## Statistical Physics of Wave Interactions: A Unified Approach to Mode-Locking and Random LasersThis thesis reveals the utility of pursuing a statistical physics approach in the description of wave interactions in multimode optical systems. To that end, the appropriate Hamiltonian models are derived and their limits of applicability are discussed. The versatility of the framework allows the characterization of ordered and disordered lasers in open and closed cavities in a unified scheme, from standard mode-locking to random lasers. With the use of replica method and Monte Carlo simulations, the models are categorized on the basis of universal properties, and nontrivial predictions of experimental relevance are obtained. In particular, the approach makes it possible to nonperturbatively treat the interplay between disorder and nonlinearity and to envisage novel and fascinating physical phenomena such as glassy random lasers, providing a novel way to experimentally investigate replica symmetry breaking. |

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### Contents

1 | |

2 Multimode Laser Theory for Open Cavities | 9 |

3 Analytic Solution of the NarrowBandwidth Model | 39 |

4 Beyond Mean FieldMode Locked Lasers | 93 |

5 Conclusions and Perspectives | 124 |

Appendix AStability Analysis of the RS Solution | 129 |

Appendix BStability Analysis of the 1RSB Solution | 137 |

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Statistical Physics of Wave Interactions: A Unified Approach to Mode-Locking ... Fabrizio Antenucci No preview available - 2016 |

### Common terms and phrases

1RSB phase 1RSB solution Antenucci approximation complex corresponding coupling Crisanti defined distribution dynamics eigenvalue electromagnetic emission experimental finite fixed free energy frequency comb gain curve Glassy behavior Hamiltonian intensity fluctuation overlap interaction Ising model Langevin equation lasing modes lasing threshold Lett Leuzzi linear locking lasers magnetization matrix mean field mean-field approximation metastable mode locking mode-locked lasers Monte Carlo noise nonlinear nontrivial number of quadruplets obtained optical optical bistability overlap matrices particular passive mode locking peaks Phase diagram phase transition Phase Wave photonic photonic parameters Phys pumping rate Quantum quenched disorder random lasers replica symmetry breaking resonator Sect slow amplitude modes spectra spectrum spherical constraint spin Spin Glass spin-glass spinodal line stationarity equations statistical mechanics Statistical Physics temperature theory thermodynamic zero