A time-domain uniqueness theorem for electromagnetic wavefield modeling in dispersive, anisotropic media

A uniqueness theorem for the initial-/boundary-value problem arising in the (analytic or computational) modeling of electromagnetic wavefields in arbitrarily dispersive and anisotropic media is presented. It is known that for media where the dispersion takes place via electrically conductive and/or linear magnetic hysteresis losses only, a uniqueness theorem for the initial-/boundary-value problem can be constructed by using direct time-domain arguments in the pertaining energy balance (Poynting's theorem). The case of arbitrary dispersion in the medium's electric and magnetic behavior, however, withstands such an approach. Here, as an intermediate step, the one-to-one correspondence between the causal time-domain field components and material response functions in the constitutive relations on the one hand and their time Laplace transforms for (a set of) real, positive values of the transform parameter on the other hand, seems a necessary tool. It is shown that this approach leads to simple, explicit, sufficiency conditions on the relaxation tensors describing the medium's electric and magnetic behavior, in which the property of causality proves to play an essential role.