T-Matrix Method for Large-Scale Arrays of Scatterers with Overlapping Circumscribing Spheres

The superposition T-matrix method based on entire-domain vector spherical wave functions (VSWFs) is a powerful technique for analyzing multiple scattering problems in electromagnetic systems. However, its applicability is somewhat limited by the challenges of computing T-matrices for arbitrarily shaped scatterers and the restriction that circumscribing spheres cannot overlap. In this paper, we integrate the superposition T-matrix method with the generalized transition matrix (GTM) approach to efficiently compute the scattering fields of large-scale arrays composed of arbitrarily shaped scatterers with overlapping circumscribing spheres. First, each element is enclosed by a reference surface, allowing the unknowns on the element to be transferred to the reference surface using the GTM method. The T-matrix that characterizes the element can be derived from the GTM defined on the reference surface. For arrays containing identical scatterers, both the GTM and the T-matrix are calculated only once. Next, when the circumscribing spheres of the reference surfaces in the array do not overlap, mutual couplings can be efficiently computed using the addition theorem of VSWFs. When the circumscribing spheres overlap, the GTM method is employed to determine the coupling between the elements. Finally, a system equation based on the VSWFs expansion coefficients of the scattered fields of all elements is formulated and directly solved. Numerical examples are provided to validate the accuracy, versatility, and efficiency of the proposed method.