  Speckle patterns generated in a disordered medium carry a lot of information
despite the apparent complete randomness in the intensity pattern. When the
medium possesses $\chi^{(2)}$ nonlinearity, the speckle is sensitive to the
phase of the incident fundamental light, as well as the light generated within.
Here, we examine the speckle decorrelation in the fundamental and
second-harmonic transmitted light as a function of varying power in the
fundamental beam. At low incident powers, the speckle patterns produced by
successive pulses exhibit strong correlations, that decrease with increasing
power. The average correlation in the second-harmonic speckle decays faster
than in the fundamental speckle. Next, we construct a theoretical model, backed
up by numerical computations, to obtain deeper physical insights on the faster
decorrelations in the second-harmonic light. Whilst providing excellent
qualitative agreement with the experiments, the model sheds important light on
the contribution of two effects in the correlations, namely, the generation of
second-harmonic light, and the propagation thereof.
