Introducing Defects into Periodic Structures
During the early 1990s, the optical physics community rediscovered the idea that a wave can be guided in a uniform medium between a pair of periodic structures, in effect forming a waveguide with side walls composed of periodic structures, if the periodic structures are operated in their stop-bands (called photonic bandgaps by them). That community was unaware that the identical concept was published many years ago in the microwave community (Larsen and Oliner, 1967). They designed a specific structure, and rigorously calculated the dispersion characteristics of waveguide modes, and also confirmed the guided-wave characteristics through the measurement. In this chapter, we will start from revisiting such a simple but important structure. In addition to the ppwg-like mode, the surface state supported by the asymmetry semi-infinite 1D periodic stratified medium will also be discussed. Secondly, the dispersion relation of waveguide, particularly on the leaky-wave phenomenon, in the channel sandwiched by a pair of 2D dielectric or metallic periodic structures will be discussed. Finally, the correlation between the scattering and guiding characteristics of the above-mentioned structure will be elucidated for interpreting the resonant transmission.
5.1 A Parallel-Plane Waveguide having a Pair of 1D Semi-Infinite Periodic Structures as its Side Walls
As shown in Figure 5.1, a parallel-plane waveguide consists of side walls made up ...