Oscillator Signals, Computer Modelling

A simple approach is to obtain overall rate constants for the pumping reactions from the pulse shape of the emission signal. 

It can be shown 2 that for quasi-steady state conditions of a laser oscillator the intensity of stimulated emission is proportional to the pumping, 

Since this condition is satisfied during the decay of the HF laser emission in certain cases (fast photolysis, low pressure), the time profile of the output intensity reflects the time dependence of the pumping. The pumping term P (t) can be described solely as the formation of the inversion by the reaction as long as losses due to vibrational deactivation are negligible. 

With the assumption of negligible vibrational deactivation, the formation of the vibrational inversion is governed by the microscopic rate constants kv for product formation at the various vibrational levels. The multi-line laser signal, however, results from the total inversion of all lasing P-branch lines which may be written as 

Cascading emission of several vibrational quanta can be accounted for by multiplying k by a constant factor. 

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