Analysis of Super-Gaussian Statistics of N-Harmonic Fields by Nonlinear Gaussian Expansions

In this paper, we propose a new approach to the analysis of stochastic processes (such as fluctuating laser fields) with super-Gaussian statistics: the expansion of stochastic processes in terms of first and higher powers of Gaussian components, which are used like a basis set. We apply this approach to treat the super-Gaussian correlation effects observed in coherent anti-Stokes Raman scattering experiments using frequency-doubled pump-laser fields. Our results give much better agreement with experimental data than previous theories do.