Generalized Transition Matrix for Arbitrarily Shaped Scatterers or Scatterer Groups

This paper presents a numerical method to evaluate the electromagnetic scattering characteristics of arbitrarily-shaped scatterers by using a generalized transition matrix. Each scatterer is regarded as a one-port device. By choosing a reference surface containing the scatterer, an associated generalized transition matrix is defined uniquely to describe the relationships between the rotated tangential incident field components and the rotated tangential scattered field components on the reference surface. The reference surface can be moved to a new surface with a regular shape, and the generalized transition matrix defined on the new reference surface can be obtained easily. The reference surface can be extended to contain a group of scatterers with arbitrary shapes and different materials. When the associated generalized transition matrix defined on a regularly-shaped reference surface is obtained, the scattered fields from that scatterer or scatterer group can be calculated simply by multiplying the rotated tangential incident fields on the reference surface with the generalized transition matrix, and not necessary to consider its internal structure again. Since the generalized transition matrix only concerns with the fields on the reference surface, it is valid for various incident fields with arbitrarily incidence angles. Two-dimensional examples are provided to verify the method.