Time-domain asymptotic solution for transmitted Gaussian pulse through a plane dielectric interface

In this paper, we shall derive a time-domain asymptotic solution for the transmitted Gaussian pulse wave observed in the rarer medium when the Gaussian pulse is incident on a plane dielectric interface from the denser medium. The validity of the time-domain asymptotic solution is confirmed by comparing with the reference solution calculated numerically. We will show that the evanescent pulse wave and the lateral wave type transmitted pulse wave are observed in the far and shallow region.