Analysis of temperature and thermo-optical properties in optical materials. 1: Cylindrical geometry

Modeling of optical and electro-optical devices requires the implementation of material properties over a broad temperature range. Because optical, thermo-optical, elasto-optical and gain properties of solid-state laser materials depend on temperature, their exact magnitude is needed for designing such optical devices. 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. Some examples are presented for thermally induced optical effects in solid-state laser gain-media 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 assess the thermal and optical characteristics, high pumping loads require cryogenic cooling to maintain low thermal lensing and thermally induced dioptric power depends quadratically on the heat rate.