Homogenization of time harmonic Maxwell equations and the frequency dispersion effect

Youcef Amirat (1) , Vladimir Shelukhin (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 LIH - Lavrentyev Institute of Hydrodynamics

We perform homogenization of the time-harmonic Maxwell equations in order to determine the effective dielectric permittivity epsilon(h) and effective electric conductivity sigma(h). We prove that epsilon(h) and sigma(h) depend on the pulsation omega; this phenomenon is known as the frequency dispersion effect. Moreover, the macroscopic Maxwell equations also depend on omega; they are different for small and large values of omega.

Domaines: Equations aux dérivées partielles [math.AP]

Youcef Amirat, Vladimir Shelukhin. Homogenization of time harmonic Maxwell equations and the frequency dispersion effect. Journal de Mathématiques Pures et Appliquées, 2011, 95, pp.420-443. ⟨10.1016/j.matpur.2010.10.007⟩. ⟨hal-00655381⟩