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;Iv/Is) = γ0(y;0)/(1 + Iv/Is)^m(y)where y =√ln 2 ΔvL/ΔvD. Ivis the intensity of the incident radiation at line center, Isis the saturation intensity, and ΔvL, ΔvDare 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 Iscan easily be determined from gain saturation measurements by using the table of m(y) provided.