Two-Dimensional Scattering of Line Source Electromagnetic Waves by a Layered Obstacle

We consider the scattering problem of line source electromagnetic waves using a multi-layered obstacle with a core, which may be a perfect conductor, a dielectric, or has an impedance surface. We formulate this problem in two dimensions and we prove some useful scattering relations. In particular, we state and prove a reciprocity principle and a general scattering theorem for line source waves for any possible positions of the source. These theorems can be used to approximate the far-field pattern in the low-frequency theory. Moreover, an optical theorem is recovered as a corollary of the general scattering theorem. Finally, we obtain a mixed reciprocity relation which can be used in proving the uniqueness results of the inverse scattering problems.

Automated summary

This paper investigates the scattering problem of line source electromagnetic waves in a multi-layered obstacle. The authors formulate this problem in two dimensions and prove several useful scattering relations, including a reciprocity principle and a general scattering theorem. These theorems can be utilized to approximate the far-field pattern in the low-frequency theory. Additionally, an optical theorem is derived as a corollary of the general scattering theorem. The authors also obtain a mixed reciprocity relation that can be employed in proving the uniqueness of inverse scattering problems.