Consisting of sub-wavelength scatterers or holes arranged on a plane, the metasurface, as a two-dimensional form of the metamaterial, permits flexible and efficient modulation of the amplitude, phase, polarization and other characteristics of the light with an unprecedented degree of freedom, which is expected to break through the limitations of traditional optics and realize ultra-light, ultra-thin, high-performance, and novel-functional optical devices. In recent years, metasurfaces have attracted increasing research interest in both academia and industry, and a wide range of applications have been achieved in the field of imaging, holography, quantum optics, displacement metrology, virtual reality, optical encryption, and ultrafast optics. Based on the elucidation of the basic design principles of metasurfaces, this review covers the main development directions, research progress, and challenges of current metasurface applications.

The design principles of metasurfaces are now well established and can be understood in three dimensions the most basic meta-atom and its scattering effect, metasurface as an array of meta-atoms, and the topmost design methods. For the first dimension, the physical image of the electromagnetic modulation of the meta-atom is explained, and the three main types of phase modulation mechanisms are introduced, that are, the resonant phase, the propagation phase, and the geometric phase. The selection of appropriate phase modulation mechanisms is significant for realizing the design of metasurfaces with different functions. For the second one, generalized refraction and reflection laws are introduced. For the last one, the forward design method and its theoretical basis are presented.

How these mechanisms are utilized to realize a variety of applications is described in detail, including polarization multiplexing, wavelength multiplexing, wide bandwidth, large field-of-view, multilayer cascades, and nonlocal metasurfaces, covering the most important and recent developments. 1) Polarization multiplexed devices (Fig.3). When operating at a single wavelength, it is theoretically elucidated that a hybrid phase modulation mechanism can achieve arbitrary polarization and phase modulation under the ideal situation of sufficient design freedom of meta-atoms. Based on this theory, the latest research progresses are presented, such as the multiplexing for arbitrary orthogonal states of polarization, multichannel polarization multiplexing, etc.2) Wavelength multiplexed devices (Fig.4). To achieve independent phase modulation of the incident light at different wavelengths, intelligent strategies of space division multiplexing, decoupling with other multiplexing channels, and other methods have been proposed, leading to applications such as full-color holographic displays. 3) Broadband devices (Fig.5). The problem of achromaticity in metalenses has been a difficult problem in this field for several years. Through dispersion engineering, theories and methods for designing achromatic metalenses have been developed, and both polarization-sensitive and polarization-insensitive achromatic lenses have been realized. Recently, the novel idea of quasi-achromatic metalenses has also been proposed to relax the bandwidth limitation of achromaticity. 4) Incident angle multiplexed and wide field-of-view devices (Fig.6). Incident angle multiplexed metasurfaces can be designed by both forward methods and inverse methods such as topology optimization. By selecting the suitable target phase distribution for wide field-of-view imaging and introducing the concept of effective aperture or virtual aperture, metalenses with wide field-of-view have been designed and realized. 5) Multilayer cascaded metasurfaces (Fig.7). The distance between layers in cascaded metasurfaces determines the relationship between adjacent layers, according to different theoretical models and design methods. By cascading multiple layers of metasurfaces, design tasks that are difficult to achieve with a single metasurface can be achieved, such as hysteresis and chromatic aberration correction of metasurface lenses, and novel functions such as dual-wavelength and dual-focus metasurface lenses can be obtained. 6) Nonlocal metasurfaces (Fig.8). By exploiting the nonlocal effect of metasurfaces, the transverse-momentum-dependent electromagnetic response can be modulated to realize novel functions that are difficult to achieve for local metasurfaces, such as image differentiation and free-space compression, which is a latest trend in metasurface design.

Metasurfaces still face many challenges from science and engineering. In terms of the metasurface design, it is still a common problem of the field to realize devices with higher performance and larger size. On the one hand, it is important to clarify the theoretical performance limits of metasurfaces and the constraints of design methods to guide the future development of the metasurface design. On the other hand, it is also essential to make breakthroughs in design methods, such as the further development and promotion of inverse design. In terms of fabrication and manufacturing, there is still a long way to go for the industrialization and commercialization of metasurfaces due to the limitations of the fabrication accuracy, process compatibility, large-scale manufacturing cost, etc. We believe that metasurfaces will play a transformative role in the near future of optics contributing to their ultra-light and ultra-thin planar architectures, powerful electromagnetic modulation properties to support flexible device designs, ease for integration and miniaturization of optical systems, and the promise of low-cost, high-volume manufacturing.