Author(s)

Evagelia S. Athanasiadou¹, Paraskevi Roupa^2*

¹Department of Mathematics, University of Athens, Athens, Greece.
²Department of Informatics and Telecommunications, University of Athens, Athens, Greece.

A time-harmonic plane acoustic wave is scattered by a piecewise homogeneous obstacle with a penetrable or impenetrable core. We construct in the close form an integral representation for the far field pattern in which we have incorporated the physical and geometrical characteristics of the scatterer. Through this representation, we obtain the far field pattern for this scatterer. We prove scattering relations between the far field patterns of two scattering problems due to two distinct incident waves on the same scatterer. In particular, we prove reciprocity and general scattering theorems. The optical theorem, connecting the total power that the scatterer extracts from the incident plane wave either by radiation or by absorption with the corresponding far field pattern of an incident plane wave, is recovered as a corollary of the general scattering theorem. Moreover, if we consider incident waves to be both a plane and a spherical, we derive a mixed reciprocity theorem. We define the corresponding far field operators and using these relations, we prove some properties that can be used for solving inverse scattering problems.

Two-Dimensional Electromagnetic Scattering, Piecewise Obstacle, Reciprocity Principle, Optical Theorem

Athanasiadou, E. and Roupa, P. (2022) On the Far Field Pattern for Acoustic Scattering by a Piecewise Homogeneous Obstacle in Two Dimensions. Journal of Applied Mathematics and Physics, 10, 2951-2964. doi: 10.4236/jamp.2022.1010198.