ABSTRACT
This chapter shows that the idea of local Fourier analysis, the theoretical territory of Fourier Modal Method (FMM) can be expanded to the development of novel theories. It proposes the generalized S-matrix method (GSMM) and the unification of local Fourier modal method (LFMM) and GSMM are developed for modeling nanophotonic networks. Using the perfect matched layer approach, nonperiodic structures were successfully modeled and analyzed by FMM. Nanophotonic networks are composed of a wide variety of photonic devices. To study the collective dynamics of such nanophotonic networks, an understanding of the theory of nanophotonic networks is necessary. The development of rigorous and efficient mathematical modeling of nanophotonic networks is an urgent and important theme at present. Practical nanophotonic networks, optical fields are usually localized on engineered structures or devices such as waveguides and resonators. The mathematical model of a nanophotonic network is made up of two key subtheories, LFMM and GSMM.
