Spatial self-phase modulation of a laser beam propagating through liquids with self-induced natural convection flow

In this work, the results of experimental and theoretical investigations of diffraction ring patterns are reported. Diffraction rings are formed due to the self-phase modulation of a continuous wave laser beam propagating through a solution of dye in ethanol. The self-phase modulation of the laser beam is the result of the changes in the refractive index due to the heating of the sample by a small absorbed fraction of the laser power. To find the thermal nonlinearity inside the liquid irradiated by a Gaussian laser beam, we have solved the heat transfer equation including conduction and convection effects in a liquid medium. The temporal dynamics and structural characteristics of the diffraction ring patterns are studied theoretically on the basis of a Fresnel–Kirchhoff diffraction integral in the approximation of an optically thin absorbing medium. The simulation results show that when a Gaussian laser beam is transmitted through a liquid medium the intensity distribution pattern in the far-field first forms a series of circular diffraction rings, but after a period of time the rings change to half circular symmetry due to convection.