ABSTRACT
This chapter describes the mathematical generalization of FMM for local FMM (LFMM). It describes the framework of LFMM, and analyzes the S-matrix for a single super-block structure within the framework of LFMM. LFMM for a single-super-block with three-dimensional permittivity and permeability profile variation is the cornerstone for the multi-super-block LFMM. The mathematical extention of LFMM of single-super-blocks to LFMM of multi-super-blocks can be straightforwardly attained by the S-matrix method with a block S-matrix and a boundary S-matrix that are newly derived for super-block structures. The chapter also examines the MATLAB® standard package of local fourier modal analysis with practical examples of photonic crystal device modeling. LFMA adopts the optical isolation assumption in analyzing nanophotonic networks, which means that optical energy can be transferred only through predetermined waveguide channels in integrated nanophotonic networks.
