Propagation of double-exponential pulse through Debye medium

The saddle point method is applied to the problem of signal propagation through Debye medium. The steepest descent method is used to calculate the propagation of a double-exponential pulse through Debye medium, and the results are compared with those obtained through Hosono's (1980) method and finite-difference time-domain (FDTD) method. It is found that a Gaussian function can be used to approximate the propagated signal for sufficiently long propagation distance and the analytical representations for the amplitude, center, and width of the propagated pulse are obtained based on the first-order asymptotic representation. An analytical approximation of the saddle points valid for late time is also obtained.