Quantitative study of laser beam propagation in a thermally loaded absorber

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Abstract
The effect of thermal loading on the propagation of Gaussian laser beams in a solid-state absorber is modeled by a novel quantitative scheme. The zeroth-order Gaussian beam solution of the wave equation in a homogeneous, cylindrically symmetric absorbing medium is used as the source term in the heat equation to calculate the temperature field. Modifications in the beam parameters caused by the temperature dependence of the absorption coefficient and the index of refraction are then calculated as first-order corrections. The formulation identifies a dimensionless parameter that controls the strength of thermal effects. Numerical results that show the dependence of crystal transmission and the spatial beam spot-size variation on incident pump power are presented. In particular, the power transmission of the crystal is found to decrease with increasing incident power, and power-dependent thermal lensing is observed. The asymptotic behavior of the solutions yields explicit formulas for the focal length of the thermal lens and the power transmission of the crystal. These explicit formulas should prove useful as a rule of thumb for experimentalists.