RICAM Colloquium - Maxence Cassier
December 12, 2024, 15:30, SP2 416-2
ABSTRACT:
In this talk [1], we investigate mathematical models for electromagnetic wave propagation in dispersive
isotropic passive linear media, that is in particular media such as metamterials for which
the dielectric permittivity Ɛ and magnetic permeability μ 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 [1, 2] and its connection to Herglotz-
Nevanlinna functions. We consider successively the cases of so-called local media and then of general
passive media. In particular, we will discuss connections between mathematical properties of models
(e.g. stability, “energy conservation [1, 3, 4]”, ...), physical assumptions (e.g. passivity) and
the existence of two Herglotz-Nevanlinna functions of the frequency: ωƐ and ωμ that determine
the dispersion of the material. We will also present dispersion and spectral analysis of this rather
general class of electromagnetic media.
Joint work with Patrick Joly (INRIA Poems) and Maryna Kachkanovska (INRIA Poems)