Spatially autoresonant stimulated Raman scattering in nonuniform plasmas

New solutions to the coupled three-wave equations in a nonuniform plasma medium are presented that include both space and time dependence of the waves. By including the dominant nonlinear frequency shift of the material wave, it is shown that if the driving waves are sufficiently strong in relation to the medium gradient , a nonlinearly phase-locked solution develops that is characteristic of autoresonance. In this case, the material electrostatic wave develops into a front starting at the linear resonance point and moving with the wave group velocity in a manner such that the intensity increases linearly with the propagation distance. The forms of the other two electromagnetic waves follow naturally from the Manley–Rowe relations. © 2008 American Institute of Physics. DOI: 10.1063/1.2884717