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.

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

“…The values of the thermal conductivity coefficient ( ) k T of YAG depend significantly on the doping rate (see [17,23] and references therein). For instance, for 0.5 at.% Nd:YAG, thermal conductivity decreases about 25% as compared with undoped YAG.…”

“…is introduced. Now it is easy to obtain the general solution for the temperature distribution [23] ( )…”

“…The results of [8] were reproduced in the first edition of the monograph [9]. However, in the second edition of this monograph, the generalization of these results for the temperature-dependent thermo-optic coefficient ( ) / β = T n T d d contained some errors in derivation [23]. Linear approximations of the thermo-optic coefficient and of the free expansion coefficient ( ) α T were proposed in [12], which can be used in a wide enough range of absolute temperatures T. However, the assumption that the contribution of the spatial element z d of AE at a point r to the OPD due to the thermo-optic change of the refractive index, or due to end-face bulging, is proportional to ( ) ( )…”

“…One of the main causes for the occurrence of thermal aberrations and the enhancement of thermal lensing is nonuniform radial pump distribution [1][2][3][4][5][6]. However, the temper ature dependence of the thermal, mechanical and optical parameters of AE is also a very important factor influencing the values of optical power and thermal aberrations [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

“…The temperature dependence of the thermal conductivity and of other parameters of the YAG is also very important for a consistent description of thermal lensing because it causes the radial temperature distribution to have higher nonparabolic terms, even for homogeneous heat loading in the AE [7][8][9][15][16][17][18][19][20][21][22][23]. It has been shown [8] that the spherical aberration induced due to the temperature-dependent thermal conductivity of AE can be compensated by a proper choice of parabolic pumping distribution.…”