Formation of a reflected wave under propagation of a pulse with high peak intensity through a Kerr medium

Propagation through a Kerr medium of short pulses depending only on the longitudinal coordinate is investigated. High values of the peak intensity are considered for which the nonlinear part of the relative permittivity is on the order of unity. When a short pulse propagates through such a medium, the leading edge of the pulse is extended, while the trailing edge runs into the slowly propagating central part of the pulse; shock waves are generated at the trailing edge, giving rise to high spatial frequencies and backward reflected radiation. The duration of the pulse increases due to the high-frequency jet that forms at the trailing edge, and the peak intensity decreases. The spectrum of the backward reflected radiation is investigated as a function of the peak intensity of the pulse and the characteristics of the time dispersion of the medium.