In the early 1980s, the late luminary Tito Arecchi was the first to highlight the existence of chaos in a laser model. Since then, along with several colleagues, he developed many important lines of research in this field, such as generalized multistability, laser with injected signal, laser with delayed feedback and the worldwide accepted classification of lasers of A, B and C, depending on their typical relaxation rates. Later, chaos control and synchronization were investigated in lasers and other systems, providing innovative schemes. Very recently, in his last contribution to laser physics, the model of the laser with feedback demonstrating its universal features was revisited.This book aims to present the research activity of Prof. Arecchi and his colleagues in the domain of nonlinear dynamics of lasers, since his seminal works of 1982 till the latest. Also included is our last contribution on jerk dynamics of laser's minimal universal model and a brief history of the discovery of laser where the reader will discover or rediscover many anecdotes about it.
Author(s): F. Tito Arecchi, Jean-Marc Ginoux, Riccardo Meucci
Series: Topics in Systems Engineering, 4
Publisher: World Scientific
Year: 2023
Language: English
Pages: 148
City: Singapore
Contents
In memoriam — Tito Arecchi (11 December 1933–15 February 2021)
Acknowledgments
List of Figures
List of Tables
1. Laser Physics and Laser Instabilities
1.1 Introduction
1.2 Semiclassical theory
1.3 Fundamental results of the semiclassical theory
1.4 References
2. Generalized Multistability and its Control in a Laser
2.1 Introduction
2.2 Two-level non-autonomous laser model
2.2.1 Rescaled form
2.2.2 Jacobian matrix
2.3 Two-level autonomous laser model
2.3.1 Fixed points
2.3.2 Jacobian matrix
2.4 Control of generalized multistability
2.5 Discussion
2.6 References
3. Minimal Universal Model for Chaos in Laser with Feedback
3.1 Introduction
3.2 Minimal universal model
3.2.1 Dimensionless form
3.2.2 Fixed points
3.2.3 Jacobian matrix
3.2.4 Bifurcation diagram
3.2.5 Numerical computation of the Lyapunov exponents
3.3 Experimental part
3.4 Discussion
3.5 Conclusions
3.6 Appendix
3.7 References
4. Slow Invariant Manifold of Laser with Feedback
4.1 Introduction
4.2 Slow–fast dynamical system
4.3 Stability analysis
4.3.1 Fixed points, Jacobian matrix and eigenvalues
4.3.2 Bifurcation diagram
4.3.3 Numerical computation of the Lyapunov characteristic exponents
4.4 Slow invariant manifold
4.5 Discussion
4.6 References
5. Phase Control in Nonlinear Systems
5.1 Introduction
5.2 Phase control of intermittency in dynamical systems
5.2.1 Crisis-induced intermittency and its control
5.2.2 Experimental setup and implementation of the phase control scheme
5.2.3 Phase control of the laser in the pre-crisis regime
5.2.4 Phase control of the intermittency after the crisis
5.3 Conclusions and discussions
5.4 References
6. The Jerk Dynamics of Laser’s Minimal Universal Model
6.1 Introduction
6.2 Preliminaries
6.3 The jerk form of laser’s minimal universal model
6.3.1 Jerk form in z
6.3.2 Stability analysis
6.3.4 Bifurcation diagram
6.3.5 Numerical computation of the Lyapunov exponents
6.4 Experimental part
6.5 Discussion
6.6 References
7. A Short History of the Discovery of LASER
7.1 The nature of light
7.2 The birth of Quantum Mechanics
7.3 From MASER to LASER
7.4 LASER applications
7.5 References
Appendix A Appendix
A.1 Laser rate equations
A.1.1 Stationary solutions
A.2 First normalization
A.2.1 Stationary solutions
A.2.2 Linear stability analysis
A.3 Second normalization
A.3.1 Stationary solutions
A.3.2 Linear stability analysis
A.4 Third normalization
A.4.1 Stationary solutions
A.4.2 Linear stability analysis
Appendix B Appendix
Bibliography
Index
