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Proceedings Paper

Volterra differential constitutive operators and locality considerations in electromagnetic theory
Author(s): Dan Censor; Timor Melamed
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Paper Abstract

Macroscopic Maxwell's theory for electrodynamics is an indeterminate set of coupled, vector, partial differential equations. This infrastructure requires the supplement of constitutive equations. Recently, a general framework has been suggested, taking into account dispersion, inhomogeneity and nonlinearity, in which the constitutive equations are posited as differential equations involving the differential operators based on the Volterra functional series. The validity of such representations needs to be examined. Here it is shown that for such representations to be effective, the spatiotemporal functions associated with the Volterra differential operators must be highly localized, or equivalently, widely extended in the transform space. This is achieved by exploiting Delta-function expansions, leading in a natural way to polynomial differential operators. The Four-vectors Minkowski space is used throughout, facilitating general results and compact notation.

Paper Details

Date Published: 24 June 2002
PDF: 11 pages
Proc. SPIE 4806, Complex Mediums III: Beyond Linear Isotropic Dielectrics, (24 June 2002); doi: 10.1117/12.472972
Show Author Affiliations
Dan Censor, Ben-Gurion Univ. of the Negev (Israel)
Timor Melamed, Ben-Gurion Univ. of the Negev (Israel)


Published in SPIE Proceedings Vol. 4806:
Complex Mediums III: Beyond Linear Isotropic Dielectrics
Akhlesh Lakhtakia; Graeme Dewar; Martin W. McCall, Editor(s)

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