Transverse effects in the four-wave-mixing: The influence of the Gauss-Laguerre functions

A well known nonlinear device is the four-wave-mixing. The interaction of these three beams inside the nonlinear medium leads to the generation of a fourth beam, the signal beam intensity. In taking into account the transverse spatial structure of the signal beam, an improvement of the model is obtained. In this aim, we can write the electric field as spatial modes. The Gauss-Laguerre function Unl, solution of the paraxial propagation equation, may be used in this idea. This device is used to the study of two cases: the probe is a spatial mode of empty space and we can study the measure of the susceptibility and make a comparison between the Gauss-Laguerre model and the plane-wave model. Or the probe is a spatial mode of the Raman nonlinear propagation and we observe an enhancement of the fundamental Raman mode according to the other Raman modes.