Generalized nihility media from transformation optics

Nihility media in the previous literature are usually understood as media with epsilon = mu = 0. Transformation optics opens a new perspective for capturing the essence of such media. From this perspective, we generalize the definition of nihility media as transformation media derived from volumeless geometrical elements. A volumeless geometrical elements can be either a point (P), a line (L), or a surface (S). Their corresponding transformation media are therefore called P-, L-, or S-type nihility media, respectively. The previous defined nihility media with epsilon = mu = 0 is a special case under the P-type nihility media. The constructions of nihility media by metamaterials are discussed. The eigenfields in different types of nihility media are derived. The interactions between an externally incident wave and a slab of nihility media in a free space background are analyzed. Furthermore, we discuss compensated bilayers composed of nihility media. It is shown that for a slab of P-type nihility media, a normally incident wave can perfectly transmit through, while all obliquely incident waves are completely blocked; for a slab made of L-type nihility media, both normally and obliquely incident waves can transmit with some reflections, which can be eliminated by adding a compensating L-type nihility media; for a slab of S-type nihility media, all field components can perfectly transmit through.