Introduction To Yasuura'S Method Of Modal Expansion With Application To Grating Problems

In this chapter we introduce the theory of the Yasuura's method based on modal expansion and explain the methods of numerical computation in detail for several grating problems. After a sample problem we discuss the methods for solving two types of problems that require additional knowledge and steps, that is, scattering by a dielectric cylinder and diffraction by a grating. Some numerical results are shown to give an evidence of an experimental rule for the number of linear equations in formulating the least-squares problem that determines the modal coefficients. After confirming the rule we show a couple of examples of practical interest, i. e., scattering by a relatively deep metal grating, plasmon surface waves on a metal grating placed in conical mounting, scattering by a metal surface modulated in two directions, and scattering by periodically located dielectric spheres. To provide supplementary explanations of particular problems, four appendices are given; H-wave scattering from a cylinder, the normal equation and related topics, conical diffraction by a dielectric grating, and comparison of modal functions and the algorithm of the smoothing procedures.