  We investigate spatial localization in a quadratic nonlinear medium in the
presence of randomness. By means of numerical simulations and theoretical
analyses we show that, in the down conversion regime, the transverse random
modulation of the nonlinear susceptibility generates localizations of the
fundamental wave that grow exponentially in propagation. The localization
length is optically controlled by the pump intensity which determines the
amplification rate. The results also apply to cubic nonlinearities.
