Abstract
Transformation optics has shown great ability in designing devices with novel functionalities, such as invisibility cloaking. A recent work shows that it can also be used to design metasurfaces which usually come from the concept of phase discontinuities. However, metasurfaces from transformation optics have very complicated material parameters. Here in this work, we propose a practical design, a sub-wavelength metallic grating with discrete and gradient index materials. Such a design not only inherits some functionalities of metasurfaces from phase discontinuities, but also shows richer physics. Our work will also provide a guidance to recent activities of acoustic metasurfaces, especially for those made of extremely anisotropic metamaterials.