Ma Yaoguang, Gao Yubin
The National Key Laboratory of Extreme Optical Technology and Instrumentation of Zhejiang University, the School of Optoelectronic Science and Engineering, Zhejiang University, the Intelligent Photonics Research Center of Jiaxing Research Institute, and the Hangzhou International Science and Technology Innovation Center of Zhejiang University
introduction
In 1968, Veselago first proposed the concept of left-handed materials (LHM) and systematically studied their electromagnetic properties. Since then, a new field of metamaterials has been born. Metamaterials are macroscopic composites composed of spatially arranged periodic or non-periodic subwavelength structures (such as metal rings, metal rods, etc.), and their functions are no longer determined by the chemical composition of the material alone, but are closely related to the structure. This means that, through careful structural design, metamaterials can possess a wealth of electromagnetic properties that natural materials cannot provide, so that human ability to control electromagnetic waves is expected to reach an unprecedented level.
As a two-dimensional form of metamaterial, metasurfaces achieve specific electromagnetic manipulation properties by arranging metaatoms – subwavelength-level scatterers or pores – on a two-dimensional plane. In terms of working principle, compared with metamaterials, metasurfaces can occupy a smaller physical space based on phase mutations at the interface rather than phase accumulation, and thus have lower losses to meet the needs of practical applications. At the same time, its compact size is also suitable for applications such as integrated nanophotonics and novel microwave antenna designs. In addition, the reduction of dimensionality significantly reduces the difficulty of processing and manufacturing devices.
Design principles for metasurfaces
Essentially, a metasurface is a two-dimensional array of metaatoms. From the perspective of metaatoms, metasurfaces can be divided into two categories: homogeneous metasurfaces and heterogeneous metasurfaces: the former is composed of the same kind of metaatoms arranged periodically, and the electromagnetic control characteristics of the entire metasurface can be reduced to a single metaatom under periodic boundary conditions, while the latter uses a variety of metaatoms of different shapes, sizes or rotation angles, each of which produces a specific electromagnetic response, and can achieve rich and complex applications through the careful arrangement of various metaatoms.
It can be seen that the working principle of homogeneous metasurfaces is the basis for further understanding of heterogeneous metasurfaces, and the core of understanding homogeneous metasurfaces lies in understanding metaatoms. Homogeneous metasurfaces can be regarded as a special case of heterogeneous metasurfaces, but they also have their own unique applications in terms of perfect absorbers, polarization control, transmittance or reflectance enhancement, etc.
1. The basic principle and phase regulation mechanism of metaatoms
A metaatom is a subwavelength metallic or dielectric structure. The study of the interaction of subwavelength structures with light can be traced back to Mie's famous paper published in 1908. In that paper, Mie used electromagnetic theory to derive a strict solution for the interaction of a monochromatic plane wave with a homogeneous sphere of arbitrary radius to a homogeneous sphere of material in a homogeneous medium. In subsequent studies, although some studies have tried to extend the spherical structure to non-spherical structures, the strict analytical form of the electromagnetic field solution is relatively complex, and a certain approximation is often adopted in practice.
In metasurfaces, metaatoms often adopt cylindrical, rectangular, and special-shaped columns (the column cross-section is H-shaped, V-shaped, cross-shaped, etc.), and the scattering fields of different metaatoms are coherent with each other. Among them, the classical method for modeling and analyzing homogeneous metasurfaces is the effective medium theory. This theory attempts to find a correspondence between the metaatomic structure and the bulk material parameters, but there are many limitations. In fact, studies such as Mie theory or equivalent media theory are rarely directly applied to the design of metaatoms (especially in the design of heterogeneous metasurfaces). In general, computational electromagnetics methods (e.g., finite difference in time domain (FDTD) methods are commonly used to perform full-wave simulations of metaatoms to solve for their electromagnetic response characteristics.
The phase control mechanism of metaatoms is of great significance for the design of metasurfaces with different functions. In the current metasurface design, three types of phase control mechanisms are most widely used: resonant phase, propagation phase, and geometric phase.
2. Generalized laws of refraction and reflection
For heterogeneous metasurfaces, the electromagnetic response properties are a function of two-dimensional space. The generalized law of refraction and reflection can be used to describe the effect of abrupt phase changes in the spatial distribution at the interface on the refractive and reflective properties of light between two media.
In 2011, Yu et al. defined the laws of generalized refraction and reflection respectively, and experimentally verified them using metasurfaces. In the experiment, the scattering field amplitude of all metaatoms should be consistent, and the spacing of adjacent metaatoms in the array should be much smaller than the wavelength to ensure that the spherical waves emitted from a single metaatom follow the Huygens principle, superimposed to produce refracted and reflected waves with plane wavefronts, as shown in Figure 1. The idea and steps of deriving this law were mentioned by Li Xiaotong et al. in 2007.
Fig. 1 FDTD simulation results of the scattered electric field for each metaatom in the V-shaped metaatomic array used to deflect the beam
3. Forward design theory of metasurfaces
In the traditional forward design strategy, the metasurface is divided into periodically arranged elements, and the elements generally adopt a square or regular hexagon with a fixed lattice constant (for square cells, the lattice constant is its side length, also known as the element size) to cover the entire surface, and a metaatom is placed in the center of each element according to the electromagnetic response requirements of the target design (the metaatom is selected from a database of metaatoms constructed by traversing structural parameters in advance), and the electromagnetic control effect of the metasurface on the incident light is equivalent to the splicing of the electromagnetic response of the local metaatom。 This approximation is called a local periodic approximation (LPA).
The effectiveness of this approximation is illustrated by taking the dielectric metasurface as an example: in subwavelength metaatoms, the main source of the cluster electromagnetic response of the metaatomic array is the Michaelis resonance within a single metaatom and its interference with each other, rather than the combination of adjacent metaatoms or the diffraction mode at the entire lattice level. From the point of view of pattern analysis, the limitation of the local periodic approximation is that it ignores the influence of the formation of a trans-unit pattern between adjacent metaatoms, which in many cases cannot be ignored.
It is precisely because of the above limitations of traditional forward design strategies that in recent years, the reverse design method of metasurface, which has been gradually developed based on optimization theory or deep learning technology, has played an increasingly important role in breaking through the performance limitations of devices and realizing novel designs with complex functions.
The direction of development of metasurface applications
1. Polarization-multiplexed metasurfaces
One of the advantages of metasurfaces over traditional optical components is to introduce independent phase control for the light incident and exit in a specific polarization state through the polarization-sensitive metaatom design, so as to realize polarization multiplexing. For single-wavelength designs, arbitrary polarization and phase manipulation can be described by a symmetrical and unitary Jones matrix.
In 2023, Xiong et al. broke the linear correlation between the phase control of each channel when the number of polarization multiplexed channels is higher than 3 by introducing uncorrelated noise, thus breaking through the basic limit of metasurface polarization multiplexing under the Jones matrix limit. As shown in Figure 2, a holographic metasurface can be experimentally multiplexed with up to 11 independent linear polarization channels, which is the highest capacity of polarization multiplexing reported to date.
Fig.2. Holographic image of an 11-channel polarization-multiplexed metasurface under incident light in different polarization states (experimental results)
In addition to the above-mentioned holographic fields, the hybrid phase control mechanism also has important applications in the field of polarization imaging. In 2019, Rubin et al. in Capasso's group proposed the concept of matrix Fourier optics and realized matrix gratings using metasurfaces, which can diffract incident light with different polarization states at fixed wavelengths to specific diffraction orders to separate them from each other, and then be used for polarization imaging of full Stokes.
2. Wavelength-multiplexed metasurfaces
Color holographic display has always been the goal pursued in the field of holographic metasurfaces. In order to realize the color holographic display, the target color image is first decomposed into the components of the three primary colors of red, green and blue, and then the metasurface is designed, and independent phase control is introduced to the incident light of the three wavelengths of red, green and blue, so that the holographic images corresponding to the color components are generated respectively, and finally the color holographic images are synthesized. It is important to note that additional algorithms may be required to correct for chromatic aberration (due to the wavelength-dependent nature of diffraction) and holographic distortion at large fields of view. The design method of wavelength multiplexing devices is introduced by taking color holographic metasurfaces as an example.
Using the strategy of space division multiplexing, as shown in Figure 3(a), the metasurface element contains multiple metaatoms, and each wavelength component corresponds to one (or two) metaatoms. By rotating the metaatoms of the corresponding wavelengths, the geometric phase is introduced, so that the whole unit can meet the phase control requirements of each wavelength at the same time. At the same time, in order to avoid crosstalk of holographic images between wavelengths, the transmittance of metaatoms corresponding to one wavelength is required to be as 0 as possible at other wavelengths, which can be achieved through careful structural design or by additional color filters pre-empting the Fabry-Perot (FP) cavity, as shown in Figure 3(b). In 2016, Wang et al. used this method to achieve a full-color holographic display, as shown in Figure 3(c). The disadvantage of this approach is that, in addition to the loss of device efficiency, the cell size is doubled, so the maximum field of view of the holographic display is severely limited. As a variant of the space division multiplexing strategy, as shown in Figure 3(d), the metaatoms responsible for the different wavelength components do not necessarily have to be placed in the same cell, but can be arranged in a certain pattern (and by the way, the function of color printing patterns can also be realized), but the corresponding constraints need to be imposed when computationally generating holograms. Based on this method, the color holographic display results achieved by Huang et al. in 2019 are shown in Figure 3(e).
Fig.3 Wavelength multiplexed metasurface. (a) Schematic diagram of metasurface element for space division multiplexing, (b) Schematic diagram of the principle of the pre-color filter of the metasurface, (c) Schematic diagram of the principle of color holographic display results based on the principle shown in (a) (experimental results, the same below) ;(d) a variant of the space division multiplexing strategy, and (e) color holographic display results based on the principle shown in (d).
3. Incident angle multiplexing and metasurfaces with large field of view
In 2017, Kamali et al. in Faraon's group conducted a preliminary exploration of metasurface devices for multiplexing the angle of incidence. Using the strategy of forward design, U-shaped metaatoms are used to cover the complete phase regulation at different incident angles. Based on this, the holographic metasurfaces with different holographic images were generated by introducing independent phase distributions to the incident light with incident angles of 0° and 30° respectively. In fact, this response is related to non-local effects, so the forward design approach faces certain limitations. In 2018, Lin et al. used topology optimization to realize the design of an aberration-corrected cylindrical lens with a numerical aperture of 0.35 at 0°, 7.5°, 15°, and 20° incidence angles for the angle-dependent target phase. However, its five-layered metasurface structure is difficult to achieve with existing processing technology. It can be seen that it is difficult to realize a large field of view metasurface device with the idea of multiplexing the angle of incidence.
The core factor limiting the field of view is various off-axis aberrations, especially coma (which can lead to asymmetry in imaging and have a serious impact on image quality). Although the hyperbolic phase distribution has the advantage of being free of spherical aberration and distortion, it introduces severe coma. Therefore, new phase distributions must be introduced to accommodate imaging applications with large fields of view. It should be noted that the phase distribution of a monolithic planar metasurface cannot perfectly correct for both spherical aberration and coma, and any phase distribution will be a trade-off between spherical aberration, coma, numerical aperture, and efficiency.
4. Multi-layered metasurfaces
Most of the above discussions are based on monolithic metasurfaces. By analogy with traditional optical design, it is not difficult to imagine that by cascading multiple layers of metasurfaces to cooperate with each other, it is expected to achieve design tasks that are difficult to accomplish on a single metasurface, such as aberration correction of metalenses, generation of high-purity vortex beams, or novel functions such as optical neural networks and secret sharing. The distance between layers in a cascaded metasurface determines the relationship between adjacent layers of metasurface, which corresponds to different theoretical models and design methods.
When the spacing between the layers of the metasurface is far enough away, there is no coupling relationship between the adjacent layers of the metasurface, and the target phase and layer spacing of each layer of the metasurface are optimized by considering the whole system in advance through traditional optical design methods such as ray tracing, and the design of each layer of the metasurface is carried out independently according to the target phase requirements, and the theory and method are completely consistent with that of the monolithic metasurface.
In 2016, Arbabi et al. used a double-layer metasurface with a layer spacing of 1 mm and a metaatomic material of amorphous silicon to achieve a fisheye objective with an F number of 0.9, a field of view of more than 60°, an operating wavelength of 850 nm, and an absolute focusing efficiency of 70% (the diameter of the effective focusing circular area is 15 μm), as shown in Figure 4. However, the limitations of the interlayer distance in the range of hundreds of microns are also very obvious: first, it cancels out the advantages of ultra-thin metalenses, and second, it brings new design and performance limitations, which cannot fully exploit the advantages of multilayer metasurfaces.
Fig.4. Multi-layered metasurfaces. (a) Image taken with a double-layer metasurface at a scale bar of 100 μm. The inset is a magnified view of the image at the position indicated by the rectangle, with the same contour color corresponding to the field of view of 0°, 15°, and 30°, all at a scale of 10 μm.
5. Non-local metasurfaces
In recent years, the coupling between metaatoms has gradually attracted attention, and non-local metasurfaces have been proposed and developed, resulting in a variety of novel device designs, which are widely used in optical simulation and image processing, spatial compression, imaging, thermal control and other fields. Non-locality means that the electromagnetic response of an element on a metasurface is not only related to that element (as is approximated by LPA), but also depends on all elements in the adjacent region (the size of the adjacent region is positively correlated with the strength of the nonlocality). The direct manifestation of the non-local effect is the dependence of the electromagnetic response on the angle of incidence of the incident light. This feature, also known as spatial dispersion, is something that needs to be avoided or even eliminated in traditional forward design. Non-local metasurfaces do the opposite, maximizing the spatial dispersion characteristics of metasurfaces.
In 2021, Song et al. experimentally demonstrated that non-localized and high optical figure of merit metasurfaces can significantly enhance the interaction between light and matter compared with traditional metasurfaces with high localization and low optical figure of merit, and realize completely decoupled optical functions at different wavelengths. This metasurface can be used in ordinary eyeglasses to achieve functional decoupling in the visible and near-infrared spectral ranges: for visible light, a zero-order transmittance of more than 85% and an average diffraction of as low as 0.07% are maintained to ensure proper imaging of the glasses, and on the other hand, the positive incident near-infrared light from the eyeball is redirected to the 60° camera to allow imaging of the eyeball, covering a wide range of eye rotation angles ± 80°, and the image resolution is sufficient to quantify the sclera, The size and movement of the iris and pupils for eye tracking.
Future outlook
Compared with traditional optical components, metasurfaces have an ultra-light and ultra-thin planar architecture, and their powerful electromagnetic control characteristics support flexible design to achieve high-performance or multifunctional multiplexing optics in wavelength, polarization, angle of incidence and other dimensions, easy to integrate and realize the miniaturization of optical systems, and is expected to achieve low-cost large-scale manufacturing. However, in terms of design and fabrication, metasurfaces still face a variety of challenges from science and engineering.
This article is rewritten and published in the journal "Metasurfaces: Design Principles and Application Challenges", and has been authorized by the author
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