The concept of negative refraction is attracting a lot of attention. The initial ideas and the misconceptions that have arisen are discussed in sufficient detail to understand the conceptual structure that binds negative refraction to the existence of backward wave and forward wave phenomena. A presentation of the properties of isotropic media supporting backward waves is followed by a discussion of negative phase velocity media, causality, anisotropic crystals and some connections to photonic crystals. The historical background is always coupled to a detailed presentation of all the issues. The paper is driven numerically and is illustrated with the outcomes of original FDTD simulations

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Surface wave propagation at the interface between different types of gyrotropic materials and an isotropic negatively refracting medium, in which the relative permittivity and relative permeability are, simultaneously, negative is investigated. A general approach is taken that embraces both the gyroelectric and gyromagnetic materials, permitting the possibility of operating in either the low GHz, THz or the optical frequency regimes. The classical transverse Voigt configuration is adopted and a complete analysis of nonreciprocal surface wave dispersion is presented. The impact of the surface polariton modes upon the reflection of both plane waves and beams is discussed in terms of resonances and an example of the influence upon the Goos-Hänchen shift is given.