Preface

The rates of competition of limited resources from different subsystems of a generic system would lead into chaotic states. This could happen in natural systems as well as in engineering systems, in particular nonlinear photonic ones. In energy storage systems if there is more than one storage element or subsystem then competition for energy would occur, and when they try to extract from or deposit their energy into each other, chaotic, bifurcation, or both phenomena would occur. The system can thus behave in a nonlinear manner, and hence the term nonlinear systems.

The most commonly known energy storage systems are those containing capacitors and inductors as charge and discharge competing elements, and photon storages with positive feedback into the resonance subsystem such as fiber lasers. Thus, higher-order differential equations can be employed to represent the dynamics of the evolution of the amplitude of the current or voltages or field amplitudes of the lightwaves in such systems.

This book selects to treat the nonlinear systems in terms of fundamental principles and associated phenomena as well as their applications in signal processing in contemporary optical systems for communications and laser systems with a touch of mathematical representation of nonlinear equations, which provides some insight into the nonlinear dynamics at different phases.

Therefore, Chapters 1 and 2 give an introduction to nonlinear systems and some mathematical representations, especially the routes to chaos and bifurcation and a brief introduction of nonlinear fiber lightwave lasing systems. Chapters 3, 4, 6, 7, and 8 describe the nonlinear phenomena in fiber lasers including both passive and active energy storage cavities, that is when the cavity is or is not modulated by an external excitation source. Soliton pulses with the lightwaves as the carrier under their envelopes are experimentally and theoretically demonstrated. Sequences of a single soliton as well as multiple numbers of solitons assembled in a group, the multibound solitons, are given and demonstrated. The interactions due to the phase states of the lightwaves under the soliton envelope lead to the binding states of these bound solitons, and their dynamics are treated in detail in Chapter 4. In Chapter 4 we then examine the evolution of these bound solitons when they are transmitted through single-mode optical fibers, which compose a phase variation system.

The evolution of the amplitude and phases of optical pulses through a guided medium can be represented by the well-known nonlinear Schrödinger equation (NLSE). Using this equation we studied different dynamics of solitons in fiber ring lasers and processing of optical systems in advanced optical communications systems. Two advanced applications are the processing of an ultrafast data pulse sequence in the optical domain via the representation of their bispectra. The bispectrum is a modern nonlinear processing technique that has been found to be the most appropriate match with our optical nonlinear systems. Furthermore the nonlinear transfer function of the NLSE can be derived via the use of the Volterra series that allows us to compensate for the distortion of pulses transmitted through the single-mode optical fiber in the digital electronic processing domain. This is described in the last chapter of this book.

The motivation and materials for this book were provided mainly by advanced research conducted in the universities of Osaka Prefecture and the Faculty of Physics of the University of Science of Ho Chi Minh City, Australian Universities, Nanayang Technological University of Singapore and in Advanced Technology Research Laboratories of Siemens, Hua Wei and Nortel Networks where one of the editors, Le N. Binh, has spent several fruitful years. An international workshop was held in 2010 at the University of Science of Ho Chi Min (HCM) City to address some issues treated in this book.

The research endeavors of many other people have contributed significantly to some sections of this book, especially research doctoral graduates of Le Binh over the years, in particular the following scholars, Dr. Lam Quoc Huy, Dr. Wenn Jing Lai, Dr. Nam Quoc Ngo, and Dr. Nguyen Duc Nhan.

We wish to thank contributors of a number of chapters of the book and especially Ashley Gasque of CRC Press for her encouragement and assistance in the formation of this book.

Le Nguyen Binh, Munich, Spring 2011

Dang Van Liet, HCM City, 2011