Plane Wave Scattering by a Dielectric Circular Cylinder in the Vicinity of a Conducting Strip (TM Case)

Scattering of plane electromagnetic waves by a dielectric circular cylinder in the vicinity of a conducting strip is presented. Two methods of solution are introduced. The first is an exact solution in which the scattered field from conducting strip is expressed in terms of Fourier series of radial and angular Mathieu function of unknown coefficient. Meanwhile the scattered field from the circular cylinder is expressed in terms of Fourier series of Bessel functions of unknown coefficient. The unknown coefficient can be obtained by enforcing the boundary conditions. The application of the boundary condition requires the use of the addition theorem of Mathieu to Bessel functions and vice versa. The second method is based in an asymptotic technique introduced by Karp and Russek for solving scattering by wide slit. The technique assumes the total scattered field from the strip and the dielectric cylinder as the sum of the scattered fields from the individual element due to a plane incident wave plus scattered fields from factious line sources of unknown intensity located at the center of every element. The line sources account for the multiple scattering effect. By enforcing the boundary conditions, the intensity of the line sources can be calculated. Numerical examples are calculated using both methods showing excellent agreement in all cases.