volume | PIER Journals

Abstract

In this study, we developed a multilevel multiple scattering theory (ML-MST) for the numerical solutions of multiple scattering equations. We formulated multiple scattering theory using vector cylindrical waves (VCW) in the MST-VCW formulation and the translational addition theorem with exciting fields in VCW. A problem with this formulation is that neighboring scatterers can have overlapping circles. In this study, multiple scattering theory is formulated using the method of moments (MoM) in the MST-MoM formulation, with the exciting field in terms of MoM unknowns. The ML-MST is developed by separating the scattering from other scatterers into neighbor and non-neighbor contributions, resulting in 2-level interactions. We then replace the MST-VCW neighbor scattering with the corresponding MST-MoM neighbor scattering. The ML-MST eliminates the issues of overlapping circles of neighbors. We apply the ML-MST formulations to the problem of band diagrams of photonic crystals by summing the scattering from non-neighbors using broadband Green's functions (BBGF). The result is the multilevel Korringa-Kohn-Rostoker (KKR) equation. Numerical illustrations were performed for the 2D case. The accuracy of the solutions was validated by comparing {them} with COMSOL simulations. The CPU time of the ML-MST was more than two orders of magnitude lower than that of COMSOL.

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Professor Leung Tsang

Dr. Enes Koc

Professor Tien-Hao Liao