Determination of nonlinear susceptibilities by transforming random variables

High-peak-power lasers are typically used as pump sources in nonlinear optical measurements. Intrinsic to these sources are pulse-to-pulse output energy instabilities. We report on how pump instabilities affect the measurement of nonlinear susceptabilites and develop theory which relates statistical parameters of a general, arbitrary pump energy probability distribution to those of its corresponding mth harmonic output. The relation leads to a simple method of data analysis whereby pump instabilities can be used as a tool in determining the nonlinear susceptibility of a material.