Boundary-condition-transfer method for two-dimensional resonant scattering by lossy dielectric cylinders of arbitrary cross-section

The scatterers are taken as infinitely long lossy dielectric cylinders of arbitrary cross-section. The excitation is either a TM polarized (E_z is the only electric field component) or a TE polarized (H_z is the only magnetic field component) plane wave or a line-source. A plane wave incident obliquely on the cylinder can be decomposed into its TM and TE polarized components. The cross-section of the scatterer is located in the x-y plane and the cylinder axis is taken as the z-axis. The permittivity and the conductivity of the scatterer are independent of the z-coordinate, but they can vary over the cross-section of the cylinder