Review of Planar Optical System: Lens Based on Metasurfaces

Abstract

Metalenses, a novel class of advanced planar optical devices based on metasurfaces developed in recent years, enable the design of incident light’s amplitude, phase, and polarization with high degrees of freedom to meet application requirements. This review systematically summarizes the latest research advances in the field of metalenses. It first elucidates their fundamental physical principles and modulation mechanisms. Based on constituent materials, metalenses are categorized into plasmonic and dielectric types. Functionally, they are classified as tunable metalenses, wide-field-of-view (wide-FOV) metalenses, and achromatic metalenses, highlighting some of the most recent progress in the field. This review aims to deliver a systematic overview of metalens technology while proposing novel design paradigms for advanced optical systems.

1. Introduction

Optical lenses, as the core component for manipulating light waves, have been the cornerstone of imaging, focusing, and sensing systems for centuries. However, traditional optical lenses based on the principles of refraction or diffraction face several inherent limitations: one is that they achieve the accumulation of the optical path through the propagation of light in the optical medium, thereby controlling the phase distribution of the emitted electromagnetic light field [1,2,3,4]. To achieve this, the lens need to have a certain surface curvature and corresponding thickness, and thus the physical volume and weight are often large, limiting their application in portable and integrated devices. Secondly, the precision machining of complex surfaces is not only costly but also poses manufacturing challenges. Thirdly, Chromatic dispersion in optical imaging systems stems from wavelength-dependent refractive indices, preventing polychromatic light from converging at a single focal point [5,6]. Traditional lenses use a combination of multiple lenses for aberration correction, such as spherical aberration, chromatic aberration, astigmatism, etc., which will further increase the complexity and size of the system. Most fundamentally, their performance is constrained by the diffraction limit, which restricts the further improvement of imaging resolution.

To break through these bottlenecks, metasurfaces and one of their most important applications, the metalens, came into being. A metasurface is a two-dimensional periodic structure based on subwavelength-size units that has emerged in recent years [7,8,9]. The core idea lies in obtaining special electromagnetic properties that do not exist in nature by carefully designing the geometry, size, orientation, and arrangement of these nanostructural units [10,11,12,13,14]. The local phase [15,16], amplitude [17,18], and polarization state [19,20,21,22,23,24,25] of light waves can be flexibly and precisely regulated at the subwavelength scale. Based on this feature, applications such as metalensrd [26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53], optical holographic metasurfaces [54,55,56,57,58,59], vortex light generators [60,61,62,63,64], and perfect absorbers [65,66,67,68,69,70,71] have emerged.

A metalens can be defined as a planar optical device that uses metasurfaces to perform the functions of a conventional lens. Its core advantage is significantly different from that of traditional lenses: metalenses are essentially two-dimensional planar structures, and their thickness is usually at the wavelength level or even subwavelength scale, greatly reducing the volume and weight of the device [72]. By designing meta-atoms, the phase, amplitude, and polarization of light waves can be finely regulated independently or collaboratively, providing unprecedented freedom for achieving complex optical functions. At present, metalenses have shown relevant application cases in different wavelength ranges such as ultraviolet [73,74,75,76,77,78], visible light [41,46,79,80,81], infrared [30,82,83,84,85,86,87,88,89,90,91], terahertz [92,93,94,95,96,97,98,99,100], and microwave [101,102,103,104,105,106,107,108,109], demonstrating their wide application and unique advantages. The performance of a metalens mainly depends on the design of its subwavelength structural units. This endows it with extremely high design flexibility, enabling it to achieve specific optical responses that are even difficult to achieve with traditional optics through computational optimization, such as special aberration correction and multi-functional integration. Its planar structure and micro-nanoscale features make it highly compatible with mature semiconductor planar processes, paving the way for building miniaturized, integrated optical systems on chips.

Firstly, we explain the fundamental principles of metalenses, the three modulation methods used to achieve wavefront control, and the limitations of the phase gradient method. The introduction of generalized Snell’s law has had a transformative impact on optics. Secondly, we introduce two different types of metalenses made of different materials—plasmonic metalenses and dielectric metalenses. Thirdly, some functions of metalenses are explored, such as the realization of tunable control, large-field-of-view imaging, and achromatic imaging. Next, we briefly introduce the progress of applying deep learning to metalenses. Finally, a brief introduction is given to the application of artificial intelligence and deep learning in optical design and the field of superlenses. The research directions, application fields, and challenges of the metalens are summarized and prospected.

2. Basic Principles

2.1. Generalized Snell’s Law

Within the optical domain, traditional optical devices rely on the accumulation of a gradual phase along the optical path to change the wavefront of propagating light. However, this approach faces limitations when dealing with complex optical phenomena and demands. In 2011, the Capasso team at Harvard University first introduced the abrupt phase at the interface of two media, derived abnormal refraction and reflection from a one-dimensional perspective based on Fermat’s principle, and proposed the generalized Snell’s law. It provides new degrees of freedom for controlling light, enabling the adjustment of the phase and amplitude of the optical wavefront within an extremely small scale [110]. This is of great significance to transform optics and integral optics, promoting the thinning and integration of optical lenses and laying the foundation for the design of two-dimensional metasurfaces.

The generalized law of refraction is derived as follows: as shown in Figure 1, a light beam with an incident angle of θ_i impinges on an interface with phase discontinuity. As can be inferred from Fermat’s principle, light rays always propagate along paths that yield an extreme value of the required travel time. In other words, the travel time of a light ray along its actual path from one point to another is stationary with respect to small variations of the path—meaning the first-order derivative of the phase along the actual optical path is zero. Assuming that the two paths are infinitely close to the actual optical path, the phase difference between them is zero. That is:

$$\left[k_0{n}_{i}sin\left({\theta }_i\right)dx+\left(\Phi +d\Phi \right)\right]-\left[k_0{n}_{t}sin\left({\theta }_t\right)dx+\Phi \right]=0$$

(1)

where θ_t denotes the refraction angle; Φ and dΦ represent the phase shifts induced by phase discontinuity at the interface when the two optical paths pass through it, respectively; dx is the distance between the two intersection points on the interface; n_i and n_t are the refractive indices of the media on both sides of the interface; and k₀ = 2π/λ₀, where λ₀ is the wavelength in vacuum. If the phase gradient along the interface is designed to be a constant, the generalized Snell’s law of refraction can be derived from Equation (1):

$$sin\left({\theta }_t\right)n_t-sin\left({\theta }_i\right)n_i={\displaystyle \frac{{\lambda }_{0}d\Phi }{2\pi dx}}$$

(2)

The generalized law of refraction establishes the beam passing through the metasurface; the relationship between the sudden phase gradient and beam deflection provides a theoretical basis for the design of metasurfaces.

Based on Snell’s law and the generalized Snell’s law, in order for the incident light to converge at the same point after passing through the lens, taking the ideal thin lens as an example, the angle θ between the emergent light and the optical axis should satisfy the formula:

$$f=rtan\theta$$

(3)

where f is the focal length of an ideal thin lens, and r is the distance from the incident position to the optical axis. For metalenses that rely on the phase modulation effect of metasurface subwavelength structural units, the exit angle of light is regulated by controlling the gradient of additional phase variation on the surface of the planar lens. Taking the normal incidence of a plane wave as an example, as shown in Figure 2, the focal length of the lens is f. When light passes through the microstructural units in the metalens, an additional phase $\phi$ is introduced, $\Phi$ (r) is the phase at position r, and $\Phi$ (r + $d$r) is the phase at position r + $d$r. There exists a gradient of variation in the additional phase ${\displaystyle \frac{d\phi }{dr}}$ between adjacent units, which is referred to as the phase gradient ($d\phi$ = $\Phi$ (r + $d$r) − $\Phi$ (r)). By substituting Equation (3) into the generalized Snell’s law in Equation (2), the functional relationship between the phase gradient ${\displaystyle \frac{d\phi }{dr}}$ (which must be satisfied at a position r from the center of the metalens) and r can be derived:

$${\displaystyle \frac{d\phi }{dr}}={\displaystyle \frac{n_i{k}_{0}r}{\sqrt{r^2+f^2}}}$$

(4)

Integrating the above equation with respect to r yields the phase relation function at this point:

$$\phi =-n_i{k}_0\sqrt{r^2+f^2}+C$$

(5)

The additional phase at the center of the metalens is zero, and the refractive index of the vacuum is usually set to 1. The expression is obtained:

$$\phi =-k_0\left(\sqrt{r^2+f^2}-f\right)$$

(6)

The above equation is the fundamental formula for the focusing and imaging of a metalens.

2.2. Phase Gradient Method

The phase gradient method is one of the core technologies for the design and characterization of metalenses. Its basic principle is to achieve anomalous reflection and refraction of light by introducing phase discontinuities at the interface. Based on the generalized Snell’s law, the phase gradient can provide effective wave vector components for transmitted and reflected photons, enabling light to propagate in a preset direction. The advantage of this method lies in its ability to break through the limitations of traditional diffractive optical elements, realize high-efficiency single-beam manipulation, and avoid the generation of multiple diffraction orders. However, although the phase gradient method shows great potential in the field of metalenses, it still faces many limitations in practical application, which seriously restrict the further development and industrial application of metalens technology. Some limitations of the phase gradient method are listed below:

• The ideal phase gradient method requires the phase to vary continuously with spatial position (e.g., beam deflection needs to satisfy the relation “phase gradient = 2$\pi$sinθ/$\lambda$”, where θ is the deflection angle and $\lambda$ is the wavelength). However, the phase of a metalens is provided by “discrete elements”—each element can only achieve a limited number of discrete phase values (e.g., divided into 8-level or 16-level phases within the range of 0~2$\pi$), which fails to cover a continuous phase distribution. The discretized phase gradient will generate “step errors”, causing part of the incident light to be unable to propagate in the preset direction. Instead, the light is converted into parasitic diffraction orders (e.g., stray light appearing beside the main beam), which reduces the energy utilization efficiency of the metalens.
• The phase gradient of metalens exhibits a strong wavelength dependence, which is jointly determined by the intrinsic dispersion characteristics of the material and the geometric dispersion of the structure. The chromatic aberration caused by the intrinsic dispersion of the element structure material and the diffraction effect of the structural geometry will seriously affect the imaging quality of the metalens. This wavelength dependence manifests as a significant shift in the focal length with changes in the wavelength, which severely limits the performance of the metalens in broadband applications.
• Most metalenses based on the phase gradient method (such as nanopillar metalenses and V-shaped antenna metalenses) are polarization-sensitive—their phase response to the elements is only effective for a specific polarization state (e.g., p-polarization or s-polarization of linearly polarized light, or left-handed or right-handed circular polarization of circularly polarized light), and they have almost no phase manipulation capability for light of other polarization states.
• The design of the phase gradient method is based on the “normal incidence” assumption—the preset phase gradient can only meet the requirement of “optical path difference matching” when the incident light is perpendicular to the metalens surface. When the incident light is obliquely incident (incident angle θ > 0), the optical path difference of the incident light on the metalens surface changes, resulting in a deviation between the actual phase gradient and the preset value.
• The phase gradient of a metalens is jointly determined by the size, shape, and spacing of subwavelength elements. Typically, the size of these elements is on the order of 100–1000 nm (approaching the lithography limit). The phase gradient method imposes extremely high precision requirements on the fabrication process, and any minor process error will cause the phase gradient to deviate from the designed value.

2.3. Modulation Methods

The main principles of electromagnetic wave forward control using metasurfaces can be roughly divided into three types: the resonant phase, propagation phase, and geometric phase [110,111,112].

The research on metasurfaces initially focused primarily on the resonant phase. By leveraging the resonance effect generated between electromagnetic waves and artificial microstructures, it is feasible to achieve electromagnetic wave manipulation phenomena such as anomalous refraction, polarization conversion, and focusing of electromagnetic waves. Through the design and adjustment of the geometric parameters of these nanostructures, strong local resonance can be induced at specific frequencies, which alters the phase response of electromagnetic waves and enables fine control over the entire wavefront. For instance, within the target spectral range, intense Mie scattering resonance can be excited in nanoparticles made of high-refractive-index dielectric materials. By adjusting the size of the nano-units, the excited electric dipoles and magnetic dipoles can be regulated (Figure 3a), thereby satisfying the so-called “first Kerker condition” and further achieving a maximum phase shift of 2π under near-unit transmittance (Figure 3b) [113]. Despite significant progress in the research of resonant phase metasurfaces, due to the effects of saturation and ohmic loss, the energy of incident electromagnetic waves is largely dissipated inside the microstructure units, resulting in low efficiency of resonant phase metasurface devices.

Propagation phase metasurfaces primarily achieve phase control by leveraging the phase difference accumulated during electromagnetic wave propagation. Nanostructures in such metasurfaces are regarded as truncated waveguides [114], where the phase accumulation is related to the effective refractive index and height of the nanostructures. Instead of adjusting the thickness to modify the propagation phase of the incident light beam, the optical wavefront is regulated by tuning the size of each unit to alter the effective refractive index of the medium—this enables the realization of desired functionalities while maintaining a planar design. As shown in Figure 3c, which presents the magnetic energy density of amorphous silicon nanocolumns (treated as truncated waveguides), the light field is confined inside the nanocolumns. This confinement helps reduce the coupling between adjacent nanocolumns. Figure 3c also illustrates the relationship between the phase and transmittance of the nanocolumns and the variation in their radius, demonstrating that phase control can be achieved by adjusting the geometric dimensions of the nanocolumns [115]. Furthermore, the accumulation of the propagation phase is closely associated with the refractive index of the material. Therefore, the modulation units of propagation phase-based metasurfaces are mainly constructed from high-refractive-index dielectric materials. Increasing the effective refractive index can effectively reduce the thickness of the metasurface.

Figure 3. (a) Field distributions for electric and magnetic dipoles [113]. (b) Amplitude and phase modulation by adjusting the dimensions of resonant meta-atoms [113]. (c) Magnetic energy distribution of amorphous silicon cylinders [115]. (d) Schematic diagram of the geometric phase of the Poincaré sphere.

Figure 3. (a) Field distributions for electric and magnetic dipoles [113]. (b) Amplitude and phase modulation by adjusting the dimensions of resonant meta-atoms [113]. (c) Magnetic energy distribution of amorphous silicon cylinders [115]. (d) Schematic diagram of the geometric phase of the Poincaré sphere.

Geometric phase metasurfaces achieve phase control by utilizing the geometric path difference generated during the polarization state conversion of electromagnetic waves [56]. Their design is primarily based on the Pancharatnam–Berry (PB) phase principle. When circularly polarized light is normally incident on a unit structure and the structure is rotated counterclockwise by an angle α, polarization change occurs as the light passes through the anisotropic medium, and the cross-polarized component carries an additional phase factor of exp (2iα). According to this principle, an additional phase difference—referred to as the PB phase—is generated when the light beam undergoes polarization conversion. Its modulation mechanism can be represented using the Poincaré sphere, which describes polarization states: as shown in Figure 3d, each point on the Poincaré sphere corresponds to a specific polarization state. When an electromagnetic wave starts from the north pole of the Poincaré sphere, evolves along the path C1-C3, and finally returns to the initial point, the additional phase factor generated is equal to half of the solid angle Ω enclosed by the path C1-C3, i.e., 2φ. Therefore, by simply varying the azimuth angle of the anisotropic microstructures from 0 to π, the geometric phase metasurface can provide a phase coverage ranging from 0 to 2π, enabling accurate modulation of the electromagnetic wavefront [116].

3. Plasmonic Metalenses

Plasmonic metalenses can be classified into surface plasmonic polaritons (spp-based metalenses) and local surface plasmonic resonance (lprs-based metalenses) based on their principles and characteristics. Surface plasmon polaritons (SPPs) are electromagnetic waves that travel along the interface between a metal and a dielectric. These surface waves are produced by the interaction between free electrons in the metal and the incident light wave, resulting in collective oscillations of the electrons. As an electromagnetic mode at the metal–dielectric interface, the wave vector of SPPs is greater than that of free-space light waves, providing a physical basis for breaking through the diffraction limit. The core of the SPP metalens is to achieve the recovery and amplification of evanescent waves by designing the nanoscale structure excitation and regulating the SPP propagation phase.

In 1998, Ebbesen et al. reported a groundbreaking phenomenon of extraordinary optical transmission through subwavelength hole arrays, where light transmission efficiency exceeded conventional theoretical predictions [117]. This effect originates from the coupling between incident light and surface plasmons on metal interfaces, enabling efficient transmission of wavelengths significantly larger than the aperture diameter. Leveraging this principle, plasmonic metalenses can achieve diffraction-unlimited imaging resolution and precise beam manipulation. In 2005, Zhang Xiang’s team experimentally achieved a silver film SPP metalens. The metalens imaging structure, as shown in Figure 4a, is mainly composed of a 35 nm thick metallic silver film, a 40 nm thick chromium Cr mask layer with a pattern, and a 40 nm thick PMMA spacer layer. A 60 nm resolution was achieved in the ultraviolet band, breaking the traditional diffraction limit [118]. In 2009, Verslegers et al. studied the phase modulation of incident light waves using nanoslit arrays of different widths to achieve angle compensation, thereby improving the focusing and performance of optical devices at different incident angles [119]. In 2013, Luo Xiangang’s research team proposed a reflective metalens imaging lithography structure as shown in Figure 4b [120]. The metal film layer is placed behind the photoresist, and the evanescent wave is compensated and amplified by SPP reflection resonance. The photoresist region between the mask and the reflected metal film layer is imprinted, thereby effectively improving the depth of field, contrast, and fidelity of the imaging. A super-resolution imaging pattern of “OPEN” discrete characters with a feature size of about 50 nm and an exposure depth of about 40 nm, as well as a dense line photoresist pattern with a half-period of 32 nm and an exposure depth of 30 nm, was obtained under a 365 nm mercury lamp light source, as shown in Figure 4c. In 2016, Zhang et al. proposed a novel plasmonic metalens based on a metal slit with an auxiliary groove as shown in Figure 4d [121]. When the lens is illuminated by vertically incident light, only inward-propagating surface plasmon polaritons can be excited and then focused at the center of the lens to form a hot spot. The researchers conducted a theoretical analysis of this focusing effect by altering the groove parameters and the polarization state of the incident light. The study found that the phenomenon existed for both circular and linear polarization states of the incident light (Figure 4e). Under the optimized groove parameters, the focal intensity of the lens can reach 2.5 times that of the grooved lens, whether illuminated by linearly polarized light or circularly polarized light. In 2016, Xu et al. presented a resonant plasma metasurface lens with flexible SPP-focusing capability [122], as shown in Figure 4f. The plasma device is driven by electromagnetic-induced transparency (EIT), which consists of two intrinsically coupled resonators. The coupling between these plasmonic elements makes it possible to produce strong metasurface lenses and enhance SPPs. However, the resistance loss of the metallic material leads to energy dissipation, reducing the efficiency of the lens. In addition, there are issues such as bandwidth limitations and difficulty in achieving full 2π phase coverage, which restrict the application of the metalens based on surface plasmonic polaritons.

Localized surface plasmon resonance (LSPR) enables tunable resonance frequencies by controlling the dimensions and geometry of metallic nanostructures, achieving subwavelength-scale light manipulation through localized field enhancement. Compared to propagating surface plasmon polaritons, LSPR exhibits superior field confinement and greater design versatility. In 2011, Yu et al. of the Cappaso team [110] proposed the generalized Snell’s law and proved that the interface phase gradient can be manipulated arbitrarily for the transmitted beam. The team designed eight phase-modulated V-shaped antennas that continuously increase at π/4 intervals and can fully cover 2π. The structural schematic diagram and simulation results are shown in Figure 4g. In 2012, Aieta et al. of this team applied the concept of optical phase discontinuity to the design of a metalens without spherical aberration [16]. This lens is composed of V-shaped gold nanoantennas and achieves high numerical aperture focusing without spherical aberration by applying a hypercurved surface phase distribution on the wave cross-section, but its focusing efficiency is relatively poor. In 2013, Ni et al. demonstrated metasurface holograms via Babinet-complementary nanoantenna arrays, fabricated by patterning shape-variant nanoholes in glass-supported metal films (Figure 4h). Achieving 10% overall efficiency, this design eliminated energy loss to higher-order diffraction modes compared to conventional holography [57]. In 2023, Liu et al. designed an ultrathin plasma metalens with a device thickness of only 0.1 λ. The metalens unit is in a symmetrical complementary ring-separated form, as shown in Figure 4i. The designed metalens achieved a high transmission efficiency of 80% and a high focusing efficiency of 50% on the focal plane with F = 4.6 λ in the simulation. The ultra-thin plasma metalens design has a medium to large numerical aperture of 0.67 [123].

Plasmonic metalenses leveraging surface plasmon polaritons employ precisely engineered nanostructures—notably nano-gaps and corrugated surfaces—to generate propagating surface waves. This mechanism facilitates simultaneous wavefront manipulation and phase engineering, enabling subwavelength light concentration beyond conventional diffraction limits. Conversely, metalenses exploiting localized surface plasmon resonance (LSPR) capitalize on resonant nanoantennas and tailored nanodisk arrays to produce intense electromagnetic field confinement. Such near-field enhancement, often reaching orders of magnitude intensity amplification, positions these platforms as prime candidates for ultra-compact photonic devices and label-free biosensors with single-molecule sensitivity. Nevertheless, fundamental limitations persist: intrinsic ohmic losses in metallic components cause substantial energy dissipation, while narrow resonance bandwidths constrain operational flexibility. The most persistent challenge remains achieving complete 2π phase modulation—critical for aberration-free focusing—due to insufficient scattering cross-sections and dispersion mismatches. These material-centric constraints currently impede high-efficiency implementations across the electromagnetic spectrum.

4. Dielectric Metalenses

Dielectric metalenses are a new type of optical component based on subwavelength-resonant nanostructures. The core principle is to control the amplitude, phase, and polarization components of electromagnetic waves by designing medium nanostructures with high refractive indices and introducing phase mutations at the interface, thereby achieving complete control of the wavefront. In contrast to plasmonic metalenses, which rely on metallic materials and cause high ohmic losses, dielectric metalenses can avoid high ohmic losses associated with optical frequencies. So far, dielectric metalenses can be roughly classified into three different types based on the mechanism by which they control the phase of the light field: Pancharatnam–Berry phase-type dielectric metalenses, high-contrast-type dielectric metalenses, and Huygens-type dielectric metalenses. There are also differences in the design of metasurfaces with different mechanisms.

The Pancharatnam–Berry phase-type dielectric metalens, abbreviated as the PB phase-type dielectric metalens, achieves complete control of the wavefront by rotating the structural units to generate the same amplitude and different geometric phases. The structural units that constitute PB phase-type metasurfaces have the same geometric shape and anisotropy, that is, each structural unit has a certain rotation angle. In 2016, Khorasaninejad M et al. [26] designed and fabricated all-dielectric metalenses with a numerical aperture (NA) as high as 0.8 at visible light wavelengths based on the PB phase control mechanism using titanium dioxide (TiO₂) nanofin structures with a high aspect ratio. As shown in Figure 5a, the metasurface structure unit is a structure of titanium dioxide nanofins arranged at different rotation angles on a quartz substrate. The material used in the metasurface is titanium dioxide, a dielectric material with a high refractive index and almost no absorption loss in the visible light band, which can achieve a high transmission efficiency. In this study, researchers used a similar method to design metalens structures operating at three visible light wavelengths of 660 nm, 532 nm, and 405 nm. The research results show that the metalens can achieve diffractive limit focusing at all three visible light wavelengths, with focusing efficiencies as high as 86%, 73%, and 66%, respectively. Moreover, using the metalens for imaging display can generate a sub-wavelength resolution and provide an image quality of up to 170 magnification, which is comparable to the image quality obtained by the most advanced commercial lenses. Therefore, it has a wide range of applications in microscopy, imaging, and spectroscopy. In 2018, Liang H et al. [124] achieved 2π transmission phase coverage by introducing PB phase and rotating single-crystal silicon nanoblock structures. They also utilized a hybrid optimization algorithm to rationally arrange the positions of structural units, thereby realizing a metalens with high numerical aperture and high transmission in the visible light band, as shown in Figure 5b. The research results show that the numerical aperture of the metalens in air is as high as 0.98, 67% light concentration efficiency is achieved in the green spectral region (532 nm), and a working bandwidth of 274 nm is achieved. Furthermore, uniquely, the metalens can be directly immersed in a uniform medium environment such as oil. The results show that an ultra-high numerical aperture of 1.48 can be achieved in experiments, and theoretically it can reach 1.73.

High-contrast all-dielectric metasurfaces [29] achieve various optical functions by using structural units with high refractive indices arranged in an ordered manner on a low refractive index substrate according to a certain algorithm for amplitude-phase control of light. High contrast refers to a significant difference in refractive index between the structural units and the substrate. Studies have shown that in high-contrast metasurfaces, each structural unit can be regarded as a truncated waveguide that achieves phase accumulation over subwavelength distances, and each waveguide supports Fabry–Perot multiple resonances, including electric dipole, magnetic dipole, electric quadrupole, and higher-order multi-dipole resonances. Due to the high refractive index of the structural units and the high refractive index difference with the surrounding medium, most of the energy of the incident light wave is confined within the structural units, making it almost impossible for adjacent structural units to produce optical coupling effects, thereby delaying the phase of light propagation. Therefore, taking advantage of the waveguide effect of high refractive index dielectric units provides a new approach to achieving efficient all-dielectric metasurfaces. In 2016, the Capasso group at Harvard University [114] achieved a polarization-independent, highly focused metalens in the visible light band using high-contrast all-dielectric metasurfaces. In this study, metalenses operating at three different wavelengths of 405 nm, 532 nm, and 660 nm were designed. The lens structure and the electric field distribution at the focal point of the metalens measured experimentally are shown in Figure 5c. Metasurface structures are composed of titanium dioxide cylinders of different diameters arranged on a glass substrate. Research has found that to achieve phase control of 2π, the structural units should maintain a sufficiently large height. Therefore, the thickness of the metalens is set at 600 nm. For the three designs with different working wavelengths, the half-height width of the focal points obtained by the metalens almost reached the diffraction limit. Moreover, the metalenses with numerical apertures (NA) of 0.6 and 0.85 achieved focusing efficiencies of up to 90% and 60%, respectively, at visible wavelengths. Meanwhile, researchers experimentally demonstrated that the metalens can also achieve high-resolution imaging. In 2019, Gao Song et al. [125] proposed and designed an efficient transmission dual-functional all-dielectric metasurface. The designed metasurface can achieve two functions of beam abnormal deflection and focusing within the visible light range. As shown in Figure 5d, the structural unit that constitutes the metasurface structure is a rectangular amorphous silicon (A-Si) nanocapsular. When the length and width of the rectangle vary, the corresponding transmission amplitude and phase shift of the rectangular structural unit can be obtained, and then the selected nanocapsular can be reasonably arranged. The gradient phase distribution corresponding to the X-polarized incident and the hyperbolic phase profile corresponding to the Y-polarized incident can be obtained, thereby enabling two functions: focusing on X-polarized light and abnormal deflection of Y-polarized light. In addition, the simulation results show that the transmission efficiency of the metasurface at visible light wavelengths can be as high as 83%.

The Huygens-type all-dielectric metasurface [126] is an all-dielectric metasurface designed based on the Huygens principle. The equivalent principle states that by inducing an electromagnetic response within the structural unit, it can induce electrical and magnetic surface currents, thereby forming a Huygens wave source. By adjusting the structural unit to achieve the purpose of regulating amplitude and phase, the desired wavefront can be produced to enable various optical functional devices. Furthermore, Huygens all-dielectric metasurfaces are composed of dielectric materials without inherent losses and can achieve high efficiency when operating in transmission mode, thus finding wide applications throughout the electromagnetic spectrum. In 2014, Manuel Decker et al. achieved for the first time at the theoretical level an all-dielectric Huygens metasurface operating at near-infrared frequencies using silicon nanoparticles [113]. As shown in Figure 5e, the structure consists of an array of subwavelength lossless silicon nanodisks embedded in a uniform dielectric environment. Research shows that by controlling the inherent properties of the resonance of electric and magnetic dipoles, namely their relative electric and magnetic polarization rates, mass factors, and their spectrum positions, silicon nanodisks can be design to exhibit properties close to those of an ideal Huygens source. By taking advantage of the main feature of Huygens sources, namely the spectral overlap of equal-intensity cross-electric dipole and magnetic dipole resonances, 360° full transmission phase coverage and high transmission rates close to 100% efficiency of the Huygens metasurface can be achieved, and they have experimentally demonstrated this concept. In fact, since the concept was proposed, researchers have reported a variety of optical functions based on all-dielectric Huygens metasurfaces, including beam deflection, beam focusing, and holography and dispersion control. In 2018, Zhang Li et al. designed and experimentally achieved a highly efficient ultrathin mid-infrared transmissive-type Huygens-type metasurface [49]. The material used was lead telluride (PbTe), a sulfur-based compound with an extremely high refractive index, to construct meta-atoms. As shown in Figure 5f, the structural design adopts a novel concept that combines rectangular and H-shaped structures, effectively compensating for the defect of low efficiency caused by single-type structures. The research results show that the metasurface achieves a highly efficient beam deflector in the mid-infrared band by introducing a linear phase gradient through the generalized Snell’s law and realizes a one-dimensional cylindrical lens and a two-dimensional planar lens with a diffraction limit focusing ability by rearranging the surface phase profile.

5. Tunable Metalenses

Variable focal length capability is one of the core requirements of optical systems such as cameras, microscopes, and telescopes. The traditional implementation relies on complex mechanical moving lens groups, resulting in bulkiness, a slow response, high power consumption, and wear and tear. The advent of metalenses, with their ultra-thin, planarized, integrable features, offers a revolutionary approach to achieving fast, compact electro-controlled or optically controlled zoom without mechanical movement. The basic principle is to dynamically change the physical properties (such as refractive index, orientation, shape, position) of the subwavelength structural units that make up the metasurface through external stimuli, thereby regulating the phase distribution of the incident light wavefront in real time and achieving dynamic adjustability of the focal length. Depending on the modulation mechanism of the nanostructure, it can be classified into three categories: optical modulation, electrical modulation, and mechanical modulation.

The first type is the light-controlled tunable metalens, which is used to control the polarization state and other characteristics of the light source. In 2018, Groever et al. designed a space-multiplexing metalens by combining the PB phase and the propagation phase using titanium dioxide nanorods [127]. It is capable of synchronous and spatially separated imaging of light opposite circularly polarized light, breaking through the traditional chiral lens method that relies on the PB phase and achieving independent imaging focusing of two circularly polarized lights without the cost of 50% efficiency, as shown in Figure 6a. The circular polarization-dependent imaging effect was verified in the visible light band, with a polarization contrast of over 20 decibels and an efficiency of up to 70%. Despite a low numerical aperture of only 0.05, the metalens achieved diffraction-limited focusing. Yao et al. achieved a spin-decoupled multifocal metalens using a pure geometric phase and were able to continuously control the focus-intensity ratio by the polarization state of the incident wave [128]. When the polarization direction of the incident light changes, the focal point also changes (Figure 6b). In addition, the intensity of multiple foci can be adjusted by controlling the ellipticity of the incident light. Because there is no need to scan a large number of parameters, only the geometric phase is used instead of the simultaneous use of the propagation phase and the geometric phase, which has the simplicity of design spin decoupling metalenses. However, the proposed metalens has a theoretical transmittance of less than 50%. Fu et al. demonstrated a reconfigurable stepping zoom metalens with high integration density, enabling focal length switching via incident wave polarization reversal [129] (Figure 6c).

Electrically tunable metalenses constitute a second category, utilizing electric fields or voltages to dynamically modulate optical properties for precise control over focal length, beam steering, and phase. This approach enables rapid response and fine-tuning capabilities, making it particularly suitable for applications requiring real-time parameter reconfiguration—such as varifocal lenses, optical modulators, and switches. It delivers reproducible high-efficiency adjustment to meet dynamic control demands in modern optical systems. In 2020, Shen et al. designed a transmission-type terahertz metalens combining a dielectric metasurface with an optical patterned liquid crystal, achieving tunable chromatic aberration correction [130]. When a voltage bias is applied to the liquid crystal, its geometric phase modulation disappears, and only the resonant phase is retained in the metalens. Therefore, the device function changes from achromatic focusing to dispersive focusing (Figure 6d). By integrating two functions in a single metalens, this technology has broad application prospects in spectroscopy and imaging systems. In the same year, Fan et al. fabricated a zoom metalens that could switch between numerical apertures 0.21 and 0.7 by placing a twisted nematic (TN) liquid crystal beneath the metalens substrate (analog data) [131]. Depending on the voltage applied to the electrode, the TN liquid crystal changes the polarization state of the incident light, thereby causing the incident light of different polarization states to form different foci (Figure 6e). The combination of this metalens with the TN liquid crystal has the advantages of high imaging quality and fast response speed (sub-millisecond), and thus has great application potential in biomedical and optical technology fields. Due to its special optical and electrical properties, graphene has attracted extensive attention from researchers around the world. In 2020, Zhang et al. proposed an electrically tunable metalens composed of a single layer of non-structured, doped graphene loaded with ribbon-shaped metallic strips of varied widths and gaps (Figure 6f) [132]. Operating at 10 THz, the metalens exhibited significant tunability in both focal length and focusing efficiency, as the Fermi level of the graphene was varied. The focal point could be shifted over a range of 90.4 µm, with a maximum focusing efficiency of 61.62%. In the same year, Naeem Ullah et al. also proposed a graphene zoom metalens with polarization conversion function [133,134], as shown in Figure 6g. The metalens consists of a bottom dielectric substrate, a metal film with C-shaped holes, and an upper whole sheet of graphene. The angle β between the symmetry axis of the C-shaped hole and the X-axis is 45°, and the phase delay produced by the metalens unit structure is affected by the radius R of the entire C-shaped hole, the size of the opening angle, and the Fermi level E_F of graphene. The X-polarized incident light is modulated by the metalens to Y-polarized light, and the focal length is tuned by regulating the Fermi level with an external gate voltage. As shown in Figure 6g, when the applied voltage changes from 0 V to 2 V, the focal length of the metalens changes from 7.13 mm to 8.25 mm.

Mechanically tunable metalenses constitute a third category, achieving dynamic focus control through strain-induced structural reconfiguration. By applying tensile or compressive forces to flexible substrates, these devices directly modulate the spatial arrangement and periodicity of meta-atoms, thereby altering phase distributions and focal lengths without electrical control. Ee and Agarwal et al. developed a zoom metalens on a stretchable polydimethylsiloxane (PDMS) substrate (Figure 6h). Under uniform strain, increased meta-atom spacing induces spatial phase redistribution, enabling continuous focal tuning at 632.8 nm. Experimental characterization demonstrated that the monotonic focal length increases with the stretching ratio, while the operating wavelength can be extended by optimizing the meta-atom geometry and materials [135]. The target wavelength of this zoom lens is 632.8 nm, but it can be adjusted by changing the geometry and material of the meta-atoms. In recent years, graphene has been used to achieve a certain range of focal length adjustment for the realization of zoom metalenses [136]. Graphene, due to the absence of a band gap, has no dispersion characteristics over a wide band range from ultraviolet to terahertz. This advantage makes it highly suitable for designing broadband devices. By laterally stretching the graphene oxide metalens, its focal length can be adjusted by more than 20% at a single wavelength (red, green, and blue light). In addition, the rotation of the metalens binder can also achieve focal length adjustment [108,137,138,139]. Iwami et al. designed a Moire metalens with an axially asymmetric binary-lens structure. The focal length can be adjusted through the mutual rotation of the binary-lens metalens [140] (Figure 6i,j). The numerical aperture of the metalens shown is 0.5 at the target wavelength of 900 nm. Compared with other mechanisms such as Alvarez lenses [141,142] and micro-electromechanical systems (MEMSs) [143,144,145,146], the advantage of this mechanism is that the focal length adjustment range is wider, covering negative values to positive values.

Figure 6. Tunable metalenses. (a) Metalens focusing LCP/RCP light at distinct positions [127]. (b) Spin-decoupled multifocal metalens architecture [128]. (c) Structural schematic of the tunable metalens [129]. (d) LC-integrated metalens switching achromatic→dispersive focus under voltage bias [130]. (e) Side-view of electrically tunable metalens modulating polarization via applied voltage [131]. (f) Schematic diagram of the graphene-based tunable metalens [132]. (g) Schematic of the graphene zoom metalens unit cell with polarization-conversion functionality; intensity distributions in the y-z plane at gate voltages of 0 V and 2 V [133]. (h) Focal length tuning via substrate stretching [134]. (i) Phase distribution of one of two lenses [140]. (j) Phase distributions of second lens and combined moiré metalens for various mutual rotation angles [140]. (k) Dual cubic-phase metasurface tunable lens schematic [141]. (l) MEMS-tunable metalens operating principle [143].

Figure 6. Tunable metalenses. (a) Metalens focusing LCP/RCP light at distinct positions [127]. (b) Spin-decoupled multifocal metalens architecture [128]. (c) Structural schematic of the tunable metalens [129]. (d) LC-integrated metalens switching achromatic→dispersive focus under voltage bias [130]. (e) Side-view of electrically tunable metalens modulating polarization via applied voltage [131]. (f) Schematic diagram of the graphene-based tunable metalens [132]. (g) Schematic of the graphene zoom metalens unit cell with polarization-conversion functionality; intensity distributions in the y-z plane at gate voltages of 0 V and 2 V [133]. (h) Focal length tuning via substrate stretching [134]. (i) Phase distribution of one of two lenses [140]. (j) Phase distributions of second lens and combined moiré metalens for various mutual rotation angles [140]. (k) Dual cubic-phase metasurface tunable lens schematic [141]. (l) MEMS-tunable metalens operating principle [143].

Other mechanical drive mechanisms, such as Alvarez lenses and adjustable metalenses with integrated micro-electromechanical systems (MEMSs), have been confirmed. S. Colburn et al. developed a large-sized tunable metalens system based on the Alvarez lens principle, achieving nonlinear adjustment of focal length through the lateral micro-movement of the bicubic phase metasurface with 1 cm aperture (Figure 6k) [141]. Since the focal length of the Alvarez lens is inversely proportional to the displacement, this mechanism has a large tuning range, but it is not suitable for portable lens platforms because a micrometer translation stage is required to drive the metasurface laterally. E. Arbabi et al. implemented a MEMS-based tunable metalens comprising two metasurfaces: a static layer (NA ≈ 0.8) on glass substrate and a movable membrane element (NA ≈ 0.8) [143]. Electrostatic actuation modulates their separation distance for focal adjustment (Figure 6l), with object/image-side numerical apertures of 0.16 and 0.014, respectively. Using this mechanism, high-speed electrical focusing and imaging distance scanning were achieved.

Table 1. Parameter characteristics of tunable metalenses.

Mechanism	Wavelength	NA	Eff.	Focal Length	Ref.
Light-controlled	532 nm	0.05	70%	18 mm	[127]
Light-controlled	0.6 Thz	—	21.8–24.5%	0, ±1, 4 mm	[128]
Light-controlled	658 nm	0.21	23.1–35.1%	60 μm	[129]
Electric controlled	0.9–1.4 Thz	0.13	26.1%/33.9%	12 mm	[130]
Electric controlled	650 nm	0.2–0.7	40%/70%	10 μm/45 μm	[131]
Electric controlled	10 Thz	—	61.62%	161.1–251.5 μm	[132]
Electric controlled	360 μm	0.21	—	7.13–25 mm	[133]
Mechanically controlled	632.8 nm	—	—	150–250 μm	[145]
Mechanically controlled	900 nm	0.5	>60%	±1.73–±5 mm	[147]

summarizes the relevant parameters in the research on tunable metalenses presented in this paper.

6. Large-Field-of-View Metalenses

In an imaging system, the field of view (FOV) of the lens is one of the key indicators for imaging. In traditional optics, the field of view is often expanded by cascading multiple optical components. This is because the rotational symmetry of a single lens under oblique incidence is disrupted, leading to an angle-related coma. At the same time, it also brings about another problem, that is, the complexity, volume, and weight of the imaging system increase sharply. Luneburg lenses with spherical symmetry in geometry can also converge to expand the FOV, and the FOV can be close to or even greater than 180°, but the manufacturing process is extremely difficult and incompatible with current planar manufacturing techniques. Metalenses offer a new path to achieve lightweight, wide-field-of-view optical systems because of the precise wavefront controllability of their subwavelength structural units. In practical applications, metalenses capable of imaging in a large field of view are more attractive and in high demand. Recent advancements have enhanced their efficiency and functionality, enabling metasurface diffractive optical elements to have comparable or better performance than traditional optical elements [28,29,45,59,148]. The core challenge of large-field-of-view metalenses is that when the incident light deviates from the optical axis, the demand for phase compensation increases dramatically with angle nonlinearity, and the linear or quadratic phase distribution of traditional metalenses cannot meet the precise convergence of off-axis beams, resulting in blurred, distorted, and reduced efficiency edge field-of-view imaging.

For this reason, Capasso et al. proposed large-field-of-view imaging metasurfaces on curved substrates in 2013 [149]. Thanks to the development of MEMS technology, this technique uses curved metasurfaces integrated on the substrate to eliminate spherical aberration, coma aberration, etc. in a large field of view, as shown in Figure 7a. Although this metasurface can achieve large-field-of-view imaging, it is complex and cumbersome, which is not conducive to integration. To address this issue, Arbabi et al. designed a dual-lens microplanar camera based on high-contrast metasurfaces [27] and achieved aberration resolution imaging at a 60° field of view at 850 nm, as shown in Figure 7b. This design employs cylindrical Si nanocapsules as phase modulation units, which can focus light in any polarization direction. Under normal incident conditions, the focusing efficiency can reach 70%. In 2017, the research team from the Institute of Optics and Electronics, Chinese Academy of Sciences experimentally demonstrated a 2D metasurface based on the ordered rotation of elements (Figure 7c). By converting the rotational symmetry of off-axis incident light into translational symmetry, this metasurface solved the off-axis aberration problem of traditional planar lenses and realized a 2D planar lens operating in the visible light region. This metalens featured an ultra-large field of view (exceeding 160°), a long depth of focus, polarization selectivity, and subwavelength resolution (with a full width at half maximum of approximately 427 nm) [150]. In 2018, Guo et al. proposed a method to expand the field of view of metalenses by converting rotational symmetry to translational symmetry and extending the local catenary light field [147]. They designed and fabricated an ultra-thin metalens with a double-layer geometric metasurface structure. In the microwave band (optimized frequency of 19 GHz), this metalens achieved a polarization conversion efficiency of over 80% (when the incident angle was tilted by 60°), wide-angle beam steering of ±60° (with a scanning range of 120°×120°), and a maximum diffraction efficiency of 93%. In 2020, Fan et al. [151] employed the damped least squares method to optimize the Strehl ratio of the incident angle and designed a metalens based on an aperture diaphragm. This metalens is composed of cylindrical GaN units arranged in a hexagonal lattice, as shown in Figure 7d. Experiments proved that the NA of the designed polarization-insensitive metalens was 0.25 and the FOV was 170°. Under the irradiation of an incident electromagnetic wave with a wavelength of 532 nm, the metalens was able to achieve diffraction-limit convergence at all angles. In 2021, Zhang Fei et al. proposed an isophase streamline optimization strategy based on catenary optics and designed and fabricated a CMOS-compatible silicon-based streamlined metasurface [152]. Through pure geometric phase modulation, this metasurface achieved a diffraction efficiency of nearly 100% in the infrared band (940 nm/10.6 μm bands), a diffraction-limited field of view of 178° in the near-infrared region, and a scanning range of more than 170° in the long-wavelength infrared region. They successfully developed an integrated infrared metalens camera (including a long-wavelength infrared thermal imaging camera and a near-infrared wide-field camera), which also featured low thermal sensitivity and polarization selectivity. This research provides a new solution for compact infrared systems in scenarios such as surveillance, unmanned aerial vehicles, and medical applications.

After extensive research on large-field-of-view metalenses, researchers gradually put them into practical use. Engelberg et al. [153] applied a metalens with a FOV of 30° to a digital single-lens reflex camera, and the outdoor photographs taken indicated that the metalens had a good imaging effect. Likewise, Chen et al. [154] presented a planar camera composed of a silicon nitride metalens array mounted on a CMOS image sensor as shown in Figure 7e. By optimizing the phase profile of the metalens, the planar camera was able to form distortion-free images with a field of view greater than 120°. Lee et al. [155] experimentally demonstrated the existence of an AR and VR display composed of large-field-of-view metalenses obtained through nanoimprinting lithography technology. The imaging schematic diagram is shown in Figure 7f. The metalenses are composed of polycrystalline silicon nanorods with different spatial rotation angles, and with the assistance of three dichroic mirrors, it is capable of achieving panchromatic imaging with a FOV of 90°.

Table 2. Parameter characteristics of large-field-of-view metalenses.

FOV	Aberration Correction Strategy	NA	Eff.	Ref.
10°	Spherical Substrate + Equal Optical Path Phase Distribution	0.5	—	[149]
>60°	Cascaded Dual Metalenses + Phase Cooperative Optimization	0.55	70%	[27]
>160°	Symmetry Transformation	—	<10%	[150]
120°	Symmetry Transformation	0.89	80%	[147]
170°	Optimized Phase Profile	0.25	82%	[151]
178°	Suppression of Off-Axis Coma Aberration	0.49	Nearly 100%	[152]

summarizes the relevant parameters in the research on large-field-of-view metalenses presented in this paper.

Figure 7. Wide-FOV metalenses: (a) Curved metalens architecture [148]. (b) Dual-layer infrared metalens with extended spectral bandwidth [27]. (c) Scanning electron microscope (SEM) image of one section of the fabricated 2D metalens [150]. (d) Unit cell schematic of aperture-stop integrated metalens [151]. (e) Planar camera module implementation [154]. (f) VR/AR near-eye display prototypes [155].

Figure 7. Wide-FOV metalenses: (a) Curved metalens architecture [148]. (b) Dual-layer infrared metalens with extended spectral bandwidth [27]. (c) Scanning electron microscope (SEM) image of one section of the fabricated 2D metalens [150]. (d) Unit cell schematic of aperture-stop integrated metalens [151]. (e) Planar camera module implementation [154]. (f) VR/AR near-eye display prototypes [155].

7. Achromatic Metalenses

Chromatic aberration is the main source of aberration in the imaging of metalenses. According to the principle in the generalized Snell’s law that the phase gradient determines the deflection direction of the beam, metalenses have the characteristic of no spherical aberration, but due to the large chromatic aberration of the phase required for focusing varying with wavelength, although these devices are composed of weakly dispersive materials, their chromaticity is still very high. This leads to a significant dispersion effect during focusing and imaging. This can be attributed to two separate factors: one is the dispersion caused by the different responses of the periodic lattice to different wavelengths [30,54]. Dispersion is the accumulation of different phases due to the propagation of light at different wavelengths through free space [82,156]. Dispersion effects can significantly reduce the performance of panchromatic optical applications. Eliminating the dispersion effect requires a combination of multiple optical components, which inevitably makes the overall structure of the lens group redundant and complex, while significantly increasing the optimization and manufacturing cost of the lens group. Therefore, the use of wideband dispersion-free metalenses is of great significance for lightweight and integrated optical systems as well as for the promotion of metalenses to replace traditional lenses in various fields. In response to this issue, researchers have explored the dispersion control of metalenses.

In 2015, Aieta et al. designed a one-dimensional achromatic metalens that can operate with minimal axial focal length drift at several discrete wavelengths using a low-loss dielectric resonator, as shown in Figure 8a [54]. The focal length of the metalens is 7.5 mm. Later, Arbabi et al. extended the study to a two-dimensional plane, achieving a two-dimensional achromatic metalens operating at two discrete wavelengths of 915 nm and 1550 nm, as shown in the Figure 8b. The NA of the metalens is 0.46, and the experimental results show that the focusing efficiencies of the metalens at these two wavelengths are 22% and 65%, respectively [30]. Although some pioneering work has achieved multi-wavelength achromatic metalenses capable of eliminating chromatic aberrations at multiple discrete wavelengths [30,33,46,47,54,79,157,158,159], achieving wideband achromatic metalenses remains crucial. In 2017, a team from Nanjing University designed an achromatic lens with a bandwidth range of 1200 nm to 1680 nm, an NA of 0.268, a designed focal length of 100 μm, and a diffraction efficiency of 12%. As shown in Figure 8c, its achromatic scheme is to design a metasurface unit structure in the shape of a coupled waveguide. By regulating the different modes generated by the waveguide at different wavelengths, the compensation ability for dispersion is obtained [47]. In this study, the degree of freedom for its achromatic design is derived from the coupling effect of the waveguide, yet the coupling effect also prevents the metasurface device from achieving higher diffraction efficiency. In 2018, Wang et al. designed an achromatic metalens that operates in transmission mode throughout the entire visible light region using GaN-integrated resonance units [46]. When the incident wavelength varies within the range of 400 nm to 660 nm, the focal length of the metalens remains constant, demonstrating a high average efficiency of up to 40% across the entire visible spectrum. This represents a substantial advancement in wideband achromatic metalenses. To eliminate the influence of the PB phase and endow the metalens with polarization insensitivity, the Capasso team designed a broadband achromatic metalens ranging from 460 nm to 700 nm, with an achromatic bandwidth of 240 nm [33]. In this research, a variety of modulation units composed of different structural combinations were adopted, and all the modulation units had axial symmetry. The design concept was to apply the metasurface element of the coupled waveguide while designing a better phase gradient to compensate for dispersion, as shown in Figure 8d. However, in the Capasso team’s study, the achromatic devices had a smaller aperture of 26.4 μm and a narrower achromatic bandwidth range. When the aperture of the achromatic metalens was further increased, more elementary structures were needed to compensate for the dispersion of the metalens. As a result, the size of the device was limited in the study.

Multilayer integration represents a key strategy for achromatic metalenses. This approach employs vertically stacked architectures to reduce lateral design constraints while enhancing out-of-plane degrees of freedom. Avayu et al. demonstrated a tri-layer achromatic metalens (Figure 8e) using vertically aligned nanodisks of distinct materials (Al/Ag/Au), where each layer was optimized for material-specific localized surface plasmon resonances at red (650 nm), green (550 nm), and blue (450 nm) wavelengths [79]. Alternatively, Arbabi et al. implemented spatially multiplexed dielectric metalenses via segmented super-atom interleaving [160]. Two amorphous silicon (a-Si) nanopost arrays, designed respectively for 915 nm and 1550 nm wavelengths, were integrated to achieve dual-wavelength focusing at a common focal plane (Figure 8f).

In addition, other scholars have obtained different achromatic schemes through other means in recent years. In 2020, Ou et al. designed a broadband achromatic polarization device with high polarization isolation, operating in the 3500 nm to 4750 nm band and with an achromatic bandwidth of 1250 nm. The experiment demonstrated achromatic focused vortex beam generators with different topological charge numbers and a focusing lens with high polarization isolation, as shown in Figure 8g. The work provides new ideas for eliminating chromatic aberration through the birefringent properties of primitives [88]. In 2020, Fatih Balli et al. designed an ultra-wideband achromatic metalens in the visible to mid-infrared band of 450 nm to 1700 nm, as shown in Figure 8h. The authors mixed two structures into a single unit to achieve a higher numerical aperture and used a nanopore structure to enhance the transmittance. However, there are also problems such as reduced diffraction efficiency as the wavelength increases [161].

Table 3. Parameter characteristics of achromatic metalenses.

Material	Wavelength	Focal Length	Eff.	Focal Length Deviation	Ref.
Si	1300 nm 1550 nm 1800 nm	7.5 mm	Nearly 10%	The focal spot approaches the diffraction limit	[54]
Au-SiO2-Au	1200–1680 nm	100 μm	<12.44%	The focal spot approaches the diffraction limit	[47]
GaN	400–660 nm	235 μm	40%	The focal spot approaches the diffraction limit	[46]
TiO2	460–700 nm	67 μm	30%	<9%	[33]
Al, Ag, Au	450 nm 550 nm 650 nm	1 mm	5.8–8.7%	<10%	[79]
a-Si	915 nm, 1550 nm	286 μm	37%, 30%	<5%, <12%	[160]
Si	3.5–5 μm	200 μm	40%	<5%	[88]
Resin	450–1700 nm	36 μm	60%	<6%	[161]

summarizes the relevant parameters in the research on achromatic metalenses presented in this paper.

8. Deep Learning in Metalenses

It is worth noting that recent artificial intelligence design methods have been mentioned and studied, and deep learning reverse design methods have been used in various fields [162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209]. The domain of artificial intelligence (AI), and specifically deep learning (DL), has undergone a metamorphosis over the past decade, transitioning from an academic pursuit with niche applications to the foundational technology underpinning the Fourth Industrial Revolution [210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250]. This progress is a multifaceted saga of architectural innovation, data availability, and computational scale, leading to capabilities that continuously redefine the possible.

The design of traditional optical lenses is a centuries-old discipline governed by well-established principles of ray optics and aberration theory. Engineers rely on sequential optimization of surface curvatures, spacings, and material choices to minimize aberrations like spherical, chromatic, and coma. While highly successful, this process is often iterative, time-consuming, and limited to conventional rotational symmetric geometries. The integration of deep learning has begun to disrupt this established paradigm, introducing a data-driven and highly computational approach that can uncover novel designs beyond human intuition. The research progress in applying DL to lens design has followed a logical progression of increasing complexity. Initially, DL was used as a surrogate model or accelerator for existing processes. Neural networks, typically fully connected networks or CNNs, were trained on large datasets of lens parameters (e.g., surface radii, thicknesses, glass types) and their corresponding optical performance metrics (e.g., MTF, spot size, wavefront error) generated by traditional ray-tracing software like Zemax or Code V. Once trained, these networks could predict the performance of a new lens design in milliseconds, replacing simulations that could take minutes or hours. This rapid prediction enabled exhaustive global optimization searches (e.g., using genetic algorithms or particle swarm optimization) that were previously computationally prohibitive, allowing designers to explore a much wider region of the design space and escape local minima. In 2019, Sengsong An et al. proposed a novel neural-network-based approach for the design of metasurface devices. This neural network could quickly determine the physical feasibility of a target design based on given nano-atom design constraints (e.g., size and geometry) and generate the optimal design that is closest to the preset performance targets [251]. In 2020, Sengsong An et al. put forward a deep-learning-based modeling method for metasurface units. By utilizing a convolutional neural-network-based network architecture, the accurate spectral response of nano-units was obtained. The proposed deep learning network workflow exhibits strong generalization ability, enabling accurate prediction of nano-atom features not present in the training dataset. Furthermore, a transmissive metalens operating at a frequency of 57 THz was designed using the well-trained network architecture [252].

The next evolutionary step has been direct inverse design. Here, the goal is to bypass traditional optimization loops entirely. A deep learning model, often a generative adversarial network (GAN) or a Conditional Variational Autoencoder (CVAE), is trained to generate a complete lens system configuration (a set of construction parameters) directly from a high-level performance specification. For instance, one could input desired values for focal length, f-number, field of view, and overall size, and the network would output a viable starting design. This approach is particularly powerful for designing non-conventional optics, such as aspheric lenses, freeform optics, or gradient-index (GRIN) lenses, where the design space is vast and non-intuitive. DL models can discover complex, highly aspheric surfaces that would be very difficult for a human to conceive, often yielding designs with superior performance and fewer elements [253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277]. In 2018, Zhaocheng Liu et al. from the University of Georgia proposed the use of generative adversarial networks for the inverse design of metasurfaces [278]. By training a generator and a discriminator, they took data combining spectral responses and noise as the input to the generator, which then outputted 2D images of metasurfaces. Compared with traditional neural networks, GANs can generate a wide variety of metasurface structures and enhance the generalization ability of inverse design. However, GANs suffer from significant instability—model training is prone to collapse, making it difficult to achieve Nash equilibrium. In 2022, Yang Yang et al. proposed an inverse network (IN) model to assist in metasurface design [279]. The IN was trained by cascading an inverse design network (IDN) and a pre-trained forward prediction network (FPN). The metasurface unit structure consists of a silica substrate and a titanium dioxide cross-shaped structure. The forward prediction network and the inverse network have the same architecture, both composed of five fully connected layers with the same number of neurons. The IDN and FPN are connected end-to-end, and the IDN is further trained using the pre-trained FPN with fixed parameters. The prediction error of the FPN is used as a supervision signal to further address the issue of non-unique solutions in the inverse design process.

The most sophisticated and powerful paradigm is end-to-end design. In this approach, the lens design is not an isolated process but is integrated with its final application, such as image classification, object detection, or computational photography. A single deep learning model encompasses the entire pipeline: the physics of the optical system (often made differentiable) and the digital image processing algorithms. The loss function is based on the final task performance (e.g., accuracy of image classification, quality of a reconstructed image), and gradients are back propagated all the way back to the physical parameters of the lenses. This allows the optical system to be co-optimized with the algorithm that will process its output, leading to holistic designs where the optics and software work in concert. For example, a lens might be designed to produce a peculiar, non-sharp intermediate image that is intentionally optimized to be perfectly decoded by a specific neural network to produce a final image of much higher quality than a traditional lens could provide [280,281,282,283,284,285,286,287,288,289]. In 2023, Jiang et al. developed an efficient end-to-end inverse design framework for multi-wavelength achromatic metalenses and demonstrated an achromatic metalens operating at four visible wavelengths and under arbitrary linear polarization, with an NA of 0.3 and a diameter of 115 μm [290]. In the same year, the research group led by Xianguang Luo proposed a physics-data-driven method. By adopting an intelligent optimizer, this method enables adaptive modification of the size of meta-atoms based on the size of their surrounding atoms. Compared with previous inverse design methods, this approach significantly improves design efficiency, reducing the design time by five orders of magnitude [291].

Metalenses, flat optics composed of dense arrays of subwavelength nanostructures (meta-atoms) that phase-shift light, represent a paradigm shift in optics, promising to replace bulky, heavy, curved lenses with thin, flat, lightweight surfaces. However, their inverse design—finding the precise arrangement of nanoscale elements to produce a desired macroscopic wavefront transformation—is a problem of staggering complexity. The design space is hyper-dimensional, and simulating the electromagnetic response of each element is computationally expensive. This is where AI and DL transition from being useful tools to becoming essential enablers, unlocking the full potential of metalens technology.

The research potential of AI in the metalens field is vast and can be categorized by its role in the design and application pipeline: nanostructure design, system-level optimization, and the creation of intelligent meta-systems. (1) AI for Inverse Design of Meta-Atoms and Metasurfaces: The core challenge is mapping geometric parameters of a meta-atom (e.g., shape, width, height, rotation) to its complex optical response (phase, amplitude, polarization shift). DL is perfect for this. Forward surrogate models are trained to predict a meta-atom’s response in milliseconds, replacing slow numerical simulations (FDTD, FEM). More importantly, inverse models, particularly using generative adversarial networks (GANs) and Conditional Variational Autoencoders (CVAEs), can accept a desired electromagnetic response and generate a corresponding nanostructure geometry. This allows for the discovery of highly efficient, non-intuitive, and topologically complex meta-atom designs that human designers would never conceive of. Furthermore, AI can design achromatic meta-atoms—structures that provide the same phase shift across a broad bandwidth—a critical hurdle for commercial metalens applications. By optimizing for a complex, multi-wavelength response, DL can solve problems that are analytically intractable. (2) AI for End-to-End and Multi-Functional Metalens Design: The true power of AI lies in moving beyond designing individual elements to optimizing the entire metalens for a specific task. This involves end-to-end differentiable modeling. A deep learning framework is constructed that includes the model of the metalens (its phase profile), the model of light propagation (e.g., angular spectrum method), and the final task-specific loss function. For a computational imaging task, the loss could be the quality of the final reconstructed image. Gradients of this loss are backpropagated through the entire digital pipeline to directly optimize the phase profile of the metalens. The physical nanostructures are then designed to implement this optimized profile. This co-design of optics and a processing algorithm leads to radically new optical systems. For instance, a metalens can be designed to produce a purposefully scrambled output that is not a clear image but is instead optimally encoded for a subsequent neural network to denoise, super-resolve, or classify with maximum accuracy. AI is also critical for designing multi-functional metalenses that perform different operations (e.g., focusing, beam steering) for different wavelengths or polarization states, a task of immense complexity that DL can navigate efficiently. (3) AI for Reconfigurable and Intelligent Metasystems: The future lies in dynamic metasurfaces using materials like phase-change chalcogenides (GST), liquid crystals, or MEMS. AI will be the “brain” that controls these systems. Deep Reinforcement Learning (RL) agents can be trained to control the tuning elements of a dynamic metalens in real-time to achieve a goal, such as compensating for atmospheric turbulence, adapting to different scene depths, or switching between imaging modalities. This points toward the development of truly intelligent meta-optical systems that can perceive their environment and self-optimize their function accordingly. For example, an AI-controlled metalens on a smartphone could automatically switch between a wide-angle landscape mode, a high-resolution zoom mode, and a depth-sensing mode for augmented reality, all without any moving parts.

In conclusion, AI is not just a tool for designing metalenses; it is the key to transforming them from static, single-purpose optical components into dynamic, intelligent, and multifunctional systems that will form the core of next-generation cameras, sensors, displays, and optical processors.

9. Summary and Outlook

Since the concept of metamaterials was proposed, researchers have conducted extensive studies on them and achieved numerous advancements [253,284,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313]. As a revolutionary achievement in the field of metamaterials, metalenses precisely control the amplitude, phase, and polarization state of light waves through subwavelength structural units, breaking the physical limitations of traditional optical lenses. This paper introduces the most fundamental principle of metalenses composed of two-dimensional metamaterials—the generalized Snell’s law—and presents three methods for achieving electromagnetic wave phase control through metalenses. It provides diverse control means for the design of metasurface unit structures and promotes the transformation of metalenses from concept to practical application. In terms of material systems, two types of metalenses—plasma type and dielectric type—are introduced. Early research on metalenses mainly focused on plasmonic metalenses. Dielectric metalenses have become the mainstream at present due to their low loss characteristics in electromagnetic wave control. In terms of functional expansion, three types of metalenses—tunable metalenses, wide-field-of-view metalenses, and achromatic metalenses—are introduced. Metalenses have made breakthroughs in these core performance aspects: tunable metalenses achieve precise focal length adjustment through light control, electrical control, mechanical modulation, etc., with response speed reaching sub-millisecond level. The large-field-of-view metalens, through schemes such as curved substrate design and double-layer structure optimization, has expanded the field of view angle to 170° and has verified its application potential in fields such as AR/VR display [314,315,316] and planar cameras. Achromatic metalenses gradually expand the achromatic bandwidth from discrete wavelengths to ultra-wideband through strategies such as multi-wavelength design, vertical stacking structure, and birefringent unit regulation, providing the possibility for panchromatic imaging. Overall, metalenses have shown great potential to replace traditional lenses and build the next generation of compact optical systems thanks to their planarization; miniaturization; high integration; and the ability to precisely control the phase, amplitude, and polarization of light waves.

At present, the main limitations of metalenses include cost issues and core performance issues. The cost issue makes it extremely difficult to match the precision of centimeter-scale components with that of nanometer-scale components, which requires extremely high costs, and the processing of materials related to metalenses also poses further demands and challenges to the existing industrial processing foundation, such as the more common electron beam etching and atomic layering, although they can meet the processing precision requirements of the nanometer scale. However, the processing region is only at the millimeter level and the cost is very high. With the development and progress of new manufacturing process technologies (such as nanoimprinting [317,318,319,320,321,322], interference lithography [323,324,325], grayscale photolithography [326,327], etc.), it is believed that metalens technology that can achieve large-sized, high-performance, and industrial assembly line production will be developed in the near future. In addition, as metalenses are diffractive imaging elements, the dispersion problem remains a major obstacle to their practical application. Currently, achromatic metalenses still have issues such as limited bandwidth and reduced efficiency at large apertubles. It is necessary to further explore new dispersion control mechanisms (such as design of equivalent parameters of metamaterials and multi-physics field coupling control) and combine them with artificial-intelligence-assisted optimization algorithms. Achieving wide-band (such as visible light to near-infrared), large-aperture, and high-efficiency achromatic focusing is needed to meet the requirements of panchromatic imaging and spectrum analysis. The development of metalenses with larger bandwidths is one of the future research trends.