Simple and phenomenological rate equations approach for the modeling of optically pumped terahertz gas lasers

We report on a simple but effective rate equation system for optically (infrared) pumped terahertz (THz)-emitting gas lasers and take the ¹³CH₃F gas as an illustration. We discuss several simplifications on individual terms of the system, resulting in reduced computing time by two orders of magnitude and in more physically intuitive results. To account for the spatial diffusion of molecules, we introduce an averaged wall collision rate instead of the position gradient terms. We self-consistently calculate the infrared absorption coefficient, the transition probability, and the population inversion. We investigate dependencies of the threshold pump power and THz output power as a function of the gas pressure. Our model can predict a wide operation regime (gas bottle-neck pressure beyond 1000 mTorr) either by increasing the nominal wall collision rate, or by increasing the molecule temperature from room temperature to 500 K. No significant computing power is needed, as the calculations can be done within a few seconds if running the algorithm on a standard personal computer.