Conditions for reducing spherical thermal aberrations in transversally pumped YAG rods

Abstract

Temperature dependences of the thermal conductivity and thermo-optic coefficient are often neglected when thermal lensing in laser crystals is investigated, though their influence is very significant. In this paper, the general solution of heat transfer equation with temperature dependent thermal conductivity is found in an integral form, which is very convenient for analytical and numerical analysis. Using this solution, the possibility to eliminate spherical aberration by a proper choice of the pump parabolicity parameter is investigated in detail. The inaccuracies in the definition of optical path differences used in a few previous works for the case of temperature dependent thermo-optic coefficient are explained. It is shown that the use of a correct definition increases the value of the parabolic coefficient at which the elimination of spherical aberrations may be realized as compared with the original work of Hodgson and Weber. It is also found that nearly the same shapes of pumping are required for elimination of spherical aberrations for both radial and tangential polarization.