Instabilities and Chaos in Quantum Optics (Paperback, Softcover Repri)

1. Introduction.- 1.1 A Heuristic Approach to Instabilities.- 1.2 About This Book.- References.- I Instabilities and Chaos in Active Systems.- 2. Instabilities and Chaos in Single-Mode Homogeneous Line Lasers.- 2.1 Background.- 2.2 Transient Decay Toward a Stable State.- 2.3 Deterministic Chaos.- 2.3.1 Historical Aspects.- 2.3.2 Dynamical Aspects.- 2.3.3 Information Aspects.- 2.3.4 Role of Transients: The Hyperchaos.- 2.4 The Modulated Laser.- 2.5 The Laser with Injected Signal (LIS).- 2.6 Instabilities in a Laser with Feedback.- 2.7 The Bidirectional Ring Laser.- 2.8 Conclusion.- 2.A Appendix: A Simple-Minded Approach to Laser Equations.- 2.A.1 The Laser Equations.- 2.A.2 Adiabatic Elimination of Polarization - Modulation and Injection.- 2.A.3 Linear Stability Analysis of Class B Solutions.- 2.A.4 Laser with Injected Signal (LIS).- 2.A.5 The Bidirectional Class B Ring Laser.- References.- 3. Experimental Measurements of Transitions to Pulsations and Chaos in a Single Mode, Unidirectional Ring Laser with an Inhomogeneously-Broadened Medium.- 3.1 Background.- 3.2 The Single-Mode, Inhomogeneously-Broadened, Unidirectional Ring Laser.- 3.2.1 Background.- 3.2.2 Experimental Set-Up.- 3.2.3 Thresholds for Transitions from Stable to Pulsed Behavior.- 3.2.4 Changes in the Pulsation Pattern Above the Second Threshold.- 3.2.5 Confirming and Characterizing the Chaos.- 3.3 Discussion.- References.- 4. Single- and Multi-Mode Operation of a Laser with an Injected Signal.- 4.1 Background Information.- 4.2 Equations of Motion and the Steady-State Configuration.- 4.3 Linear Stability Analysis in the Mean-Field Limit.- 4.4 Adiabatic Elimination of the Atomic Variables.- 4.5 Dynamical Behavior of the Single-Mode Model.- 4.6 Power Spectra and Lyapunov Exponents.- 4.A Appendix: Derivation of (4.14).- 4.B Appendix: List of the Coefficients of (4.29).- 4.C Appendix: List of Coefficients in (4.31).- References.- 5. Experimental Observations of Single Mode Laser Instabilities in Optically Pumped Molecular Lasers.- 5.1 Background.- 5.2 Optically Pumped Far Infrared Lasers.- 5.2.1 Resonant Pumping.- 5.2.2 Detuned Pumping.- 5.2.3 Single-Mode Laser Instability in Near Resonantly Pumped Mid-Infrared Systems.- 5.3 Conclusion.- References.- 6. Quantum Treatment of Amplified Spontaneous Emission in High-Gain Free-Electron Lasers.- 6.1 Introduction.- 6.2 The Quantum Hamiltonian Model.- 6.3 Classical Limit and Classical Treatment of Amplified Spontaneous Emission.- 6.4 The Basic Equations of the Linear Quantum Regime.- 6.5 Analysis on Resonance and for Sufficiently Long Times.- 6.6 "Harmonic Oscillator" Limit.- 6.7 "Classical" Limit.- 6. A Appendix.- References.- Additional References with Titles.- II Instabilities and Chaos in Passive Systems.- 7. Global Bifurcations and Turbulence in a Passive Optical Resonator.- 7.1 Background Material.- 7.2 Model and Theory.- 7.3 Bifurcation and Global Phase Portraits.- 7.4 The Plane-Wave Map.- 7.4.1 The Newhouse Sink Phenomena.- 7.4.2 Boundary Crisis.- 7.5 Gaussian Beams (2D Problem).- 7.5.1 Stability of the Plane-Wave Map to Transverse Spatial Perturbations.- 7.5.2 Solitary Waves as Fixed Points of the Infinite Dimensional Map.- 7.5.3 Many Routes to Optical Turbulence.- 7.6 Gaussian Beams (3D Problem).- 7.7 Summary.- References.- 8. Experimental Verification of Regenerative Pulsations and Chaos.- 8.1 Regenerative Pulsations.- 8.2 Ikeda Instabilities.- 8.2.1 Experimental Setup.- 8.2.2 Review of Period Doubling.- 8.2.3 Universality.- 8.2.4 Nature of Transitions.- 8.2.5 Effects of Noise.- 8.2.6 Other Waveforms/Alternate Paths.- 8.2.7 Test for Chaos in High-Speed Optical Systems.- 8.3 Instabilities in Sodium Vapor.- 8.3.1 Optically Thick.- 8.3.2 Optically Thin.- 8.4 Issues for Fast Chaotic Systems.- References.- 9. Instabilities and Routes to Chaos in Passive All-Optical Resonators Containing Molecular Gases.- 9.1 Background.- 9.2 Theory of Instabilities in Passive Nonlinear Resonators.- 9.2.1 The Basic Model.- 9.2.2 Phys