Bifurcation to Standing and Traveling Waves in Large Laser Arrays

Abstract

Arrays of semiconductor diode lasers are promising devices for applications that require high optical power from a laser source (high-speed optical recording, high-speed printing, free-space communications, pumping of solid-state lasers) [1]. Experimental and numerical studies of arrays consisting of a small number of lasers have shown that they are unstable devices and may exhibit a large variety of spatio-temporal responses [2-5]. In order to control these instabilities by various external mechanisms (injection locking, periodic modulations), systematic bifurcation studies are needed. The laser equations are however stiff and accurate solutions for a large population of lasers require long computation times. Asymptotic methods based on the limit of weak coupling [6] also fail to provide simple phase equations because the semiconductor laser is not a limit cycle oscillator. We have recently reformulated the laser equations as a weakly perturbed system of coupled conservative oscillators which eliminate part of the stifness of the problem and allow an analytical study of the first Hopf bifurcation as the coupling strength is progressively increased. If N is even, the Hopf bifurcation is simple and corresponds to a transition from a nonuniform steady state to a time periodic standing wave solution [7]. However, if N is odd, bifurcation to periodic standing and traveling wave solutions are both possible. This multiple bifurcation problem is difficult analytically but can be simplified if we consider the limit N large.