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We define a reciprocity gap functional for electromagnetic scattering in chiral media. We assume that a perfectly conducting scatterer is embedded in a piecewise homogeneous isotropic background ch...

An inverse scattering problem of time-harmonic chiral electromagnetic waves for a buried partially coated object was studied. The buried object was embedded in a piecewise isotropic homogeneous background chiral material. On the boundary of the scattering object, the total electromagnetic field satisfied perfect conductor and impedance boundary conditions. A modified linear sampling method, which originated from the chiral reciprocity gap functional, was employed for reconstruction of the shape of the buried object without requiring any a priori knowledge of the material properties of the scattering object. Furthermore, a characterization of the impedance of the object&rsquo, s surface was determined.

The scattering problem of a time-harmonic dependent plane elastic wave by a multi-layered thermoelastic body in an isotropic and homogeneous elastic medium is considered. The direct scattering problem is formulated. Integral representations for the total exterior elastic field and the total interior thermoelastic fields as well as expressions for the far-field patterns are obtained containing the physical parameters of the interior thermoelastic layers. A reciprocity type theorem, a general type scattering theorem and an optical type theorem for plane wave incidence are presented and proved.

In the present work the scattering of time-harmonic plane thermoelastic waves from a rigid triaxial thermoelastic el- lipsoidal scatterer in a homogeneous and isotropic environment is considered. The direct scattering problem is formulated. Using low-frequency theory a corresponding inverse scattering problem is studied. In particular, a method for specifying the size and the orientation of the thermoelastic ellipsoid using measurements of the leading order terms of the low-frequency expansion of the scattered field is presented. Corresponding results for the case of the sphere and the spheroid can be obtained considering them as geometrically degenerate forms of the ellipsoid for appropriate values of its geometrical parameters.

The scattering of a time-harmonic plane electromagnetic wave by a penetrable chiral obstacle in an achiral environment is considered. An extension of the standard method of fundamental solutions is applied in order to obtain numerically the solution of the problem. The electric fields are expressed in terms of the fundamental solutions of the corresponding equations in dyadic form. Completeness and linear independence for appropriate systems of functions are proved which will be used in order to solve approximately the above scattering problem. Using the transmission conditions, the scattering problem is transformed into a linear algebraic system with coefficient matrix which consists of chiral and achiral blocks. When the measure of chirality vanishes, our results cover the case of an achiral dielectric scatterer.

The scattering problems of time-harmonic electromagnetic plane waves by a penetrable or an impenetrable ellipsoidal scatterer are considered. A low-frequency formulation of the corresponding direct scattering problems using the Rayleigh approximation is described. A method for solving inverse electromagnetic scattering problems for ellipsoids using near-field data is presented. A finite number of measurements of the zeroth low-frequency approximation of the electric scattered field lead to specify the orientation as well as the size of the ellipsoids. This method is applied for the cases of the perfectly conductive, the impedance, the lossless dielectric and the lossy dielectric ellipsoids. Especially for the case of penetrable ellipsoids, using additionally the leading order term of the low-frequency expansion of the magnetic scattered field, the physical parameters of the ellipsoids are also specified. Corresponding results for spheres and spheroids considering them as geometrically degenerate forms of the ellipsoid are presented.

In the present work, the scattering problem of an elastic wave by a penetrable thermoelastic body in an isotropic and homogeneous elastic medium is considered. The corresponding scattering problem is formulated in a suitable compact form, and taking into account the physical parameters of the thermoelastic body and integral representations for the total exterior elastic and the total interior thermoelastic field are presented. Using asymptotic analysis of the fundamental solution of the Navier equation, expressions of the far-field patterns are obtained, and reciprocity theorems for plane and spherical wave incidence are established. Finally, a general scattering theorem for plane wave incidence is also presented. Copyright © 2016 John Wiley & Sons, Ltd.

The scattering problem of time-harmonic elastic waves from a triaxial rigid ellipsoidal obstacle is considered. The direct scattering problem is formulated. A method using near-field data for solving the corresponding inverse scattering problem in order to specify the size and the orientation of the ellipsoid is described. A matrix with elements given in terms of measurements of the leading low-frequency coefficient of the scattered field is constructed. The eigenvalues of this measurement matrix provide information for the semi-axes of the ellipsoid whereas the eigenvectors together with a rotation matrix whose elements are given in terms of the Euler angles are used to specify the orientation of the ellipsoid. Corresponding results for geometrically degenerate cases of the ellipsoid such as spheroids, spheres, needles and disks are obtained for appropriate values of the geometrical parameters.

The scattering problem of a time-harmonic electromagnetic plane wave by a dielectric ellipsoid with a perfectly conductive confocal ellipsoidal core is considered. A method for solving an inverse electromagnetic scattering problem for the layered ellipsoid using near-field data or far-field data is presented. The size and the orientation of the layered ellipsoid can be obtained, using a finite number of measurements of the low-frequency approximation of the electric scattered field or the electric far-field pattern. Corresponding results for the dielectric ellipsoid and the perfectly conductive ellipsoid are presented considering them as physically degenerate forms of the layered ellipsoid. Moreover, results for the layered sphere and the layered spheroid may be obtained, considering them as geometrically degenerate forms of the layered ellipsoid.

We analyse a scattering problem of electromagnetic waves by a bounded chiral conductive obstacle, which is surrounded by a dielectric, via the quasi-stationary approximation for the Maxwell equations. We prove the reciprocity relations for incident plane and spherical electric waves upon the scatterer. Mixed reciprocity relations have also been proved for a plane wave and a spherical wave. In the case of spherical waves, the point sources are located either inside or outside the scatterer. These relations are used to study the inverse scattering problems. doi:10.1017/S144618111800007X

In this work we study scattering of a plane electromagnetic wave by a multi-layered chiral body in free space. In the interior of the scatterer exists a core which is either a perfect conductor or a dielectric. We obtain integral representations of the scattered fields which consist of a chiral and an achiral counterpart incorporating the boundary and transmission conditions. We introduce a dimensionless version of the scattering problem and we prove the reciprocity principle and a general scattering theorem for the far-field patterns. Finally, we define Herglotz functions and we state the general scattering theorem in terms of the far-field operator which expresses the superposition of the far-field pattern.