Fast-time dynamics of a coupled laser system: the Ginzburg-Landau equation

摘要

Abstract: Under a continuum approximation we derive a complex Ginzburg-Landau equation describing either a set of weakly coupled class A lasers, or the fast-time dynamics of a set of weakly coupled class B lasers. We show that phase locked behavior is described by the so-called Stokes wave solution and by performing a linear stability analysis we confirm analytically some numerical observations - namely that the Stokes wave can often be made unstable for perturbations of sufficiently short wavelength and that the coupling phase plays at least as significant a role in determining the spatio-temporal behavior of the system as does the coupling strength. As with our previous work on the simulation of discrete systems a stable phase-locked solution is found to be particularly difficult to achieve as the relative coupling phase approaches $pi@/2. The continuum approach also highlights other scalings, not immediately apparent from the discrete model. The coupling strength, for example, is shown to set the scale of spatial fluctuations.!7