Stability and bifurcations of periodically modulated, optically injected laser diodes

Recent experiments using lasers subject to external injection [T. B. Simpson, Opt. Commun., 170, 93 (1999)] have shown remarkable locking performances when a small reference current modulation is added to the dc-bias current. The locking problem is studied analytically by using a multiple scale perturbation method. We derive a slow time amplitude equation for the laser rapid limit-cycle oscillations. The solution of this equation is then investigated both analytically and numerically using a continuation method. We find that the intensity of the laser field can be time periodic (locking) or quasiperiodic (unlocking) and that there exist two distinct bifurcation mechanisms leading to locking. Finally, we compare bifurcation diagrams based on our amplitude equation with diagrams obtained from the laser original equations and find a good quantitative agreement.