Propagation of the short pulse in medium with resonant relaxation

Abstract

The new analytical representation of fundamental solution (Green’s function) describing the short pulse propagation in medium with single process of resonant relaxation is presented. This analytical solution is based on the generalized local response function of linear media [3]. It contains well-known Lorentz’s and Debye’s models of relaxing media as particular cases. The variation of pulse shape while its propagation, described by the obtained solution, shows a variety of forms of pulse propagation and general laws of pulses dynamics beginning from pure relaxation behavior and up to resonant one. The derived solutions are correct also for active media for linear regime of the pulse propagation. In the paper [3] the equation of state, that describes local response of arbitrary linear medium in a vicinity of thermodynamic state, is derived by use of thermodynamic approach. This equation of state (1) for corresponding values of parameters describes as particular cases exponential relaxation processes in medium (Debye’s model), as well as resonant relaxations (Lorenz’ model):