Method for realizing dual-polarization broadband Laplace differentiator based on non-local metasurface

Abstract

The invention discloses a method for realizing a dual-polarization broadband Laplacian differentiator based on a non-local metasurface, and belongs to the application fields of nano photonics, optical calculation and optical field information regulation and control. The non-local metasurface works in a transmission mode and is composed of a square ring unit array made of a single-layer amorphous silicon material. By designing and selecting geometric parameters of the square ring, the non-local metasurface respectively excites bound state modes with different angle dispersion capabilities in a quasi-continuous domain under irradiation of p polarized light and s polarized light, and an optical transfer function required by optical Laplacian differential operation can be realized in a real airspace. And generating a processing file of the corresponding non-local metasurface according to the determined geometric dimension of the square ring unit. And processing the transmission-type non-local metasurface by adopting a micro-nano processing technology of electron beam etching. In a working wave band, when a target image directly enters the non-local metasurface under irradiation of p polarized light and s polarized light, two-dimensional second-order edge contour information of the target image can be directly obtained under the dual-polarization channel.

Description

Technical Field

[0001] This invention relates to a method for realizing a dual-polarization broadband Laplacian differentiator based on a nonlocal metasurface, and more particularly to a method for directly realizing a broadband Laplacian differentiator in the spatial domain in p-polarization and s-polarization channels based on a transmissive dielectric optical nonlocal metasurface, which is used to realize second-order two-dimensional edge detection of target images, belonging to the fields of nanophotonics, optical simulation image processing and light field information manipulation technology. Background Technology

[0002] Differentiators can capture high-frequency components of an incident light field and filter out low-frequency components, thus enabling edge detection of target objects in image processing. Compared to traditional electronic or digital differentiators, optical analog differentiators utilize the specific optical transfer function of optical devices to differentiate the incident light field, facilitating faster identification and extraction of target object feature information. This is crucial for the development of various modern technologies, including autonomous driving, medical imaging, and head-mounted display applications.

[0003] Generally, there are two methods for realizing optical analog differentiation: Fourier spatial filtering and Green's function methods. Regardless of the method used, the core objective is to enable the device to perform differential operations using an optical transfer function. The former mainly uses a 4f filtering system consisting of a pair of optical lenses and a filter to apply a spatial mask in the frequency domain, differentiating and filtering the target image to obtain a differential image. However, this system is relatively large, hindering miniaturization and integration into existing commercial imaging systems. The latter method focuses on designing an optical transfer function with an angular dispersion response to the incident light field and performing edge detection directly in the spatial domain. By eliminating the need for a 4f system lens assembly, it enables a more compact differential image processing system, simplifying complexity and promoting scalability for integrated applications. However, for traditional optical devices, designing an optical transfer function with an angular dispersion response using the Green's function method to realize optical analog differentiation is extremely challenging. In recent years, artificial nanostructures called optical metasurfaces have been found to improve this problem.

[0004] Metasurfaces, as ultrathin artificial engineering structures, can precisely control the amplitude, phase, and polarization of incident light fields at the micro- and nanoscale. Therefore, they possess significant advantages and broad application prospects in holographic imaging, precision measurement, optical simulation calculations, and optical image processing. Current research shows that metasurface differentiators can achieve unidirectional first-order differentiation and edge detection through optical resonance, the photon spin Hall effect, and Pancharatnam-Berry phase. However, common images possess two-dimensional information. Therefore, limiting differentiation and edge detection to one-dimensional or single-directional aspects cannot meet practical needs or fully demonstrate the powerful capabilities of metasurfaces. To obtain all edge information of any image in a single exposure, the simplest method is to design a Laplacian differentiator, which can perform edge detection for two-dimensional second-order images. Based on the Green's function method, designing nonlocal metasurfaces with angle selectivity to the incident light field is an effective strategy for realizing the optical transfer function required for Laplacian differentiation. For example, nonlocal metasurfaces can be used to excite Fano resonances or guided mode resonances to achieve Laplacian differentiation. However, these schemes also face limitations, including some differentiators that only function in theoretical designs and are practically unmanufacturable. Furthermore, some differentiators rely on a single polarization channel, are limited by narrow bandwidth, have low resolution, and require additional polarization equipment or digital post-processing, all of which hinder their performance and operational efficiency. These issues significantly limit the practical application of Laplace differentiators. Summary of the Invention

[0005] The purpose of this invention is to provide a method for realizing a broadband Laplacian differentiator with dual polarization channels based on a nonlocal metasurface. By designing a nonlocal metasurface to excite bound state modes in a quasi-continuous domain with different angular dispersion capabilities under p-polarized and s-polarized light illumination, a Laplacian differentiator with large numerical aperture, high resolution, and wide bandwidth can be directly realized in the spatial domain for the p-polarized and s-polarized channels based on this nonlocal metasurface. This enables the realization of two-dimensional second-order edge contour information of the target image under dual polarization channels. This invention is applied to optical systems such as optical image processing, optical simulation calculation, and machine recognition, solving related engineering and technical problems.

[0006] The objective of this invention is achieved through the following technical solution.

[0007] This invention discloses a method for realizing a dual-polarization broadband Laplacian differentiator based on a nonlocal metasurface. The nonlocal metasurface used to realize the dual-polarization channel Laplacian differentiator is composed of a square ring array of a single layer of amorphous silicon material, operating in transmission mode. It has a simple structure and is easy to fabricate. A minimum square ring unit structure with selected geometric parameters is designed so that the nonlocal metasurface obtains bound state modes in a quasi-continuous domain sensitive to the incident angle within the operating wavelength range of the dual-polarization channel, thereby satisfying the optical transfer function required for optical Laplacian operations in the spatial domain, i.e., ensuring that the optical transfer function and the incident angle satisfy a quadratic relationship. Based on the determined geometric dimensions of the square ring unit, a corresponding fabrication file for the nonlocal metasurface is generated. Such a transmission-type nonlocal metasurface is fabricated using electron beam etching micro / nano fabrication technology. In the operating wavelength range for exciting the bound state modes in the quasi-continuous domain, when the target image irradiated by p-polarized light and s-polarized light is directly incident on the optical resonant metasurface, clear second-order two-dimensional edge contour information of the target image is directly obtained in the spatial domain behind the metasurface.

[0008] The method for realizing a dual-polarization broadband Laplace differentiator based on a nonlocal metasurface disclosed in this invention includes the following steps:

[0009] Step 1: A single-layer nonlocal metasurface for realizing a dual-polarization broadband Laplacian differentiator is constructed from a square ring array of amorphous silicon material with identical structural dimensions. By designing the geometry of the square ring units, the single-layer nonlocal metasurface can achieve dual polarization channels under p-polarization and s-polarization, obtaining bound state modes in different quasi-continuous domains with selective characteristics for incident angles, thereby obtaining the optical transfer function required for the nonlocal metasurface to perform two-dimensional second-order edge detection of images. When the input light field passes through the nonlocal metasurface under the dual polarization channels, the light field information is processed separately, and the result of the Laplacian operation can be obtained by recording the output light field information separately.

[0010] To perform second-order two-dimensional optical spatial simulation differential operations in real space for p-polarized and s-polarized cases respectively, the nonlocal metasurface should function as an optical Laplacian operator for the transmitted light field of the target object under both polarization channels, so that the distribution of the transmitted electric field of the target image exhibits the following characteristics: in This represents the Laplace operator, whose mathematical form is: This is equivalent to designing the optical transfer function of a nonlocal metasurface in the p-polarization and s-polarization channels in k-space to meet the operational requirements of the Laplace operation, as shown in Equation (1).

[0011]

[0012] Where the subscripts s and p represent the polarization of the incident light and the transmitted light, respectively, and the horizontal wave vector distribution is k. || =ksin(θ), where k represents the incident wave vector, and θ and These represent the incident angle and azimuth angle of the incident light, respectively. k x and k y Let x and y represent the components of the wave vector along the two orthogonal axes, respectively. Therefore, for a nonlocal metasurface to perform Laplace differentiation in both p-polarized and s-polarized channels, the optical transfer function in both polarization channels must satisfy a quadratic function relationship with respect to the plane wave vector of the incident light field. Simultaneously, when the incident angle is normal, the transmittance of the nonlocal metasurface should be zero, while when the incident angle becomes oblique, the transmittance of the nonlocal metasurface in both p-polarized and s-polarized channels increases accordingly, satisfying the quadratic function relationship.

[0013] Performing the Laplace operation in the real space domain is equivalent to filtering out the low-frequency information components of the incident light field in k-space, while the high-frequency information components are transmitted according to the aforementioned rules. This allows the nonlocal metasurface to function as a high-pass filter in both p-polarization and s-polarization channels. This optical characteristic of performing a high-pass filter in dual polarization channels is achieved by exciting a nonlocal metasurface with bound states in a quasi-continuous domain dominated by different electromagnetic resonance modes in both p-polarization and s-polarization channels.

[0014] The principle of high-pass filtering under dual polarization channels is as follows: In a normally incident symmetric system, the bound states in the quasi-continuous domain have not yet been excited. At this time, both polarization channels exhibit bound states in the continuous domain of the non-radiative dark mode, which helps to obtain near-zero transmittance under normally incident conditions. When the incident light is tilted and obliquely incident, the symmetry of the entire system is broken. The bound states in the quasi-continuous domain with radiation characteristics are excited in the p-polarized and s-polarized channels respectively, thereby affecting the spectral transmission characteristics, causing the spectral transmission amplitude to increase with the increase of the oblique incident angle.

[0015] As a preferred embodiment, the specific method for realizing the desired spectral properties of the nonlocal metasurface is as follows:

[0016] The height H and period P of the square ring unit are set, the working wavelength is selected from 1150nm to 1500nm, the material is amorphous silicon, and the transmission spectrum of the square ring structure unit with different combinations of outer side length L and inner hole side length w is scanned using optical electromagnetic calculation tools. Based on the transmission results of scanning different incident angles under p-polarization and s-polarization channels, the structural parameters required for the transfer function of the nonlocal metasurface to realize a dual-polarization broadband Laplace differentiator are determined.

[0017] Preferably, the electromagnetic calculation tools can be FDTD and COMSOL, which are based on the finite element time-domain (FTD) method.

[0018] Step Two: Determine the transmission spectral response of the square ring structure constituting the nonlocal metasurface within the working wavelength range of 1150 nm to 1500 nm, ensuring that the normal incident transmittance of the nonlocal metasurface is close to zero over a wide working wavelength range. When the incident light becomes obliquely incident, the transmittance of the nonlocal metasurface in both p-polarized and s-polarized channels increases with the increase of the oblique incident angle, providing the necessary conditions for realizing broadband Laplace operations under dual polarization. Simultaneously, the resonance modes at the working position under p-polarization and s-polarization are analyzed using electromagnetic mode analysis methods, and the bound states in the quasi-continuous domains of different electromagnetic resonance modes are determined by analyzing the corresponding electromagnetic field distribution. Furthermore, by analyzing the effects of changes in incident angle and azimuth angle on the transmission spectrum under p-polarization and s-polarization, the constraint conditions for polarization and azimuth angle for realizing a broadband Laplace differentiator under dual polarization channels using the designed nonlocal metasurface are determined.

[0019] Step 3: Based on Step 1 and Step 2, the geometric parameters of the square ring unit of the nonlocal metasurface used to realize the dual-polarization broadband Laplace differentiator must satisfy the following conditions:

[0020] Condition 1: For the transmission spectral response in the near-infrared spectral region, the nonlocal metasurface satisfies that the transmittance at the normally incident resonance wavelength is zero or close to zero. When the incident light becomes obliquely incident, the transmittance of the nonlocal metasurface at the resonance wavelength under p-polarization and s-polarization increases with the increase of the incident angle, and each has a predetermined bandwidth range.

[0021] Condition 2: The physical conditions for exciting bound states in the quasi-continuous domain under dual polarization channels are met. The bound states in the quasi-continuous domain are determined based on electromagnetic intrinsic properties. The electromagnetic resonance modes of the bound states in the quasi-continuous domain under p-polarization and s-polarization channels are determined by analyzing the specific resonance modes corresponding to the resonance positions based on the electromagnetic field mode distribution. Ultimately, based on the electromagnetic field distribution, the resonance positions are determined to be bound states in the quasi-continuous domain dominated by magnetic quadrupole resonance and bound states in the quasi-continuous domain dominated by magnetic dipole resonance, respectively, under the p-polarization and s-polarization channels.

[0022] Condition 3: The relationship between the transmission spectrum of the nonlocal metasurface and the angle under both p-polarization and s-polarization channels satisfies a quadratic function relationship. The angle includes the incident angle and the incident azimuth angle. This allows the Laplace differentiator to be dependent on the polarization state and the incident azimuth angle. Simulation software is used to simultaneously satisfy the above conditions, thus ultimately determining the designed nonlocal metasurface.

[0023] The geometric parameters include the height H, period P, outer side length L, and inner hole side length w of the square ring.

[0024] Based on the above conditions that the geometric parameters of the square ring element must satisfy, the geometric parameters of the square ring element are determined, and the corresponding nonlocal metasurface processing file is generated.

[0025] Step 4: Using the fabrication file of the nonlocal metasurface obtained in Step 3, fabricate the required transmission-type nonlocal metasurface sample using a micro / nano fabrication method primarily based on electron beam etching. The target image and nonlocal metasurface are directly illuminated using p-polarization and s-polarization, and Laplacian differential operations and corresponding two-dimensional second-order image edge detection are performed directly in the spatial domain under these two polarization channels.

[0026] This invention is used to directly perform second-order two-dimensional image edge detection processing on spatial target objects under p-polarization and s-polarization channels respectively. It extends the light field information modulation function and image information processing capability of optical nonlocal metasurfaces from the frequency domain to the real space domain, significantly compressing the volume of optical systems, avoiding additional alignment requirements, and facilitating integration into multifunctional optical image processing systems.

[0027] Beneficial effects:

[0028] 1. The present invention discloses a method for realizing a dual-polarization broadband Laplace differentiator based on a nonlocal metasurface. Based on a nonlocal metasurface, a high NA and wide bandwidth Laplace differentiator is realized simultaneously under both p-polarization and s-polarization channels. By designing a square ring structure with identical geometric parameters, bound states in the quasi-continuous domain dominated by different electromagnetic resonance modes are excited in the p-polarization and s-polarization channels, respectively, so that the optical transfer function of the nonlocal metasurface in the p-polarization and s-polarization channels meets the requirements for performing Laplace differential operator operations.

[0029] 2. The method for realizing a dual-polarization broadband Laplace differentiator based on a nonlocal metasurface disclosed in this invention expands the ability of optical metasurfaces to process optical field information by directly realizing the Laplace differentiator in the real space domain, and realizes a nonlocal metasurface modulated by bound states in the quasi-continuous domain.

[0030] 3. Compared with the traditional 4f filtering scheme using glass lenses to perform differentiator function, the method of realizing a dual-polarization broadband Laplace differentiator based on a nonlocal metasurface disclosed in this invention can quickly complete the optical edge detection processing of the image without the need for additional lens combinations during the experiment, which significantly compresses the spatial volume of the optical imaging system and is conducive to promoting high integration.

[0031] 4. The method for realizing a dual-polarization broadband Laplace differentiator based on a nonlocal metasurface disclosed in this invention uses a nonlocal metasurface that is a passive device, which has lower power consumption and faster speed compared to traditional electronic or digital image edge detection.

[0032] 5. The method for realizing a dual-polarization broadband Laplacian differentiator based on a nonlocal metasurface disclosed in this invention directly performs second-order two-dimensional image edge detection and recognition on the target image. The edge detection effect is more practically valuable than that of only first-order or only one-dimensional edge detection.

[0033] 6. The method for realizing a dual-polarization broadband Laplace differentiator based on a nonlocal metasurface disclosed in this invention can extend the dual-polarization broadband optical analog differentiation and image second-order two-dimensional edge detection methods to the visible light, near-infrared or microwave bands by using a time-domain finite element difference method and a finite element method to find other square ring structures that constitute the nonlocal metasurface.

[0034] 7. The method for realizing a dual-polarization broadband Laplace differentiator based on a nonlocal metasurface disclosed in this invention can replace the silicon material of the nonlocal metasurface with titanium dioxide or germanium material, and then use the time-domain finite element difference method and the finite element method to find the size of other square ring structures, thereby obtaining a larger numerical aperture and a wider bandwidth working area.

[0035] 8. The method for realizing a dual-polarization broadband Laplace differentiator based on a nonlocal metasurface disclosed in this invention can perform edge detection on common amplitude targets, as well as on transparent biological cells or phase objects.

[0036] 9. The method for realizing a dual-polarization broadband Laplace differentiator based on a nonlocal metasurface disclosed in this invention utilizes the dependence characteristics of the nonlocal metasurface on the p-polarization and s-polarization channels to modulate light wave information of different polarization states, and can be applied to applications such as autonomous driving, mixed reality, and optical image encryption. Attached Figure Description

[0037] Figure 1 This invention relates to a method for realizing a dual-polarization broadband Laplace differentiator based on a nonlocal metasurface.

[0038] Figure 2 This is a schematic diagram of a method for realizing a dual-polarization broadband Laplace differentiator based on a nonlocal metasurface in an embodiment of the present invention.

[0039] Figure 3 These are the scanning results of the geometric parameters, resonance characteristics, and transmission spectrum of the square ring unit structure in the embodiments of the present invention;

[0040] Wherein: (a) is a schematic diagram of the square ring structure constituting the nonlocal metasurface. (b) is the transmission spectrum of the nonlocal metasurface under p-polarized light with incident light angles increasing from 0° to 25°. (c) is the transmission spectrum of the nonlocal metasurface under s-polarized light with incident light angles increasing from 0° to 25°. (d)-(e) are the top and side views of the positions of bound states in the continuous and quasi-continuous domains of the nonlocal metasurface at the resonance wavelength of 1300 nm under p-polarization, relative to the electric field Ez. (f)-(g) are the top and side views of the positions of bound states in the continuous and quasi-continuous domains of the nonlocal metasurface at the resonance wavelength of 1265 nm under s-polarization, relative to the magnetic field Hz. (h) is the optical transfer function and quadratic fit of the nonlocal metasurface at wavelengths of 1350 nm and 1285 nm under p-polarization and s-polarization, respectively.

[0041] Figure 4 These are the scanning results of the two-dimensional angular dispersive spectra of the square ring unit structure under different polarizations in the embodiments of the present invention;

[0042] Where: (a)-(f) are the two-dimensional angular transmission spectra of the nonlocal metasurface under the maximum incident angle range and arbitrary azimuth combination at the corresponding working wavelength when irradiated by p-polarized light. (g)-(l) are the two-dimensional angular transmission spectra of the nonlocal metasurface under the maximum incident angle range and arbitrary azimuth combination at the corresponding working wavelength when irradiated by s-polarized light.

[0043] Figure 5 This is the experimental optical path diagram used in the embodiments of the present invention;

[0044] Wherein: 1—incident laser source, 2—half-wave plate, 3—imaging target, 4—actually processed nonlocal metasurface sample, 5—microscope objective, 6—long focal length imaging lens, 7—CCD.

[0045] Figure 6 These are experimental results of single-wavelength images under p-polarization and s-polarization according to embodiments of the present invention;

[0046] Wherein: (a) and (b) are the imaging results of a dog illuminated by p-polarized light at 1350 nm with and without a nonlocal metasurface, respectively. (c) is a magnified view of (b). (d) and (e) are the imaging results of a dog illuminated by p-polarized light at 1285 nm with and without a nonlocal metasurface, respectively. (f) is a magnified view of (e).

[0047] Figure 7 These are experimental results of broadband image processing of nonlocal metasurfaces under p-polarization and s-polarization in embodiments of the present invention.

[0048] Wherein: (a) and (b) are broadband imaging results of the dog and pigeon images by CDD with nonlocal metasurfaces, respectively. (c)-(d) are intensity comparisons of the tangents at the same position in Figure (a) and Figure (b), respectively.

[0049] Figure 8 This is the imaging result of a nonlocal metasurface on various biological cells under p-polarization and s-polarization in an embodiment of the present invention.

[0050] Wherein: (a) to (d) are CDD imaging results of onion epidermal cells, pumpkin vesicle tissue, pepper epidermal cells, and fly wings without nonlocal metasurfaces, respectively. (e) to (h) are CDD imaging results of onion epidermal cells, pumpkin vesicle tissue, pepper epidermal cells, and fly wings under 1350 nm p-polarized light illumination with nonlocal metasurfaces, respectively. (i) to (l) are CDD imaging results of onion epidermal cells, pumpkin vesicle tissue, pepper epidermal cells, and fly wings under 1285 nm s-polarized light illumination with nonlocal metasurfaces, respectively. Detailed Implementation

[0051] To better illustrate the purpose and advantages of this invention, the following description, in conjunction with the accompanying drawings and embodiments, further explains the invention. The technical problems solved by the present invention and its beneficial effects are also described. It should be noted that the described embodiments are merely intended to facilitate understanding of the invention and do not constitute any limitation thereof.

[0052] Example: A method for realizing a dual-polarization broadband Laplace differentiator based on a nonlocal metasurface.

[0053] like Figure 1 As shown in the figure, the method for realizing a dual-polarization broadband Laplace differentiator based on a nonlocal metasurface disclosed in this embodiment is specifically implemented as follows:

[0054] Step 1: To realize a dual-polarization broadband Laplace differentiator based on a nonlocal metasurface, the nonlocal metasurface first needs to possess the optical transfer function required for implementing the Laplace differentiator in both p-polarized and s-polarized channels, thus enabling the manipulation of image light field information. The dimensions of the square ring are designed to excite bound states in a quasi-continuous domain with different angular responses in the working wavelength range for p-polarized and s-polarized light at different incident angles, thereby ensuring that the optical transfer function of the transmission spectrum satisfies the requirements for executing the Laplace differential operator. The specific implementation method for optical transfer function modulation is as follows:

[0055] Step 2: The designed nonlocal metasurface consists of an array of identical square rings. The operating wavelength range is 1100 nm to 1500 nm, and amorphous silicon is selected as the material. The substrate material used in the simulation has a refractive index of n = 1.45. Using the finite-difference time-domain method (FDTD), a combined scan was performed on the height H, outer side length L, inner side length w, and period P of the square ring structure, ultimately obtaining a square ring structure with dimensions of H = 450 nm, L = 450 nm, w = 50 nm, and P = 600 nm. Simultaneously, the electromagnetic field distribution at the resonance position was analyzed using Comsol software. It was determined that the bound states in the quasi-continuous domain with different angular responses under p-polarization exhibit magnetic dipole resonance modes, while the bound states in the quasi-continuous domain with different angular responses under s-polarization exhibit magnetic quadrupole resonance modes. Furthermore, it was determined that the spectral response of the nonlocal metasurface to different incident angles under these corresponding parameters meets the requirements for realizing a Laplace differentiator.

[0056] Step 3: Based on the processing file of the corresponding nonlocal metasurface obtained in Step 2, fabricate the nonlocal metasurface using a micro-nano processing method mainly based on electron beam etching.

[0057] Step 4: Use p-polarized and s-polarized light to incident on the nonlocal metasurface, and perform corresponding Laplacian differentiation processing and second-order two-dimensional image edge detection imaging according to the actual input target light field.

[0058] Figure 2 This is a schematic diagram of a method for realizing a dual-polarization broadband Laplace differentiator based on a nonlocal metasurface in an embodiment of the present invention;

[0059] In both p-polarization and s-polarization channels, images of a puppy and a pigeon were projected onto a nonlocal metasurface as test images. Then, second-order two-dimensional edge detection results, obtained by Laplacian differentiation, were immediately obtained after processing the image on the nonlocal metasurface. The experiment could be performed directly in the spatial domain.

[0060] Figure 3 This invention confirms the geometric parameters of the smallest unit of the nonlocal metasurface, the dispersive spectral scanning results at different incident angles in p-polarized and s-polarized channels, and the bound state modes in the quasi-continuous domain in p-polarized and s-polarized channels. Furthermore, the azimuth response at the resonance wavelength of 1350 nm p-polarized and 1285 nm s-polarized surfaces was studied, revealing that the nonlocal metasurface does indeed meet the expected performance for second-order two-dimensional edge detection.

[0061] Figure 4The results of the dispersive spectral scanning of nonlocal metasurface pairs under different wavelengths and different incident angles for p-polarized and s-polarized light in the embodiments of the present invention show that the nonlocal metasurface pairs can indeed meet the requirements for performing second-order two-dimensional edge detection in p-polarized and s-polarized channels, which is consistent with expectations.

[0062] Figure 5 This is the experimental optical path diagram used in the embodiments of the present invention.

[0063] First, an infrared light source excites the incident light, which is then polarized by a half-wave plate and incident on the target image. The light field information formed by the target image then illuminates the designed nonlocal metasurface. After passing through an imaging system composed of a microscope objective and lenses, the light is finally received by an infrared CCD. The experimental results for the Laplace differential effect on images of dogs and pigeons, onion epidermal cells, pumpkin vesicle cells, pepper skin cells, and a portion of a fly's wing are as follows: Figure 6 , Figure 7 and Figure 8 As shown.

[0064] Figure 6 The figures show experimental results of nonlocal metasurfaces in this invention for images of puppies and pigeons under p-polarization at 1350 nm and s-polarization at 1285 nm.

[0065] Figure 7 The figures show experimental results of nonlocal metasurfaces in this invention on images of puppies and pigeons under p-polarized light from 1285 nm to 1450 nm and s-polarized light from 1270 nm to 1300 nm.

[0066] Figure 8 This is an experimental result image of onion epidermal cells, pumpkin vesicle cells, pepper skin cells, and partial wing images of a nonlocal metasurface in an embodiment of the present invention under p-polarization at 1350 nm and s-polarization at 1285 nm.

[0067] Compared to traditional electronic or digital image edge detection methods, this method can process images at the speed of light. This greatly improves image processing speed and can accurately capture subtle edge information in images, significantly enhancing the accuracy and robustness of edge recognition.

[0068] In summary, the method for realizing a dual-polarization broadband Laplacian differentiator based on a nonlocal metasurface disclosed in this embodiment can excite bound-state modes in the quasi-continuous domain with angle selectivity in both p-polarization and s-polarization channels. This allows for the manipulation of the optical transfer function required by the optical Laplacian operator in both polarization channels, thereby enabling two-dimensional second-order edge detection of the input image over a wide bandwidth. This method can be applied to multifunctional optical imaging systems such as biomedical image processing, effectively solving related engineering problems. Furthermore, the proposed method can achieve high numerical aperture and wide bandwidth imaging applications. Combined with the ultrathin characteristics and spatial square manipulation capabilities of nonlocal metasurfaces, this nonlocal metasurface can be directly and effectively integrated with existing systems such as microscopes, completing large amounts of data processing in a high-speed, parallel, real-time, and low-power manner, providing a solid foundation for future machine vision, autonomous driving, and mixed reality display imaging.

[0069] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for realizing a dual-polarization broadband Laplace differentiator based on a nonlocal metasurface, characterized in that: Includes the following steps, Step 1: A single-layer nonlocal metasurface for realizing a dual-polarization broadband Laplacian differentiator is constructed from a square ring array made of amorphous silicon material with identical structural dimensions. By designing the geometry of the square ring units, the single-layer nonlocal metasurface can realize dual polarization channels under p-polarization and s-polarization, respectively obtaining bound state modes in different quasi-continuous domains with selective characteristics for incident angles. This yields the optical transfer function required for the nonlocal metasurface to perform two-dimensional second-order edge detection of images. When the input light field passes through the nonlocal metasurface under the dual polarization channels, the light field information is processed separately. By recording the output light field information separately, the result of the Laplacian operation can be obtained. Step 2: Determine the transmission spectral response of the square ring structure constituting the nonlocal metasurface in the working wavelength range of 1150 nm to 1500 nm, so that the normal incident transmittance of the nonlocal metasurface is close to zero in a wide working wavelength range; when the incident light becomes obliquely incident, the transmittance of the nonlocal metasurface in the p-polarized and s-polarized channels should increase with the increase of the oblique incident angle, respectively, providing the necessary conditions for realizing the broadband Laplace operation under dual polarization; at the same time, the resonance modes of the working position under p-polarization and s-polarization are analyzed according to the electromagnetic mode analysis method, and the bound states in the quasi-continuous domain of different electromagnetic resonance modes are determined by analyzing the corresponding electromagnetic field distribution; in addition, by analyzing the influence of the change of incident angle and azimuth angle on the transmission spectrum under p-polarization and s-polarization respectively, the constraint conditions of polarization and azimuth angle for realizing the broadband Laplace differentiator of the designed nonlocal metasurface in dual polarization channels are determined. Step 3: Based on Step 1 and Step 2, the geometric parameters of the square aperture unit of the nonlocal metasurface used to realize the dual-polarization broadband Laplace differentiator must satisfy the following conditions: Condition 1: For the transmission spectral response in the near-infrared spectral region, the nonlocal metasurface satisfies that the transmittance at the normally incident resonance wavelength is zero or close to zero; when the incident light becomes obliquely incident, the transmittance of the nonlocal metasurface at the resonance wavelength under p-polarization and s-polarization increases with the increase of the incident angle, and has a predetermined bandwidth range respectively. Condition 2: The physical conditions for exciting bound states in the quasi-continuous domain under dual polarization channels are met; the bound states in the quasi-continuous domain are determined based on electromagnetic intrinsic characteristics; the electromagnetic resonance modes of the bound states in the quasi-continuous domain under p-polarization and s-polarization channels are determined based on the specific resonance modes corresponding to the resonance positions according to the electromagnetic field mode distribution analysis; finally, based on the electromagnetic field distribution, the resonance positions are determined to be bound states in the quasi-continuous domain dominated by magnetic quadrupole resonance and bound states in the quasi-continuous domain dominated by magnetic dipole resonance under p-polarization and s-polarization channels, respectively. Condition 3: The relationship between the transmission spectrum and the angle of the nonlocal metasurface under both p-polarization and s-polarization channels satisfies a quadratic function relationship; the angle includes the incident angle and the incident azimuth angle; thus realizing the dependence of the Laplace differentiator on the polarization state and the incident azimuth angle; the above conditions are satisfied simultaneously through simulation software, thereby finally determining the designed nonlocal metasurface; The geometric parameters include the height H, period P, outer side length L, and inner hole side length w of the square ring; The geometric parameters of the square ring element are determined based on the above conditions that the geometric parameters of the square ring element must satisfy, and the corresponding nonlocal metasurface processing file is generated. Step 4: Using the nonlocal metasurface fabrication file obtained in Step 3, prepare the required transmission-type nonlocal metasurface sample using a micro-nano fabrication method mainly based on electron beam etching; directly irradiate the target image and nonlocal metasurface with p-polarization and s-polarization, and directly perform Laplacian differential operations and corresponding two-dimensional second-order image edge detection in the spatial domain under these two polarization channels.

2. The method for realizing a dual-polarization broadband Laplace differentiator based on a nonlocal metasurface as described in claim 1, characterized in that: In step one, To perform second-order two-dimensional optical spatial simulation differential operations in real space for p-polarized and s-polarized cases respectively, the nonlocal metasurface should function as an optical Laplacian operator for the transmitted light field of the target object under both polarization channels, so that the distribution of the transmitted electric field of the target image exhibits the following characteristics: in This represents the Laplace operator, whose mathematical form is: This is equivalent to designing the optical transfer function of a nonlocal metasurface in the p-polarization and s-polarization channels in k-space to meet the operational requirements of the Laplace operation, as shown in Equation (1). Where the subscripts s and p represent the polarization of the incident light and the transmitted light, respectively, and the horizontal wave vector distribution is k. || =ksin(θ), where k represents the incident wave vector, and θ and These represent the incident angle and azimuth angle of the incident light, respectively. k x and k y Let x and y represent the components of the wave vector along the two orthogonal axes, respectively. Therefore, for a nonlocal metasurface to perform Laplace differential operations in both p-polarized and s-polarized channels, the optical transfer function in both polarization channels must satisfy a quadratic function relationship with respect to the plane wave vector of the incident light field. Simultaneously, when the incident angle is orthogonal, the transmittance of the nonlocal metasurface should be zero, while when the incident angle becomes oblique, the transmittance of the nonlocal metasurface in both p-polarized and s-polarized channels increases accordingly, satisfying the quadratic function relationship. Performing the Laplace operation in the real space domain is equivalent to filtering out the low-frequency information components of the incident light field in k-space, while the high-frequency information components are transmitted according to the above rules, so that the nonlocal metasurface has the function of a high-pass filter in the p-polarization and s-polarization channels; this optical characteristic of performing a high-pass filter in dual polarization channels is achieved by exciting a nonlocal metasurface with bound states in the quasi-continuous domain dominated by different electromagnetic resonance modes in the p-polarization and s-polarization channels. The principle of high-pass filtering under dual polarization channels is as follows: In a normally incident symmetric system, the bound states in the quasi-continuous domain have not yet been excited. At this time, both polarization channels are bound states in the continuous domain of the non-radiative dark mode, which helps to obtain near-zero transmittance under normally incident conditions. When the incident light is tilted and obliquely incident, the symmetry of the entire system is broken. The bound states in the quasi-continuous domain with radiation characteristics are excited in the p-polarized and s-polarized channels respectively, thereby affecting the spectral transmission characteristics, so that the spectral transmission amplitude increases with the increase of the oblique incident angle.

3. The method for realizing a dual-polarization broadband Laplace differentiator based on a nonlocal metasurface as described in claim 2, characterized in that: The specific method for achieving the desired spectral properties of the nonlocal metasurface is as follows: The height H and period P of the square ring unit are set, the working wavelength is selected from 1150nm to 1500nm, the material is amorphous silicon, and electromagnetic calculation tools are used to scan the transmission spectrum of the smallest unit of the square ring structure under different combinations of outer side length L and inner hole side length w. Based on the transmission spectrum results under different incident angles obtained by actual scanning, the structural parameters required for the transfer function of the nonlocal metasurface to perform the Laplace differential function under both p-polarized and s-polarized polarization channels are determined. When the p-polarized and s-polarized input light fields pass through the nonlocal metasurface, the light field information under different polarization conditions is processed respectively, and the result of the Laplace operation is obtained by recording the output light field.

4. The method for realizing a dual-polarization broadband Laplace differentiator based on a nonlocal metasurface as described in claim 3, characterized in that: The electromagnetic calculation tools mentioned above employ the time-domain finite element difference method, the FDTD software based on the finite element method, and the multiphysics simulation software COMSOL.

5. The method for realizing a dual-polarization broadband Laplace differentiator based on a nonlocal metasurface as described in claim 1, 2, 3, or 4, characterized in that: This technology enables direct second-order two-dimensional image edge detection of spatial target objects in both p-polarization and s-polarization channels. It extends the optical field information modulation function and image information processing capability of optical nonlocal metasurfaces from the frequency domain to the real space domain, significantly compressing the volume of optical systems, avoiding additional alignment requirements, and facilitating integration into multifunctional optical image processing systems.

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