Mutually injecting semiconductor lasers: simulations for short and zero delay

Distant lasers with mutual optical injection are subject to a delayed coupling. We consider the barely investigated case of delays shorter than the relaxation oscillation period. In order to illuminate the role of these short delays, the ultimate zero-delay limit is considered as a reference. We use a traveling wave equation model, which fully resolves the spatio-temporal distributions of optical fields and carriers in the lasers and treats the wave propagation between the lasers by delayed boundary conditions. Wavelength detuning between the otherwise identical single-mode DFB lasers is used as primary bifurcation parameter. The zero-delay reference exhibits a synchronisation scenario typical for coupled oscillators. The nonsynchronised regimes represents a self-pulsation of the nonlinear carrier-photon system. Additional effects appear when including a short delay. Resonances of the cavity formed by the laser pair cause a staircase dependence on detuning of the pulsation frequency. Irregular dynamics is observed at the borders of the locked regions as well as at the edges of the stairs.