Mathematical models for dispersive electromagnetic waves: An overview

Publication type:
Paper in peer-reviewed journals
Computers and Mathematics with Applications, vol. 74 (11), pp. 2792-2830
Keywords :
spectral theory; energy and dispersion analysis; Maxwell's equations in dispersive media; Herglotz functions; passivity and dissipativity; Lorentz materials;
In this work, we investigate mathematical models for electromagnetic wave propagation in dispersive isotropic media. We emphasize the link between physical requirements and mathematical properties of the models. A particular attention is devoted to the notion of non-dissipativity and passivity. We consider successively the case of so-called local media and general passive media. The models are studied through energy techniques, spectral theory and dispersion analysis of plane waves. For making the article self-contained, we provide in appendix some useful mathematical background.
    author={Maxence Cassier and Patrick Joly and Maryna Kachanovska },
    title={Mathematical models for dispersive electromagnetic waves: An 
           overview },
    doi={10.1016/j.camwa.2017.07.025 },
    journal={Computers and Mathematics with Applications },
    year={2017 },
    volume={74 (11) },