Nonlinear dynamics in directly modulated semiconductor ring lasers
ABSTRACT In this paper, we have theoretically studied the dynamical behavior of current modulated semiconductor ring lasers (SRLs). As we vary the amplitude and frequency of the modulation around a fixed bias current, different dynamical states including periodic, quasi-periodic and chaotic states are found. As in other single mode semiconductor lasers, the modal intensities in a SRL present chaotic behavior for driving frequencies comparable to the relaxation oscillation frequency. In this regime the two counter-propagating modes vary in phase. However, for modulation frequencies significantly lower than the relaxation oscillation frequency, we reveal the existence of chaotic oscillations where the two counter-propagating modes are in anti-phase. In order to get a more complete understanding of the dynamics of SRLs at low modulation frequencies, we derive a reduced model using asymptotic methods. This reduced model uncovers a topological resemblance between current-modulated SRLs and the periodically driven Duffing-Van der Pol oscillator.