Modulation and amplification of wave packets in amplifiers with a travelling refractive-index wave

We study the conditions of frequency modulation, spectral broadening, and amplification of a Gaussian pulse – a whispering-gallery-mode (WGM) wave packet (WP) – propagating along a spiral trajectory on the surface of an active cylindrical optical waveguide, in which a travelling refractive-index wave (TRIW) is generated. Analytical expressions are obtained for the dependences of the duration, chirp, and spectral width on the distance travelled by the pulse along the waveguide, as well as on the parameters of the waveguide and the radiation launched into it. It is shown that the interaction of a wave packet with the TRIW leads to a strong frequency modulation of the amplified pulse with the conserved linearity of the chirp. It is demonstrated that this circumstance can be used to generate pico- and subpicosecond pulses with peak powers above 100 kW.