Characteristic basis function method for solving large problems arising in dense medium scattering

Electromagnetic scattering from a dense medium consists of a large number of dielectric scatterers is of great interest. For these dense media, multiple scattering and coherent wave mutual interactions must be taken into account and many exiting analytical and approximation theories may require the use of pair distribution function and/or configurational symmetries. To incorporate mutual coupling effects, the use of characteristic basis functions (CBFs) has recently been proposed (R. Mittra et al., IEEE MTT-S Microwave Symp. Workshop, 2002). In this method, the mutual coupling effects are included through the use of higher-level basis functions, referred to the primary and secondary CBFs. The coefficients of these CBFs are solved directly using the Galerkin method. In this paper, we implement the CBF method for dense medium scattering. These CBFs, however, are constructed differently using the Foldy-Lax equations (L. Tsang et al., Optics Lett., vol. 17, no. 5, pp. 314-316, 1992) in which mutual coupling effects among all scatterers can be included systematically. Our results in this paper show that a small number of CBFs is sufficient.