Instabilities and Chaos in Quantum Optics
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1 Instabilities and Chaos in Quantum Optics Editors: E T. Arecchi and R. G. Harrison With 135 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
2 Contents 1. Introduction. By F.T. Arecchi and R.G. Harrison A Heuristic Approach to Instabilities About This Book 4 References 7 Part I Instabilities and Chaos in Active Systems 2. Instabilities and Chaos in Single-Mode Homogeneous Line Lasers. By F.T. Arecchi (With 26 Figures) Background Transient Decay Toward a Stable State Deterministic Chaos Historical Aspects Dynamical Aspects Information Aspects Role of Transients: The Hyperchaos The Modulated Laser The Laser with Injected Signal (LIS) Instabilities in a Laser with Feedback The Bidirectional Ring Laser Conclusion A Appendix: A Simple-Minded Approach to Laser Equations A.1 The Laser Equations 40 2.A.2 Adiabatic Elimination of Polarization Modulation and Injection 42 2.A.3 Linear Stability Analysis of Class В Solutions 44 2.A.4 Laser with Injected Signal (LIS) 45 2.A.5 The Bidirectional Class В Ring Laser 45 References 47 VII
3 3. Experimental Measurements of Transitions to Pulsations and Chaos in a Single Mode, Unidirectional Ring Laser with an Inhomogeneously-Broadened Medium By N.B. Abraham, A.M. Albano, Т.Н. Chyba, L.M. Hoffer, M.F.H. Tarroja, S.P. Adams, and R.S. Gioggia (With 14 Figures) Background The Single-Mode, Inhomogeneously-Broadened, Unidirectional Ring Laser Background Experimental Set-Up Thresholds for Transitions from Stable to Pulsed Behavior Changes in the Pulsation Pattern Above the Second Threshold Confirming and Characterizing the Chaos Discussion 68 References Single- and Multi-Mode Operation of a Laser with an Injected Signal. By D.K. Bandy, L.A. Lugiato, and L.M. Narducci (With 18 Figures) Background Information Equations of Motion and the Steady-State Configuration Linear Stability Analysis in the Mean-Field Limit Adiabatic Elimination of the Atomic Variables Dynamical Behavior of the Single-Mode Model Power Spectra and Lyapunov Exponents 98 4.A Appendix: Derivation of (4.14) В Appendix: List of the Coefficients of (4.29) С Appendix: List of Coefficients in (4.31) 106 References Experimental Observations of Single Mode Laser Instabilities in Optically Pumped Molecular Lasers By D.J. Biswas, R.G. Harrison, CO. Weiss, W. Klische, D. Dangoisse, P. Glorieux, and N.M. Lawandy (With 8 Figures) Background Optically Pumped Far Infrared Lasers Resonant Pumping Detuned Pumping Single-Mode Laser Instability in Near Resonantly Pumped Mid-Infrared Systems Conclusion 120 References 121 VIII
4 6. Quantum Treatment of Amplified Spontaneous Emission in High-Gain Free-Electron Lasers By R. Bonifacio and F. Casagrande Introduction The Quantum Hamiltonian Model Classical Limit and Classical Treatment of Amplified Spontaneous Emission The Basic Equations of the Linear Quantum Regime Analysis on Resonance and for Sufficiently Long Times "Harmonic Oscillator" Limit "Classical" Limit A Appendix 137 References 138 Additional References with Titles 138 Part II Instabilities and Chaos in Passive Systems 7. Global Bifurcations and Turbulence in a Passive Optical Resonator. By J.V. Moloney (With 22 Figures) Background Material Model and Theory Bifurcation and Global Phase Portraits The Plane-Wave Map The Newhouse Sink Phenomena Boundary Crisis Gaussian Beams (2D Problem) Stability of the Plane-Wave Map to Transverse Spatial Perturbations Solitary Waves as Fixed Points of the Infinite Dimensional Map Many Routes to Optical Turbulence Gaussian Beams (3D Problem) Summary 169 References Experimental Verification of Regenerative Pulsations and Chaos. By M.W. Derstine, J.L. Jewell, H.M. Gibbs, F.A. Hopf, M.C. Rushford, L.D. Sanders, and K. Tai (With 19 Figures) Regenerative Pulsations Ikeda Instabilities Experimental Setup Review of Period Doubling Universality 183 IX
5 8.2.4 Nature of Transitions Effects of Noise Other Waveforms/Alternate Paths Test for Chaos in High-Speed Optical Systems Instabilities in Sodium Vapor Optically Thick Optically Thin Issues for Fast Chaotic Systems 197 References Instabilities and Routes to Chaos in Passive All-Optical Resonators Containing Molecular Gases By R.G. Harrison, W.J. Firth, and I.A. Al-Saidi (With 20 Figures) Background Theory of Instabilities in Passive Nonlinear Resonators The Basic Model Physical Interpretation of the Ikeda Instability Fabry-Perot Resonators Universality Trapping Bifurcation Points Nonlinear Absorption Characteristics of Molecules Ammonia Sulphur Hexafiuoride Molecular Energy-Level Scheme Optical Bistability and Instability Generation in Optical Resonators Ring Resonator Fabry-Perot Resonator Fabry-Perot Resonator with Sulphur Hexafiuoride Conclusion 234 References Transmission Properties of a Sodium-Filled Fabry-Perot Resonator. By G. Giusfredi, S. Cecchi, E. Petriella, P. Salieri, and F.T. Arecchi (With 8 Figures) Background Experimental Set-Up Discussion Optical Bistability by Zeeman Pumping Optical Tristability Multistability Self-Pulsing 245 References 249 Subject Index 251 X
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