Asymptotic solution with higher-order approximation for transient whispering gallery mode radiation field excited by a UWB pulse source

Abstract

Asymptotic solution with higher-order approximation has been derived for the transient whispering gallery (WG) mode radiation field excited by a Gaussian-type modulated ultra-wideband pulse source. Time-domain asymptotic solution is obtained by applying the saddle point technique to evaluate the inverse Fourier transform for the transient WG mode radiation field. Asymptotic solution with higher-order approximation provides the new physical phenomena that the instantaneous angular frequency changes as the function of a time and the shape of the Gaussian beam is expanded in terms of a time. The validity of the asymptotic solution has been confirmed by comparing with the reference solution.