Analytical solution of steady state heat equation in nonlinear thermal-lensing effect

Abstract

The main interaction of laser beam with materials is to create a temperature distribution, which is the introduction to investigating effects such as thermal-lensing, nonlinear absorption and refraction, and laser-induced damage effects. The correct prediction of this temperature profile can be important in the accurate calculation of thermal expansion volumetric stresses that cause optical aberrations in optical devices and photonic and laser materials. In this letter, new approach has been used to solve the heat equation of laser beam radiation to a thin sample and an exact solution for the time-independent heat equation in a laser-irradiated sample was obtained. Considering appropriate boundary conditions, the steady-state temperature distribution without any approximation was obtained which includes the lower incomplete gamma function. Based on the temperature distribution, the nonlinear changes of absorption and refractive indexes resulting from thermal effects can be accurately calculated. This model was extended for both Gaussian and top-hat beams.