Analytical approach for studying a time-domain cavity problem

A time-domain cavity problem for the system of Maxwell's equations with time derivative and dynamic constitutive relation for a dielectric with temporal dispersion is solved within the framework of the evolutionary approach. The field vectors and polarization vector for the dielectric are presented as the modal expansions in terms of the solenoidal and irrotational modal basis vectors. The modal amplitudes are scalar and time-dependent herein. Cauchy problems are obtained for the modal amplitudes. Every Cauchy problem exhibits how the process progresses in time (i.e., evolves, shortly) starting from a given initial state up to the state at a time of observation. That is why we call our approach as evolutionary.