Attractors and basins of the locking–unlocking bistability in a semiconductor laser subject to strong optical injection

Abstract

Properties of attractors and basins of the locking–unlocking bistability in an optically injected semiconductor laser are investigated to study the bistable operating conditions. The attractors of the injection-locked and unlocked states are a fixed point and a period-one limit cycle, respectively. The presence of the intrinsic noise makes the system operated at operating conditions close to the bistability boundaries unconditionally injection-locked or unlocked, resulting in the disappearance of attractors. The basins and basin boundary exhibit fractal-like structure which causes difficulty in controlling the bistable operation near the basin boundary. The presence of the intrinsic noise induces a jump of the orbit of an initial condition close to the basin boundary from the basin of one attractor to that of the other, resulting in the increased degree of the difficulty. The possibility of such a jump is higher for an operating condition showing a more complex basin boundary. Hence, how noise of a given strength affects the operation of a system under different operating conditions is related to the dimension of the basin boundary of the system. The dimension of the basin boundary as a function of the operating condition is thus computed to quantitatively characterize the fractal structure. Both fractal–fractal and fractal–smooth metamorphoses are found to happen in the system.