Mode description of routes to chaos in external-cavity coupled semiconductor lasers

The nonlinear behaviors of routes to chaos in semiconductor lasers with external optical feedback were explored in this work. It was indicated that the relaxation oscillation was the origin of the first nonlinear instability of optical intensity under a short delay. Three types of transition routes with quasi-periodic, subharmonic oscillation, and periodic doubling to optical chaos were distinguished in terms of the delay time normalized to the inverse of the relaxation oscillation frequency of a solitary laser diode. The linearized mode theory and small-signal response were confirmed as part of the phenomena in the transitions to chaos