Wavefront reversal of focused beams (theory of stimulated Brillouin backscattering)
An analysis is made of wavefront reversal (WFR) in stimulated scattering of a pump beam with small-scale inhomogeneities, focused in a medium unbounded along the transverse coordinate. The solution is sought in the form of a pump-reversing wave with a continuously varying envelope. Allowance is also made for corrections for small-scale distortions correlated with the gradients of the pump field. An equation for the envelope derived previously by the authors is solved for the case of excitation of stimulated scattering from spontaneous noise. Hermite–Gaussian "modes" of this equation are found. The main conclusion from the solutions is that WFR in stimulated scattering of focused beams neglecting the influence of the scattered field on the pump wave not only results in narrowing of the WFR wave envelope but also in the formation of smallscale distortions which increase with distance from the beam axis. An analysis is also made of amplification of Stokes waves uncorrelated with the pump wave.