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Simulation of light beam propagation in nonlinear media

The present paper concerns simulation of nonlinear wave propagation in the ray regime. Conventionally, linear ray propagation is computed by using Hamilton's ray equations whose terms are derived from the dispersion equation. In the present case of nonlinear propagation, the terms depend on the field amplitudes which are determined by the convergence (or divergence) of the ray in the beam, therefore it is necessary to modify the original Runge-Kutta scheme, building into it some iteration mechanism such that the process converges to the values which take into account the amplitude effect. This research attempts to properly modify the existing propagation formalism. The results display self-focusing effects characteristic of nonlinear optics problems. The influence of weak losses on the beam propagation and its self-focusing is also discussed. Some displayed results, obtained by simulating the modified formalism, seem to be physically plausible and are in good agreement with experimental results reported in the literature.