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This paper reports a detailed numerical study of the synchronization properties of two mutually delay-coupled semiconductor lasers in the framework of the Lang-Kobayashi model. By computing high-definition stability diagrams, we predict the complex distribution of periodic and chaotic laser oscillations on the coupling versus detuning control parameter plane. Such diagrams provide details concerning the behavior of the laser intensities, quantify objectively the synchronization between their electric fields, and display in-phase and out-of-phase laser behavior. In addition, we also describe the presence of a conspicuous abrupt change in the optimal shift for the greatest value of the cross-correlation function when varying the detuning between the optical angular frequencies of the lasers. (C) 2016 Optical Society of America

We report a numerical characterization of the stability of semiconductor lasers with delayed feedback under the simultaneous variation of the delay time τ and the pump current P. Changes in the number of External Cavity Modes are studied as a function of the delay time while the Regular Pulse Package regime is characterized as a function of the pump current. In addition, we describe some remarkable structures observed in the τ × P control plane, delimiting where these and other complex regimes of laser operation exist.

We report on a systematic investigation of the stability of a CO2 laser subjected to delayed electro-optical feedback. Such a laser roughly displays three operational intervals of stability, which we characterize using high-resolution stability charts and a video. Contrary to current belief, we find delays smaller than ∼1 μs to strongly “clean complexity,” namely, to prevent chaos and periodic pulsations with many spikes. In contrast, complex pulsations and chaos are significantly enhanced for τ>1 μs. In this range, one finds a complex alternation of periodic and chaotic phases, which are sensitive to the delay duration.

We describe some remarkable continuous deformations which create and destroy peaks in periodic oscillations of the Mackey–Glass equation, a paradigmatic example of a delayed feedback system. Peak creation and destruction results in richer bifurcation diagrams which, in addition to the familiar branches arising from period-doubling and peak-adding bifurcations, may also display arbitrary combinations of doubling and adding, leading to highly complex mosaics of stability domains in control parameter space. In addition, we show that the onset of higher dimensionality does not alter the prevailing dynamics instantaneously and, remarkably, even may have no effect at all, a result that cannot be predicted analytically with standard methods.