Small-scale fluctuations of laser beam fluence at the large B-integral in ultra-high intensity lasers

Analytical expressions for the spatial spectrum of fluence fluctuations of a laser pulse propagating in a medium with Kerr nonlinearity have been obtained. It is shown that inhomogeneities with a spatial scale much larger than the critical scale of self-focusing grow insignificantly even at large values of the B-integral. Experiments using BK7 glass and a KDP crystal as a nonlinear medium confirm the obtained theoretical results. This may be interesting for pulse post-compression, frequency doubling, and other experiments using transmission optical elements in ultra-high intensity lasers.