Complex dynamics of delay-coupled semiconductor lasers: fundamentals and applications

Abstract

Introduction: The present thesis is devoted to the study of semiconductor lasers subject to delayed optical feedback and coupling. The complex spectral and dynamical properties of these systems have been investigated using state-of-the-art telecommunications detection technologies. With such tools, we have been able to experimentally characterize previously unknown features in our delay-coupled systems. Along this work, both fundamental and applied results are presented for the different experiments investigated. Results: The first part of the thesis is focusing on the system of the single delayed feedback laser. The problem of feedback characterization is approached from a time scale perspective, relating the dynamical regimes to the characteristic frequencies of the delayed feedback laser. We have empirically found that the ratios of these characteristic frequencies completely determine the dynamical behavior. This constitutes a model independent approach that can be used, for example, to test the validity of numerical models that aim at explaining the dynamical behavior of these lasers. Furthermore, the general extent of our approach is validated by measuring various laser diodes with distinct characteristics. Specific properties of the dynamics of the single laser with feedback system have also been characterized by means of the intensity autocorrelation function. For this purpose, the experimental autocorrelation is compared with the autocorrelation obtained from a model of a stochastic linear oscillator with delay. The relation between the model parameters and the experimental system parameters is analyzed and discussed together with the limits of validity of this approach. In the second part, systems with two delay-coupled lasers are studied. The phenomenon of chaos synchronization is explored in two different configurations: a unidirectional coupling configuration where the delayed feedback laser signal is optically coupled to a second laser, and a bidirectional scheme of two mutually coupled lasers with self-feedback. In the first configuration, the relation between the consistency of the dynamics and the synchronizability with the second laser is studied. In the latter scheme, the robustness of the synchronized state is characterized against detuning in parameters and noise. The knowledge gained in the synchronization experiments is used to implement a classical public-channel secure-key exchange protocol in the bidirectional coupling scheme. This protocol is demonstrated experimentally, and its advantages and weaknesses are analyzed. Finally, we present a practical photonic implementation of a dynamical system experiencing two different delay times depending on the state of the system. The stationary spectral characteristics of this experimental system are studied and the conditions for the dynamics to occur in separated states are highlighted. We have also investigated the real-time intensity and optical spectrum dynamics to demonstrate the existence and properties of state-dependent delay dynamics. Qualitatively similar properties can be found from a proper numerical model of this system. Conclusions: Altogether, we have presented fundamental and applied aspects of semiconductor lasers optically coupled with delay. The presented phenomenology is of immediate potential use for a variety of applications that range from photonics-based reservoir computing to chaos communications. In addition, the presented fundamental insights can potentially be extended to other classes of dynamical systems. Contents: Resum (iv) Abstract (vi) List of Publications (vii) 1 Introduction (1) 1.1 Motivation (1) 1.2 Semiconductor Laser Devices (2) 1.3 Nonlinear Dynamics of Semiconductor Lasers (5) 1.3.1 Delayed Optical Feedback Effects on the Emission of Semiconductor Lasers (6) 1.4 Chaos Synchronization in Optically-Coupled Semiconductor Lasers (11) 1.5 Outline of this Thesis (14) 2 Semiconductor Lasers Subject to Delayed Optical Feedback: Similarity Properties in the Dynamics (17) 2.1 Introduction (17) 2.1.1 Strong and Weak Chaos Regimes (18) 2.1.2 Chapter Outline (18) 2.1.3 Contributions to the Work in the Present Chapter (19) 2.2 Experimental Methods (19) 2.2.1 Semiconductor Lasers (19) 2.2.2 Feedback Experiments in Fiber-Based Setups (20) 2.2.3 Acquisition Conditions (21) 2.3 Characteristic Frequencies of Delayed Feedback Lasers (21) 2.3.1 Autocorrelation Function of the Intensity Dynamics (24) 2.4 Invariant Dynamics Signature (25) 2.4.1 Physical Mechanism for Weak and Strong Chaos (27) 2.5 Full Rescaling of the Dynamics (30) 2.6 Dynamical Regimes (32) 2.6.1 Low Feedback Strengths (32) 2.6.2 Intermediate Feedback Strengths (34) 2.6.3 High Feedback Strengths (34) 2.7 Comparison with Numerical Modelling (35) 2.8 Similarity Properties in Quantum Dot Lasers (38) 2.8.1 Brief Introduction to Quantum Dot Lasers Particularities (38) 2.8.2 Invariant Dynamics Signature in Quantum-Dot Lasers (40) 2.9 Discussion and Summary (42) 3 Properties of the Autocorrelation Function of a Laser with Feedback (45) 3.1 Introduction (45) 3.1.1 Chapter Outline (46) 3.1.2 Contributions to the Work in the Present Chapter (46) 3.2 Experimental Methods (46) 3.2.1 Experimental Technique to Determine the Delay Time (47) 3.3 Autocorrelation Function of a Linear Stochastic Delay Model (47) 3.4 Comparison of the Autocorrelation Functions of the Laser and the Linear Model (51) 3.5 Limits of Validity of the Linear Approximation (53) 3.6 Parameters Extraction from the Fit of the Autocorrelation Function (56) 3.6.1 Time Delay Extraction (58) 3.7 Summary and Discussion (59) 4 Chaos Synchronization in Delay-Coupled Semiconductor Lasers (61) 4.1 Introduction (61) 4.1.1 Chapter Outline (63) 4.1.2 Contributions to the Work in the Present Chapter (63) 4.2 Experimental Methods (64) 4.2.1 Experimental Setups for Synchronization Experiments (64) 4.2.2 Cross-Correlation Analysis (66) 4.3 Correlations and Synchronization of Unidirectionally Coupled Lasers in Open-Loop Configuration (66) 4.4 Synchronization of Two Mutually-Coupled Semiconductor Lasers with a Passive Relay (73) 4.4.1 Influence of Spectral Detuning (76) 4.4.2 Isochronous Synchronization Regime (78) 4.4.3 Noise-Induced Desynchronization Events: Bubbling (79) 4.5 Summary and Discussion (86) 5 Bidirectional Secure Key Exchange using Chaotic Semiconductor Lasers (89) 5.1 Introduction (89) 5.1.1 Chapter Outline (93) 5.1.2 Contributions to the Work in the Present Chapter (93) 5.2 Experimental Methods (94) 5.3 Encrypted-Key Distribution Scheme (95) 5.3.1 Simultaneous Bidirectional Key Exchange Protocol (96) 5.3.2 Particularities of the Experimental Setup (96) 5.3.3 Proof of Concept (99) 5.4 Security Analysis of Our Scheme (102) 5.5 Discussion and Summary (106) 6 State-Dependent Delay Dynamics in Semiconductor Lasers (109) 6.1 Introduction (109) 6.1.1 Chapter Outline (111) 6.1.2 Contributions to the Work in the Present Chapter (111) 6.2 Experimental Methods (111) 6.3 Experimental Results (114) 6.4 Numerical Modeling (124) 6.5 Switching Characteristics (127) 6.6 Summary and Discussion (129) 7 Concluding Remarks (131) A Appendix A (137) A.1 Laser Sources (137) A.2 Feedback Experiments in Fiber-Based Setups (140) A.3 Signal Detection (141) A.4 List of Instruments and Components (142) Abbreviations (145) Bibliography (147)