Analysis of the optical extraction efficiency in gas-flow lasers with different types of resonator

The celebrated Rigrod model [J. Appl. Phys. 34, 2602 (1963)] has recently been shown to be inadequate for calculating the output power of gas-flow lasers when the quenching of excited species is slow and the optical extraction efficiency is high [Opt. Lett. 20, 1480 (1995)]. The previous analysis of two-level systems is presented here in detail and extended to include the chemical oxygen-iodine laser (COIL). For both two-level systems and COIL's, we obtained simple analytic formulas for the output power, which should be used instead of the Rigrod model. We present the formulas for Fabry-Perot, stable, and unstable resonators. Both the saturation parameter and the extraction efficiency differ from those appearing in the Rigrod model. The highest extraction efficiency is achievable for both stable and unstable resonators with uniform intensity distribution over the resonator cross section and is greater than that calculated by the Rigrod model. A rather surprising conclusion is that the extraction efficiency of unstable resonators can be increased substantially if one increases the length of the part of the mirrors lying downstream of the optical axis. The derived formulas are applied to describe published experimental results of supersonic COIL's. The dependence of the power on the threshold gain is evaluated and from this the plenum yield of singlet oxygen is estimated. The value of the yield is in better agreement with experimental measurements than that obtained by the Rigrod model.