Modeling of thermal lensing in a [1 1 1]-cut Nd:YAG rod with temperature-dependent parameters and different pumping profiles

Temperature dependences of the thermo-optical coefficients of YAG crystals are often neglected when thermal lensing in laser rods is investigated, though their influence is very significant. It is especially significant for transversally non-uniform thermal loading. An analytical solution of the heat transfer equation with only the radial heat flow is found in the integral form, which is very convenient for numerical simulations. Uniform, top-hat, parabolic, Gaussian, super-Gaussian and annular heat source distributions are used in the calculations. The generalization of the thermally-induced refractive index change for long enough [1 1 1]-cut YAG rods to the case of temperature-dependent YAG parameters is developed and applied to the calculation of the corresponding optical path differences. Different definitions of the optical power of the aberrated thermal lens (TL) are discussed in detail. It is shown that for each of the heat source distributions, the temperature dependences of the YAG parameters significantly increase (1.5-1.8 times) the paraxial optical power of the induced TL.