Manipulation of light with α transformation media

A type of transformation media called α media is proposed by performing a direct transformation to the metric tensor of another kind of media, called seed media. Light rays in an α medium correlate to those in its seed medium through a simple displacement or rotation relation. Three types of commonly encountered anisotropic media are covered by the concept of α media: (1) media of slab shape, having continuous translational symmetry with respect to two Cartesian coordinate components; (2) media of cylindrical shape, having cylindrical rotational symmetry and continuous translational symmetry along the longitudinal direction; (3) media of spherical shape, having spherical rotational symmetry, with two principal axes along the symmetry directions, and with the material parameters in the same sign. Optical properties of such media can be effectively interpreted through recalling the properties of certain isotropic media, i.e., their seed media. Conversely, from simple isotropic media in which light trajectories are well known, one can design α media for manipulating light. Based on this fact, several optical devices, including frequency demultiplexers, beam splitters, focusing lenses, and radiation controllers, are designed and numerically verified. The famed invisibility cloak derived from a conventional coordinate transformation is revisited from the α media perspective.