Antiphase and in-phase dynamics in laser chain models with delayed bidirectional couplings

Abstract

The radiation dynamics of a closed chain of lasers with optoelectronic delayed coupling is analyzed. We consider bidirectional couplings of two designs: (i) diffusion type with feedback and (ii) bidirectional type without feedback. Assuming that the number of lasers is sufficiently large, we propose integro-differential models for spatially distributed variables with periodic boundary conditions. The critical value of the coupling coefficient is determined at which the stationary state of laser generation spontaneously becomes unstable due to the presence of a delay in the coupling lines. Bifurcations of asymptotically infinite dimension are described. For both types of coupling, we obtain the same two-dimensional complex partial differential equation of the Ginzburg–Landau type (with the difference only in the coefficients) for the slowly varying amplitude of the fundamental harmonic. Using the simplest homogeneous solution of such a quasi-normal form, the oscillations of laser radiation in chains, which can be anti-phase or in-phase depending on the time delay and the design of the couplings, are analytically described.