Nonlinear and stochastic dynamics of semiconductor lasers: Modulation, transient dynamics and synchronization

The aim of this Thesis is the study how the interplay of deterministic nonlinear dynamics and stochastic dynamics of semiconductor laser (SCLs) influences information processing and synchronization in these devices with the aim of exploiting the constructive effects that appear combining these two ingredients. The interplay of deterministic nonlinear dynamics, current modulation and noise leads to phenomena such as low frequency fluctuations, stochastic and coherent resonances, excitability and synchronization. This Thesis is based on the numerical study of two well-known models for two different types of SCLs. The vertical-cavity surface-emitting lasers (VCSELs) are characterized by allowing the emission of two linear orthogonal polarizations due to the cylindrical geometry of the cavity. The edge-emitting lasers (EELs) can emit multi-longitudinal-modes with a polarization that is fixed by the rectangular cavity geometry. Our investigation is based on the use of widely accepted models that describe the statistic and dynamic behavior of these SCLs qualitatively and quantitatively. The non-linearity of a system can be observed when it is perturbed. A simple way to introduce a perturbation in the SCLs is through a modulation of the current injection. Its effect on VCSELs is studied with the spin-flip model, which describes the time evolution of the polarized optical fields and the carriers of each polarization. The results show that an asymmetric triangular current modulation with an appropriate asymmetry induces the emission of pulses of maximum amplitude and a duration of less than a nanosecond. These appear even when the current is on average below the solitary laser threshold, with a reduction of the emission threshold larger than the 20%. When the modulation occurs between three levels of constant current, properly chosen, a finite amount of noise allows logical operations encoded in the polarization emitted by the VCSEL. This effect is known as logical stochastic resonance. The research shows how the combination of noise, nonlinear effects and bistability allows a significant reduction of the system response time and enables a wide range of parameters where the system provides a robust and reliable response. High dimensional dynamics occur when the laser light is reflected from an external mirror with a certain delay. When the injection current is close to the threshold, the intensity becomes unstable inducing low-frequency fluctuations. This dynamics can be reproduced accurately using the model of Lang-Kobayashi (LK) for a single mode EEL, which provides the temporal evolution of the optical field and the carriers number. This research concludes that in a wide range of system parameters these fluctuations are chaotic transients. The statistics of these transient is not affected by moderate noise intensities, while observing the influence of different light-matter interactions in both the duration and the statistics of the transient times. The comparison of the obtained results with a low-dimensional phenomenological model shows how noise plays a relevant role in long-term transients when the dimensionality of the system is small. In this Thesis we also studied the occurrence of synchronization without delay in a set of non-identical lasers, when a sufficiently large number of elements are coupled through a central laser without dynamics, but with time delay in the coupling. Using a generalization of the LK model is shown that the kind of transition to the synchronization can be controlled by the injection current of the outer lasers, so an abrupt or a progressive transition to the synchronization can be obtained by increasing the number of lasers in the system. These two transitions are identified as the quorum sensing synchronization and crowd synchronization respectively. The effect of delay in the coupling is investigated for the first time in this type of synchronization.