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Table of Contents
Supervisor's Foreword; List of Publications; Acknowledgments; Contents; 1 Introduction; References; 2 Multimode Laser Theory for Open Cavities; 2.1 Modes Description of Open Systems; 2.1.1 Fox
Li Modes; 2.1.2 Quasimodes; 2.1.3 Constant-Flux States; 2.2 Field Quantization for Open Cavities; 2.2.1 Normal Modes; 2.2.2 Resonator and Channel Modes; 2.2.3 System-and-Bath Hamiltonian; 2.2.4 Langevin Equations; 2.2.5 Comparison with the Constant Flux States; 2.3 Quantum Theory of a Two-Mode Laser in an Open-Cavity; 2.3.1 Atom-Field Interaction; 2.3.2 Properties of the Lasing Mode
2.4 Semiclassical Multimode Theory2.4.1 Linear Regime; 2.4.2 Lasing Regime; 2.5 Hamiltonian Formulation; 2.5.1 Purely Dissipative Case (mathcalHI=0); 2.5.2 General Case (mathcalHI neq0); References; 3 Analytic Solution of the Narrow-Bandwidth Model; 3.1 Formulation of the Main Mean-Field Model; 3.2 Quenched Disordered Systems in a Nutshell; 3.3 Replicated Partition Function; 3.4 Replica Symmetry Breaking Solutions with mathcalR Steps; 3.5 Phase Diagram at Fixed Effective Field; 3.5.1 Fieldless Case; 3.5.2 Nonzero Field
Magnetized Solutions; 3.6 Phase Diagram at Fixed Coupling Averages
3.7 Random First Order Transition and Complexity3.8 Conversion to Random Laser Parameters; 3.8.1 Unfolding the Field Equation; 3.9 Intensity Overlap Matrix; References; 4 Beyond Mean Field
Mode Locked Lasers; 4.1 Power Condensation; 4.2 Passive Mode Locking with Frequency Comb; 4.2.1 Definition of the Model; 4.2.2 Previous Studies of 4-Body Models; 4.3 Numerical Analysis; 4.3.1 Efficient Monte Carlo Simulation: The Synchronous Update; 4.3.2 Observables of Interest; 4.3.3 Details of the Simulations; 4.4 Numerical Results; 4.4.1 Lasing Threshold and Metastability
4.4.2 Phase Wave and Absence of Global Magnetization4.4.3 Two Point Correlation Functions; 4.4.4 Electromagnetic Pulse and Phase Delay; 4.4.5 Gain and Intensity Spectra; References; 5 Conclusions and Perspectives; Appendix AStability Analysis of the RS Solution; Appendix BStability Analysis of the 1RSB Solution
Li Modes; 2.1.2 Quasimodes; 2.1.3 Constant-Flux States; 2.2 Field Quantization for Open Cavities; 2.2.1 Normal Modes; 2.2.2 Resonator and Channel Modes; 2.2.3 System-and-Bath Hamiltonian; 2.2.4 Langevin Equations; 2.2.5 Comparison with the Constant Flux States; 2.3 Quantum Theory of a Two-Mode Laser in an Open-Cavity; 2.3.1 Atom-Field Interaction; 2.3.2 Properties of the Lasing Mode
2.4 Semiclassical Multimode Theory2.4.1 Linear Regime; 2.4.2 Lasing Regime; 2.5 Hamiltonian Formulation; 2.5.1 Purely Dissipative Case (mathcalHI=0); 2.5.2 General Case (mathcalHI neq0); References; 3 Analytic Solution of the Narrow-Bandwidth Model; 3.1 Formulation of the Main Mean-Field Model; 3.2 Quenched Disordered Systems in a Nutshell; 3.3 Replicated Partition Function; 3.4 Replica Symmetry Breaking Solutions with mathcalR Steps; 3.5 Phase Diagram at Fixed Effective Field; 3.5.1 Fieldless Case; 3.5.2 Nonzero Field
Magnetized Solutions; 3.6 Phase Diagram at Fixed Coupling Averages
3.7 Random First Order Transition and Complexity3.8 Conversion to Random Laser Parameters; 3.8.1 Unfolding the Field Equation; 3.9 Intensity Overlap Matrix; References; 4 Beyond Mean Field
Mode Locked Lasers; 4.1 Power Condensation; 4.2 Passive Mode Locking with Frequency Comb; 4.2.1 Definition of the Model; 4.2.2 Previous Studies of 4-Body Models; 4.3 Numerical Analysis; 4.3.1 Efficient Monte Carlo Simulation: The Synchronous Update; 4.3.2 Observables of Interest; 4.3.3 Details of the Simulations; 4.4 Numerical Results; 4.4.1 Lasing Threshold and Metastability
4.4.2 Phase Wave and Absence of Global Magnetization4.4.3 Two Point Correlation Functions; 4.4.4 Electromagnetic Pulse and Phase Delay; 4.4.5 Gain and Intensity Spectra; References; 5 Conclusions and Perspectives; Appendix AStability Analysis of the RS Solution; Appendix BStability Analysis of the 1RSB Solution