Numerical modeling of microscale heat transfer effects in thermally stimulated nonlinear optical materials

The significance of microscale heat transfer mechanisms during short pulsed laser radiation of thermally stimulated nonlinear optical materials is investigated. In nonlinear optical materials, the index of refraction is a function of the incident intensity and temperature. A numerical simulation code is developed in order to couple the nonlinear optical effects and the thermal effects. The numerical simulation code includes radial conduction effects which are significant at high incident intensities. The heat transfer model used for problems involving long laser pulse durations, nanoseconds or greater, is based on the diffusion equation or Fourier's Law. For shorter pulses, picoseconds or less, the numerical simulation code includes the Hyperbolic Two Step, Hyperbolic One Step and Parabolic Two Step microscale heat transfer models. The microscale models include the effects of the short time or small spatial scale present in many of today's laser interactions. Significant differences occur between the temperature predictions of the microscale models and the diffusion equation. Numerical simulations of experimental and analytical results are presented in order to verify the numerical simulation code. The hyperbolic one step results reveal that during the initial heating period of the Z-Scan experiment a steep temperature gradient exists which propagates at a finite speed in the radial direction. These results differ significantly from those predicted from the diffusion equation and result in large differences in the predicted instantaneous transmittance values for picosecond or shorter pulse widths. After a sufficiently long time, approximately four times the relaxation time, the thermal response predicted by the hyperbolic one step model converges to that predicted by the diffusion equation, along with the calculated instantaneous transmittance values.