Transient response of circular waveguide modes on refractive index change in core

We present an analytical solution of a problem of a circular waveguide mode transformation due to time refractive index change in a core. The scenario is that a natural mode propagates in the waveguide at the moment when the refractive index changes abruptly in time along all length of the waveguide. Ideal dielectric waveguide and waveguide with perfectly conducting wall are considered. The comparative analysis is performed