A simple theory for the Raman spike

The classical stimulated Raman scattering system describing resonant interaction between two electromagnetic waves and a fast relaxing medium wave is studied by introducting a systematic perturbation approach in powers of the relaxation time. We separate amplitude and phase effects for these complex fields. The analysis of the former shows the existence of a stagnation distance after which monotonous energy transfer begins from one electromagnetic wave to the other and this quantity is calculated. Concerning phase effects we give the conditions for the formation of a Raman spike from an initial fast and large phase jump in one of the waves. The spike evolution and width estimated from the reduced model agree with the results from numerical simulations of the original system.