Proceedings Article | 31 October 2014
KEYWORDS: Thermal optics, Finite element methods, Refractive index, Glasses, Laser glasses, Rod lasers, Photoelasticity, Distortion, Adaptive optics, Nd:YAG lasers
This paper focuses on the three main effects that can induce wave-front distortion due to thermal lensing in laser gain media: 1) thermo-optic (dn/dT); 2) stress-optic; and 3) surface deformation (e.g., “end-bulging” of a laser rod). Considering the simple case of a side-pumped cylindrical rod which is air- or water-cooled along its length, the internal temperature distribution has long been known to assume a simple parabolic profile. Resulting from this are two induced refractive index variations due to thermo-optic and stress-optic effects that also assume a parabolic profile, but generally not of the same magnitude, nor even of the same sign. Finally, a small deformation on the rod ends can induce a small additional lensing contribution. We had two goals in this study: a) use finite-element simulations to verify the existing analytical expressions due to Koechner1 and Foster and Osterink; and b) apply them to glasses from the SCHOTT laser glass portfolio. The first goal was a reaction to more recent work by Chenais et al. who claimed Koechner made an error in his analysis with regard to thermal stress, throwing into doubt conclusions within studies since 1970 which made use of his equations. However, our re-analysis of their derivations, coupled with our FE modeling, confirmed that the Koechner and Foster and Osterink treatments are correct, and that Chenais et al. made mistakes in their derivation of the thermally-induced strain. Finally, for a nominal laser rod geometry, we compared the thermally-induced optical distortions in LG-680, LG-750, LG-760, LG-770, APG-1, and APG-2. While LG-750, -760, and -770 undergo considerable thermo-optic lensing, their stress-optic lensing is nearly of the same magnitude but of opposite sign, leading to a small total thermal lensing signature.
