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Studying time-dependent behavior in lasers is analytically difficult due tothe saturating non-linearity inherent in the Maxwell-Bloch equations andnumerically demanding because of the computational resources needed todiscretize both time and space in conventional FDTD approaches. We describehere an efficient spectral method to overcome these shortcomings in complexlasers of arbitrary shape, gain medium distribution, and pumping profile. Weapply this approach to a quasi-degenerate two-mode laser in different dynamicalregimes and compare the results in the long-time limit to the Steady State AbInitio Laser Theory (SALT), which is also built on a spectral method but makesa more specific ansatz about the long-time dynamical evolution of thesemiclassical laser equations. Analyzing a parameter regime outside the knowndomain of validity of the stationary inversion approximation, we find that foronly a narrow regime of pump powers the inversion is not stationary, and thatthis, as pump power is further increased, triggers a synchronization transitionupon which the inversion becomes stationary again. We provide a detailedanalysis of mode synchronization (aka cooperative frequency locking), revealinginteresting dynamical features of such a laser system in the vicinity of thesynchronization threshold.

Spectral method for efficient computation of time-dependent phenomena in complex lasers