Unitary analysis of T-matrix method in 2D dielectric scattering by TE wave incident

As a numerical method for dealing with irregular boundaries, T-matrix method does not use the electromagnetic field boundary conditions directly to solve problems. However its physical nature is based on analytic wave functions, as for the irregular boundary, it is also available by analytic continuity. So if the cross-section of a particle tends to circle, the extension area should equals to zero. Therefore in theory, the results obtained by T-matrix should be identical with the classical analytic solutions. In this paper, the full analysis of T-matrix structure is given, and when the boundary of a dielectric is limited to the cylindrical one, unitary transition from T-matrix method to analytic solutions in two dimensional scattering is completed by TE wave incident.