| We consider high frequency electromagnetic pulse propagation in complex materials. The physical problem is modeled by Maxwell's equations in a weak or variational form, and well-posedness results are established for materials that admit specific constitutive relationships for polarization. Our first result concerns nonlinear materials with Debye polarization dynamics. Next, we develop and analyze a more general framework that includes multiple polarization mechanisms, as well as uncertainty and variability at the molecular level through distributions of parameters in these mechanisms. Propagation characteristics are illustrated in the case of nonlinear Debye polarization dynamics and are compared to linear results. |
