When thinking about traditional optical materials one invokes a notion of homogeneous media, where imperfections or variations in the material properties are minimal on the length scale of the wavelength of light λ (Fig. 1.1 (a)). Although built from discrete scatterers, such as atoms, material domains, etc., the optical response of discrete materials is typically “homogenized” or “averaged out” as long as scatterer sizes are significantly smaller than the wavelength of propagating light. Optical properties of such homogeneous isotropic materials can be simply characterized by the complex dielectric constant ε. Electromagnetic radiation of frequency ω in such a medium propagates in the form of plane waves E,H ̴ ei(k·r− ωt) with the vectors of electric field E(r,t), magnetic field H(r,t), and a wave vector k forming an orthogonal triplet. In such materials, the dispersion relation connecting wave vector and frequency is given by εω2 = c2k2, where c is the speed of light. In the case of a complex-valued dielectric constant ε, one typically considers frequency to be purely real, while allowing the wave vector to be complex. In this case, the complex dielectric constant defines an electromagnetic wave decaying in space, |E|, |H| ̴ e−Im(k)·r, thus accounting for various radiation loss mechanisms, such as material absorption, radiation scattering, etc.

Another common scattering regime is a regime of geometrical optics. In this case, radiation is incoherently scattered by the structural features with sizes considerably larger than the wavelength of light λ (Fig. 1.1(b)).