This book is an edited version of lectures given by the authors at the 1985 Summer School on Lase Physics. The School was held in Jilin University in Changchun, Peoples' Republic of China. Contents: The book is divided into 2 parts, the first is ''An Outline of Laser Physics and Laser Instabilities'': An Introduction to the Theory of the Laser: The Rate Equations; The Interaction of Light and Matter: The Classical Picture; The Basic Laser Equations: Homogeneously Broadened Systems; Steady State Behavior of a Homogeneously Broadened Ring Laser; Linear Stability Analysis: The Resonant Case; The Adiabatic Elimination of the Fast Variables; Linear Stability Analysis: The General Case; The Single Mode Laser: Deterministic Chaos; Dynamical Behavior of the Maxwell-Bloch Equations; The Spectral Analysis of the Output Field; Theory of a Laser with Inhomogeneous Broadening. The second part is on the ''principles of Laser Physics and Laser Instabilities'': Background Notes for the Discussion of Experimental Laser Systems; Amplified Spontaneous Emission; The Two-Level Atom; Laser Cavities and Modes; Types of Laser Systems and Classification of Lasers; the Xe 3.51 ..mu..m Laser; Chaos in Single Mode Lasers; Forced Laser Systems, Modulated Lasers and Lasers with an Injected Signal; Dynamical Phenomena in Multimode Laser Systems.
This book is an edited version of lectures given by the authors at the 1985 Summer School on Lase Physics. The School was held in Jilin University in Changchun, Peoples' Republic of China. Contents: The book is divided into 2 parts, the first is ''An Outline of Laser Physics and Laser Instabilities'': An Introduction to the Theory of the Laser: The Rate Equations; The Interaction of Light and Matter: The Classical Picture; The Basic Laser Equations: Homogeneously Broadened Systems; Steady State Behavior of a Homogeneously Broadened Ring Laser; Linear Stability Analysis: The Resonant Case; The Adiabatic Elimination of the Fast Variables; Linear Stability Analysis: The General Case; The Single Mode Laser: Deterministic Chaos; Dynamical Behavior of the Maxwell-Bloch Equations; The Spectral Analysis of the Output Field; Theory of a Laser with Inhomogeneous Broadening. The second part is on the ''principles of Laser Physics and Laser Instabilities'': Background Notes for the Discussion of Experimental Laser Systems; Amplified Spontaneous Emission; The Two-Level Atom; Laser Cavities and Modes; Types of Laser Systems and Classification of Lasers; the Xe 3.51 ..mu..m Laser; Chaos in Single Mode Lasers; Forced Laser Systems, Modulated Lasers and Lasers with an Injected Signal; Dynamical Phenomena in Multimode Laser Systems.
The instabilities in homogeneously broadened lasers, which we described in the previous chapter, have a paradigmatic importance because they arise in models which allow one to perform the linear-stability analysis in a simple analytic form. The treatment of the corresponding instabilities in the case of in homogeneously broadened lasers is substantially more complex in general. However, it is very interesting because, as we shall see, the instabilities arise in parametric domains that are much more accessible from the experimental viewpoint. A related issue is that of the possibility of multimodal emission in a laser. It is common knowledge that in order to attain multimode emission it is necessary to have a sort of in homogeneity in the gain medium, because in a completely homogeneous configuration all modes interact with all atoms, and the arising competition among modes implies that only one of them survives. There are basically two main kinds of in homogeneity, the first is of spatial nature and the other is of spectral nature. The first kind is realized in Fabry–Perot lasers, because different cavity modes interact with atoms at different spatial positions in the cavity thanks to the standing-wave configuration of the field and to the consequent phenomenon of spatial hole- burning (see Section 14.2 and Fig. 14.1). This circumstance is capable of weakening the mode–mode competition and allowing multimode operation. In unidirectional ring lasers, on the other hand, there is an “inhomogeneous” configuration in the case of inhomogeneous broadening, because different groups of atoms have different transition frequencies and therefore interact with different modes thanks to the spectral hole-burning (see Section 15.2 and Fig. 15.3). Again, this weakens the mode–mode competition and allows multimode operation. However, these are qualitative considerations, and the only reliable and quantitative method to determine the possibility of multimodal operation is the linear-stability analysis of the single-mode stationary solutions.
Modeling lasers may be realized with different levels of sophistication. Rigorously it requires a full quantum treatment but many laser dynamical properties may be captured by semiclassical or even purely classical approaches. In this book we deliberately chose the simplest point of view, i.e. purely classical equations, and try to extract analytically as much information as possible. The basic framework of our approach is provided by the rate equations . In their simplest version, they apply to an idealized active system consisting of only two energy levels coupled to a reservoir. They were introduced as soon as the laser was discovered to explain (regular or irregular, damped or undamped) intensity spikes commonly seen with solid state lasers (for a historical review, see the introduction in). These rate equations are discussed and sometimes derived from a semiclassical theory in textbooks on lasers. They capture the essential features of the response of a single-mode laser and they may be modified to account for specific effects such as the modulation of a parameter or optical feedback. The most basic processes involved in laser operation are schematically represented in Figure 1.1. N 1 and N 2 denote the number of atoms in the ground and excited levels, respectively. The process of light–matter interaction is restricted to stimulated emission and absorption.
This chapter concludes the discussion about temporal instabilities and self-oscillations, considering the instabilities that arise in the systems analyzed in Chapter 13, with the exception of optical bistability, which has been discussed separately in Chapter 11. Section 25.1 focuses on the laser with an injected signal. As already mentioned in Section 13.1, in this system self-pulsing instabilities are rather ubiquitous, and on exploring the parameter space one meets an extremely rich variety of oscillatory behaviors. For example, under extremely high-gain conditions, breathing, spiking and chaos have been identified over various ranges of the driving field strength [294]. In this section we show some results that arise under parametric conditions that are more accessible experimentally. We illustrate especially the coexistence, for the same parametric values, of different oscillatory behaviors that are reached by starting from different initial conditions. On the other hand, Section 25.2 deals with a laser with a saturable absorber. In this system even the full scenario of stationary intensity solutions in the single-mode model is very complex. For the sake of simplicity, in this section we focus on a simpler rate-equation model that is obtained from the single-mode model of Eqs. (13.13)–(13.17) by adiabatically eliminating the atomic polarization of both active and passive medium. As in Chapter 13, we assume that the atomic transition frequencies are equal and also coincide with a cavity frequency. In this way all the variables in the model can be assumed real, and the linearization around the stationary solution described in Section 13.2 leads to a cubic eigenvalue equation. The spontaneous oscillations which arise from this instability are called repetitive passive Q-switching in the literature. Section 25.3 considers the stability of the stationary solutions of the degenerate optical parametric oscillator described in Section 13.4 and outlines the scenario of period doubling and chaos that arises under appropriate parametric conditions.
Abstract This book is an introduction to quantum optics for students who have studied electromagnetism and quantum mechanics at an advanced undergraduate or graduate level. It provides detailed expositions of theory with emphasis on general physical principles. Foundational topics in classical and quantum electrodynamics, including the semiclassical theory of atom-field interactions, the quantization of the electromagnetic field in dispersive and dissipative media, uncertainty relations, and spontaneous emission, are addressed in the first half of the book. The second half begins with a chapter on the Jaynes-Cummings model, dressed states, and some distinctly quantum-mechanical features of atom-field interactions, and includes discussion of entanglement, the no-cloning theorem, von Neumann’s proof concerning hidden variable theories, Bell’s theorem, and tests of Bell inequalities. The last two chapters focus on quantum fluctuations and fluctuation-dissipation relations, beginning with Brownian motion, the Fokker-Planck equation, and classical and quantum Langevin equations. Detailed calculations are presented for the laser linewidth, spontaneous emission noise, photon statistics of linear amplifiers and attenuators, and other phenomena. Van der Waals interactions, Casimir forces, the Lifshitz theory of molecular forces between macroscopic media, and the many-body theory of such forces based on dyadic Green functions are analyzed from the perspective of Langevin noise, vacuum field fluctuations, and zero-point energy. There are numerous historical sidelights throughout the book, and approximately seventy exercises.
This is a book chapter in the following descried book: This book collects together the lecture courses and seminars given at the Les Houches Summer School 2008 on Long-Range Interacting Systems, reviewing the state-of-the-art developments in this field and providing an essential background to future studies, all in writing that is accessible to Masters and PhD students and researchers wishing to enter this field. Leading scientists in different fields of mathematics and physics present their views on this fast growing and interdisciplinary field of research, exploring such topics as fundamental problems of probability, transport theory, equilibrium and non-equilibrium statistical mechanics, condensed matter physics, astrophysics and cosmology, physics of plasmas, and hydrodynamics. In particular, the book examines the thermodynamic and dynamical properties of systems with long-range interactions, which have been poorly understood until recently.
Preface. List of symbols. 1. Introduction. 2. Basic properties and types of lasers. 3. Laser resonators. 4. The intensity of laser light. Rate equations. 5. The basic equations of the semiclassical laser theory. 6. Applications of semiclassical theory. 7. Ultrashort pulses. 8. Instability hierachies of laser light. Chaos, and routes to chaos. 9. Optical bistability. 10. Quantum theory of the laser I. A first approach via quantum mechanical Langevin equations. Coherence, noise and photon-statistics. 11. Quantum theory of the laser II. A second approach via the density matrix equation and quantum classical correspondence. 12 A theoretical treatment of the two-photon laser. 13. The laser - trailblazer of synergetics. References. Subject index.