I. G. Stratis

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.

On the Error of the Optical Response Approximation in Chiral Media

We study the equations modelling the evolution of electromagnetic fields in chiral media with dispersion. We prove existence and uniqueness of solutions of these equations and provide estimates for the error of the optical response approximation for chiral media.

Electromagnetic fields in linear and nonlinear chiral media: a time-domain analysis

We present several recent and novel results on the formulation and the analysis of the equations governing the evolution of electromagnetic fields in chiral media in the time domain. In particular, we present results concerning the well-posedness and the solvability of the problem for linear, time-dependent, and nonlocal media, andresults concerning the validity of the local approximation of the nonlocal medium (optical response approximation). The paper concludes with the study of a class of nonlinear chiral media exhibiting Kerr-like nonlinearities, for which the existence of bright and dark solitary waves is shown.

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.

Transmission problems in the theory of elastic hemitropic materials

The purpose of this article is to investigate mixed transmission-boundary value problems for the differential equations of the theory of hemitropic (chiral) elastic materials. We consider the differential equations corresponding to the time harmonic dependent case, the so called pseudo-oscillation equations. Applying the potential method and the theory of pseudodifferential equations we prove uniqueness and existence theorems of solutions to the Dirichlet, Neumann and mixed transmission-boundary value problems for piecewise homogeneous hemitropic composite bodies and analyze their regularity properties. We investigate also interface crack problems and establish almost best regularity results.

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.

The Singular Sources Method for an Inverse Transmission Problem

We employ the singular sources method introduced in [4] to solve an inverse transmission scattering problem for the Helmholtz equation or D, respectively, where the total field u satisfies the transmission conditions on the boundary of some domain D with some constant β. The main idea of the singular sources scheme is to reconstruct the scattered field of point sources or higher multipoles (·, z) with source point z in its source point from the far field pattern of scattered plane waves. The function (z, z) is shown to become singular for z→∂D. This can be used to detect the shape D of the scattering object.Here, we will show how in addition to reconstructions of the shape D of the scattering object, the constant β can be reconstructed without solving the direct scattering problem. This extends the singular sources method from the reconstruction of geometric properties of an object to the reconstruction of physical quantities.

Electromagnetic Scattering Problems in Chiral Media: A Review

ABSTRACT Time-harmonic electromagnetic waves are scattered by a homogeneous chiral obstacle. It is shown that the corresponding transmission problem has a unique solution. This transmission problem is reduced to a pair of uniquely solvable coupled integral equations over the interface between the obstacle and the surrounding medium. Some scattering relations are established, and the spectrum of the far-field operator is studied and related to that of the T-matrix. If the far-field pattern is known for all incident waves with a fixed wave number, uniqueness of the obstacle and its material parameters is established.

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.