6 July 1994 Fast-time dynamics of a coupled laser system: the Ginzburg-Landau equation
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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.
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Ziping Jiang, Ziping Jiang, Martin W. McCall, Martin W. McCall, } "Fast-time dynamics of a coupled laser system: the Ginzburg-Landau equation", Proc. SPIE 2099, Nonlinear Dynamics in Lasers and Optical Systems, (6 July 1994); doi: 10.1117/12.179645; https://doi.org/10.1117/12.179645

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