volume | PIER Journals

2005-11-28

Electromagnetic Fields in Self-Dual Media in Differential-Form Representation

Ismo Veikko Lindell

Prof. Ismo Veikko Lindell

Department of Electrical and Communications Engineering

Helsinki University of Technology

Finland

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Progress In Electromagnetics Research, Vol. 58, 319-333, 2006

doi:10.2528/PIER05072201

Abstract

Four-dimensional differential-form formalism is applied to define the duality transformation between electromagnetic fields and sources. The class of linear media invariant in any non-trivial duality transformation is labeled as that of self-dual media. It is shown that the medium dyadic of a self-dual medium, which represents a mapping between the two electromagnetic field two-forms, satisfies a quadratic algebraic equation. Further, it is shown that fields and sources in a self-dual medium can be decomposed in two uncoupled sets each self-dual with respect to a duality transformation. Also, for each of the decomposed fields the original medium can be replaced by a simpler effective medium. Splitting the electromagnetic problem in two self-dual parts can be used to simplify the solution process because differential equations for fields are reduced to those with second-order scalar operators. This is applied to find plane-wave solutions for the general self-dual medium.

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Ismo Veikko Lindell, "Electromagnetic Fields in Self-Dual Media in Differential-Form Representation," Progress In Electromagnetics Research, Vol. 58, 319-333, 2006.
doi:10.2528/PIER05072201

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