Tesis doctoral de María Cristina Martínez González
In this thesis we have presented the results of a set of experimental investigations of the dynamics of delay-coupled semiconductor lasers. The characterization of these systems includes topics such as the processing of information by coupled lasers, the choice of a leader in their lag-synchronized dynamics, or how chaos arises in two coupled semiconductor lasers. ¿ the transition to chaos of a semiconductor laser through a quasiperiodic state was reported in the past adding an optical feedback or through mutual coupling. we studied the quasiperiodic route to chaos of two semiconductor lasers mutually coupled through two independent unidirectional paths. The transition from unidirectional to bidirectional coupling was implemented by increasing the coupling strength of one of the paths, while keeping the other constant. We have seen how the transition from stable unidirectional injection to chaos arises through a quasiperiodic state. adjusting the currents and temperatures of the lasers in a unidirectional configuration, we maximize the injection by choosing optical frequencies sufficiently close to each other. In this regime, the output intensity of the receiver laser is forced to oscillate at the relaxation oscillation frequency of the driver, with a delay time introduced by the interaction. When the back injection is slightly increased, the external modes of the other cavity are excited and the laser output becomes quasiperiodic. This quasiperiodic behavior is produced by a competition between the external compound-cavity modes and the relaxation oscillation frequencies of both lasers. When the mutual coupling is sufficiently high the chaotic behavior appears. ¿ we have examined how a system of two coupled chaotic oscillators behaves under conditions of lag synchronization. Our experimental setup consists on two semiconductor lasers coupled via mutual injection of their emitted fields, and allows for the control of the coupling directionality. Our results show that the laser leading the dynamics changes depending on the coupling scenario. When one of the lasers has autonomous chaotic dynamics, in the form of irregularly spaced sudden power dropouts (low-frequency fluctuations), and this dynamics is injected into a solitary laser (which is stable in the absence of injection), the injecting laser obviously leads the dynamics. Such role, however, can be transferred to the other laser by converting the coupling from unidirectional to bidirectional. The transition occurs via a state in which the two lasers alternate randomly the leader and laggard roles. This type of behavior is not only restricted to the low-frequency dynamics that we have studied experimentally, but also to fully developed chaotic dynamics (coherence collapse) that occurs for higher pump currents, as shown by numerical simulations. our model also shows that the type of dynamics can be changed in a continuous way by acting upon the optical feedback strength affecting the laser with independent dynamics. we have discussed the potential of this system for bidirectional chaotic communications. Our experimental results show that whenever one of the lasers leads the dynamics, the other laser (the laggard) is able to operate as a chaos-pass filter. However, we have not been able to send information bidirectionally in an effective way. Numerical simulations show that, even though the maximum cross-correlation is similar in both the unidirectional and bidirectional cases, sudden synchronization losses in the latter situation prevent the system from being used as a reliable setup for bidirectional chaotic communications. ¿ when two coupled nonlinear systems are perturbed by two independent periodical signals, it is possible to observe a resonance at their outputs at a third frequency not present in the input, what is known as a ghost resonance. we have given experimental and numerical evidence of the existence of such a ghost resonance in two mutually coupled semiconductor lasers. The resonance is not trivial, since it persists in the case of incommensurate input frequencies, showing a behavior that agrees with theoretical predictions. Similar results have been obtained in simpler theoretical models and in single semiconductor lasers with optical feedback, but to our knowledge this was the first experimental observation in coupled systems. in a second part, we have shown experimentally that coupling between two excitable systems, specifically two semiconductor lasers with optical feedback, is able to mediate the processing of distributed inputs, applied in the form of pump current modulations of different frequencies. For large enough coupling strengths, the laser outputs have the form of synchronized trains of power dropouts which become entrained to a frequency that is not present in the input signals. When these signals are harmonics of a missing fundamental, as in the previous case, the response occurs at precisely the fundamental frequency. On the other hand, in the case where the two input frequencies are equally shifted from these harmonics, the system responds following a linear law, which arises from analyzing the linear summation of the two input modulationsthe superposition law holds even though the two signals acting upon a given laser are clearly different, one of them being electrical (through direct pump current modulation) and the other optical (through injection from the other laser). This type of response to complex input signals has been reported in the human brain with psychophysical experiments and magnetoencephalographic recordings, which highlights the importance of understanding the integration of distributed inputs by networks of information processing elements. ¿ we have experimentally and numerically shown that the introduction of a global noise can stabilize the isochronal solution in two mutually coupled semiconductor lasers. departing from a low frequency regime, in the synchronized state of the system with a well defined leader of the dynamics, we simultaneously added the same amount of colored noise to the pump current of the two lasers. For low amplitude, the noise is not capable of affecting the dynamics of the system, but for higher values of the amplitude the laser outputs synchronize without delay. a more detailed study showed that there is a threshold in the noise correlation time above which the fast dynamics of the system is not affected. The envelope of the dynamics (the dropout events) is affected by the colored noise for large enough noise intensity, but a cross-correlation study of the numerical output intensities shows a threshold in the correlation time above which the fast dynamics cannot synchronize with zero lag. For noise correlation times smaller than that threshold, and eventually in the white noise limit, the isochronal solution of the total dynamics of the system is stabilized. ¿ we have experimentally studied the route towards synchronization in a small network of three semiconductor lasers coupled with distributed delay times. Our results show that clusters emerge generically as the system goes towards synchronization for increasing coupling strength. A detailed study of the coupling between each pair of lasers showed that the cluster in the three laser system was formed by the pair of lasers with highest mutual coupling. The lasers which have most affinity (less detuning, highest parameter mismatch, and as a consequence highest coupling) will maintain the synchronized behavior for decreased injected light, whereas the third laser needs more coupling to belong to the synchronized system. The overlap of some of the peaks in the rf spectrum in the clustering state, denotes that it is an intermediate stage before a complete loss of synchronization. the experimental observations are satisfactorily reproduced by a rate equation model of the lang-kobayashi type. The model is valid for a laser emitting in a single longitudinal mode. The lasers in the experiments emit multiple longitudinal modes, and yet the agreement between the experiment and the model predictions is surprisingly good. This can be explained as due to the out of phase dynamics of the longitudinal modes. Because of the competition for the common carrier reservoir,the longitudinal modes oscillate in antiphase, such that the total output (that is, the sum of the modal intensities) is similar to that of a single-mode laser. The numerical simulations performed in this experiment helped us to understand which is the determining factor for the choice of lasers forming the cluster. We showed that the coupling determines which laser enters the cluster and which one loses the synchronization first.
Datos académicos de la tesis doctoral «Dynamical behavior of delay-coupled semiconductor lasers«
- Título de la tesis: Dynamical behavior of delay-coupled semiconductor lasers
- Autor: María Cristina Martínez González
- Universidad: Politécnica de catalunya
- Fecha de lectura de la tesis: 30/01/2009
Dirección y tribunal
- Director de la tesis
- Jordi García Ojalvo
- Tribunal
- Presidente del tribunal: ramon Vilaseca alavedra
- ingo Fischer (vocal)
- claudio rubén Mirasso santos (vocal)
- Javier Martín buldu (vocal)