Nonlinear dynamics in directly modulated semiconductor ring lasers

In this paper, we have theoretically studied the dynamical behavior of current modulated semiconductor ring laser (SRLs). As we very the amplitude and frequency of the modulation around a fixed bias current, different dynamical states including periodic, quasi-periodic and chaotic state 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 frquencies significantly lower than the relaxation oscillation frequency, we reveal the existence of chaotic oscillations where the two counter-propagating modes are in ati-phase.