A distinctive discussion of the nonlinear dynamical phenomena of semiconductor lasers. The book combines recent results of quantum dot laser modeling with mathematical details and an analytic understanding of nonlinear phenomena in semiconductor lasers and points out possible applications of lasers in cryptography and chaos control. This interdisciplinary approach makes it a unique and powerful source of knowledge for anyone intending to contribute to this field of research. By presenting both experimental and theoretical results, the distinguished authors consider solitary lasers with nano-structured material, as well as integrated devices with complex feedback sections. In so doing, they address such topics as the bifurcation theory of systems with time delay, analysis of chaotic dynamics, and the modeling of quantum transport. They also address chaos-based cryptography as an example of the technical application of highly nonlinear laser systems.

This book is the first comprehensive volume on nonlinear dynamics and chaos in optical systems. A few books have been published recently, but they summarize applied mathematical methodologies toward understanding of nonlinear dynamics in laser systems with small degrees of freedom focusing on linearized perturbation and bifurcation analyses. In contrast to these publications, this book summarizes nonlinear dynamic problems in optical complex systems possessing large degrees of freedom, systematically featuring our original experimental results and their theoretical treatments. The new concepts introduced in this book will have a wide appeal to audiences involved in a rapidly-growing field of nonlinear dynamics. This book focuses on nonlinear dynamics and cooperative functions in realistic optical complex systems, such as multimode lasers, laser array, coupled nonlinear-element systems, and their applications to optical processing. This book is prepared for graduate students majoring in optical and laser physics, but the generic nature of complex systems described in this book may stimulate researchers in the field of nonlinear dynamics covering different academic areas including applied mathematics, hydrodynamics, celestial mechanics, chemistry, biology, and economics.

By recirculating light in a nonlinear propagation medium, the nonlinear optical cavity allows for countless options of light transformation and manipulation. In passive media, optical bistability and frequency conversion are central figures. In active media, laser light can be generated with versatile underlying dynamics. Emphasizing on ultrafast dynamics, the vital arena for the information technology, the soliton is a common conceptual keyword, thriving into its modern developments with the closely related denominations of dissipative solitons and cavity solitons. Recent technological breakthroughs in optical cavities, from micro-resonators to ultra-long fiber cavities, have entitled the exploration of nonlinear optical dynamics over unprecedented spatial and temporal orders of magnitude. By gathering key contributions by renowned experts, this book aims at bridging the gap between recent research topics with a view to foster cross-fertilization between research areas and stimulating creative optical engineering design.

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.

After the first time chaos could be controlled, for the last quarter of century, a diversity of publications have been devoted to the development of new control schemes and their applications to different laser systems. This book assembles several review papers which analyze and describe the most important achievements in controlling laser dynamics and synchronization of laser systems. The papers report a variety of interesting dynamical phenomena encountered in different types of lasers and related to control techniques. For the last 20 years laser physics and nonlinear dynamics have undergone a crucial progress. Understanding lasers as dynamical systems involves concepts associated mostly with the nonlinear nature of these systems. Since the appearance of the pioneering work of E. Ott, C. Grebogi and J. A. Yorke in 1990, who proposed a method for controlling chaos, active attempts for applying this method and other control methods to laser systems have been conducted. Many research works were directed not only to the observation and identification of dynamical regimes in lasers, but also to control laser dynamics and chaos. Considerable progress has been made in research and development of semiconductor and fiber lasers. The special interest these lasers stir up is explained by their easy operation, small size, low price, and, of course, their successful application in communications. However, in spite of the huge progress in laser physics and nonlinear dynamics, only few reviews have been devoted to this topic. The book has an interdisciplinary character because the topic of this book is a great mixture of four big areas of science: laser physics, nonlinear dynamics, control theory, and synchronization. Each area was developed independently till the first nonlinear control of laser dynamics has been realized. The aim of this book is to address a broad readership: students, researchers, engineers, technicians, who work with lasers, as well as scientists conducting interdisciplinary research; it is intended for both theoreticians and experimentalists. The intention of this book is to give the reader a good understanding of nonlinear laser dynamics, not only in one specific type of laser but rather in many different types of lasers, as each control method or coupling is introduced. Four chapters of the book are devoted to laser dynamics control and describe the most important achievements of the last two decades in this topic. These chapters review already classical and relatively new results on stabilizing unstable periodic orbits in chaotic lasers and other control methods providing the reader with an extensive bibliography. The book also contains four chapters devoted to synchronization of coupled lasers. Special attention in the book is given to experimental applications of different control methods and synchronization phenomena in different laser systems. Editing this book has been a rewarding experience for me. Since 1979, I have been associated with lasers, beginning as a postgraduate student at the Institute of Physics of the Belarus Academy of Sciences in Minsk when I helped build a CO2 laser for a research project under Professor Vladimir V. Churakov direction. He was the first person to instil in me an enthusiasm for optics and light. I then was very fortunate to do my thesis work under supervision of Academician of the Byelorussian Academy of Sciences Boris Ivanovich Stepanov, who encouraged me to reduce ideas to simple concepts. Being very diligent, he nonetheless, also was a cheery person. He used to say that a real scientist has to work more than 24 hours per day, write monographs and must never stay too much time in one research area, but should change direction from time to time. I also thank Dr. Boris F. Kuntsevich for helping me to understand the fundamental theory of laser oscillations. At that time, in the late 70s - early 80s, since there were no personal computers we had to search for analytical solutions of laser equations. This was a good exercise to learn the foundation of laser physics. I am grateful to my colleagues Drs. Vladimir O. Petukhov and Ivan M. Bertel, who played a key role in my experimental practice helping me to install and equip my first experimental setup. Being a part of a stimulating group of young researchers at the Laboratory of General Spectroscopy during the growth of the field of laser spectroscopy was an unparalleled opportunity. We built CO2 lasers and tried to stabilize them for spectroscopy applications. For a long period of time Dr. Viacheslav N. Chizhevsky and I worked together, he got me involved in the world of chaos and helped me take my first steps into numerical simulations with MATLAB; together we carried out many experiments with CO2 lasers. He shared his ideas with me and I deeply appreciate all our fruitful discussions. Back then, we thought (about) laser was a stable device and treated any instabilities and chaos as a consequence of mechanical vibrations or bad alignment. It was only in 1964 that the Russian physicists A. Z. Grazyuk and A. N. Oraevskii found in numerical studies of the equations describing a simplest (homogeneously broadened, single-mode, traveling wave, resonantly tuned) laser, a time-dependent solution that consisted of pulses, varying irregularly with time. They even used at that time the term chaotic to describe this irregular pulsing behavior. Laser dynamics stagnated in a rudimentary state for more than one decade until in 1975, when the German theoretical physicist G. Haken concluded, from the isomorphy of a laser with Lorenz equations, that lasers could exhibit a non-periodic, pulsing emission, that is a chaotic emission. Even though, in the early 80s we did not believe that the Lorenz-Haken instability was inherent to real laser systems; thinking it was only an academic curiosity invented by theoreticians far removed from the daily reality of experimental laser physics, nonlinear laser dynamics was born and in 1982 after the first clear experimental evidence of laser chaos, was baptized by F. T. Arecchi These results, sharpening the perception of lasers as unstable systems, were then followed by a large number of experimental and theoretical investigations. Many researchers tried to exploit the new acquired knowledge of laser dynamics in some applications. Even though, the principal aim was still focused on avoiding instabilities to obtain a stable laser emission. Curiously, we had observed chaos in a bidirectional ring CO2 laser long before it was discovered by Prof. Arecchi's group. However, we did not pay serious attention to these findings, thinking it was the same chaotic behavior that had been previously observed in solid-state lasers. Moreover, we could not even publish our results in public scientific journals because in the Soviet Union of the 80's, during the period of Cold War, laser subjects were classified as top secret and not even the word laser was allowed to be used in open scientific literature. To evade this ban and get permission to publish our results, we had to replace the word laser by synonym words optical quantum generator . Many scientists who dealt with lasers were not allowed to go abroad and participate in international conferences. I was mainly a laser experimentalist until 1997, when I went to Canada with my own means to participate in the Summer School on Nonlinear Dynamics in Biology and Medicine organized by Leon Glass and Michael C. Mackey at McGill University in Montreal, where we took very useful lectures and practical exercises on theoretical modeling of physiological systems. Thanks to these lectures I came to realize that the world obeys universal dynamical laws, and also discovered for myself that many phenomena observed in lasers are present in a wide class of dynamical systems. This instilled in me the idea that a laser can serve as a very useful instrument to elaborate new methods for controlling nonlinear dynamics and chaos, which can be applied then to other systems, including biological and medical ones. Professor Arecchi and coworkers developed the same idea in their recent works; they do mention such similarity in the first chapter of this book. During the economically difficult period of the perestroika many scientists from the former Soviet Union had to abandon science and either go work for the industry or establish their own business. Some of the science-loving researchers who yet insisted on working at universities and research institutes had to paint roofs and towers or buy and resell things in order to survive. Many of us were looking for a job abroad. I was very fortunate to be invited first in 1992 by Professor Michel Herman from Physical Chemistry Laboratory at the University of Brussels where I spent three months working with dye lasers and fast Fourier spectroscopy. Then, thanks to Professor Ramón Corbalán who invited me to create the Laboratory of Infrared and Far Infrared Lasers at Universitat Autónoma de Barcelona, I spent almost seven years in Spain, where we carried out a series of interesting experiments on laser dynamics control. During that period I was happy to visit other universities and laser laboratories, such as the laboratory of Professor Pierre Glorieux at Université de Lille (France) and Professor Fortunato Tito Arecchi at Institute de Ottica Applicata in Florence (Italy), where we carried out several collaborative experiments with CO2 lasers. I also thank Professor Ari Olafson for the kind hospitality he extended to me in Reykjavik where I spent four unforgivable months in 1996 working at the University of Iceland. Finally, to round out my scientific carrier I was invited to Mexico in 1999 where I presently work as a Research Professor at Centro de Investigaciones en Optica in Leon, Guanajuato. I wish to thank Dr. Vicente Aboites, physicist and philosopher, for his kind invitation. Although the laser technology in Mexico is not yet advanced, the government is making a great effort to help develop national laser science and technology. I thank CONACYT (National Council for Science and Technology) for partial support of the publication of this book through project No. 46973-E, in particular, and research on lasers and applications, in general. Working in the field of lasers and nonlinear dynamics at several different institutions has provided me with a broad perspective that I hope has successfully contributed to the manner in which many of the concepts are presented in this book. I thank all of the authors who contributed to this book and to the reviewers who worked under great time pressure to complete the reviewing process in a relatively short time. I sincerely hope this book will stimulate new discussions and fundamental issues to a deeper level of understanding of laser dynamics and to develop new approaches to control and synchronization of laser systems. The results of this exercise could be also useful on the definition of scientific and technological programs related to this topic.

Monograph on laser dynamics, intended for those involved with laser optics, nonlinear dynamics, atomic physics, solid state physics molecular physics and spectroscopy. Subjects covered include the history of laser dynamics, theoretical models of nonlinear dynamics, and practical usage.

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

This book describes the fascinating recent advances made concerning the chaos, stability and instability of semiconductor lasers, and discusses their applications and future prospects in detail. It emphasizes the dynamics in semiconductor lasers by optical and electronic feedback, optical injection, and injection current modulation. Applications of semiconductor laser chaos, control and noise, and semiconductor lasers are also demonstrated. Semiconductor lasers with new structures, such as vertical-cavity surface-emitting lasers and broad-area semiconductor lasers, are intriguing and promising devices. Current topics include fast physical number generation using chaotic semiconductor lasers for secure communication, development of chaos, quantum-dot semiconductor lasers and quantum-cascade semiconductor lasers, and vertical-cavity surface-emitting lasers. This fourth edition has been significantly expanded to reflect the latest developments. The fundamental theory of laser chaos and the chaotic dynamics in semiconductor lasers are discussed, but also for example the method of self-mixing interferometry in quantum-cascade lasers, which is indispensable in practical applications. Further, this edition covers chaos synchronization between two lasers and the application to secure optical communications. Another new topic is the consistency and synchronization property of many coupled semiconductor lasers in connection with the analogy of the dynamics between synaptic neurons and chaotic semiconductor lasers, which are compatible nonlinear dynamic elements. In particular, zero-lag synchronization between distant neurons plays a crucial role for information processing in the brain. Lastly, the book presents an application of the consistency and synchronization property in chaotic semiconductor lasers, namely a type of neuro-inspired information processing referred to as reservoir computing.

Disorder is everywhere, inherently present in nature, and is commonly believed to be a synonymous with disturbance. As a consequence, the methodical and customary study of the dynamics of the electromagnetic field, both in the linear and nonlinear optical regimes, leans to rule out it from the treatment. On the other hand, nonlinearity enriches the physical disciplines and brings them closer to reality with respect to the linear approximation. Nonlinearity allows to stimulate a wide and rich ensemble of optical responses that beautifies the role of matter in the active processes with electromagnetic fields. Independently of each other, both of these mechanisms foster localization of light. What happens when light enlightens their synergistic interaction? When pushed together, light, disorder and nonlinearity make new and intriguing phenomena emerge. This text provides a comprehensive investigation of the role of disorder in the nonlinear optical propagation both in transparent media and lasers. Eventually, disorder promotes and enhances complex nonlinear dynamics opening new perspectives in applied research driven by the processes of localization of the electromagnetic field. The first experimental study of laser emission in granular media unveils how randomness magnifies and largely affect laser-matter interactions. Viola Folli in her research work touches and deepens the leading milestones of the new science named Complex Photonics.