Derivation of the Lamb coefficients in four frequency ring laser

In order to study the laser multi-modes coupling effects,theoretical deduction of four frequency ring laser at Ja=1→Jb=2 transition was conducted with the third-order perturbation method from the Lamb semi-classical self-consistent theory.The Lamb coefficients in the non-Doppler limit general case including the population pulsation effects were derived.The analysis shows that the conclusion drawn can be generally applied,which is helpful to the quantitative study on the laser multi-modes coupling fine effects.