Abstract. Metamaterials are composed of periodic subwavelength metal/dielectric structures that resonantly couple to the electric and/or magnetic components of the incident electromagnetic fields, exhibiting properties that not found in nature. This class of micro-and nano-structured artificial media have attracted great interest during the past 15 years and yielded ground-breaking electromagnetic and photonic phenomena. However, the high losses and strong dispersion associated with the resonant responses and the use of metallic structures, as well as the difficulty in fabricating the micro-and nanoscale 3D structures, have hindered practical applications of metamaterials. Planar metamaterials with subwavelength thickness, or metasurfaces, consisting of single-layer or few-layer stacks of planar structures can be readily fabricated using lithography and nanoprinting methods, and the ultrathin thickness in the wave propagation direction can greatly suppress the undesirable losses. Metasurfaces enable a spatially varying optical response (e.g., scattering amplitude, phase, and polarization), mold optical wavefronts into shapes that can be designed at will, and facilitate the integration of functional materials to accomplish active control and greatly enhanced nonlinear response. This paper reviews recent progress in the physics of metasurfaces operating at wavelengths ranging from microwave to visible. We provide an overview of key metasurface concepts such as anomalous reflection and refraction, and introduce metasurfaces based on the PancharatnamBerry phase and Huygens' metasurfaces, as well as their use in wavefront shaping and beam forming applications, followed by a discussion of polarization conversion in fewlayer metasurfaces and their related properties. An overview of dielectric metasurfaces reveals their ability to realize unique functionalities coupled with Mie resonances and their low ohmic losses. We also describe metasurfaces for wave guidance and radiation control, as well as active and nonlinear metasurfaces. Finally, we conclude by providing our opinions of future developments in this rapidly developing research field.

{The development of artificially structured electromagnetic materials, termed metamaterials, has led to the realization of phenomena that cannot be obtained with natural materials 1 . This is especially important for the technologically relevant terahertz (1 THz 5 10 12 Hz) frequency regime; many materials inherently do not respond to THz radiation, and the tools that are necessary to construct devices operating within this range-sources, lenses, switches, modulators and detectors-largely do not exist. Considerable efforts are underway to fill this 'THz gap' in view of the useful potential applications of THz radiation [2][3][4][5][6][7] . Moderate progress has been made in THz generation and detection 8 ; THz quantum cascade lasers are a recent example 9 . However, techniques to control and manipulate THz waves are lagging behind. Here we demonstrate an active metamaterial device capable of efficient real-time control and manipulation of THz radiation. The device consists of an array of gold electric resonator elements (the metamaterial) fabricated on a semiconductor substrate. The metamaterial array and substrate together effectively form a Schottky diode, which enables modulation of THz transmission by 50 per cent, an order of magnitude improvement over existing devices 10 . A great deal of research into metamaterials has used microwave radiation; this is in part due to the ease of fabrication of sub-wavelength structures at these frequencies. Indeed, negative refractive index media 11,12 composed of negative permittivity 13 (e 1 , 0) and negative permeability 14 (m 1 , 0) metamaterial elements was first demonstrated at microwave frequencies. This has led to intense theoretical, computational and experimental studies of exotic phenomena, such as perfect lensing 15 and cloaking 16,17 . Recently, researchers have ventured to create functional metamaterials at near-infrared and visible frequencies [18][19][20] . Considerably less work has concentrated on THz frequencies 21,22 . However, the design flexibility associated with metamaterials provides a promising approach, from a device perspective, towards filling the THz gap.Metamaterials are geometrically scalable, which translates to operability over many decades of frequency. This engineering tunability is in fact a distinguishing and advantageous property of these materials. However, for many applications it is desirable to have real-time tunability. For instance, short-range wireless THz communication or ultrafast THz interconnects 23,24 require switches and modulators. Current state-of-the-art THz modulators based on semiconducting structures have the desirable property of being broadband, which is of relevance to THz interconnects, but are only able to modulate a few per cent 10 and usually require cryogenic temperatures 25 . Therefore, further improvement of the performance characteristics are required for practical applications. Here we present an efficient active metamaterial switch/modulator operating at THz frequencies. Although the modulation is based...

Polarization is one of the basic properties of electromagnetic waves conveying valuable information in signal transmission and sensitive measurements. Conventional methods for advanced polarization control impose demanding requirements on material properties and attain only limited performance. We demonstrated ultrathin, broadband, and highly efficient metamaterial-based terahertz polarization converters that are capable of rotating a linear polarization state into its orthogonal one. On the basis of these results, we created metamaterial structures capable of realizing near-perfect anomalous refraction. Our work opens new opportunities for creating high-performance photonic devices and enables emergent metamaterial functionalities for applications in the technologically difficult terahertz-frequency regime.