Medium metasurface optical edge detection device and method based on dual-polarization-state Mie resonance

Abstract

The invention discloses a dielectric metasurface optical edge detection device and method based on dual-polarization-state Mie resonance, the method shows a non-local dielectric metasurface which is high in robustness and easy to prepare, and the device can achieve polarization-independent edge detection with excellent efficiency and high numerical aperture (NA). By simultaneously utilizing Mie resonance in the s polarization state and the p polarization state, isotropic two-dimensional second-order differential operation under any polarization condition (including non-polarization illumination) is realized. According to the design scheme, real-time image edge extraction can be achieved, the average peak efficiency reaches 30%, the working bandwidth of 40 nm is achieved at the center wavelength of 1064 nm, and high-quality edge detection can be kept under the numerical aperture of 0.5. The work provides a new method for realizing polarization-independent edge detection, and paves a way for practical application of an optical calculation and imaging system.

Description

Technical Field

[0001] The present invention belongs to the field of optical analog computing, and particularly relates to a dielectric metasurface optical edge detection device and method based on dual-polarization Mie resonance. Background Art

[0002] Image processing, as a fundamental and rapidly developing key technology in the fields of science and engineering, its core methods - edge detection and data compression technologies based on differential operations - currently mainly rely on integrated electronic computing systems to achieve. With the continuous increase in the demand for image data accuracy and complexity in emerging technology fields such as autonomous driving, computer vision, medical imaging, and augmented / virtual reality (AR / VR), digital image processing technology has correspondingly developed to a highly refined stage. Although electronic computing can handle complex computing tasks, it is essentially limited by high energy consumption and relatively low computing efficiency. In contrast, optical analog computing can achieve real-time image feature extraction and data processing without analog-to-digital conversion by regulating the light-matter interaction. This innovative paradigm can complete large-scale real-time operations with extremely low energy consumption.

[0003] Traditionally, optical analog computing based on the principles of Fourier optics usually uses a 4f optical filtering system to achieve. However, the inherent size limitation of such systems makes it difficult to achieve compact integration. In recent years, the research focus has shifted to planar optical analog computing systems. Among them, using nanophotonic materials is an effective way to miniaturize the system - with the progress of metasurface design and fabrication technology, this solution has become practically feasible.

[0004] The non-local characteristics of the metasurface enable it to directly regulate optical signals in momentum space in real space, and only a single-layer ultrathin metasurface structure is required to achieve optical analog image processing. Existing research has shown that planar optical structures including photonic crystal slabs and metasurfaces can achieve optical analog computing such as differential operations and equation solving by regulating resonance effects. For example: 1) By designing Fano resonance and bound states in the continuum (BICs), optical differential operations with Laplace response were first achieved in a single polarization state; 2) Subsequently developed polarization-insensitive quasi-BIC metasurfaces increased the numerical aperture to 0.08; 3) Based on the latest progress in band engineering, broadband dual-polarization optical differentiation was further achieved, further improving the numerical aperture and working bandwidth. However, the existing methods still have three key limitations: low numerical aperture, polarization dependence, and narrowband working characteristics, which jointly restrict their practical application effects. Summary of the Invention

[0005] The purpose of the present invention is to solve the above problems existing in the background art, and provide a dielectric metasurface optical edge detection device and method based on dual-polarization Mie resonance.

[0006] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A dielectric metasurface optical edge detection device based on dual polarization state Mie resonance, as Figure 1 shown, the metasurface uses fused silica as the substrate, and dielectric nanocolumns arranged in a hexagonal lattice periodic pattern are provided on the substrate. The nanocolumns are amorphous silicon with low loss and high refractive index in the near-infrared band. The dielectric nanocolumns arranged in a hexagonal lattice periodic pattern are fabricated on the substrate by photolithography. The single unit structure is as Figure 1 shown, the lattice constant a is 570 nm, the cylinder radius r is 217 nm, and the height H is 189 nm.

[0008] A method for optical edge detection using the above device, the method is: by precisely controlling its nonlocal characteristics to achieve spatial dispersion control, so that its optical transfer function (OTF) satisfies the Laplacian operator characteristics in the Fourier space, thereby realizing the key function of performing a spatial second-order differential operation on the input image. Nonlocality and locality generally exist in physical phenomena, and the nonlocality in the metasurface mainly depends on the coupling between unit structures. The design of the unit structure determines the nonlocal characteristics of the metasurface. Designing strong nonlocal characteristics can control the momentum signal in real space and realize the optical transfer function in momentum space in real space. Nonlocal metasurfaces can avoid the optical transfer function required for Fourier transform to achieve spatial differentiation and have received extensive attention. Spatial dispersion (related to the incident angle, also called angular dispersion) can be controlled in the nonlocal metasurface, thereby realizing the momentum-related optical transfer function required for spatial differentiation.

[0009] When this single-layer metasurface works as a Laplacian operator, it has several characteristics: (1) polarization independence: it can precisely modulate arbitrarily polarized incident light; (2) isotropy: directly complete two-dimensional edge detection in real space; (3) wide spectral response: simultaneously have ultra-high numerical aperture and wide-band working characteristics.

[0010] Furthermore, the method is specifically as follows:

[0011] The schematic diagram of the principle of realizing polarization-independent optical edge detection using a nonlocal dielectric metasurface is as Figure 1 shown; this single-layer metasurface, as a Laplacian operator, can precisely modulate the incident light of any polarization state and directly realize two-dimensional isotropic optical edge detection in real space; the electric field distribution of the input image in the x-y plane is E in (x,y), and the transmitted electric field after the metasurface performs the Laplacian operation is expressed as

[0012]

[0013] In the momentum space, this relationship is expressed as:

[0014]

[0015] Among them, [k x , k y represents the transverse wave vector of the incident light; E in is the total electric field strength of the incident light; Obviously, when the optical transfer function (OTF) of the metasurface satisfies , optical edge detection can be reliably achieved; Considering that polarization-independent operation needs to be applicable to any polarization state, the incident light is decomposed into two orthogonal components - s polarization state and p polarization state E in (k x , k y ) = [E s (k x , k y ), E p (k x , k y )], and the optical transfer function of the metasurface is expressed as:

[0016]

[0017] Among them, the subscripts s and p represent the polarization states of the incident light and the transmitted light respectively; E s , E p are the component electric field strengths of the s polarization state and the p polarization state of the incident light; H is the optical transfer function matrix of the structure; The two polarization conversion terms in the above formula satisfy H sp (k x , k y ) = H ps (k x , k y ) = 0, so the transmitted electric field is expressed as Equation (2):

[0018]

[0019] H ss , H sp are the components of the optical transfer function matrix of the structure when the incident light is s polarized and the transmitted light is s or p polarized; H ps , H pp are the components of the optical transfer function matrix of the structure when the incident light is p polarized and the transmitted light is s or p polarized; In a polarization-independent optical system, it is necessary to ensure that the optical transfer functions (OTFs) of the metasurface in orthogonal polarization states are highly consistent; Specifically, when the OTFs of the metasurface for the s polarization state and the p polarization state satisfy:

[0020]

[0021] At this time, the transmitted electric field is expressed as:

[0022]

[0023] This condition ensures that when light with any polarization state (including unpolarized light) is incident, the metasurface can achieve isotropic Laplacian operation, thus completing polarization-independent high-precision edge detection;

[0024] It should be particularly noted that when the transverse wave vector [k x , k y (corresponding to the incident angle θ) varies within a large angle range, it is difficult to achieve the exact consistency of the optical transfer functions (OTFs) in two polarization states even for a metasurface with a highly symmetric arrangement; therefore, to ensure the polarization-independent performance of optical edge detection, during the metasurface design process, at a sufficiently high numerical aperture, the OTFs in s polarization and p polarization should be kept consistent.

[0025] The beneficial effects of the present invention compared with the prior art are as follows: The present invention proposes a non-local dielectric metasurface with a simple structure and easy processing, which exhibits nearly the same optical response to any polarized light, as Figure 1 shown. This metasurface operates in the near-infrared band with a central wavelength of 1064 nm and is composed of an array of amorphous silicon cylindrical nanocolumns deposited on a glass substrate (relative dielectric constant εr = 12.94 @ 1064 nm). Only three geometric parameters are required to define this metasurface with a hexagonal lattice arrangement: the lattice constant a, the cylinder radius r, and the height H. Through systematic optimization by combining the genetic algorithm simulated by the finite-difference time-domain method (FDTD), the present invention finally determines the optimal parameter combination as a = 570 nm, r = 217 nm, and H = 189 nm. More importantly, this general structure that satisfies the optical transfer function (OTF) required for differential operation can be easily extended to other spectral bands. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 Schematic diagrams of the design of a polarization-independent spatial differential metasurface and the unit structure of the metasurface.

[0027] Figure 2 (a) Transmission amplitude varying with wavelength and incident angle in p polarization state. (b) Transmission amplitude and phase at different incident angles at the working central wavelength in p polarization state. (c) Transmission amplitude varying with wavelength and incident angle in s polarization state. (d) Transmission amplitude and phase at different incident angles at the working central wavelength in s polarization state. (e) Transmission amplitude varying with wavelength and incident angle in unpolarized state. (f) Transmission amplitude and phase at different incident angles at the working central wavelength in unpolarized state.

[0028] Figure 3Two-dimensional spatial dispersion under different polarization states. (a)(b) Transmission amplitude and transmission phase distributions of the p-polarization state in momentum space. (c)(d) Transmission amplitude and transmission phase distributions of the s-polarization state in momentum space. (e)(f) Transmission amplitude and transmission phase distributions of the unpolarized state in momentum space.

[0029] Figure 4 Polarization-independent spatial differentiation results. (a) Input image, with a size of 200×200 pixels and a pixel size of λ (1064×1064 nm). (b) Differentiation output result when the polarization is maintained in the x direction. (c) Differentiation output result when the polarization angle is maintained in the y direction. (d) Differentiation output result in the unpolarized state. (e) Output intensity distribution diagrams under the three illumination conditions of (b)(c)(d).

[0030] Figure 5 Output images under different wavelengths of incident light in the unpolarized state within the broadband working wavelength range. Respectively, (a) 1025 nm. (b) 1035 nm. (c) 1045 nm. (d) 1055 nm. (e) 1075 nm. (f) 1085 nm. (g) 1090 nm. (h) 1095 nm. (i) Comparison diagram of the intensity distributions at the positions corresponding to the white solid lines in Figure b for each wavelength. Detailed implementation manners

[0031] The technical solutions of the present invention will be further described below in conjunction with the accompanying drawings and embodiments, but are not limited thereto. Any modification or equivalent replacement of the technical solutions of the present invention, without departing from the spirit and scope of the technical solutions of the present invention, shall be covered by the protection scope of the present invention.

[0032] Based on the optical simulation calculation of a planar optical structure, the present invention has significant advantages in terms of system miniaturization, loss reduction, and calculation speed compared to traditional systems that require complex optical configurations. However, there are three key limitations in existing metasurface solutions for analog image processing: polarization dependence, efficiency limitation, and numerical aperture (NA) limitation. This study demonstrates a robust and easy-to-fabricate nonlocal dielectric metasurface that can achieve polarization-independent edge detection with excellent efficiency and high numerical aperture (NA). By simultaneously utilizing Mie resonances in both s-polarization and p-polarization states, the present invention realizes isotropic two-dimensional second-order differentiation operations under arbitrary polarization conditions (including unpolarized illumination). The proposed design can achieve real-time image edge extraction, with an average peak efficiency of 30%, a working bandwidth of 40 nm at the central wavelength of 1064 nm, and can maintain high-quality edge detection at a numerical aperture of up to 0.5. This work provides a new method for achieving polarization-independent edge detection and paves the way for the practical application of optical computing and imaging systems.

[0033] Example 1:

[0034] Based on the devices and methods of the present invention, to verify the polarization-independent characteristics of the nonlocal optical response, the present invention calculates the transmission amplitude and phase responses of the designed metasurface to p-polarized, s-polarized, and unpolarized light, as Figure 2 shown. Figure 2 (a) shows the variation of the simulated p-polarized transmission amplitude |tpp| with wavelength and incident angle. At the central operating wavelength of 1064 nm, the transmission amplitude approaches zero within a 40-nm bandwidth at normal incidence. As the incident angle increases to θmax = 30°, the transmission amplitude gradually increases, showing a moderate sensitivity to the incident angle. To confirm that the optical transfer function (OTF) of the metasurface conforms to the characteristics of an even-order differentiator, the present invention extracts the transmission response related to the incident angle at a wavelength of 1064 nm ( Figure 2 (indicated by the white dashed line in (a)). As Figure 2 (b) shows, the results show that the transmission amplitude (red solid line) has an obvious quadratic relationship with the incident angle and is in good agreement with the ideal Laplace response (red dashed line, satisfying |tpp| ∝ kx 2 = sin 2 θ). In addition, the phase response of the metasurface (green curve) hardly changes with the incident angle, which is consistent with the ideal phase characteristics.

[0035] Figure 2 (c)(d) show the variation of the s-polarized transmission amplitude with wavelength and incident angle. There is only a slight difference in the maximum amplitude value (0.95) at θ = 29°. Generally speaking, the amplitude response of unpolarized light ( Figure 2 (e)(f)) is highly consistent with both s- and p-polarized states. Thus, it can be seen that the unpolarized response of the designed metasurface fully meets the OTF requirements for differential operations, not only conforming to the theoretical formula (3), but also approaching the ideal response. It should be particularly noted that currently, there are still great challenges in constructing a metadevice to achieve an approximately consistent angular-sensitive transmission spectrum for s- and p-polarized states within a numerical aperture NA = 0.5.

[0036] To verify the isotropic characteristics of the designed metasurface in the two-dimensional edge detection of incident images, the present invention calculates the variation of the transmission amplitude and phase in the momentum space ( Figure 3 ). The transmission amplitude of the p-polarized state monotonically increases with the transverse wave vector and reaches the maximum value when the numerical aperture NA is as high as 0.5. At the same time, this amplitude hardly changes with the azimuth angle φ ( Figure 3 (a)(b)), fully demonstrating that the metasurface has a highly symmetric optical response. In addition, the transmission phase remains nearly uniformly distributed throughout the momentum space - which is a necessary condition for implementing the Laplace operation. The performance of the s-polarized state is highly similar to that of the p-polarized state ( Figure 3(c)(d)), only the variation trend of the amplitude with the wave vector is slightly different from that of the p-polarized state.

[0037] Since both the p-polarized and s-polarized states exhibit strong isotropy and phase stability, the optical response of the unpolarized state naturally shows ideal spatial isotropy: its transmitted amplitude has a quadratic relationship with the spatial frequency, and the phase distribution is uniform ( Figure 3 (e)(f)). Most importantly, this isotropic optical response that meets the requirements of the Laplace differential operation OTF ensures that the designed metasurface can function as a two-dimensional second-order spatial optical analog differential operator.

[0038] To evaluate the isotropic effect of edge detection, the present invention numerically simulates the output images of the nonlocal metasurface under different polarization states. A flower with a complex geometric structure is selected as the input image ( Figure 4 (a)), which not only contains edge features in the x and y directions but also has various randomly oriented curve contours. In particular, the petal area is distributed with fine and dense detail features, which can fully test the edge detection quality of the metasurface. According to the Nyquist-Shannon sampling theorem, the size of the input image is set to 200×200 pixels (about 212 μm), and the size of a single pixel unit is λ (1064×1064 nm).

[0039] The simulation results show that under illumination with polarization maintained in the x direction ( Figure 4 (b)) and polarization maintained in the y direction ( Figure 4 (c)), the output signals can clearly distinguish the flower edge from the internal area. The designed metasurface can not only accurately detect relatively simple leaf edges but also precisely analyze the detailed contours of the complex petal area, fully demonstrating its high-resolution edge detection ability. The output results under unpolarized light illumination ( Figure 4 (d)) are almost completely consistent with those under polarized state illumination. To quantitatively evaluate the detection efficiency, the present invention analyzes Figure 4 (a) the output intensity distributions at the red dotted line under three illumination conditions: the intensity curves in the case of polarization maintained in the x direction, the case of polarization maintained in the y direction, and the unpolarized state case are highly consistent, with only a slight deviation at the position of x = 115λ due to the slight difference in the transmitted amplitude ( Figure 4 (e)).

[0040] Furthermore, a quantitative evaluation is carried out through the peak efficiency ηpeak≡Iout / Iin (setting the input intensity Iin = 1). The maximum peak efficiencies of all three cases exceed 0.3, and the unpolarized state reaches the excellent level in the current field of optical edge detection of metasurfaces with ηpeak = 0.39. This nonlocal metasurface can achieve efficient and isotropic differential operations, and can completely obtain the edge information in all directions of the image without missing the detail features in a specific orientation.

[0041] In addition to achieving isotropic and efficient optical edge detection, this nonlocal metasurface also has the characteristic of operating in a wide spectral range. In the present invention, unpolarized light is used to irradiate the input flower image, and output images at different wavelengths are obtained in the wavelength range of 1025 - 1095 nm (the actual working bandwidth can be wider, and the edge peak efficiency < 73.5%). Figure 5 ) It is found that at the two limit wavelengths of the working bandwidth, 1035 nm and 1090 nm, the field strength in the inner region of the flower in the output image has reached 70% of the edge intensity Figure 5 (b)(g)), and it is difficult to distinguish the pattern edge from the main body according to the Rayleigh criterion, presenting the characteristics of bright-field imaging. When the wavelength approaches the central wavelength, only a weak light field distribution appears in the main region of the image, but its intensity is significantly lower than that of the edge region Figure 5 (b)), and sufficient edge contrast is still maintained. In the working band of 1055 - 1085 nm Figure 5 (d)-(f)), the light intensity distribution is only concentrated on the image edge, and the intensity of the main region can be ignored, realizing pure contour extraction.

[0042] Based on the analysis of the output images at different wavelengths, it can be confirmed that this metasurface can achieve efficient isotropic edge detection within a 40-nm working bandwidth (1045 - 1085 nm). To more intuitively show the detection performance at different wavelengths, Figure 5 (i) The intensity distribution curves at the white dotted line are compared: the peak-to-valley values of the intensities corresponding to the wavelengths of 1045 - 1085 nm are significantly different (the valley value is close to zero), while the valley intensities of the curves at the wavelengths of 1035 nm and 1090 nm reach 70% of the peak value, resulting in difficult edge recognition. Through quantitative calculation, the peak efficiency ηpeak of the edge detection image is stably between 30% and 45% (the average efficiency > 30%, specifically referring to the ratio of the edge intensity to the input light intensity here), which is consistent with the quantization standard of the aforementioned polarization-independent experiment. Obviously, this metasurface not only achieves isotropic edge detection with a large numerical aperture (NA = 0.5), but also maintains efficient edge enhancement characteristics in a wide spectral range, providing a reliable guarantee for practical applications.

[0043] The present invention proposes a polarization-independent dielectric metasurface, which makes the optical transfer functions (OTFs) of both s-polarization and p-polarization meet the requirements for constructing an optical analog differentiator by regulating the nonlocal optical response. This metasurface can be used as a Laplacian differentiator to achieve isotropic two-dimensional second-order image edge detection with a numerical aperture of 0.5 in a 40-nm wide spectral range, and the average efficiency of the edge intensity exceeds 30%, and can completely obtain the full-direction edge information of the image. This excellent edge detection performance has important application value in the field of image processing and can be integrated with existing systems such as autonomous driving, computer vision, medical imaging, and AR / VR in the future to provide new solutions for intelligent optical information processing.

Claims

1. A dielectric metasurface optical edge detection device based on dual-polarization Mie resonance, characterized in that: The metasurface uses fused silica as a substrate, and dielectric nanocolumns arranged in a hexagonal lattice periodic pattern are provided on the substrate. The nanocolumns are made of amorphous silicon with low loss and high refractive index in the near-infrared band. The dielectric nanocolumns arranged in a hexagonal lattice periodic pattern are fabricated on the substrate by photolithography. The lattice constant a is 570 nm, the cylinder radius r is 217 nm, and the height H is 189 nm.

2. A method for optical edge detection using the device according to claim 1, characterized in that: The method is as follows: By precisely controlling its nonlocal characteristics to achieve spatial dispersion control, enabling its optical transfer function (OTF) to satisfy the characteristics of the Laplace operator in the Fourier space, thereby realizing the key function of performing a second-order spatial differential operation on the input image.

3. The method according to claim 2, wherein: The specific method is as follows: The single-layer metasurface acts as a Laplacian operator, capable of precisely modulating incident light of any polarization state and directly realizing two-dimensional isotropic optical edge detection in real space; the electric field distribution of the input image in the x-y plane is E in (x, y), and the transmitted electric field after the metasurface performs the Laplacian operation is expressed as In the momentum space, this relationship is expressed as: where [k x , k y represents the transverse wave vector of the incident light; E in is the total electric field strength of the incident light; obviously, when the optical transfer function (OTF) of the metasurface satisfies , optical edge detection can be reliably achieved; considering that polarization-independent operation needs to be applicable to any polarization state, the incident light is decomposed into two orthogonal components - s polarization state and p polarization state E in (k x , k y ) = [E s (k x , k y ), E p (k x , k y )], and at this time the optical transfer function of the metasurface is expressed as: where the subscripts s and p represent the polarization states of the incident light and the transmitted light, respectively; E s , E p are the electric field strengths of the s-polarization state and the p-polarization state components of the incident light; H is the optical transfer function matrix of the structure; in the above formula, the two polarization conversion terms satisfy H sp (k x , k y ) = H ps (k x , k y ) = 0. Therefore, the transmitted electric field is expressed as Equation (2): H ss , H sp is the optical transfer function matrix component of the structure when s-polarization state is incident and s- or p-polarization state is transmitted; H ps , H pp The optical transfer function matrix component of the structure when p-polarization state is incident and s- or p-polarization state is transmitted; in polarization-independent optical systems, it is necessary to ensure that the optical transfer function (OTF) of the metasurface in orthogonal polarization states is highly consistent; specifically, when the OTF of the metasurface for s- and p-polarization states satisfies: At this time, the transmitted electric field is expressed as: This condition ensures that when incident with any polarization state (including unpolarized light), the metasurface can achieve isotropic Laplace operation, thereby completing polarization-independent high-precision edge detection; It should be particularly noted that when the transverse wave vector [k x , k y (corresponding to the incident angle θ) varies within a large angular range, it is difficult to achieve a perfect match of the optical transfer functions (OTFs) in both polarization states even for a metasurface with a highly symmetric arrangement; therefore, to ensure the polarization-independent performance of optical edge detection, during the metasurface design process, at a sufficiently high numerical aperture, the OTFs in s-polarization and p-polarization should be kept consistent.

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