Coherent effects in the multimode dynamics of inhomogeneously broadened ring lasers

This study investigates how coherent effects manifest in the dynamical behavior of the laser above the instability threshold. In the numerical simulations, the free spectral range is kept fix and equal to unity, to homogeneous linewidth ratio, and consider weak inhomogeneous broadening, twice larger than the homogeneous one. Significant differences are observed in the temporal and spectral behavior of the laser, which could not be captured by the rate equations, for which there is no distinction among the different cases considered. Therefore, this study demonstrates that the rate equations can describe properly the multimode dynamics only for short cavities, and for longer cavities the Maxwell-Bloch equations are necessary. The numerical integration of the dynamical equations turned out to be very time consuming for the smaller values of the decay rate of the population inversion, because in that limit the equations become very stiff. In order to overcome that problem a set of generalized rate equations is derived, that maintain all the necessary information about coherence, but are much less stiff. The authors checked that these equations provide the same results as the complete model, but with much shorter computation times.