Thermal lensing and aberrations modeling of a Brewster cut end pumped laser rod by BEM and optimization of the pumping-beam waist

In this article, the temperature distribution in a volume of a Ti:Sapphire laser rod with a Brewster cut in a steady state has been calculated using Boundary Element Method (BEM). High speed and superior accuracy are among the dominant characteristics of this method. Calculating the temperature distribution and refraction index, we calculated the applied phase shift on the transmitted beam of the rod, obtained dioptric power of the rod in tangential and sagittal planes, and investigated its variation according to the increase in the power and spot size of the pump beam. Afterwards, a self-consistent algorithm was used to optimize the spot size of the pump beam under condition of maximum overlap between pump and laser beam. Finally, in order to investigate the accuracy of the calculation, the temperature distribution was calculated using ANSYS software and a very good accommodation was observed between the two results. The only difference was that the calculation process in ANSYS software was four times longer than that using BEM.