Causal Dynamic Constitutive Relations for Lossy Dispersive Dielectrics

The relationship between a polarization vector and an electric field applied to a lossy dielectric media of Lorentz type is considered in a novel format of Maxwell’s equations. Dynamic processes are studied via solving Newton’s equation of motion for the polarization vector, where a given applied electric field stands at its right-hand side as a force term. The applied field can have a beginning and an end in time. The causal solution is obtained via solving the motion equation by the method of matrix exponential. Two examples are exhibited where the problem is solved explicitly in the class of the real-valued functions of time.