An Operator Approach to the Analysis of Electromagnetic Wave Propagation in Dispersive Media: Part 1—General Results

Maxence Cassier () and Patrick Joly ()
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Maxence Cassier: Aix Marseille University, CNRS, Centrale Med, Institut Fresnel
Patrick Joly: Institut Polytechnique de Paris, POEMS, CNRS, INRIA, ENSTA Paris

Chapter 108 in Operator Theory, 2026, pp 3355-3410 from Springer

Abstract: Abstract In this chapter, we investigate the mathematical models for electromagnetic wave propagation in dispersive isotropic passive linear media for which the dielectric permittivity ε $$\varepsilon $$ and magnetic permeability μ $$\mu $$ depend on the frequency. We emphasize the link between physical requirements and mathematical properties of the models. A particular attention is devoted to the notions of causality and passivity and its connection to the existence of Herglotz functions that determine the dispersion of the material. We consider successively the cases of the general passive media and the so-called local media for which ε $$\varepsilon $$ and μ $$\mu $$ are rational functions of the frequency. This leads us to analyze the important classes of non-dissipative and dissipative generalized Lorentz models. In particular, we discuss the connection between the mathematical and physical properties of models through the notions of stability, energy conservation, dispersion and modal analyses, group and phase velocities, and energy decay in dissipative systems.

Keywords: Maxwell’s equations; Electromagnetic passive media; Metamaterial; Generalized Lorentz models; Dispersion analysis; Spectral theory; Herglotz functions; Energy decay rate (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-16356-1_77

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DOI: 10.1007/978-3-032-16356-1_77

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