A simplified model for predicting gain, saturation, and pulse length for gas dynamic lasers

A single time-scale model is developed to describe the 10.6-μ laser energy extraction from an initially inverted N
2
-CO
2
catalyst mixture where the energy is stored primarily in the N
2
vibration. This condition is typical of high-pressure gas dynamic lasers, but the methods are general and applicable to other systems. In the absence of external pumping, the nitrogen can be regarded as an energy source that is depleted on a time scale
\tau = \tauNAT(1 + I_{0}/I), \tauNAT
being the minimum possible time scale governed by collisional processes, τ determines the pulse time for
Q
-switched laser mixtures or the required streamwise cavity length for CW gas dynamic lasers. The derived saturation intensity I
0
also appears in the expression for saturated gain (for collision broadened cases)
g = g_{0}/(1 + I/I_{0})
, where g
0
is approximately the small signal gain at a given nitrogen vibrational temperature, g
0
decays on the same intensity-dependent time scale τ as the nitrogen vibrational energy.