Thermal effects in end-pumped solid state lasers - influence on resonator stability, beam quality, and output power
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A theoretical analysis is given of the magnitudes of thermal effects in end-pumped high-power solid state lasers, and their influence on the laser output characteristics, particularly the beam quality and conversion efficiency. The theory of thermal lensing and stress-induced birefringence found in laser textbooks for the case of top-hat pump- and resonator modes, is extended to cover the more general case of Gaussian modes. Analytic expressions for these cases are derived. Expressions are also derived for the reduction of the birefringence loss, which can be achieved by inserting a quarterwave plate between the laser rod and the laser end mirror. An analysis is given of the tolerance of laser resonators to thermal lensing, providing guide lines for the choice of resonator parameters in order to ensure sufficient resonator stability margins. Finally, a few examples are given of the results of rigorous numerical simulations of an end-pumped Nd:YAG laser. It is found that the analytic theory provides fairly good guide lines concerning the choice of resonator parameters in many cases, but there are also cases where the numerical simulations provide quite surprising results. In particular, it is found that good performance can be obtained even if the thermal focal length on the laser rod axis is substantially shorter than the limit for a stable resonator. For optimal choices of resonator parameters and pump beam diameter, it is found that a 50 W pump beam at 808 nm can be converted to more than 20 W output at 1064 nm, with a beam quality of M2 < 2.