A formulation of gain saturation for partially homogeneous laser transitions

The gain of a partially homogeneous line at line center is shown to saturate according to the following formula: γ0(y;I v /I s ) = γ0(y;0)/(1 + I v /I s ) m(y) where y =√ln 2 Δv L /Δv D . I v is the intensity of the incident radiation at line center, I s is the saturation intensity, and Δv L , Δv D are the Lorentzian and Doppler linewidths. Numerically calculated values for m(y) are tabulated, and show that m(y) approaches ½ as y → 0 and 1 as y → ∞ in accordance with the known limiting cases of inhomogeneous and homogeneous broadening, respectively. When y is known, the saturation intensity I s can easily be determined from gain saturation measurements by using the table of m(y) provided.