Effects of laser spatial incoherence with finite correlation length on the space-time behavior of backscattering instabilities

The average space-time behavior of backscattering instabilities in the presence of a purely spatial incoherence of the laser beam is investigated analytically. It is found that the divergence of the strongly damped limit of the average backscattered light amplitude [cf. H. A. Rose and D. F. Dubois, Phys. Rev. Lett. 72, 2883 (1994)] must be replaced by the onset of an absolutelike instability characterized by a local, space dependent growth rate. The validity of the results is discussed in the regime where the breakdown of our model is caused by the onset of absolutely unstable hot spots. The time asymptotic behavior of the instability in this regime is computed heuristically. The average Green's function for the backscattered light is computed analytically in the case where the laser incoherence is characterized by an exponentially decaying correlation function.