Periodic optical systems, resonators, and inhomogeneous media

Abstract

Introduction In this chapter we shall use a variety of analytic techniques to analyze periodic optical systems and understand their behavior. These are optical systems in which a ray crosses a repeating pattern of interfaces, a so-called stratified medium , or passes through a sequence of optical components that repeat in a periodic fashion along the axis. These periodic systems include multi-layer structures that have special reflective or transmissive properties and structures whose dielectic properties vary symmetrically in two or three dimensions. Such periodic structures are often called photonic crystals. Periodic lens sequences are axisymmetric arrangements of multiple lenses arranged along an axial direction. They can be described as stable or unstable. Stable lens sequences have the ability to confine a propagating bundle of rays near to the axis in such a way that the rays never deviate by more than a certain finite distance from the axis and remain confined. Periodic lens sequences can also be used to study the paths of light rays bouncing back and forth between pairs of mirrors – optical resonators . This will allow us to deduce the stability condition for such resonators. Plane waves in media with complex refractive indices The relative permittivity and the relative permeability characterize a medium in terms of its difference from a vacuum. Most materials that are important in a discussion of lasers and optical devices are not strongly magnetic, and it is generally legitimate to assume that for such materials μ r = 1.