Statistical properties of partially coherent beams transmitted through nonlinear Kerr thin layers

Abstract

Investigation of the propagation of partially coherent beams through nonlinear media is very difficult because of the need to deal with the fourth- or higher-order correlation function. Here a simple theoretical model is proposed to derive analytical results on the transmission of partially coherent beams through nonlinear Kerr thin layers. Considering only the self-phase modulation effect and neglecting the diffraction effect, the exact probability density function of the transmitted field at arbitrary two points has been derived and found to be not Gaussian. Statistical properties of the transmitted Gaussian Schell-model beams are studied in detail. The moment theorem is no longer valid so that the fourth-order correlation function cannot be decomposed as the sum of products of the second-order correlation functions. Numerical results are presented to see the effects of nonlinearity on the deviation from Gaussian statistics.