Depolarization holographic method based on polarization multiplexing metasurface

Abstract

The invention provides a polarization multiplexing metasurface-based depolarization holographic method, which comprises the following steps of: describing a polarization state of light by using Jones calculation, and defining a propagation model of a wave; the pixel pitch of the metasurface and the height of the nanorod are determined, and a function between the length and width (l, w) of the nanorod and the modulation phase is obtained; a strict coupling wave analysis RCWA method is used, and electromagnetic response of the nanostructure is simulated under local period approximate LPA; fitting the libraries of phi xx and phi yy through a linear quadratic polynomial at each wavelength so as to represent a Jones matrix of the metasurface; introducing a noise function fnoise, applying the noise function fnoise to the metasurface, and calculating the complex amplitude of the metasurface by using an agent model; and establishing a joint optimization process, optimizing the metasurface geometric diagram and the SLM phase diagram, generating a focal length stacking hologram of the target image data set, and performing verification by using a CITL calibration model. According to the method, the image quality can be improved.

Description

Technical Field

[0001] The present disclosure relates to the field of image processing, and particularly to a depolarization holographic method based on polarization multiplexed metasurfaces. Background Art

[0002] The latest progress in holographic display technology has mainly benefited from advanced computer-generated holography (CGH) algorithms, which have successfully achieved excellent image quality. However, the improvement of CGH algorithms is gradually affected by the physical limitations of display systems, and the technology development tends to saturate. A fundamental problem faced by holographic display technology is whether there are still unexploited degrees of freedom. If these undeveloped degrees of freedom can be discovered, it will bring new development opportunities for CGH algorithms, thereby improving the performance of holographic displays.

[0003] The physical limitations of holographic display are mainly related to the coherence of light. In particular, the speckle noise generated by coherent light poses a challenge to the quality of holographic images. Speckle noise not only reduces the clarity of the image but also interferes with the natural accommodation response of the human eye in holographic images. Traditional speckle reduction techniques often require a compromise in image resolution or rely on high-speed spatial light modulators (SLMs) to reduce the speckle intensity through temporal averaging of multiple frames of images. Therefore, using a single static optical element to reduce speckle noise would be a significant advantage.

[0004] Among the various properties of light, the polarization state has been widely used in a variety of imaging and display applications. In particular, the incoherence of orthogonal polarization states is extremely beneficial to the development of holographic display technology. However, due to the lack of a suitable optical platform capable of performing polarization-dependent light modulation, research in this field has been long neglected. Fortunately, in 2016, researchers introduced a new type of optical element called metasurface, which can modulate the optical response of light at the subwavelength scale, providing a new way to solve this problem. Metasurfaces can provide independent phase distributions for two orthogonal polarization states of incident light, which is a unique property that is difficult to achieve with traditional optical elements. In addition, the pixel-level optical response modulation of metasurfaces enables optimized designs and makes it an ideal optical platform for holographic displays. Summary of the Invention

[0005] In response to the above-mentioned problems, the present invention proposes a depolarization holographic method based on polarization multiplexing metasurface, which characterizes the wave propagation containing polarization information through Jones vector and Jones matrix; uses RCWA simulation and library fitting technology to establish a differentiable metasurface proxy model to overcome the physical limitations brought by phase modulation limitation and material dispersion; the proxy model utilizes the polarization channel of the holographic display through metasurface technology to simultaneously generate two holographic images with orthogonal polarization states; the designed joint optimization process constitutes a fully differentiable optimization path, aiming to maximize the polarization multiplexing effect while taking into account the physical limitations of the metasurface, and integrating it into the CGH optimization algorithm, thereby realizing depolarization holography and improving the overall image quality.

[0006] The solution of the present disclosure includes the following steps:

[0007] The Jones calculus is used to describe the polarization state of light. The polarization state is represented by a 2×1 Jones vector, and the optical element is described by a 2×2 Jones matrix to define a wave propagation model.

[0008] Determine the pixel spacing of the metasurface and the height of the nanorods, and obtain the relationship function between the length and width (l, w) of the nanorods and the modulation phase;

[0009] The rigorous coupled wave analysis (RCWA) method is used to simulate the electromagnetic response of nanostructures under the local periodic approximation (LPA).

[0010] At each wavelength, φ xx ,φ yy The library is fitted by a linear quadratic polynomial to represent the Jones matrix of the metasurface;

[0011] Introducing noise function f noise and applied it to the metasurface, using a proxy model to calculate its complex amplitude based on the metasurface’s geometrical graph;

[0012] A joint optimization process is established to optimize the metasurface geometry and SLM phase image, generate focal stack holograms of the target image dataset, and experimentally validated using the CITL calibration model.

[0013] In some embodiments, the Jones vector is defined as:

[0014]

[0015] The Jones matrix is defined as:

[0016]

[0017] Define horizontal linear polarization as a vector The vertical linear polarization state is a vector v x and v y These two vectors are respectively and Complex vectors of.

[0018] In some embodiments, the following steps are included:

[0019] The angle between the horizontal line and the fast axis after passing through the SLM is set to 22.5°. The half-wave plate rotates the horizontally polarized light passing through the SLM by 45 degrees, thereby generating a diagonal polarization state;

[0020] The metasurface after the HWP applies different phase modulations to the orthogonal linear polarization states;

[0021] Among them, the Jones matrix J of the half-wave plate hwp and the Jones matrix J of the metasurface meta Are expressed as:

[0022]

[0023] Among them, J hwp and J hwp Represent the Jones matrices of the half-wave plate and the metasurface respectively, while φ xx and φ yy Represent the phase shifts introduced by the transmitted light on the corresponding polarization components.

[0024] In some embodiments, the Jones vector of the complex-valued wavefront after the metasurface is expressed as the matrix multiplication of the Jones vector of the SLM field ), the Jones matrix J of the HWP hwp and the Jones matrix J of the metasurface meta . The complex-valued wavefront and the intensity of the corresponding field at a distance z are expressed as:

[0025]

[0026] Among them, the intensity of the propagation field is expressed as the sum of the intensities of the fields evolving in two orthogonal polarization states due to mutual incoherence.

[0027] In some embodiments, two polarization states (φ xx , φ yy ) and different wavelengths are combined together, including 638nm, 520nm and 450nm, and a total of 6 libraries are obtained;

[0028] For each wavelength, a linear quadratic polynomial is used to fit the obtained Jones matrix, and its general expression is:

[0029]

[0030] where l and w are normalized values relative to the meta - surface pixel pitch, C nm , are polynomial coefficients, and J proxy is the approximate Jones matrix of the meta - surface.

[0031] In some embodiments, the expression of the noise function is:

[0032] f noise (l(x)) = l(x)*δ(x - x ∈ ) + l ∈

[0033] where * is the convolution operation, δ(·) represents the Dirac delta function, and the misalignment noise x ∈ is determined by the uniform random distribution U(-σ x , σ x ) and is used to translate the sub - surface, while the fabrication error is simulated by adding Gaussian noise .

[0034] In some embodiments, the joint optimization process steps include using a pre - calibrated metasurface surrogate model to calculate the complex - valued amplitude of the metasurface based on geometric parameters;

[0035] combining the noise function f noise and the approximate Jones matrix J proxy of the metasurface to incorporate the noise effect into the model;

[0036] where the optimization objective is to minimize the following loss function:

[0037]

[0038] where, is the loss function, φ is the SLM phase map, and {d}, d = 1,... D are the exponents of the propagation distance.

[0039] The beneficial effects of the present invention are as follows: Using Jones vectors and Jones matrices to characterize polarization - related wave propagation; creating a differentiable metasurface surrogate model by combining RCWA simulation and library fitting technology, effectively addressing the phase modulation limitation and material dispersion problems; the surrogate model utilizes metasurface technology to fully exploit the polarization channel potential of holographic displays and can create two orthogonally polarized holographic images simultaneously; the designed optimization process constitutes a fully differentiable optimization path, aiming to optimize the polarization multiplexing effect, while considering the actual physical limitations of the metasurface and integrating them into the CGH optimization algorithm, thereby achieving depolarization holography and significantly improving the image quality. Brief Description of the Drawings

[0040] Figure 1 It is a flowchart of the overall implementation of the depolarization holographic method in the related art.

[0041] Figure 2 It is a flowchart of the overall implementation of the depolarization holographic method based on polarization multiplexing metasurfaces in some examples of the present disclosure.

[0042] Figure 3 It is a flowchart of the implementation of the joint optimization process in some examples of the present disclosure.

[0043] Figure 4 It is a flowchart of the implementation of the wave propagation model CITL calibration framework in some examples of the present disclosure;

[0044] Figure 5 It is a schematic diagram of the qualitative comparison of four scenarios in the comparative experiment in some examples of the present disclosure. Detailed Description of the Embodiments

[0045] The embodiments of the technical solution of the present application will be described in detail below with reference to the drawings. The following embodiments are only used to illustrate the technical solution of the present application more clearly, so they are only examples and cannot be used to limit the protection scope of the present application.

[0046] Figure 1 It schematically shows the overall implementation flowchart of the depolarization holographic method in the related art. The existing method receives linearly polarized incident light through a spatial light modulator (SLM).

[0047] Figure 2 It schematically shows the overall implementation flowchart of the depolarization holographic method based on polarization multiplexing metasurfaces in some examples of the present disclosure. The SLM receives linearly polarized incident light. A half-wave plate (HWP) and a metasurface are placed behind the SLM. The angle between the horizontal line of the HWP and the fast axis is set to 22.5 degrees. Therefore, the HWP rotates the horizontally polarized light incident on the SLM by 45°, forming a diagonal polarization state. Since the diagonal polarization state can be separated into horizontally and vertically linearly polarized states with the same amplitude, the metasurface behind the HWP applies different phase modulations to these two orthogonal linearly polarized states.

[0048] A depolarization holographic method based on polarization multiplexing metasurfaces of the present disclosure involves steps such as model description, electromagnetic simulation, library fitting, surrogate model construction, and joint optimization process design.

[0049] In the model description stage, the present disclosure defines the Jones vector and Jones matrix notations for describing the propagation of polarized waves. Subsequently, through RCWA simulation and library fitting techniques, a differentiable metasurface surrogate model is established to overcome the physical limitations of phase modulation and material dispersion. In the construction of the surrogate model, metasurface technology is utilized to exploit the polarization channels of the holographic display and generate two holographic images with orthogonal polarization states. The joint optimization process designs a fully differentiable optimization path aimed at maximizing the polarization multiplexing effect while taking into account the physical limitations of the metasurface and integrating it into the CGH optimization algorithm.

[0050] In some examples, Jones calculus is used to describe the polarization state of light. The polarization state is represented by a 2×1 Jones vector, and an optical element is described by a 2×2 Jones matrix, defining the wave propagation model.

[0051] In these examples, the horizontal linear polarization state can be defined as the vector which is specifically represented as [1, 0] T , and the vertical linear polarization state is represented by the vector in the form of [0, 1] T . Therefore, the elements v x , v y of the Jones vector contain the complex-valued information of the horizontal and vertical polarization components. The influence of the optical element on the polarization state is calculated by matrix multiplication of the Jones matrix and the Jones vector:

[0052]

[0053] In some examples, the pixel pitch of the metasurface and the height of the nanorods are determined to obtain the relationship function between the nanorod length and width (l, w) and the modulation phase.

[0054] In these examples, a half-wave plate (HWP) and a metasurface are placed after the SLM. The angle between the horizontal line of the HWP and the fast axis is set to 22.5 degrees. Therefore, the HWP rotates the horizontally polarized light incident on the SLM by 45°, forming a diagonal polarization state. Since the diagonal polarization state can be separated into horizontal and vertical linear polarization states with the same amplitude, the metasurface after the HWP applies different phase modulations to these two orthogonal linear polarization states. The Jones matrices of the HWP and the metasurface are described as:

[0055]

[0056] where φ xx , φ yy represents the phase shift on the co-polarization component of the transmitted light.

[0057] Assume that the SLM, HWP, and metasurface are close enough and lie in the same plane. The Jones vector of the complex-valued wavefront behind the metasurface is represented as the Jones vector of the SLM field. The Jones matrix J of the HWP hwp and the Jones matrix J of the metasurface meta for matrix multiplication. Thus, the complex-valued wavefront and the intensity of the corresponding field at a distance z are represented as:

[0058]

[0059] Here, the intensity of the propagating field is represented as the sum of the intensities of the fields evolving in two orthogonally polarized states due to mutual incoherence.

[0060] Figure 2 Shows the process of electromagnetic simulation using the orthogonally polarized states of the metasurface as described in some examples of the present disclosure. After the HWP passes through the SLM, the horizontally polarized light passing through the SLM is rotated by 45 degrees to form a diagonal polarization state. Then, the polarization multiplexing metasurface provides different phase modulations for each linearly polarized state. The subsequent reconstructed fields along the two orthogonally polarized channels do not interfere with each other, resulting in a weighted intensity sum.

[0061] In the library fitting step, the rigorous coupled-wave analysis (RCWA) method is used to simulate the electromagnetic response of the nanostructure under the local periodic approximation (LPA). For each wavelength, the library of φ xx , φ yy is fitted with a linear quadratic polynomial to represent the Jones matrix of the metasurface.

[0062] In some examples, the fitting process uses the rigorous coupled-wave analysis (RCWA) to simulate the electromagnetic response of the nanostructure within the framework of the local periodic approximation (LPA). Given the known pixel pitch of the metasurface and the height of the nanorods, the modulation phase is derived as a function of the length and width (l, w) of the nanorods. Combining the two polarization states (φ xx , φ yy ) with different wavelengths, including 638 nm, 520 nm, and 450 nm, a total of 6 libraries are obtained. Then, for each wavelength, the resulting Jones matrix is fitted with a linear quadratic polynomial, and its general expression is:

[0063]

[0064] where l, w are normalized by the pixel pitch of the metasurface, C nm , are the polynomial coefficients, and J proxy is the approximate Jones matrix of the metasurface.

[0065] In the surrogate model step, a noise function f is introduced noise , and it is applied to the metasurface. Using the surrogate model, the complex amplitude of the metasurface can be calculated based on its geometry map.

[0066] In some examples, a noise function f noise is implemented to simulate potential alignment and manufacturing errors that may occur in experiments, so that the optimized metasurface is robust to these defects. The noise function is expressed as:

[0067] f noise (l(x)) = l(x) * δ(x - x ∈ ) + l ∈

[0068] where * is the convolution operation, and δ(·) represents the Dirac delta function. The misalignment noise x x is determined by the uniform random distribution U(-σ x ),σ ∈ to translate the sub-surface, and Gaussian noise is added for manufacturing errors Although the present invention only represents the dependence of the dimension x in the formula in l, it is equally applicable to the parameter w and the dimension y.

[0069] In the joint optimization process, a joint optimization process is established to optimize the metasurface geometry map and the SLM phase map, generate the focal stack holograms of the target image dataset, and use the CITL calibration model for experimental verification.

[0070] In some examples, a focal stack is selected as the optimization target because in conventional holographic display technologies, attempting to achieve the target through a single spatial light modulator (SLM) phase pattern usually encounters a highly complex and overly restrictive problem. First, using the pre-calibrated metasurface surrogate model, the complex-valued amplitude of the metasurface is calculated based on the geometric parameters. Subsequently, combining the noise function f noise and the approximate Jones matrix J proxy of the metasurface, the noise effect is taken into account in the model. The optimization objective is to minimize the following loss function:

[0071]

[0072] where is the loss function, φ is the SLM phase map, and {d}, d = 1,... D are the exponents of the propagation distances. The present invention optimizes the geometric parameters (l, w) of the deformed surface through a large dataset, where the φ of each target image can obtain the optimal result.

[0073] Figure 3Schematically shows the joint optimization process described in some examples of the present disclosure. The joint optimization of the subsurface nanostructure geometry map and the SLM phase map realizes the focal-stack hologram on the target image dataset. The SLM field evolves into two different holograms through polarization multiplexing of the subsurface. In this process, the Jones matrix of the noise reflection simulates the optical operation of the metasurface under experimental conditions. The two holograms of each polarization state propagate to all target planes and are then combined by summing through the content-guided attention (CGA) mechanism. The backpropagation gradient of the loss calculated between the reconstructed focal plane and the target focal plane updates the subsurface and SLM phase patterns.

[0074] Figure 4 [[ID=X]]Schematically shows the CITL calibration framework of the wave propagation model described in some examples of the present disclosure. The calibration framework mainly includes a multi-layer perceptron and a k model with a 3×3 kernel, which is the spatially varying phase response and the crosstalk between adjacent pixels. The source intensity a src , phase φ src and the complex fields of the Fourier plane a F , φ F are combined into f ASM [[ID=1 X]] to consider the propagation terms independent of the content. Among them, the amplitude of the light wave is first captured and reconstructed, and then the phase of the light wave at different depths is controlled by the spatial light modulator SLM. The integrated free-form microlens array f ASM further adjusts the phase and amplitude of the light wave to optimize the imaging or transmission effect. The multiplexed perceptron (MLP) processes the resulting signal while solving the crosstalk problem to ensure the clarity of the signal. According to the specific properties of the metasurface and the polarization state of the light wave, the system adjusts the parameters accordingly to adapt to conditions such as the y polarization and tilt angle. The entire process is interconnected and coordinated to form a closed-loop system, where the output of each step may serve as the input of the next step to achieve dynamic optimization and precise control.

[0075] To verify the effectiveness of the present invention, quantitative analysis is performed for four scenarios, and comparative tests are carried out with traditional holographic displays, holographic displays using a single polarization state to optimize the metasurface, and depolarized holographic display methods using two orthogonal polarization states to optimize the metasurface.

[0076] The experimental simulation content of the depolarized holographic method based on the polarization multiplexed metasurface of the present invention is as follows:

[0077] It should be noted that in the translation of the text in item , the content in the original text seems to be incomplete or there may be some errors in the tags. I have tried my best to translate it according to the overall context and translation requirements. If there are inaccuracies, please adjust according to the actual situation. Also, the text in item has been adjusted to make the translation more fluent while maintaining the original meaning as much as possible.Using depolarization holography, images are generated according to different light polarization states to obtain a polarization-related amplitude dataset for model training. This dataset contains 1600 phase patterns generated by the stochastic gradient descent method and an additional 400 phase patterns obtained by the alternating direction method of the multiplier method. Among the phase patterns generated by the stochastic gradient descent method, 800 are optimized for 2D images, and the other 800 are optimized based on the incoherent focus stack of 2D images. A total of 2000 phase maps are used for training in each channel. During the dataset creation process, the learning rate, propagation distance, and range of the initial random phase distribution are randomized. The intensity of the hologram is recorded on 7 different depth planes, covering 4 cases: a single phase pattern without a metasurface, and vertical, horizontal, and diagonal polarization with a metasurface. This enables the model to learn the polarization-related metasurface phase and amplitude, as well as other parameters of the propagation model, through CITL training. The model is trained for 10 epochs with a learning rate of 5E-4 for each channel. On the NVIDIA RTXA6000, the model training for each channel takes approximately 6 hours. Please refer to Figure 5 , the research results show that the introduction of the metasurface improves the imaging quality of the focal stack hologram. The granular speckle pattern that appears under traditional conditions becomes smoother under the optimized depolarization condition, thus improving the clarity of image details. By magnifying each image, it can be found that the optimized depolarization condition has lower intensity fluctuations and fewer granular patterns compared to the traditional condition. The speckle pattern, as high-frequency noise, appears in the mid- to high-frequency regions of the image under traditional conditions.

Claims

1. A depolarization holographic method based on polarization multiplexed metasurface, characterized in that, Including the following steps: Using Jones calculus to describe the polarization state of light, where the polarization state is represented by a 2×1 Jones vector and the optical element is described by a 2×2 Jones matrix, and defining the wave propagation model; Determining the pixel pitch of the metasurface and the height of the nanorods, and obtaining the relationship function between the length and width (l, w) of the nanorods and the modulation phase; Using the rigorous coupled-wave analysis (RCWA) method to simulate the electromagnetic response of the nanostructure under the local periodic approximation (LPA); At each wavelength, φ xx , φ yy 's library is fitted by a linear quadratic polynomial to represent the Jones matrix of the metasurface; Introduce the noise function f noise , and apply it to the metasurface. Using the surrogate model, calculate its complex amplitude according to the geometry of the metasurface; Establishing a joint optimization process to optimize the metasurface geometry map and the SLM phase map, generating the focal stack hologram of the target image dataset, and using the CITL calibration model for experimental verification.

2. The depolarization holographic method based on polarization multiplexed metasurface according to claim 1, wherein The Jones vector is defined as: The said Jones matrix is defined as: Define the horizontal linear polarization as the vector The vertical linear polarization state as the vector v x and v y These two vectors are respectively and Complex vectors of 3. A depolarization holographic method based on a polarization multiplexed metasurface according to claim 1, wherein Including the following steps: The angle between the horizontal line and the fast axis after passing through the SLM is set to 22.5°. The half-wave plate rotates the horizontally polarized light passing through the SLM by 45 degrees, thereby generating a diagonal polarization state; Applying different phase modulations to the orthogonal linear polarization states using the metasurface after the HWP; Among them, the Jones matrix J of the half-wave plate hwp and the Jones matrix J of the metasurface meta are expressed as: Among them, J hwp and J hwp represent the Jones matrices of the half-wave plate and the metasurface respectively, while φ xx and φ yy represent the phase shifts introduced by the transmitted light on the corresponding polarization components.

4. A depolarization holographic method based on a polarization multiplexed metasurface according to claim 3, characterized in that, The Jones vector representation of the complex-valued wavefront after the metasurface is the Jones vector of the SLM field The Jones matrix J of the HWP hwp and the Jones matrix J of the metasurface meta The matrix multiplication of, the complex-valued wavefront at distance z and the intensity of the corresponding field are expressed as: Among them, the intensity of the propagation field is expressed as the sum of the intensities of the fields evolving in two orthogonal polarization states due to mutual incoherence.

5. A depolarization holographic method based on a polarization multiplexed metasurface according to claim 1, wherein Combining two polarization states (φ xx , φ yy ) and different wavelengths together, including 638 nm, 520 nm, and 450 nm, a total of 6 libraries were obtained; For each wavelength, a linear quadratic polynomial is used to fit the obtained Jones matrix, and its general expression is: where l, w are the normalized values with respect to the meta - surface pixel pitch, are polynomial coefficients, and J proxy is the approximate Jones matrix of the meta - surface.

6. The depolarization holographic method based on polarization multiplexed metasurface according to claim 1, characterized in that The expression of this noise function is: f noise (l(x)) = l(x) * δ(x - x ∈ ) + l ∈ where * is the convolution operation, δ(·) represents the Dirac delta function, and the misalignment noise x ∈ is determined by the uniform random distribution U(−σ x , σ x ) for translating the subsurface, while the manufacturing error is simulated by adding Gaussian noise .

7. A depolarization holographic method based on a polarization multiplexed metasurface according to claim 1, wherein The steps of the joint optimization process include calculating the complex-valued amplitude of the metasurface based on the geometric parameters using a pre-calibrated metasurface surrogate model; Combined with the noise function f noise and the approximate Jones matrix J of the metasurface proxy , the noise effect is incorporated into the model for consideration; Among them, the optimization objective is to minimize the following loss function: wherein, is the loss function, φ is the SLM phase diagram, and {d}, d = 1, ... D are the exponents of the propagation distances.

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