Excitation by a transient signal of the real-valued electromagnetic fields in a cavity

Excitation of electromagnetic fields in a cavity is studied in the time domain. A signal, which excites the fields, stands in Maxwell's equations as the electric current density given by an integrable function of coordinates and time. The problem is solved within the framework of the evolutionary approach to electromagnetics. The modal field expansions with time-dependent modal amplitudes are derived. Exact solutions for the amplitudes are obtained as the convolution integrals with time as a variable of integration, where the signal function stands as a parameter of the integrands. Two examples of the signal functions having a beginning in time are considered: (a) a surge modeled by the double-exponential function of time and (b) a sinusoid oscillating with an arbitrary frequency.