  In this article, we explore how cryogenic cooling of the Ti:sapphire laser
crystal greatly reduces thermal lensing by over an order of magnitude because
of two factors: (i) the increase in the thermal conductivity of the crystal,
and (ii) the decrease in the temperature dependence of the refractive index. We
obtained analytical expression of the focal length of thermal lens for the pump
inside the laser crystal being a Gaussian beam. Through analysis of the laser
cavity stability, we found that in order for the relative difference between
the optimal laser cavity path lengths in the horizontal and vertical directions
to be less than 0.1%, the focal length of thermal lens should be longer than
0.5 m. Such a requirement can be met if the laser crystal is cooled to
temperatures below 100 K while being pumped at a power that is enough to
produce 100 W output. Therefore, it is very likely that an output power of 100
W can be achieved on a single Ti:sapphire laser by cryogenic cooling of the
laser crystal.
