Research Progress on Applications of Metasurface-Based Optical Image Edge Detection Technology

Abstract

With the rapid development of metasurface technology, metasurfaces have gained significant attention in optical edge detection. Owing to their precise control over the phase, amplitude, and polarization state of electromagnetic waves, metasurfaces offer a novel approach to edge detection that not only overcomes the size limitations of traditional optical devices but also significantly enhances the flexibility and efficiency of image processing. This paper reviews recent research advances in metasurfaces for optical edge detection. Firstly, the principles of phase-controlled metasurfaces in edge detection are discussed, along with an analysis of their features in different applications. Then, methods for edge detection based on polarization and dispersion modulation of metasurfaces are elaborated, highlighting the potential of these technologies for efficient image processing. In addition, the progress in multifunctional metasurfaces is presented, offering new perspectives and application prospects for future optical edge detection, along with a discussion on the limitations of metasurface-based edge detection technologies and an outlook on their future development.

1. Introduction

Optical edge detection techniques have important applications in fields such as computer vision, pattern recognition, and image processing. The goal of these techniques is to accurately identify and locate the edge features of objects in an image. Traditional edge detection methods often rely on classic image processing algorithms, such as the Sobel operator and the Canny edge detector [1,2]. These methods perform well in simple scenes but tend to struggle in more complex environments. To achieve optical edge detection, conventional imaging systems typically rely on a 4f optical system [3] (hereafter referred to as the 4f system), which regulates the spatial spectrum through Fourier transformation. However, the 4f system is bulky and requires precise optical alignment, which makes it unsuitable for integration and miniaturization. As technology advances, traditional optical devices are increasingly unable to meet the growing demands of modern society. The advent of metasurfaces has brought new solutions to edge detection technology, offering significant breakthroughs for improving efficiency and performance.

Metamaterials are a class of artificially designed and manufactured materials characterized by negative permittivity (ε) [4] and negative permeability (µ) [5], which do not occur naturally and are known as left-handed materials. These materials break through traditional material design concepts by precisely engineering structures at the microscopic scale to achieve specific macroscopic properties. Metamaterials possess unique electromagnetic properties, such as backward wave propagation, subwavelength focusing, and selective absorption. They are particularly suitable for applications in advanced optical systems such as antennas, sensors, and imaging devices [6]. Metasurfaces, as the two-dimensional equivalent of three-dimensional metamaterials [7,8,9]. They consist of subwavelength-scale structural units distributed only on the material’s surface. By tuning the geometric shape and arrangement of these surface units, metasurfaces enable precise control over the propagation of electromagnetic waves.

In 2011, Professor Federico Capasso’s research team at Harvard University proposed the generalized Snell’s law [10], which introduced phase discontinuities at the interface by modifying the geometric parameters of the unit structures, enabling precise control of electromagnetic wavefronts. Metasurfaces have found widespread and unique applications in the field of image processing. First, in image edge detection [11], differential operations are performed using special structures and optical properties to highlight edge information. Second, in image encryption [12], microscopic structural designs alter light propagation characteristics to encode or modulate images. Finally, in holographic displays [13], metasurfaces exploit their phase modulation capabilities to produce realistic three-dimensional images.

Optical edge detection has the advantages of high speed, low energy consumption, strong parallel processing capability, and large information capacity [14,15,16,17,18,19,20,21]. Compared to traditional computational methods, metasurface-based edge detection technology demonstrates several significant advantages. First, metasurfaces enable real-time optical processing, eliminating the need for complex and resource-intensive digital computations. Second, their planar and ultrathin designs allow for compact and easily integrable optical components, making them particularly suitable for miniaturized and portable devices. Third, metasurface technology exhibits excellent scalability and manufacturability, as these components can be mass-produced using nanofabrication techniques, thereby reducing costs while maintaining high performance. Lastly, metasurfaces inherently support large-scale parallel processing, enabling the simultaneous handling of multiple optical signals, which is difficult to achieve with traditional serial digital computation methods. These advantages allow metasurface-based optical components to achieve more compact and efficient system designs, driving innovation in edge detection technologies. This paper begins by introducing the design principles of metasurfaces, followed by a review of the applications and challenges of various metasurface types in optical edge detection, and concludes with a summary aimed at further advancing research and practice in this field.

2. Phase-Controlled Metasurface Edge Detection Technology

Phase modulation technology is one of the core functions of metasurfaces in optical manipulation, enabling various optical functions, such as beam shaping, focusing, and deflection. Phase modulation can be achieved by tuning the optical properties of the material or designing nanostructures, and is commonly used in fields such as holography [13] and wavefront shaping [22]. Phase-modulating metasurfaces control the phase of incident light in the gradient direction through careful design, introducing spatially varying phase delays to achieve first- or second-order differentiation along different directions. Alternatively, spatially varying nanostructures can be designed on metallic metasurfaces to control the phase distribution of surface plasmons [23], simulating first- or second-order derivative operations to extract and amplify edge information in images. This section primarily introduces edge detection using P-B phase metasurfaces and Laplacian-based metasurfaces, as well as other forms of phase-modulating metasurfaces. Phase-modulating metasurfaces offer high integration, allowing direct incorporation into optical devices and enabling edge detection in optical systems without complex post-digital processing, making them ideal for real-time imaging.

2.1. P-B Phase Metasurfaces

2.1.1. Fundamental Principles of P-B Phase

In 1956, Professor Pancharatnam discovered that when resonators are arranged in the x–y plane and rotated by an angle θ around the x-axis, the scattered waves with opposite spins acquire an additional phase factor [24]. In 1984, Professor Berry interpreted this additional phase as a geometric phase, which is equal to half of the solid angle enclosed by two paths connecting the north and south poles on the Poincaré sphere [25]. This indicates that the scattering processes with opposite spins occurring in the two resonators possess a geometric phase. Therefore, the Pancharatnam–Berry phase (hereinafter referred to as the P-B phase, which is a type of geometric phase) depends solely on the spin state of the incident light and the orientation angle of the scatterer and exhibits dispersion-insensitive characteristics, unlike resonance-related phases. Compared to traditional optical materials, metasurfaces based on P-B phases have several advantages, such as a compact planar configuration [26], multifunctionality [27], and high efficiency.

Generally, the Jones matrix of an anisotropic scatterer can be represented by Equation (1):

$$\left[\begin{array}{c}{\mathrm{E}}_{\mathrm{x}}^{\mathrm{o}}\\ {\mathrm{E}}_{\mathrm{y}}^{\mathrm{o}}\end{array}\right]=\mathrm{R}\left(-\mathsf{\theta }\right)\left(\begin{array}{cc}{\mathrm{e}}^{\mathrm{i}{\mathsf{\varphi }}_{\mathrm{x}}}& 0\\ 0& {\mathrm{e}}^{\mathrm{i}{\mathsf{\varphi }}_{\mathrm{y}}}\end{array}\right)\mathrm{R}\left(\mathsf{\theta }\right)\left[\begin{array}{c}{\mathrm{E}}_{\mathrm{x}}^{\mathrm{i}}\\ {\mathrm{E}}_{\mathrm{y}}^{\mathrm{i}}\end{array}\right]$$

(1)

where ${\mathrm{E}}_{\mathrm{x}}^{\mathrm{i}}$ and ${\mathrm{E}}_{\mathrm{y}}^{\mathrm{i}}$ represent the x and y components of the input electric field, respectively, and ${\mathrm{E}}_{\mathrm{x}}^{\mathrm{o}}$ and ${\mathrm{E}}_{\mathrm{y}}^{\mathrm{o}}$ represent the x and y components of the output electric field, respectively. R is a 2 × 2 rotation matrix that can be used for electric field transformations in different reference frames.

The corresponding transmission matrix can further be represented by Equation (2):

$$\mathrm{M}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{R}\left(-\mathsf{\theta }\right)\left(\begin{array}{cc}{\mathrm{e}}^{\mathrm{i}{\mathsf{\varphi }}_{\mathrm{x}}}& 0\\ 0& {\mathrm{e}}^{\mathrm{i}{\mathsf{\varphi }}_{\mathrm{y}}}\end{array}\right)\mathrm{R}\left(\mathsf{\theta }\right)$$

(2)

The P-B phase can also be represented on the Poincaré sphere, as shown in Figure 1a, considering light propagating through an optical system with a specific geometric configuration. As the light travels along different paths, its polarization state changes correspondingly on the Poincaré sphere. Various planar optical devices based on the P-B phase principle have been developed, such as electromagnetic wave deflectors [28], planar imaging lenses (as shown in Figure 1) [29], orbital angular momentum beam generators [30], and surface plasmon couplers [31].

Metasurfaces based on the P-B phase achieve precise control of the phase of light by manipulating the polarization state of the light. This control depends on the phase of the polarization state change and is independent of the propagation path of the light wave, relying solely on the evolution of the polarization state [32,33]. By designing the nanostructures of the metasurface, light with different polarization states undergoes different phase changes as it passes through the metasurface, resulting in spin separation of the incident photons [28,34,35,36]. By introducing spatially varying orientation angles on the metasurface, the geometric phase of the incident light can be precisely controlled at different positions, thereby achieving the desired phase distribution of the outgoing light.

2.1.2. Applications and Development of P-B Phase Metasurfaces

Placing a P-B phase metasurface in the Fourier plane of a 4f optical system, as shown in Figure 2a, leads to a lateral displacement of the left-handed circularly polarized (LCP) and right-handed circularly polarized (RCP) components of the output light field after passing through the metasurface. In the image plane, only the displaced portion of the light passes through the analyzer, which selects a specific polarization state to achieve edge detection. Specifically, the output field is approximately proportional to the first spatial derivative of the input field, highlighting the edges in the image.

Introducing a symmetric phase gradient causes the metasurface to induce radial spatial separation of linearly polarized light, extending one-dimensional edge detection to two dimensions and enabling edge detection in complex images. In two-dimensional edge detection, the output field is related to the radial component of the first spatial derivative of the input field, allowing for the detection of edges in two-dimensional space.

Xie et al. [37] developed and constructed a two-dimensional optical differentiator based on a P-B phase metasurface for performing two-dimensional edge detection tasks, featuring high resolution without the need for subsequent digital processing. Under the influence of the annular grating phase, the P-B phase metasurface radially separates the left- and right-handed components of the light beam. After removing the linearly polarized light in the central overlapping region, the remaining optical signal corresponds to the output of the two-dimensional optical differentiation, as shown in Figure 2b.

Xu et al. [38] designed an inverse metasurface, as shown in Figure 2c, which is applied to optical analog computation and all-optical image edge detection. Compared to traditional optical elements, the inversely designed P-B phase metasurface integrates more functions into a more compact size, contributing to higher integration of optical systems. Bi et al. [39] proposed an edge detection principle based on dual geometric-phase polarization-dependent interference, combining the amplitude transfer function in the 4f system with a geometric-phase metasurface, as shown in Figure 2d. This approach offers broadband response and controllable accuracy. Luo team from Hunan University [40] designed a cascaded device based on liquid crystal and P-B lenses with orthogonal polarizers, achieving highly dynamic edge resolution control. In the experiment, the adjustable range of edge resolution reached 100 µm for one-dimensional edges and 50 µm for two-dimensional edges, which can be further extended by using PBLs with shorter focal lengths, as shown in Figure 2e. By combining the P-B phase metasurface with quantum light sources, higher sensitivity edge detection was achieved [41], as shown in Figure 2f.

P-B phase metasurface technology, with its excellent wavefront manipulation capabilities and compact structure, has significantly advanced the development of optical edge detection technology. However, current P-B phase modulation metasurfaces are typically optimized for specific wavelengths or narrow spectral ranges, limiting their applicability in broadband applications and making it challenging to meet the diverse demands of complex optical environments. Additionally, most P-B phase modulation metasurfaces rely on 4f optical systems, which are bulky and structurally complex, hindering their integration into compact designs. With the gradual realization of broadband and multi-wavelength functionalities, as well as the continuous improvement in the integration of optical components, P-B phase metasurfaces are being widely explored in applications such as biomedical imaging, industrial inspection, augmented reality, and optical computing. Their development is driving optical systems toward miniaturization, intelligent design, and multifunctionality. In the future, with the introduction of new materials and the continued advancement of manufacturing techniques, the cost of P-B phase metasurfaces is expected to be further reduced, while their durability and performance will be further enhanced, accelerating the widespread adoption of this technology across various fields.

2.2. Laplace Metasurfaces

2.2.1. Fundamental Principles of Laplace Metasurfaces

The Laplacian operator is a second-order differential operator commonly used for image edge detection, with its core principle being the calculation of the second derivative of image intensity values to highlight the edges in an image. By performing spatial differentiation on light wave propagation, Laplacian metasurfaces can emphasize edge information in the image. For two-dimensional images, the Laplacian operator detects changes in pixel values by calculating the second derivative, thereby identifying edge regions in the image. Traditional edge detection methods typically rely on complex electronic signal processing, whereas Laplacian metasurfaces achieve edge detection directly through optical means, significantly improving computational efficiency.

Mathematically, the two-dimensional Laplacian operator can be expressed as Equation (3):

$${\nabla }^{2}I={\displaystyle \frac{{\partial }^{2}I}{\partial x^2}}+{\displaystyle \frac{{\partial }^{2}I}{\partial y^2}}$$

(3)

where I represent the intensity value of the image, and $x$ and $y$ represent the horizontal and vertical coordinates of the image, respectively. Through this operation, areas of the image with significant intensity variations (i.e., edges) are notably enhanced, while flat regions tend to become smoother.

In optical analog computation, the two-dimensional spatial function of the Laplacian operator is given by Equation (4):

$${\nabla }^{2}E\left(x,y\right)={\displaystyle \frac{{\partial }^{2}E\left(x,y\right)}{\partial x^2}}+{\displaystyle \frac{{\partial }^{2}E\left(x,y\right)}{\partial y^2}}$$

(4)

where $E\left(x,y\right)$ represents the electric field of the input signal, with its distribution given by Equation (5):

$$E\left(x,y\right)=\iint \tilde{E}\left(k_x,k_y\right)e^{i\left(k_{x}x+k_{y}y\right)}d{k}_{x}d{k}_y$$

(5)

where $k_x$ and $k_y$ are waves on the orthogonal axes; the optical transfer function (OTF) of the Laplacian metasurface is given by Equation (6).

$$\mathcal{L}\left(k_x,k_y\right)=-(k_x^2+k_y^2)$$

(6)

The transmission of the Laplacian metasurface is zero for normal incidence, while it increases as the incidence angle increases.

To meet the requirements of the OTF and transmission characteristics, precise control over the phase, amplitude, and polarization state of light waves can be achieved through the careful design of nanostructures and the use of novel materials. The Laplacian operator can be implemented by tuning the spatial differentiation properties of the light field through mechanisms such as guided-mode resonance, gap surface plasmon resonance (GSP), electric dipole resonance (ED), and magnetic dipole resonance (MD) supported by the metasurface [42,43,44,45]. In the design and realization of Laplacian metasurfaces, incorporating quasi-bound states in the continuum (hereafter abbreviated as BIC) has been shown to significantly enhance sensitivity to high-frequency components. This improvement is due to the high-quality factor (Q-factor) characteristic of BIC. BIC arises from interference caused by guided-mode resonance or symmetry-breaking mechanisms. This results in highly localized electric fields with exceptionally high Q-factors. By leveraging BIC, the spatial differentiation properties of Laplacian metasurfaces are substantially improved, enabling sharper edge detection and stronger responses to high-frequency components [46,47]. Moreover, studies have demonstrated that the resonance wavelength and spectral bandwidth of BIC can be precisely tuned by manipulating symmetry-breaking parameters, thereby enabling narrowband or broadband functionalities tailored to specific application requirements. This capability is critical for deploying Laplacian metasurfaces in advanced fields such as optical computing, image enhancement, and sensing. Furthermore, integrating BIC provides a robust framework for optimizing the trade-off between performance and fabrication complexity.

With specifically designed nanostructures, the high-frequency components of the optical input signal are enhanced in the spatial frequency domain, while the low-frequency components are suppressed. The optical transfer function of the metasurface in a specific spectral band can extract the spatial characteristics of the second derivative of the image, thereby generating an output optical field with edge enhancement features. Finally, by combining with other optical elements (e.g., analyzers), the edge detection results are transferred to the imaging system to complete the identification and analysis of image edges, enabling efficient edge detection and subsequent image processing [11,20].

2.2.2. Applications and Development of Laplace Metasurfaces

To overcome the limitations of traditional digital circuits in terms of computational speed and power consumption, Liu et al. [48] designed a quasi-bound state in the continuum (abbreviated as BIC) metasurface composed of silicon nanodisks. By adjusting the radius of the nanodisks to tailor the quasi-BIC resonance, the transmission characteristics as a function of the incident angle at specific wavelengths meet the requirements of the optical transfer function for the Laplacian operator. This design achieves high-quality, efficient, and uniform second-order spatial differentiation within a relatively wide wavelength range and enables isotropic two-dimensional edge detection under any incident polarization. The team led by Professor Huang Lingling at the Beijing Institute of Technology [49] proposed a silicon hollow-brick dielectric resonant metasurface based on toroidal dipole (TD) resonance for realizing Laplacian operations. This metasurface is capable of performing two-dimensional second-order edge detection, has a numerical aperture close to 0.4 and a wide operating wavelength range exceeding 100 nm, and can be directly integrated into the imaging system, as shown in Figure 3.

Hen Zhou et al. [50] demonstrated a Laplacian metasurface capable of performing isotropic second-order spatial differentiation. The metasurface, based on the excitation of quasi-BIC, provides an optical transfer function that is close to an ideal Laplacian operation, with an extended maximum incident angle. The symmetry of the mode ensures the isotropy of the Laplacian operation. This metasurface successfully achieved the Laplacian operation for one-dimensional Gaussian functions and two-dimensional spatial functions and can be used for high-quality image edge detection. Cheng Guo et al. [51] applied a two-dimensional Laplacian operator in holography and phase-shifted Bragg gratings using photonic crystal slabs, eliminating the need for bulky optical components and achieving implementation in transmission mode. This design not only reduces system complexity but also increases integration, enhancing the compactness and applicability of the system, as shown in Figure 4.

Laplacian metasurfaces combine subwavelength structure design with the Laplacian operator to achieve two-dimensional spatial differential edge detection at the optical scale. They possess advantages such as real-time operation, high efficiency, low-power consumption, and compact integration, achieving breakthroughs in experiments in the visible and near-infrared bands. Although the current manufacturing costs are high and the capabilities of frequency band expansion and dynamic regulation are limited, they have great potential in fields such as biological imaging and machine vision. Future development will focus on broadband response, multifunctional integration, the introduction of dynamically regulated materials, and the optimization of low-cost mass manufacturing technologies, to accelerate their transformation from laboratory research to practical applications.

2.3. Other Phase-Controlled Metasurfaces

In addition to P-B phase modulation, phase control also includes resonance phase modulation and propagation phase modulation. Resonance phase modulation is based on the electromagnetic resonance effect between light waves and nanostructures. The resonance interaction between light waves and nanostructures can induce localized surface plasmon resonance on metal surfaces [52,53], resulting in significant phase changes. Propagation phase modulation relies on the phase accumulation caused by the propagation path and refractive index of light waves in the medium. Its core principle is to precisely control the phase distribution of the output light by adjusting the propagation distance and the refractive index of the material.

The propagation phase differs from the geometric and resonance phases as it depends on the physical path and interaction of light waves within the material. It is suitable for broadband and high-efficiency beam manipulation, whereas the resonance phase, with its narrowband and high sensitivity, is advantageous for dynamic optical systems. The applications of metasurfaces utilizing resonance and propagation phase modulation are summarized in

Table 1. Applications of other phase modulation metasurfaces.

Name	Structure	Principle	Implementation Effect	References
Optical Resonator Array	Composed of V-shaped metallic antenna units.	Redefines the laws of reflection and refraction by introducing a linear phase gradient at the interface.	Enables arbitrary-angle reflection and refraction, generating optical vortices with orbital angular momentum.	[10]
Chiral Dielectric Metasurface	Consists of two silicon nanocubes embedded in a glass layer.	Resonance modes of electric dipoles and magnetic dipoles are used to enhance chiral optical response through multipole resonance.	Employs sputtered silicon material with low absorption loss, achieving high efficiency in the near-infrared range.	[54]
Propagation Phase Metasurface	Utilizes high-aspect-ratio gallium nitride (GaN) meta-atoms with fin-shaped and cylindrical geometries.	Achieves annular light intensity focusing and optical property optimization within specific wavelength ranges through phase manipulation.	Capable of high optical performance but exhibits significant chromatic aberration due to dispersion limitations.	[55]
Transmission Metasurface	Silicon nanorod arrays sandwiched between two DBR layers.	Leverages the combined effects of guided-mode resonance and Fabry–Pérot resonance.	Enables dynamic phase control and high transmission efficiency.	[56]
Dielectric Metasurface	Amorphous silicon nanopillars placed on a quartz substrate.	Controls the symmetry and unitarity of the Jones matrix by adjusting the geometric parameters of elliptical pillars, achieving phase and polarization conversion of the optical field.	Generates arbitrary spatially varying polarization and phase distributions, enabling dual-function optical patterns for polarization switching.	[57]
Dielectric Metasurface	Crystalline silicon is transferred onto a quartz substrate via an SOI wafer process.	Achieves phase coverage from 0 to 2π by adjusting the cylinder diameter.	Experimental transmission efficiency is 47%, with theoretical optimization potentially reaching 71%; due to the symmetry of the cylindrical structure, it is insensitive to polarization states.	[58]

. The combination of these phase modulation methods enables metasurfaces to achieve compactness, high efficiency, and intelligence in fields such as optical imaging, holographic displays, optical communications, and quantum optics, providing new solutions for advancing future optical technologies.

3. Polarization Modulation Metasurface Edge Detection Technology

3.1. Fundamental Principles of Polarization Modulation

Polarization is one of the fundamental properties of light, referring to the specific arrangement of the oscillation direction of light waves during propagation. Manipulating the polarization state of light at the micro- and nanoscale has found extensive applications in fields such as imaging [59], detection [60] and micromanipulation [61], as well as across disciplines like biology [62] and medicine [63]. Since most light in nature is unpolarized or partially polarized, polarizers are required to separate polarized light from natural light.

In classical optics, the polarization state of light is typically represented using vectors, such as Jones vectors and Stokes vectors. In 1852, Stokes introduced four parameters to describe the intensity and polarization state of light waves, as shown in Equation (7).

$$S=\left[\begin{array}{c}{S}_0\\ \begin{array}{c}{S}_1\\ S_2\\ S_3\end{array}\end{array}\right]=\left[\begin{array}{c}{E}_x^2+E_y^2\\ \begin{array}{c}{E_x^2-E}_y^2\\ 2E_x{E}_y\cos \delta \\ 2E_x{E}_y\sin \delta \end{array}\end{array}\right]=\left[\begin{array}{c}{I}_x+I_y\\ \begin{array}{c}{I}_x-I_y\\ I_{45°}-I_{-45°}\\ I_R-I_L\end{array}\end{array}\right]$$

(7)

In the equations, $\delta$ represents the phase difference between the x and y components; S₀ denotes the total light intensity, S₁ represents the intensity difference along the x and y directions, S₂ represents the intensity difference along the 45° and 135° directions, and S₃ represents the intensity difference after decomposing linearly polarized light into right circularly polarized light (RCP) and left circularly polarized light (LCP).

In 1941, Jones first proposed using vectors to represent the x- and y-components of the electric field, as shown in Equation (8).

$$E=\left[\begin{array}{c}{E}^x\\ E^y\end{array}\right]=\left[\begin{array}{c}{E}_{0x}{e}^{i{\phi }_x}\\ E_{0y}{e}^{i{\phi }_y}\end{array}\right]$$

(8)

The Jones vector describes the amplitude and phase of two orthogonal components of light at the same time and position. Its characteristics remain invariant over time and apply only to fully polarized light.

Traditional polarizers utilize the asymmetry in processes such as reflection, refraction, absorption, and scattering to decompose incident light into two orthogonal polarization states. Examples include using Brewster angle incidence, birefringence effects, or dichroism in crystals. Metasurfaces based on polarization control achieve specific optical functionalities by designing nanostructures that manipulate the propagation speed or path of different polarization states.

When light passes through anisotropic birefringent materials [64], different polarization states (typically linear polarizations along the fast and slow axes) propagate at different speeds. Metasurfaces based on birefringence effects can separate or interfere with polarization states, thereby enhancing edge information in images. The photonic spin Hall effect [65] refers to the interaction between the spin angular momentum and orbital angular momentum of light, causing photons with different polarization states to undergo spatial separation on the metasurface. When polarized light passes through a specially designed metasurface, photons with left- and right-handed polarization states are separated along different paths [66]. This effect can be used to enhance image gradients in specific directions. Moreover, metasurface-based polarization devices are gradually replacing traditional optical polarization devices, enabling the construction of more compact and multifunctional optical systems. These polarization devices can simultaneously achieve polarization angle rotation, convert linearly polarized light into circularly polarized light, or transform arbitrarily polarized light into specific polarized light, supporting a wide range of complex polarization manipulation functions.

3.2. Applications and Development of Polarization Modulation Metasurfaces

Polarization-modulated metasurfaces have advanced rapidly in the fields of edge detection and optical image processing. In 2022, Bingquan Xu et al. [67] proposed and simulated a polarization-independent spatially differentiable metasurface designed using particle swarm optimization (PSO). By optimizing the metasurface microstructures through the PSO method, the response to different polarization states was enhanced, achieving properties such as high numerical aperture, isotropy, and polarization independence. In experiments involving grayscale processing and differential operations on traffic sign images, the metasurface successfully performed high-precision edge detection, demonstrating consistent detection performance under both linearly polarized and unpolarized light conditions. As shown in Figure 5, the PSO-optimized metasurface can execute high-quality differential operations, significantly improving edge detection outcomes.

In March 2023, ZHANG et al. [68] proposed a fully optical image edge detection method based on the two-dimensional photonic spin Hall effect in anisotropic metamaterials. By designing a specific anisotropic metasurface, differently polarized light can propagate at varying speeds along the optical axis, thereby enhancing edge information in the image, as shown in Figure 6a. By altering the geometric dimensions of the metasurface, tunable one-dimensional edge detection and directional two-dimensional edge detection can be achieved, with the ability to modulate the imaging resolution by adjusting the magnitudes of transverse and in-plane displacements. In the same year, Michele Cotrufo et al. [69] proposed a silicon-based metasurface. By changing three geometric parameters, the lattice constant, hole radius, and plate thickness, this design achieves a strongly polarization-asymmetric or nearly polarization-independent response while maintaining a high degree of isotropy. It does not rely on the 4f imaging system. The metasurface with a strongly polarization-asymmetric response can enable controllable direction-dependent edge detection, as shown in Figure 6b.

PENG TANG et al. [70] proposed a polarization-independent edge detection metasurface based on the spin–orbit interaction of light. When the Fresnel coefficients r_p = r_s, variations in the incident polarization do not affect the output light intensity or transfer function. The component in the y-direction simplifies to a term independent of incident polarization, thereby achieving polarization independence. Both the output light intensity and transfer function are insensitive to incident polarization and are functionally dependent on the incident angle, as shown in Figure 7.

Polarization-modulated metasurfaces can perform multiple functions simultaneously, such as polarization angle rotation and conversion from linear to circular polarization, providing great flexibility in edge detection and other optical applications. Compared to traditional optical devices, they offer advantages such as smaller size, lighter weight, and ease of integration. However, high-precision nano-structural design and fabrication remain significant challenges. Different application scenarios require specific optical materials to achieve optimal polarization control. Recent studies have incorporated phase-change materials into metasurfaces, enabling multifunctionality and dynamic switching capabilities.

4. Dispersion Modulation Metasurface Edge Detection Technology

4.1. Fundamental Principles of Dispersion Modulation

Dispersion refers to the relationship between a material’s refractive index (n) and the frequency (or wavelength) of incident light. In optics, light waves of different frequencies (or wavelengths) propagate at different speeds within the same medium, resulting in distinct refractive indices for each frequency. This phenomenon is known as dispersion, and its characteristics directly influence the propagation path, focusing performance, and diffraction patterns of light. In the field of optics, precise control over dispersion is crucial. It is employed in ultrafast laser optical devices to achieve pulse shaping and, by minimizing chromatic aberration, ensures accurate image reproduction in imaging systems [71,72,73]. Compared to traditional refractive materials, optical metasurfaces composed of subwavelength nanostructures can introduce effective refractive indices and dispersion, enabling dynamic adjustments to the material’s dispersion curve for better integration into modern optical systems.

Metasurfaces, as artificial materials constructed from periodic subwavelength units, can be described by effective material parameters such as effective permittivity, permeability, and refractive index. Due to the inherent resonances of the building blocks of metasurfaces, their effective material parameters exhibit strong dispersion characteristics. Artificial materials with negative permittivity and negative permeability have been applied across a broad spectrum, ranging from electromagnetic waves to mechanical waves. Traditional refraction and reflection laws limit the planarization and lightweight nature of optical devices [74,75] and are associated with low diffraction efficiency and strong dispersion. With the rapid development of the metasurface field, recent advancements have proposed devices based on metal nanoslits and dielectric metasurfaces, where gradient phases are generated by appropriately adjusting the arrangement of metal nanopillars, thereby generalizing the classical Snell’s law into the generalized Snell’s law [10,76]. Non-local responses with strong spatial dispersion are crucial for achieving ideal reflection metasurfaces. In the case of ideal reflection, metasurfaces need to precisely control the propagation and interference of multiple plane waves within the same space. The non-local response mechanism with strong spatial dispersion provides more advanced control over metasurfaces in reflective optical devices, enabling more complex and precise manipulation of light fields [77].

Taking the rapidly developing metalenses as an example, topology optimization combined with adjoint and gradient descent methods is employed in the design process to alter the metasurface’s topology, enabling it to quickly converge to the optimal solution. Implementation methods include using coupled nanofins, rotating anisotropic nanofins, and employing isotropic nanostructures. Various broadband achromatic metal lenses have been realized in the visible and near-infrared bands, offering advantages such as polarization sensitivity, large numerical aperture, and wide bandwidth. However, the group delay of nanostructures is limited by their height and group refractive index. By adopting multilayer structures, the group delay range can be extended, as shown in Figure 8.

4.2. Applications and Development of Dispersion Modulation Metasurfaces

By utilizing the compensation between the structural dispersion of the MIM waveguide and the material dispersion of metals, Li et al. [78] demonstrated that plasma nanoslits can be used to construct broadband chromatic aberration-correcting lenses and designed a chromatic aberration-correcting deflector. This deflector generates phase shifts by varying the slit width distribution, enabling the deflection of the beam in the same direction across different wavelengths, with nearly identical deflection angles and chromatic aberration correction at all incident angles. Additionally, Li et al. also designed a metal lens with reverse dispersion, in which the focal length increases with wavelength, demonstrating the effectiveness and multifunctionality of dispersion engineering for customizing the dispersion of metal lenses, as shown in Figure 9a.

MKhorasaninejad et al. [79] designed a metal lens with a negative dispersion effect, in which the focal length increases with the wavelength. Experiments demonstrated a chromatic aberration correction response with a 60 nm bandwidth in the visible range. By cascading metal lenses with opposite dispersion characteristics, a wider bandwidth chromatic aberration-corrected lens can be achieved. Similar design principles can be applied to realize transmission-type chromatic aberration-corrected metal lenses, and the use of materials with higher refractive indices can increase the operating bandwidth of reflection-type chromatic aberration-corrected metal lenses, as shown in Figure 9b.

Michele Cotrufo et al. [80] introduced strong spatial dispersion effects by engineering the band structure dispersion of periodic nonlocal metasurfaces, leading to nonlocal responses that are closely related to the propagation characteristics of surrounding light waves. This nonlocal response provides metasurfaces with powerful optical control capabilities. The researchers designed two different dispersion modes, making the frequencies close to and different from the points, with the radiation linewidth being approximately equal to or slightly larger than their detuning, and the mode frequency shifting in different directions as the in-plane wave vector increases. Experiments show that by further optimizing the dispersion characteristics of the metasurfaces, their spectral bandwidth can be significantly increased and extended to scenarios involving more optical modes, thus enabling wideband, efficient, and high numerical aperture edge detection, as shown in Figure 10.

Currently, dispersion-modulated metasurfaces have achieved high numerical aperture and broad bandwidth across a wide spectral range, significantly improving the precision and efficiency of edge detection. However, the design dimensions of achromatic metalenses are constrained by the limitations of current manufacturing precision. Additionally, metasurface design often involves multiple software tools, leading to challenges such as data transmission difficulties, high learning costs, low efficiency, and poor integration. With advancements in manufacturing processes, the emergence of novel materials, and the integration of topology optimization in software design, as well as the application of deep neural network models to overcome local minimum problems, the future holds promise for the development of larger and more complex metasurface components.

5. Multifunctional Metasurface Edge Detection Technology

Multifunctional metasurfaces combine functionalities like phase, amplitude, polarization, and spectral modulation. This integration enables complex optical processing capabilities. To better classify the various functionalities and mechanisms of multifunctional metasurfaces, this study divides them into two categories: dynamic multifunctional metasurfaces and static multifunctional metasurfaces. The following sections will provide a detailed discussion of each category.

5.1. Dynamic Multifunctional Metasurfaces

Dynamic metasurfaces refer to structures that incorporate various design optimization principles or integrate dynamic materials, enabling them to dynamically adjust their optical properties in response to external conditions and achieve multiple functionalities. This adaptability makes them suitable for complex application scenarios requiring real-time responses or reconfigurable functions, such as edge detection, adaptive optical systems, augmented reality (AR), and optical communications.

Phase-change materials, liquid crystals, transparent conductive oxides, and two-dimensional materials such as graphene are novel materials capable of functional modulation through external stimuli. These materials enable efficient functional regulation in various application scenarios, facilitating the manipulation, storage, transmission, and processing of light [81].

The optical performance of metasurfaces is primarily determined by two factors: the geometric shape and size of the unit structures and the dielectric constant of the materials. Once the devices are fabricated, the geometry and size of the structures are challenging to modify, necessitating the adjustment of the dielectric constant to regulate or reconfigure the optical properties of the devices. Common methods include carrier injection [82], thermo-optic effects [83], and the Pockels effect [84]. Although these methods have been widely studied and applied, they typically result in only small changes in the dielectric constant. In contrast, phase-change materials, which alter their lattice structure under external stimuli (e.g., heat, lasers, and voltage), can significantly adjust the dielectric constant, providing a more effective solution [85,86,87,88].

Currently, phase-change materials such as vanadium dioxide (VO₂) and germanium antimony telluride (GST) are attracting considerable attention for their application in metasurfaces. These materials undergo phase transitions with temperature changes, such as from an insulating state to a metallic state or from a crystalline state to an amorphous state, thereby altering their optical properties. This feature is widely used for dynamic tuning of metasurface designs. GST exhibits significant refractive index differences and fast-switching responses between its crystalline and amorphous states [89,90,91]. A monolithic metasurface based on GSST, designed by Hu Jie et al. [92], enables dynamic switching between edge detection and focusing imaging without the need for a 4f system, as shown in Figure 11a. Its functionality arises from the optimized combination of transmission phase and geometric phase provided by GSST in different states, greatly enhancing the flexibility and precision of edge detection.

VO₂ shows outstanding performance in the dynamic control of reflection spectra, transmission spectra, and polarization states in surface plasmon metasurfaces [93,94,95,96,97]. Michele Cotrufo et al. [98] incorporated a thin layer of VO₂ into the metasurface to dynamically tune its optical properties with temperature changes. When the temperature is below 61 °C, absorption losses are minimized, and the output image maintains high contrast edge enhancement. When the temperature rises above 61 °C, the output image changes rapidly, and at temperatures above 68 °C, the edge enhancement completely disappears, as shown in Figure 11b. This design eliminates the need for a 4f system, facilitating miniaturization, and can be extended to devices with integrated local heaters, electrical effects, or externally pumped lasers for optical-induced heating to control the temperature.

The development of multifunctional metasurfaces based on phase-change materials in the field of edge detection has made significant progress. Meanwhile, dynamic multifunctional metasurfaces have also rapidly advanced in areas such as communication and quantum technologies. Examples of such dynamic metasurfaces are listed in

Table 2. Dynamic multifunctional metasurfaces.

Type	Principle	Application	References
Graphene-Based Polarization-Multiplexing Coding Metasurface	Achieves dynamic wavefront control by tuning the Fermi level and utilizing the Pancharatnam–Berry (P-B) phase.	Generates vortex beams, multi-directional reflected beams, and specularly reflected beams. Also functions as a dynamic metalens for high-capacity THz communication.	[99]
Polarization-Frequency Multiplexing Transmissive THz Metasurface	Utilizes the phase transition properties of vanadium dioxide (VO2) to switch between metallic and insulating states, combined with polarization and frequency multiplexing.	Enables high-capacity, long-distance THz communication, suitable for 6G technologies. Extends the application of dynamic metasurfaces.	[100]
Graphene and VO2-Based Multi-Wavefront Generator	Integrates dual dynamic control mechanisms using graphene’s electrically tunable properties and VO2’s thermal phase transition.	Generates diverse wavefronts, such as deflected beams, dynamic metalenses, and orbital angular momentum (OAM) beams. Applicable to THz communication, high-resolution imaging, and quantum information processing.	[101]
Tunable Holographic Metasurfaces	Using the modulation characteristics of electro-optic materials, these metasurfaces can reconfigure the phase and amplitude of light waves to meet different optical requirements.	Researchers proposed tunable holographic metasurfaces that not only enable dynamic beam deflection but also generate real-time updated holographic images for different application scenarios.	[102]
Quantum Optics-Based Metasurface	Based on the principle of P-B phase and quantum entangled photon pairs generated by spontaneous parametric down-conversion (SPDC).	Researchers rely on the non-locality of quantum entanglement, and by detecting the polarization state of entangled photons, they can switch between normal imaging mode and edge detection mode.	[11]
Tunable Metasurface	Utilizes Mie resonance and metalens focusing design to adjust optical transmission parameters, achieves precise control of convolution kernel weights, and simultaneously reduces optical crosstalk.	By leveraging Mie resonance to tune convolution kernel weights and combining it with metalens focusing functionality, it is applied to low-power optical computing, achieving high-precision (6.4-bit computational accuracy) optical convolution operations.	[103]
Graphene-Based Multifunctional Metasurface	By altering the bias voltage between the two graphene layers in a graphene sandwich structure, the Fermi level is tuned, thereby changing its electromagnetic properties.	Researchers designed a dynamically tunable reflective metasurface, where the reflection amplitude and response frequency can be controlled by two independent voltage sources.	[104]

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Dynamic multifunctional metasurfaces have significantly advanced fields like optical communication, quantum information processing, high-resolution imaging, and edge detection. Metasurfaces based on phase-change materials (e.g., VO₂ and GST), two-dimensional materials (e.g., graphene), and electro-optic materials enable dynamic control of Fermi levels, phase, and amplitude, allowing for the generation of vortex beams, orbital angular momentum (OAM) beams, and dynamic holographic images. These metasurfaces find wide applications in 6G communication, high-precision optical computing, and quantum imaging. Their advantages include multifunctional integration, high response speed, and compactness. However, challenges such as limited material stability, constrained response efficiency, and high manufacturing costs remain. Additionally, the functionalities of current dynamic metasurfaces are primarily restricted to specific spectral ranges, highlighting the need for further exploration into broadband coverage and efficient dynamic responses. Future research focuses on developing low-energy, high-stability dynamic materials and optimizing metasurface designs for multifunctional manipulation across broader spectral ranges. It also explores using artificial intelligence to enhance the precision and efficiency of dynamic control mechanisms. Dynamic multifunctional metasurfaces are poised to become a cornerstone of next-generation optical systems and photonic technologies, driving advancements across diverse fields, from communication to quantum technologies.

5.2. Static Multifunctional Metasurfaces

Static multifunctional metasurfaces achieve multiple optical functionalities using fixed structural designs and material parameters. They do not rely on external dynamic modulation. These metasurfaces primarily utilize geometric designs, composite structures, or inherent optical properties to produce predetermined optical responses. With their high stability, static multifunctional metasurfaces are particularly suitable for applications in optical imaging, sensing, and holography.

Compared to traditional single-function metasurfaces, static multifunctional metasurfaces do not solely rely on a single principle or functional module. Instead, they achieve multifunctionality through the combination of multiple optical manipulation mechanisms. For instance, phase-controlled metasurfaces can combine geometric design with spectral modulation to simultaneously enable beam shaping and edge enhancement within a single device. Similarly, polarization modulation metasurfaces can integrate polarization selectivity and wavelength separation through composite design approaches. This combination and integration of functionalities significantly enhance the versatility and applicability of metasurfaces, providing a novel design paradigm for multifunctional optical systems. Examples of static multifunctional metasurfaces are presented in

Table 3. Static multifunctional metasurfaces.

Type	Principle	Application	References
Multifunctional Modulated Metasurfaces	By multidimensional control, metasurfaces are designed to simultaneously achieve multiple functions.	Liu et al. proposed an all-dielectric metasurface that independently controls the amplitude and phase of the polarization state at visible light frequencies, realizing polarization-dependent complex amplitude holography.	[105]
All-Dielectric Metasurfaces	By leveraging fixed geometric phases and nanostructure designs, static metasurfaces achieve multi-dimensional control of light.	Realizing depth measurement using DH-PSF under incoherent light and edge detection under coherent light conditions.	[106]
On-Chip Integrated Multifunctional Metasurfaces	Utilize geometric phase, propagation phase, and detour phase to achieve full-parametric multiplexing of the Jones matrix.	Optical communication: channel multiplexing and on-chip optical data processing;Optical display and AR: high-quality holographic projections;Light field manipulation: generating holograms and OAM beams.	[107]
Deep Learning-Based Multifunctional Metasurfaces	By using a specific framework and training mechanism to train Generative Adversarial Networks (GANs), metasurfaces with multiple functions are designed.	Researchers utilized a bipolar unit cell generator network design and verified the effectiveness of this design method in realizing polarization-independent lenses through full-wave simulation of electric field distributions.	[108]

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Static multifunctional metasurfaces have demonstrated significant application potential in optical edge detection and other fields. With fixed structural designs, they efficiently manipulate light without the need for dynamic external control. These metasurfaces feature simplicity in structure, ease of integration, miniaturization, and low cost. In edge detection, these metasurfaces extract high-frequency image information directly. This makes them ideal for machine vision, microscopy, and real-time image processing. In other areas, such as optical communication, imaging displays, and quantum optics, static metasurfaces are capable of wavefront shaping, multiplexing, holographic display, and orbital angular momentum (OAM) beam generation, among other functions. However, the fixed nature of their design may limit their adaptability in complex dynamic scenarios, and further optimization is needed to balance broadband performance and efficiency. In the future, static multifunctional metasurfaces can enhance their functionality and optical efficiency through the optimization of nanostructure designs, providing innovative solutions for cutting-edge fields such as optical computing, information processing, and sensing.

6. Drawbacks and Prospects

The optical edge detection technology based on metasurfaces has demonstrated remarkable advantages. However, several issues and challenges remain in its practical applications. First, most metasurface designs are currently limited to fixed spectral bands or specific frequencies for edge detection, making it difficult to meet the demands of broadband optical systems. P-B phase metasurfaces often depend on bulky 4f optical systems, limiting their use in compact optical devices due to their size and complexity. In the future, the spectral range of P-B phase metasurfaces could be expanded by introducing novel materials or developing multi-wavelength designs based on new physical mechanisms. Meanwhile, compact optical systems can be designed to replace traditional 4f configurations, such as incorporating microlens arrays or freeform optical designs, thereby further enhancing their portability and integration.

Second, polarization metasurfaces perform exceptionally well in polarization control and edge enhancement but lack flexibility, making them unsuitable for dynamic environments or real-time responses. Dispersion-controlled metasurfaces, while showing excellent performance, are relatively small in size and have low numerical aperture (NA) values, which limit their compatibility with optical systems. Future research could focus on exploring new physical mechanisms, utilizing deep learning design and optimization methods, or combining the two approaches to design metasurfaces flexibly. This could improve the working efficiency and imaging performance of large-diameter (millimeter- or centimeter-scale) dispersion metasurfaces with high numerical apertures (greater than 0.5).

In recent years, dynamic multifunctional metasurfaces have garnered increasing attention due to their ability to integrate multiple optical functionalities and achieve dynamic modulation. However, limitations persist. Phase-change material-based metasurfaces often suffer from response delays and reduced modulation precision due to material losses. The development of dynamic metasurfaces is still in its early stages and requires significant technological advancements. With breakthroughs in new materials, future dynamic metasurfaces are expected to achieve more precise and rapid dynamic control.

Furthermore, current design tools and methods are inefficient, and the high learning cost limits their broader applications. The ultrathin nature of metasurfaces also makes their design and fabrication highly dependent on precise nanofabrication techniques. Meeting diverse optical requirements often requires complex nanostructure designs and high-resolution fabrication, leading to high costs and lengthy production cycles. Therefore, it is crucial to develop low-cost, high-throughput nanofabrication processes. Currently, available high-resolution, large-scale lithography methods include deep ultraviolet (DUV) lithography, extreme ultraviolet (EUV) lithography, and nanoimprint lithography. With the continuous improvement of fabrication processes, the development of metasurfaces will become even more rapid.

7. Conclusions

Overall, metasurfaces, with their unique ability to manipulate electromagnetic waves, have made significant progress in optical image edge detection. This paper explores the application of metasurfaces based on various principles in optical edge detection and lists the latest advancements in different metasurface devices in the field. It analyzes the current status and existing issues of different types of metasurfaces in optical edge detection and proposes corresponding solutions. Metasurfaces in optical edge detection have evolved to feature high numerical aperture, wide bandwidth, multifunctionality, and dynamic modulation, enabling efficient and dynamic edge detection in various environments. Although many metasurface devices for edge detection have been developed, their results are still at the laboratory stage, and there are several challenges to overcome before commercialization. With further breakthroughs in material science and nanomanufacturing technology, the potential of metasurfaces in optical image processing will continue to be explored. This will not only drive the entire field toward smarter and more efficient solutions but also showcase broad application prospects in fields such as biomedical imaging, quantum information processing, augmented reality, machine vision, and optical computing.