Analysis of thermal effects in laser materials, 2: Disk and slab geometry

Modeling of optical and electro-optical devices requires the implementation of properties of these device materials over a broad temperature range. The accurate evaluation of temperature is essential for the calculation of optical, thermo-optical, elasto-optical and gain characteristics of solid-state laser materials. Among thermally induced effects in optical materials one finds that thermal focus escalates with pump power as well as does its induced aberration. Derived in this paper is a closed form solution to the problems of nonlinear heat transfer and stress field, resulting in expressions for the local temperature, stress and strain, refractive index, trajectories of propagating rays, optical path difference, thermal lensing, tilt and third order aberrations, induced birefringence and depolarization. In the analysis the temperature dependent coefficients were best fitted to existing experimental data. Calculations are presented for some thermally-induced optical effects in the temperature range of 77-770 K. It is found that for large heat deposition rates the use of the nonlinear solution is uniquely necessary to accurately assess the thermal and optical characteristics, that high pumping loads require cryogenic cooling to maintain reasonably low thermal lensing and that thermally induced dioptric power quadratic dependence on the heat level. Finally, it is found that the disk configuration suffers the least adverse thermo-optical effects.