The effect of thermally induced gain gradients in solid state lasers

A dependence of the small-signal gain in solid-state lasers on the thermal loading is calculated. An average thermal power dependent gain reduction factor, η_g(𝒬), is defined in terms of the temperature coefficients of the laser gain curve, and the thermal conductivity of the laser rod. η_g(𝒬) arises from the shifts in the laser gain curve associated with the temperature gradients caused by optical pumping, and reduces the small-signal gain. The calculation of η_g(𝒬) for the specific cases of Nd:YAG and Nd;Cr:GSGG lasers indicates a reduction in the small-signal gain, from this mechanism alone, of 20-30% at high average power (200 W-cm^-3, thermal)