Investigation of CO$_2$ laser signatures

A theoretical model was developed predicting a dependence of the signature of a CO$_2$ laser on the optical length of the resonator. The form of the signature, i.e., the number of vibrationa–rotational transitions and the sequence of their appearance in the signature, is uniquely determined by two fractional remainders obtained on dividing the resonator length by the periods $|L_1|\approx2,8$ mm and $|L_2|\approx20$ cm. If there is a resonator length existing such that both remainders have the same denominator $p$, then one can observe a signature having a previously predicted sequence of vibrational–rotational transitions numbering less than $p$. For real CO$_2$ laser transition frequencies an algorithm was obtained for calculating the resonator length corresponding to a specified form of signature. It was found that the opportunities for producing a regular signature are more extensive than suggested by previous studies. The experimental results are in good agreement with those predicted by the theoretical model.