Dual integral equations technique in electromagnetic wave scattering by a thin disk

International audienceThe scattering of an arbitrary electromagnetic wave by a thin disk located in free space is formulated rigorously in terms of coupled dual integral equations (CDIEs) for the unknown images of the jumps and average values of the normal to the disk scattered-field components. Considered are three cases of the disk: (1) zero-thickness perfectly electrically conducting (PEC) disk, (2) thin electrically resistive (ER) disk and (3) dielectric disk. Disk thickness is assumed much smaller than the disk radius and the free space wavelength, in ER and dielectric disk cases, and also much smaller than the skin-layer depth, in the ER disk case. The set of CDIEs are \decoupled" by introduction of the coupling constants. Each set of DIEs are reduced to a Fredholm second kind integral equation by using the semi-inversion of DIE integral operators. The set of \coupling" equations for finding the coupling constants is obtained additionally from the edge behavior condition. Thus, each problem is reduced to a set of coupled Fredholm second kind integral equations. It is shown that each set can be reduced to a block-type three-diagonal matrix equation, which can be effectively solved numerically by iterative inversions of the two diagonal blocks and 2 x 2 matrix