtain the intensity distribution through four independent projection measurements to recover the Stokes parameters. Then, the hyopb can be reconstructed by calculating the Stokes parameters point by point, and this process may introduce alignment errors due to spatial or temporal partitioning.

[0053] Therefore, in the present invention, considering the linear superposition of vector modes, compared with measuring the polarization state with spatial contributions, the present invention provides a more effective method. When the hybrid-order Poincaré beam vector passes through a linear system with negligible polarization crosstalk, the global optical response is the linear superposition of two independent optical responses induced by two orthogonal circular polarization bases. Therefore, when characterizing the polarization state of the hybrid-order Poincaré beam, the hybrid-order Poincaré beam is first decomposed into a left-handed circularly polarized optical vortex and a right-handed circularly polarized optical vortex.

[0054] S102: Respectively emit the left-handed circularly polarized optical vortex and the right-handed circularly polarized optical vortex onto a metasurface designed by a diffractive optical neural network, and convert the left-handed circularly polarized optical vortex and the right-handed circularly polarized optical vortex into a preset number of focal points through the metasurface.

[0055] In the present invention, a spin-multiplexed diffractive metasurface is introduced, that is, a metasurface designed by a diffractive optical neural network, which can independently process two circularly polarized optical vortices, thereby generating two sets of predefined outputs.

[0056] Among them, the metasurface is an optimized micro-nano-sized planar optical device that can perform special optical processing on the input light field, such as Figure 2 shown Figure 2 is a schematic flow chart of a metasurface designed based on a diffractive optical neural network.

[0057] Specifically, the introduced metasurface, as a trained optical computing layer, processes the incident complex light field (hybrid-order Poincaré beam) into a latent feature space, and the intensity measurement at the output position is closely related to the complex amplitude coefficients of the orthogonal polarization bases.

[0058] Optionally, taking the preset number as 3 as an example for illustration, that is, the metasurface can convert the left-handed circularly polarized optical vortex and the right-handed circularly polarized optical vortex into three focal points respectively, HyOPBs = |ψ -3,3,θ,σ |.

[0059] It should be noted that the metasurface is bilayer, and the metasurface is composed of silicon nitride nanorods on a quartz substrate; the silicon nitride nanorods maintain a uniform height, and the size and azimuth angle of the silicon nitride nanorods vary spatially to achieve the phase required for the output focal points.

[0060] Converting left-handed circularly polarized light vortices and right-handed circularly polarized light vortices into a preset number of focal points through a metasurface, including: mapping left-handed circularly polarized light vortices and right-handed circularly polarized light vortices to three focal points on the focal plane through the metasurface.

[0061] The predefined amplitude and phase distributions on the focal plane are achieved through a spin-multiplexed metasurface, which is facilitated by a diffraction optical neural network. Specifically, the amplitudes and phases of the three focal points corresponding to the left-handed circularly polarized light vortex satisfy: A 1 = A 2 = A 3 = 1, The amplitudes and phases of the preset number of focal points corresponding to the right-handed circularly polarized light vortex satisfy: A 1 = A 2 = A 3 = 1, where A 1 、A 2 、A 3 are the amplitudes of the three focal points respectively, are the phases of the three focal points respectively.

[0062] During the training process, each layer consists of neuron metasurfaces, the working wavelength is 532 nm, and the 50×50 input light field is defined as a vortex beam carrying topological charge l, which is determined by the following expression:

[0063]

[0064] where r and are cylindrical coordinates; represents the beam radius, w 0 represents the waist radius of the Gaussian beam, represents the Laguerre polynomial with angular quantum number l and radial refractive index p. The present invention selects the sum of the preset number of focal points corresponding to the left-handed circularly polarized light vortex and the preset number of focal points corresponding to the right-handed circularly polarized light vortex as the basis of the hybrid-order Poincaré beam. |R l,p > = |-3,0>, |L l,p > = |3,0>. Under the illumination of the vortex beam, the diffraction metasurface exhibits the ability to convert the incident light into the designed target field U, and the propagation of the light field follows the principle of scalar diffraction theory. We define the actual output light field as O and calculate the loss function using the mean squared error (MSE):

[0065]

[0066] Use the stochastic gradient descent algorithm to backpropagate the error and update the metasurface phase to minimize the loss function.

[0067] Linearly superpose a preset number of foci corresponding to a left - handed circularly polarized light vortex and a preset number of foci corresponding to a right - handed circularly polarized light vortex to obtain a preset number of complex foci.

[0068] According to the principle of linear superposition, when the spatial positions of three foci corresponding to the left - handed circularly polarized light vortex and the right - handed circularly polarized light vortex coincide, the detected amplitude can be expressed as:

[0069]

[0070] Among them, and respectively represent the initial amplitudes of the right - handed circularly polarized light vortex component and the left - handed circularly polarized light vortex component, σ L represents the initial amplitude of the left - handed circularly polarized light vortex, θ L represents the initial phase of the left - handed circularly polarized light vortex, represents the preset phase of the focus corresponding to the left - handed circularly polarized light vortex, σ R represents the initial amplitude of the right - handed circularly polarized light vortex, θ R represents the initial phase of the focus corresponding to the right - handed circularly polarized light vortex, represents the preset phase of the focus corresponding to the right - handed circularly polarized light vortex, and i represents the position of the i - th focus.

[0071] Collect the intensities of a preset number of complex foci, and analyze the intensities of the preset number of complex foci through an electronic deep neural network model to obtain the polarization information of the hybrid - order Poincaré beam.

[0072] Among them, the polarization information includes amplitude and phase difference.

[0073] Since the intensity measurement of the beam is closely related to the complex amplitude coefficients of the orthogonal polarization bases, therefore, the intensities of a preset number of complex foci can be detected by a detector, and the mapping relationship between the intensity and the reconstructed polarization information can be determined.

[0074] Optionally, collecting the intensities of a preset number of complex foci includes: for any one of the complex foci, integrating the Poynting vector of a preset area centered on the complex focus to obtain the intensity of the complex focus.

[0075] The prediction of the polarization information of a hybrid-order Poincaré beam is essentially a regression photon problem. Due to limited nonlinearity, it is quite challenging to accurately predict vector parameters using only an optical neural network. For this reason, the present invention introduces an Electronic Deep Neural Network (EDNN), which establishes a complex mapping |I>|Q> from intensity I to polarization information Q between intensity measurement and reconstructed polarization information. The EDNN has powerful feature learning ability and nonlinear modeling ability, can process complex high-dimensional data, and is very suitable for data fitting in this case. Therefore, the present invention can quickly obtain the polarization information of a hybrid-order Poincaré beam by processing the output intensity using the EDNN.

[0076] In an exemplary embodiment, the intensity of a preset number of complex foci is analyzed by an electronic deep neural network model to obtain the polarization information of a hybrid-order Poincaré beam, including: determining the intensity ratio of the preset number of complex foci according to the intensity of the preset number of complex foci; inputting the intensity ratio into the electronic deep neural network model to obtain the polarization information of the hybrid-order Poincaré beam.

[0077] Taking the case where there are 3 complex foci as an example, the intensity ratio of the complex foci can be I 1 :I 2 :I 3 . Input I 1 , I 2 and I 3 into the electronic deep neural network model to obtain the polarization information of the hybrid-order Poincaré beam.

[0078] Among them, the electronic deep neural network model includes an input layer, a nonlinear fully connected layer, and an output layer; inputting the intensity ratio into the electronic deep neural network model to obtain the polarization information of the hybrid-order Poincaré beam includes: inputting the intensity ratio into each neuron of the nonlinear fully connected layer through the input layer respectively to obtain the feature data output by each neuron; inputting the feature data output by each neuron into the output layer to obtain the polarization information of the hybrid-order Poincaré beam.

[0079] In an exemplary embodiment, as Figure 3 shown, Figure 3 is a schematic flow chart of a method for characterizing the polarization state of a hybrid-order Poincaré beam based on a diffraction metasurface. Figure 3 In the figure (a), it is a Poincaré sphere. The two poles of the Poincaré sphere correspond to LCP and RCP vortex beams, which are orthogonal polarization bases with different topological charges. Each star point on the Poincaré sphere represents a hybrid-order Poincaré beam with a different vector field distribution. The bottom inset shows the polarization and intensity distributions of three arbitrarily selected hybrid-order Poincaré beams. Figure 3 Figure (b) in [reference] is a schematic diagram of the polarization state characterization of a single hybrid-order Poincaré beam based on a diffractive metasurface. The double-layer diffractive metasurface serves as an optical computing layer, directly processing the incident vector field (hybrid-order Poincaré beam) and converting it into three different points (complex foci) on the focal plane. Then, a detector is used to capture the corresponding intensity distribution in a single measurement. Subsequently, an electronic deep neural network is used to fit and reconstruct the polarization information of the hybrid-order Poincaré beam.

[0080] In an exemplary embodiment, as Figure 4 shown, Figure 4 Figure [reference] is a schematic diagram of the working mechanism of a spin-multiplexing diffractive metasurface for the polarization information characterization of a hybrid-order Poincaré beam. First, the hybrid-order Poincaré beam is decomposed into two orthogonal circularly polarized lights carrying optical vortices. The complex amplitude coefficients of the hybrid-order Poincaré beam are closely related to the polarization information of the hybrid-order Poincaré beam. It is worth noting that we have selected three intensity values to map the feature space because poincar <s:1>The parameter is essentially defined by three different parameters, and the commonly used two-parameter representation stems from normalization. According to Equation (1), the hybrid-order Poincaré beam can be decomposed into the complex amplitude superposition of two orthogonally circularly polarized optical vortices (on the left side of Figure (a) in Figure 4 ). We use a spin-multiplexed diffractive metasurface to independently process each orthogonally circularly polarized optical vortex, thereby generating two sets of predefined outputs (in the middle of Figure (a) in Figure 4 ), and the final combined output is related to the superposition of the complex amplitudes (on the right side of Figure (a) in Figure 4 ). Therefore, the polarization information of the hybrid-order Poincaré beam can be completely determined by analyzing the output. Figure 4 Figure (b) in Figure 4 shows the target phase distribution of the double-layer metasurface in the RCP and LCP channels. Figure 4 Figures (c) and (d) in Figure 4 are schematic diagrams of the metasurface, which consists of silicon nitride nanocolumns on a quartz substrate with a period of P = 350 nm and a height of H = 800 nm. Figure 4 Figure (c) in x provides a side view of the nanocolumns, while y Figure (d) in Figure 4 provides a top view. Figure 4 Figure (e) in x shows the phase sequence of 16 nanocolumns, including φ x and φ y . Figure 4 Figure (f) in

[0081] shows the transmittance and polarization conversion efficiency of 16 nanocolumns. Figure 4 To independently control the phases of RCP and LCP light, an efficient birefringent meta-atom that combines geometric phase and propagation phase is adopted. As shown in Figures (c) and (d) in Figure 4 , the metasurface unit consists of silicon nitride (Si 3 N 4 ) nanorods on a quartz substrate. The nanorods maintain a uniform height, while their in-plane dimensions and azimuth angles (H = 800 nm, L, W, and θ) vary spatially to achieve the desired phases, and the finite-difference time-domain (FDTD) algorithm is used to perform a parametric scan of L and W with a defined period.

[0082] According to the results of the parametric scan, a set of 16 nanocolumns is selected to provide 16 levels of soft phase, covering the entire 2π range of φ x φ y . As shown in Figure (e) in Figure 4 , the high transmittance (T x , T y ) and polarization conversion efficiency (η) of the 16 nanocolumns ensure the efficient operation of the diffractive metasurface at the working wavelength. As shown in Figure (f) in Figure 4 , the propagation phase and geometric phase of the transmitted light are respectively given by φ x , φ y and the rotation angle θ. Therefore, the required phase shift and rotation angle at each pixel are calculated according to the target phase to achieve the design of the spin-multiplexed diffractive metasurface.

[0083] In an exemplary embodiment, as Figure 5 shown, Figure 5 is a schematic structural diagram of an electronic deep neural network for reconstructing the polarization information of a hybrid-order Poincaré beam provided by the present invention.

[0084] As Figure 6 shown, Figure 6 gives a schematic diagram of characterizing the polarization information of a hybrid-order Poincaré beam driven by an electronic deep neural network model. First, 300 sets of samples with randomly distributed hybrid-order Poincaré beams are generated as the training data set, and they are assigned to the designed spin-multiplexed diffractive metasurface. The vector diffraction method is used to calculate the optical field distribution of the output field, and the Poynting vector integration method is used to determine the intensity ratio of the three focal points. By this method, the polarization information |Q> of 300 sets of hybrid-order Poincaré beams and the corresponding intensity ratio |I> are obtained. Once enough data sets are accumulated, an EDNN is established for feature extraction and inverse mapping to keep the prediction error within a low range. In Figure 6 in the figure (a), the intensity ratio |I> is used as the input, and the output is the polarization information |Q> of the hybrid-order Poincaré beam. The EDNN includes an input layer, four non-linear fully connected layers and an output layer, which constructs the inverse mapping between |I> and |Q>, which enables us to directly obtain the polarization information of the hybrid-order Poincaré beam from the EDNN. The network training error curve of the EDNN is as shown in Figure 6 in the figure (b). This method can predict the polarization information of the hybrid-order Poincaré beam without multiple measurements, and can directly characterize the vector state of HyOPBs by single detection, greatly simplifying the experimental process and avoiding registration errors.

[0085] To clearly show the results, we randomly selected 10 sets of intensity ratios and input them into the trained EDNN. The predicted polarization information of the hybrid-order Poincaré beam closely matches the target value, as shown in Figure 6 in the figure (c) and (d). Figure 6 The comparison results in the figure (e) and (f) show that the prediction of the phase difference θ is mainly distributed along the diagonal, indicating that the prediction results are relatively accurate. However, several data points of the amplitude σ deviate from the diagonal. We emphasize that increasing the data set size can improve the prediction accuracy, although this will require a large amount of computing resources and time.

[0086] Finally, to quantify the accuracy of the scheme, the mean absolute error (MAE) is used as the test error of the polarization information of the i-th hybrid-order Poincaré beam where |Q r > represents the actual value, and |Q o > represents the output value. First, the absolute error of the polarization information of the hybrid-order Poincaré beam was calculated. Figure 6 Figures (g) and (h) in

[0087] In an exemplary embodiment, as Figure 7 shown, Figure 7 is a schematic diagram of the single-shot characterization of the polarization information of the hybrid-order Poincaré beam. First, a double-layer spin-multiplexed diffraction metasurface was designed, and the relevant EDNN model was trained to achieve the single-shot characterization of the polarization information of the hybrid-order Poincaré beam. The accuracy of the single-shot characterization scheme was verified by vector simulation. Specifically, three different vector modes A (σ = 0.783, θ = 1.662), B (σ = 1.576, θ = 5.465), and C (σ = 2.347, θ = 1.472) were randomly selected from the high-order Poincaré sphere, as Figure 7 shown in Figure (a) in Figure 7 . These vector modes were used as inputs and incident on the double-layer diffraction metasurface, while the detector simultaneously recorded the intensity distribution on the output plane. The input modes are shown at the top of Figure (b) in Figure 7 , and vector simulation was used to calculate the far field.

[0088] Subsequently, the Poynting vector integral was used to calculate the energy ratio of the three foci, which was then normalized and input into the trained EDNN model. The EDNN effectively extracted the polarization information of the hybrid-order Poincaré beam of the input vector mode. Using the predicted polarization information of the hybrid-order Poincaré beam, we reconstructed the three vector modes, and the results are shown at the bottom of Figure (b) in Figure 7 . Obviously, the reconstructed vector diagram matches the input test diagram very well, demonstrating the effectiveness of the single-shot characterization scheme for the polarization information of the hybrid-order Poincaré beam proposed in the present invention.

[0089] To further evaluate the robustness of the method of the present invention, 15 different patterns were randomly selected to test the reconstruction ability of the method of the present invention. It is worth noting that these patterns are not the original 100 test sets, which confirms the generalization of the single-shot characterization scheme proposed by the present invention. The comparison between the reconstruction results and the theoretical results shows that the reconstruction error of σ is ±2.35%, and the reconstruction error of θ is ±1.54%. Obviously, the method of the present invention is significantly superior to the traditional Stokes polarization detection in terms of reconstruction accuracy, compact integration, and real-time detection.

[0090] Finally, to demonstrate the ability to characterize arbitrary vector beams, the proposed single-shot characterization scheme was used to detect hybrid-order Poincaré beams, such as Figure 8 shown Figure 8 is a schematic diagram for verifying the polarization information characterization of a hybrid-order Poincaré beam. Compared with HOPBs, the LCP and RCP optical vortices in the hybrid-order Poincaré beam have completely different topological charges, resulting in a more complex transverse polarization distribution in the combined vector beam. As shown in Fig. (a) of Figure 8 , a hybrid-order Poincaré beam characterized by the bases |-5,R> and |+3,L> is proposed. Due to the asymmetry of the optical vortices carried by LCP and RCP, the polarization state distribution changes rapidly in the transverse plane, which poses a major challenge to directly reconstructing the polarization state to predict the Poincaré parameters.

[0091] Therefore, a double-layer spin-multiplexed diffraction metasurface can be used to manage the complex polarization distribution and directly extract the polarization information of the hybrid-order Poincaré beam of the incident light field without polarization reconstruction. Two optical vortices with different topological charges are used as inputs to design the diffraction metasurface. Subsequently, vector simulations and Poynting vector integrals are performed to calculate the output energy ratio of the beam after passing through the metasurface, and this ratio is normalized and then input into the EDNN model. A total of 300 data sets are used to train the corresponding EDNN model. Next, three different patterns are randomly selected from the hybrid-order Poincaré beam sphere: A (σ = 1.185, θ = 1.662), B (σ = 1.576, θ = 5.462), and C (σ = 2.867, θ = 1.663). Figure 8 Fig. (b) of

[0092] In summary, the present invention proposes and successfully verifies a single-shot characterization scheme for the polarization information of a hybrid-order Poincaré beam using a double-layer spin-multiplexed diffractive metasurface. By combining a diffractive optical neural network with an electronic deep neural network model, the limitations of traditional Stokes parameter measurement are addressed, allowing for real-time characterization and reconstruction of hyopb. Compared with traditional methods that rely on multi-polarization projections, the present invention fully characterizes the vector properties of a hybrid-order Poincaré beam using only one intensity measurement, which is very different from traditional Stokes-based schemes. In addition, through the characterization of the hybrid-order Poincaré beam, it is demonstrated that the present invention is applicable to any vector Poincaré sphere beam. The characterization method of the present invention can rapidly, accurately, and single-shot characterize a hybrid-order Poincaré beam in a compact integrated optical sensor system, opening up new avenues for the development of high-capacity optical communication, entangled quantum information, and high-dimensional optical encryption.

[0093] When applying the polarization state characterization method of a hybrid-order Poincaré beam based on a diffractive metasurface provided by the present invention, it is not necessary to execute according to the Figure 1 sequence of the steps shown. The specific execution sequence of each step can be determined as needed, and the present invention places no restrictions thereon.

[0094] The above is the polarization state characterization method of a hybrid-order Poincaré beam based on a diffractive metasurface provided by one or more embodiments of the present invention. Based on the same concept, the present invention also provides a corresponding polarization state characterization device of a hybrid-order Poincaré beam based on a diffractive metasurface, as Figure 9 shown.

[0095] Figure 9 Schematic diagram of a polarization state characterization device of a hybrid-order Poincaré beam based on a diffractive metasurface provided by the present invention. The device 900 includes:

[0096] A decomposition module 901 for decomposing a hybrid-order Poincaré beam into a left-handed circularly polarized optical vortex and a right-handed circularly polarized optical vortex.

[0097] A diffraction module 902 for respectively emitting the left-handed circularly polarized optical vortex and the right-handed circularly polarized optical vortex onto a metasurface designed by a diffractive optical neural network, and converting the left-handed circularly polarized optical vortex and the right-handed circularly polarized optical vortex into a preset number of focal points through the metasurface.

[0098] A superposition module 903 for linearly superposing the preset number of focal points corresponding to the left-handed circularly polarized optical vortex and the preset number of focal points corresponding to the right-handed circularly polarized optical vortex to obtain a preset number of complex focal points.

[0099] An analysis module 904 for collecting the intensities of the preset number of complex focal points and analyzing the intensities of the preset number of complex focal points through an electronic deep neural network model to obtain the polarization information of the hybrid-order Poincaré beam.

[0100] For the specific limitations of the polarization state characterization device of the hybrid-order Poincaré beam based on the diffractive metasurface, reference can be made to the limitations of the polarization state characterization method of the hybrid-order Poincaré beam based on the diffractive metasurface in the above text, which will not be elaborated here. Each module in the above polarization state characterization device of the hybrid-order Poincaré beam based on the diffractive metasurface can be implemented in whole or in part by software, hardware, and their combination.

[0101] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded in the present invention.

Claims

1. A polarization state characterization method for mixed-order Poincare beams based on diffractive metasurfaces, characterized in that: include: Decomposing the mixed-order Poincare beam into left-handed circularly polarized light vortex and right-handed circularly polarized light vortex; The left-handed circularly polarized light vortex and the right-handed circularly polarized light vortex are respectively emitted onto a metasurface designed by a diffractive optical neural network, and the left-handed circularly polarized light vortex and the right-handed circularly polarized light vortex are converted into a preset number of focal points by the metasurface; Linearly superimposing a preset number of focal points corresponding to the left-handed circularly polarized light vortex and a preset number of focal points corresponding to the right-handed circularly polarized light vortex to obtain a preset number of complex focal points; The intensities of the preset number of complex foci are collected, and the intensities of the preset number of complex foci are analyzed through an electronic deep neural network model to obtain polarization information of the mixed-order Poincare beam.

2. The method according to claim 1, characterized in that The preset number is 3, and the amplitude and phase of the preset number of foci corresponding to the left-handed circularly polarized light vortex satisfy: A1=A2=A3=1, The amplitude and phase of the preset number of focal points corresponding to the right-handed circularly polarized light vortex satisfy: A1=A2=A3=1, Among them, A1, A2, and A3 are the amplitudes of the three focal points respectively. They are the phases of the three foci respectively.

3. The method according to claim 1, characterized in that The metasurface is a double layer, and the metasurface is composed of silicon nitride nanorods on a quartz substrate; the size and azimuth angle of the silicon nitride nanorods vary in space to achieve the phase required for the output focus.

4. The method according to claim 1, characterized in that: The collecting the intensities of the preset number of complex focal points comprises: For any complex focus, the Poynting vector of a preset area centered on the complex focus is integrated to obtain the intensity of the complex focus.

5. The method according to claim 4, characterized in that The magnitude of the complex focus is expressed as: Among them, A n represents the magnitude of the complex focus, and denote the initial amplitudes of the right-handed circularly polarized light vortex component and the left-handed circularly polarized light vortex component, σ L represents the initial amplitude of the left-handed circularly polarized light vortex, θ L represents the initial phase of the left-handed circularly polarized light vortex, Indicates the preset phase of the left-handed circularly polarized light vortex corresponding to the focus, σ R represents the initial amplitude of the right-handed circularly polarized light vortex, θ R represents the initial phase of the right-handed circularly polarized light vortex corresponding to the focus, It represents the preset phase of the focus corresponding to the right-handed circularly polarized light vortex, and i represents the i-th focus position.

6. The method according to claim 1, characterized in that The step of analyzing the intensities of the preset number of complex focal points by an electronic deep neural network model to obtain polarization information of the mixed-order Poincare beam comprises: Determining an intensity ratio of a preset number of complex focal points according to the intensities of the preset number of complex focal points; The intensity ratio is input into the electronic deep neural network model to obtain the polarization information of the mixed-order Poincare beam.

7. The method according to claim 6, characterized in that The electronic deep neural network model includes an input layer, a nonlinear fully connected layer and an output layer; the inputting the intensity ratio into the electronic deep neural network model to obtain the polarization information of the mixed-order Poincare beam includes: Inputting the intensity ratio to each neuron of the nonlinear fully connected layer through the input layer to obtain feature data output by each neuron; The characteristic data output by each neuron is input into the output layer to obtain the polarization information of the mixed-order Poincare beam.

8. A polarization state characterization device for mixed-order Poincare beams based on a diffractive metasurface, characterized in that: include: A decomposition module, used for decomposing a mixed-order Poincare beam into a left-handed circularly polarized light vortex and a right-handed circularly polarized light vortex; a diffraction module, for respectively emitting the left-handed circularly polarized light vortex and the right-handed circularly polarized light vortex onto a metasurface designed by a diffraction optical neural network, and converting the left-handed circularly polarized light vortex and the right-handed circularly polarized light vortex into a preset number of focal points through the metasurface; A superposition module, used for linearly superimposing a preset number of focal points corresponding to the left-handed circularly polarized light vortex and a preset number of focal points corresponding to the right-handed circularly polarized light vortex to obtain a preset number of complex focal points; An analysis module is used to collect the intensity of the preset number of complex foci, and analyze the intensity of the preset number of complex foci through an electronic deep neural network model to obtain polarization information of the mixed-order Poincare beam.

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