  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 are not found
in nature. 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,
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
Pancharatnam-Berry phase and Huygens' metasurfaces, as well as their use in
wavefront shaping and beam forming applications, followed by a discussion of
polarization conversion in few-layer 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 opportunities and challenges in this rapidly developing research
field.
