Propagation of double-exponential pulse through Debye medium

In this paper, the saddle-point method is applied to the problem of signal propagation through Debye medium. The steepest descent method is used to ca lculate the propagation of double-exponential pulse through Debye medium, a nd the results are compared with those obtained through Hosono's method and finite-difference time-domain (FDTD) method. It is found that a Gaussian f unction can be used to approximate the propagated signal for sufficiently l ong propagation distance and the analytical representations for the amplitu de, center, and width of the propagated pulse are obtained based on the fir st-order asymptotic representation. An analytical approximation of the sadd le points valid for late time is also obtained.