Abstract
Light propagation in a thermally self-induced inhomogeneous medium is investigated to find the transient spatial output field for an arbitrary incident field. The paraxial wave equation is coupled with the thermal diffusion equation to predict the output field as the index of refraction transiently changes due to absorption of light by the medium. The coupled equations are non-dimensionalized and are explicitly expressed in full non-linear form. A coupling parameter is derived to scale the degree of non-linearity. Limits for the validity of using the coupled wave-diffusion approach are given, with respect to bulk fluid motion and the transverse wave assumption. An additional constraint is given on the paraxial wave equation that arises due to the coupling with the diffusion equation. Numerical results are compared to exact solutions and experiments for Gaussian and multi-mode laser beams, which verify that this approach is accurate in the range of validity, and describes local, transient self-focusing in multi-mode beams.
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