Analytical model of the temperature distribution and the thermally induced birefringence in laser rods with cylindrically symmetric heating

Abstract

An analytical model of the thermal effects of cylindrically symmetric heating in laser rods is presented. We discuss two different methods for calculating the temperature distribution and thermal effects such as the thermally induced lens and thermal birefringence. One method is based on Taylor series; the other, on the integration of differential heating distributions. As an example, we discuss the effect of thermally induced birefringence in a Nd:YAG rod and compare the analytical solutions with finite-element simulations and experimental data. Compared with the numerical simulations, the calculations with the analytical expression are faster by several orders of magnitude and are therefore an excellent tool for optimization of the parameters related to heating and cooling of laser rods.