Theory of self-locking phenomena in the pressure broadened three-mode He-Ne laser

Taking account of pressure broadening the coefficients in Lamb's third-order amplitude and phase determining equations for three modes are evaluated in the Doppler limit, and comparison is made with other theories. After expanding the coefficients to first order in the detuning ε from the linecenter an expression is presented for the frequency range where mode locking will occur. Using experimental data of several authors for the 6328 Å Ne-transition numerical values are obtained for the pressure dependent decay rates Υ _a , Υ _b , of the upper and lower laser level and the linewidth Υ _ab ^′ , viz.:Υ _a =17.7+(12.6±0.6)P _He, Υ _b =8.3+(12.6±0.6)P _He, and Υ _ab ^′ =13.0+(91±6)P _He MHz, whereP _He is measured in torr.