ABSTRACT
Often in optics we must deal with layered media when the optical properties change only in one specific direction (say, along the z-axis), while in any plane transverse to this direction, the optical properties are invariant. Such media with dielectric and magnetic responses given by ε(z) and µ(z) as functions of only z are also referred to as stratified media. There are many examples
Wave Trends
of such media. The most useful one refers to the optical interference coatings that are essential for most optical instruments. Reflection and transmission through these structures can be handled in terms of simple 2 × 2 matrices when the constituent layers are homogeneous and isotropic. In the case of an anisotropic layered medium, we can develop a 4 × 4 matrix formulation for uniaxial materials [61, 62]. In this chapter we deal with isotropic homogeneous layers and develop the characteristics matrix formalism to obtain the refection and transmission coefficients (see also Ref. [31]). We discuss how the dispersion in such structures can be engineered to lead to slow and fast light [7]. We apply the technique to investigate the modes of a structure. We probe the effects of finite temporal width of a pulse leading to the Wigner delay [63]. The space equivalent of Wigner delay, also known as the Goos-Ha¨nchen shift [64], for a spatially finite beam is then discussed. Finally, we show how someone using such structures can realize perfect transmission and coherent perfect absorption. We will define all the necessary notions and concepts as we go along.
