We consider the scattering of time-harmonic plane waves by an infinitely long penetrable chiral cylinder. The electromagnetic scattering problem is reduced to a transmission problem for a system of two-dimensional Hel...We consider the scattering of time-harmonic plane waves by an infinitely long penetrable chiral cylinder. The electromagnetic scattering problem is reduced to a transmission problem for a system of two-dimensional Helmholtz equations. We prove the classical reciprocity principle, a general scattering theorem and an optical theorem in R<sup>2</sup>. Using Herglotz wave functions we define the corresponding far field operator. Applying the general scattering theorem useful relations are proved for the reconstruction of the scatterer. We also prove that for real chirality measure of the penetrable scatterer the far field operator has a countable number of eigenvalues which lie on a circle.展开更多
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...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.展开更多
文摘We consider the scattering of time-harmonic plane waves by an infinitely long penetrable chiral cylinder. The electromagnetic scattering problem is reduced to a transmission problem for a system of two-dimensional Helmholtz equations. We prove the classical reciprocity principle, a general scattering theorem and an optical theorem in R<sup>2</sup>. Using Herglotz wave functions we define the corresponding far field operator. Applying the general scattering theorem useful relations are proved for the reconstruction of the scatterer. We also prove that for real chirality measure of the penetrable scatterer the far field operator has a countable number of eigenvalues which lie on a circle.
文摘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.
