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In this paper electromagnetic Herglotz dyadics are used to develop a superposition method and apply it for the study of an inversion scheme for electromagnetic scattering in chiral media. The direct scattering problem for the perfect conductor is formulated and Beltrami Herglotz dyadics and dyadic electromagnetic Herglotz pairs are being used. Assuming that the incident electromagnetic field is produced by a superposition of plane incident waves, the scattered field and the corresponding far-field pattern are expressed as the superposition of the scattered fields and the corresponding to them far-field patterns respectively. Far-field operators are defined and studied and an integral equation is posed. The solvability of this equation is related to the solution of the interior perfect conductor boundary value problem. Finally, an inversion scheme is posed and a theorem for it's solvability is proved. © de Gruyter 2008.

We consider time-harmonic electromagnetic waves propagating in a homogeneous three-dimensional unbounded chiral medium where a perfect conductor has been immersed. Assuming that the incident electric field is a superposition of plane incident electric waves, the corresponding scattered field and the far-field pattern are expressed as the superposition of the scattered fields and the far-field patterns respectively. It is also proved that the sets of far-field patterns are complete if and only if there does not exist an eigenfunction to the interior perfect conductor problem that vanishes on the boundary of the scatterer which is an electric Herglotz field. The Left-Circularly Polarized and the Right-Circularly Polarized far-field operators are defined and studied and using them the electric far-field operator is defined too. The properties of the above operators and Herglotz functions are related to the solution of the interior perfect conductor boundary value problem. © 2006, Taylor & Francis Group, LLC.

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. © 2005, Taylor & Francis Group, LLC.

In this paper electromagnetic Herglotz dyadics in chiral media are considered. The basic equations for dyadic electromagnetic fields in chiral media are presented and the direct scattering problem for the perfect conductor is formulated as a dyadic one. We define Beltrami Herglotz dyadics using the corresponding vector fields and the Herglotz norm as well. It is proved that a Beltrami dyadic satisfies the Herglotz condition if and only if it is a Herglotz dyadic. A representation theorem for Beltrami Herglotz dyadics is proved and a density theorem is extended to the dyadic case. A dyadic electromagnetic Herglotz pair is defined and a growth property for it is derived. It is proved that the set of all dyadic electromagnetic Herglotz pairs is dense within the set of dyadic electromagnetic pairs which solve the Maxwell-like equations for electromagnetic scattering in chiral media.