Equilibrium bifurcations and chaotic transitions in coupled microlaser lattices

Abstract

Analytic and simulation studies for the steady-state equilibria and bifurcations of coupled microlaser arrays are described. Lateral cavity interactions affect the gain in each cavity, leading to active photonic lattice behavior, equivalent to a nonlinear coupled oscillator lattice. The coupled-cavity rate equations are employed to follow the coherent photon and carrier population in each lattice site. Fixed-point-type steady states, of constant lattice phase shift, result for low coupling strengths; the radiation envelope for these states conforms with a periodic Bloch state over the array. Bifurcations to limit cycles of increasing complexity occur at higher coupling via period doubling sequences. The associated spatial patterns of photon and carrier lattice distribution resemble photonic convection cells. Limit cycles of different periods, emanating mathematically from different original fixed points, coexist at high strengths, each one accessible from different initial conditions. The multiplicity of possible limit cycles in systems with many degrees of freedom (number of lattice sites) combined with changes in their accessibility from initial conditions offers new insights to chaotic transitions, compared to low dimensionality paradigms.