Transformation of the probability density function in an optical parametric amplifier: Application to rogue-wave-like statistics

We study how the probability density function of a weak seed intensity is transformed in a nonlinear process such as optical parametric amplification. The character of the transformation strongly depends on the amplification regime accessed: in the small-gain (undepleted-pump) regime the statistics of the seed are transferred to the statistics of the amplified signal almost unaltered. In contrast, in the gain saturation regime the modification of the statistics is considerable. In particular, we demonstrate that rogue-wave-like (long-tailed) statistics of the seed are completely suppressed, and resulting probability distribution function of the amplified signal becomes Gaussian. The theoretical findings are supported by the experiments carried out in supercontinuum-seeded noncollinear optical parametric amplifier.