Christodoulos Athanasiadis

Electromagnetic scattering by a homogeneous chiral obstacle: boundary integral equations and low-chirality approximations

Time-harmonic electromagnetic waves are scattered by a homogeneous chiral obstacle. The corresponding transmission problem is reduced to a pair of coupled integral equations over S, where S is the interface between the obstacle and the surrounding medium. This is done using a generalization of the Stratton--Chu representation that is valid for chiral media. The integral equations obtained are a generalization of those obtained by Muller for a homogeneous dielectric obstacle. Finally, we develop approximations for low-chirality obstacles. These approximations can be computed using simple modifications to existing codes for solving Mullers equations.

Scattering relations for point sources: Acoustic and electromagnetic waves

The problem of scattering of spherical waves by a bounded obstacle is considered. General scattering theorems are proved. These relate the far-field patterns due to scattering of waves from a point source put in any two different locations. The scatterer can have any of the usual properties, penetrable or impenetrable. The optical theorem is recovered as a corollary. Mixed scattering relations are also established, relating the scattered fields due to a point source and a plane wave.

Electromagnetic scattering by a homogeneous chiral obstacle : Scattering relations and the far-field operator

Time-harmonic electromagnetic waves are scattered by a homogeneous chiral obstacle. The reciprocity principle, the basic scattering theorem and an optical theorem are proved. These results are used to prove that if the chirality measure of the obstacle is real, then the far-field operator is normal. Moreover, it is shown that the eigenvalues of the far-field operator are the same as the eigenvalues of Watermans T-matrix.

On some properties of Beltrami fields in chiral media

Abstract Bohrens decomposition of the electric and magnetic fields into suitable Beltrami fields, is very important in the study of electromagnetics of chiral media. Integral representations for Beltrami fields are established, from first principles, in this work, along with the uniqueness results of Rellichs type. Applications to transmission problems for chiral media are also included.

ON THE ACOUSTIC SCATTERING AMPLITUDE FOR A MULTI-LAYERED SCATTERER

We consider the boundary-value problems corresponding to the scattering of a timeharmonic acoustic plane wave by a multi-layered obstacle with a sound-soft, hard or penetrable core. Firstly, we construct in closed forms the normalized scattering amplitudes and prove the classical reciprocity and scattering theorems for these problems. These results are then used to study the spectrum of the scattering amplitude operator. The scattering cross-section is expressed in terms of the forward value of the corresponding normalized scattering amplitude. Finally, we develop a more general theory for scattering relations.

Inverse Acoustic Scattering by a Layered Obstacle

A uniqueness theorem is proved for the inverse acoustic scattering problem for a piecewise-homogeneous obstacle under the assumption that the scattering amplitude is known for all directions of the incident and the scattered field at a fixed frequency.

Radiation relations for electromagnetic excitation of a layered chiral medium by an interior dipole

In this paper we establish certain fundamental radiation integral relations, refereed also as radiation theorems or principles, which connect the fields and far-field patterns due to the spherical wave excitation of a layered chiral obstacle by a dipole in its interior. The investigation of problems involving such types of excitations is motivated by significant applications including, for example, radiation from thin wires embedded in layered chiral media as well as from chiral in chiral composites. Reciprocity and general radiation theorems are established, relating the total, primary, and secondary Beltrami fields with the respective far-field patterns. As a consequence of the general radiation theorem, we obtain the optical theorem expressing the extinction cross section by means of the secondary Beltrami field at the dipole’s location. For an obstacle excited by a plane and a spherical wave mixed radiation-scattering theorems are derived. The theorems recover as special cases the respective known res...

Beltrami Herglotz functions for electromagnetic scattering theory in chiral media

In this article, Herglotz functions of electromagnetic fields in a chiral medium are considered. The left-circularly polarized and the right-circularly polarized Beltrami Herglotz functions are defined by an integral representation over the unit sphere where the corresponding kernels are exactly the Beltrami far-field patterns. Herglotz condition holds true for these Beltrami Herglotz functions and a density theorem is proved. It is shown that Beltrami Herglotz kernels can be obtained from the Beltrami fields without the need to expand them in eigenvectors. Using the Beltrami Herglotz functions, an electromagnetic Herglotz pair in a chiral medium is defined and it is proved that it satisfies the Herglotz condition. The corresponding far-field patterns are considered and a density theorem is obtained.

The Atkinson-Wilcox expansion theorem for electromagnetic chiral waves☆

Abstract Consider the problem of scattering of a time-harmonic electromagnetic wave by a three-dimensional bounded and smooth obstacle. The infinite space outside the obstacle is filled by a homogeneous isotropic chiral medium. In the region exterior to a sphere that includes the scatterer, any solution of the generalized Helmholtzs equation that satisfies the Silver-Muller radiation condition has a uniformly and absolutely convergent expansion in inverse powers of the radial distance from the center of the sphere. The coefficients of the expansion can be determined from the leading coefficient, “the radiation pattern”, by a recurrence relation.

A boundary integral equations approach for mixed impedance problems in elasticity

Direct scattering problems for partially coated obstacles in linear elasticity lead to interior and exterior mixed impedance boundary value problems for the equations of steady-state elastic oscillations. We employ the potential method and reduce the mixed impedance problems to equivalent boundary pseudodifferential equations for arbitrary values of the oscillation parameter. We give a detailed analysis of the corresponding pseudodifferential equations which live on a proper submanifold of the boundary of the elastic body and establish uniqueness and existence results for the original mixed impedance problems for arbitrary values of the oscillation parameter; this is crucial in the study of inverse elastic scattering problems for partially coated obstacles. We also investigate regularity properties of solutions near the curves where the boundary conditions change and establish almost best Holder smoothness results.