Periodic Impedance Surface
In the previous chapters, the rigorous MMA was developed for dealing with the scattering and guiding characteristics of a dielectric waveguide incorporating periodic structures and numerous numerical examples were demonstrated for exploring the unique physical picture of the wave process therein. In addition to the above-mentioned approach, in this chapter we will introduce an alternative approach, the periodic IBC, for analyzing the scattering properties of a plane wave by a periodic structure. As is well known, the IBC was first developed (Leontovich 1948) in the early 1940s for solving the problem of radio waves propagating over the Earth. Leontovich showed that, on the surface of a nearly perfect conductor, the IBC related the tangential electric and magnetic fields via a surface impedance defined by the electromagnetic properties of the scatterer. Because the approximate IBC relates only the electromagnetic fields outside the scatterer, the scattering fields can be assessed without considering the internal fields; therefore, such an approach can further simplify the mathematical analysis. Furthermore, a 1D periodic impedance surface was employed to successfully explain the anomalous absorption of a lossy optical grating (Hessel and Oliner 1965), which is the so-called Wood's anomaly.
In this chapter, the rigorous1 mathematical formulation for formulating the scattering of a plane wave by 1D scalar periodic impedance surfaces will be carried ...