Optical saturation and extraction from the chemical oxygen-iodine laser medium

A rate equation model for the loaded gain of a flowing chemical oxygen-iodine laser is described. It includes pumping of the upper laser level by O₂(¹Δ), deactivation by water and energy pooling with O₂(¹Δ), stimulated emission on the 3→4 transition, hyperfine relaxation (HFR) of the ²P_1/2 and ²P_3/2 iodine sublevels, and velocity cross-relaxation (VCR) of the iodine atoms. The solution of the model is obtained for the loaded gain when the medium is stimulated by a multimode field. It is shown that optical saturation of the COIL medium is governed by three parameters: the ratio of the collision to Doppler linewidth measuring how much of the total linewidth is accessed; a saturation parameter measuring the field strength required to overcome medium quenching; and a cross-relaxation parameter measuring the ability of the velocity and hyperfine relaxation to restore homogeneity to the transition. Criteria for the saturation character, homogeneous, inhomogeneous, or mixed, are established. It is shown that there are medium conditions for which conventional measures of the transition homogeneity would indicate inhomogeneous behavior when, in fact, the behavior is distinctly homogeneous. This gain model is used to parametrically examine the sensitivity of the loaded gain and optical extraction efficiency to cavity pressure and to the uncertainty in the magnitude of the velocity cross-relaxation rates. It is shown, under single-mode operating conditions, that the extraction efficiency increases as the rate of velocity cross-relaxation increases and that the saturation behavior of the medium can be totally changed by only modest changes in the cavity operating conditions. The implications when interpreting experimental data and scaling from low to high power operation are briefly discussed and it is shown that interpreting test data without consideration of the factors presented here can lead to substantial error in estimating the power available from the flow. The approach used to estimate the velocity cross-relaxation rates is discussed in an appendix