The Maxwell equations form the basis of the classical electromagnetic theory. In addition to these famous four equations, we need the constitutive relations, which connect the fields and flux densities to each other by the material parameters, permittivity and permeability. It is very natural to assume that these material parameters are in most cases positive. However, if we allow them to go negative, we face new exciting physical phenomena that have attracted mathematicians, physicists and engineers alike. For example, double-negative materials allow backward wave propagation and negative refraction enabling sub-wavelength focusing of a light beam. If only the electric permittivity is negative, such interfaces can support plasmonic resonances that are sub-wavelength oscillations of electron density excited by the incident light. Noble metals can manifest negative permittivity at visible and ultraviolet frequencies. However, the possibility of constructing double-negative materials has become closer to reality only recently alongside the research of artificial metamaterials. |