Analytical approach for studying a time-domain cavity problem

Abstract —A time-domain cavity problem for the system ofMaxwell's equations with time derivative and dynamic constitutiverelation for a dielectric with temporal dispersion is solved withinthe framework of the evolutionary approach. The eld vectorsand polarization vector for the dielectric are presented as themodal expansions in terms of the solenoidal and irrotationalmodal basis vectors. The modal amplitudes are scalar and time-dependent herein. Cauchy problems are obtained for the modalamplitudes. Every Cauchy problem exhibits how the processprogresses in time (i.e., evolves, shortly) starting from a giveninitial state up to the state at a time of observation. That is whywe call our approach as evolutionary. I. I NTRODUCTION The evolutionary approach to electromagnetics was pro-posed for solving linear and nonlinear time-domain cavity andwaveguide problems in book [1]. One can nd useful details,which regard to the cavity problem, in [2]–[4].II. S TATEMENT OF THE T IME -D OMAIN P