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Scattering Matrix Method Applied to Photonic Crystals
Published in Kiyotoshi Yasumoto, Electromagnetic Theory and Applications for Photonic Crystals, 2018
Daniel Maystre, Stefan Enoch, Gérard Tayeb
The scattering matrix method (SMM) is one of the most efficient methods for solving a problem of scattering by a large but finite number of objects. It basically takes into account separately the specific scattering properties of each object and then evaluates the coupling phenomena between them. Even though it can be presented in a quite rigorous form, it is based on a physically intuitive approach to the problem of scattering from a set of objects. One of its advantages is to be accessible to postgraduate students. Moreover, the numerical implementation does not present major difficulties. In contrast to other classical methods like Finite Difference Time Domain method (FDTD) or the finite element method, it becomes much simpler in the case of two-dimensional (2D) photonic crystals with circular cross sections or 3D photonic crystals formed by spherical inclusions. It deals with crystals of finite size regardless of whether or not they have defects of periodicity.
The Fourier modal method and its use in plasmonics and the theory of resonant diffraction gratings
Published in V. A. Soifer, Diffractive Optics and Nanophotonics, 2017
In section 1.1 the Fourier modal method is considered in the standard formulation for solving the problem of diffraction of a plane wave on two-dimensional and three-dimensional multilayered periodic diffraction structures and for the case of non-periodic structures. The considered implementation of the method is based on a numerically stable approach, known as the scattering matrix method. The method is described in detail and was used by the authors to create original computer programs for the solution of problems of diffraction on structures of various types. The readers can safely use the formulas given in section 1.1 when creating their own programs for electromagnetic modelling.
Matrix method for two-dimensional waveguide mode solution
Published in Journal of Modern Optics, 2018
Baoguang Sun, Congzhong Cai, Balajee Seshasayee Venkatesh
In addition, the matrix method, such as matrix approach, transfer matrix function (TMF) and scattering matrix method (8–10), has already been used in several works to study propagation characteristics. In the related articles, the matrix approach was presented for obtaining leakage losses and absorption losses, the TMF was useful for the analysis of dielectric waveguides, while the scattering matrix method was applied to the analysis of finite two-dimensional photonic crystals and light-wave devices. However, the above-mentioned methods are used only for a certain waveguide, such as dielectric waveguides, and there is no further discussion about the complex elements of the transfer matrix in guided modes.