Statistical mechanics models for multimode lasers and random lasers

Abstract

We review recent statistical mechanical approaches to multimode laser theory. The theory has proved very effective to describe standard lasers. We refer of the mean field theory for passive mode locking and developments based on Monte Carlo simulations and cavity method to study the role of the frequency matching condition. The status for a complete theory of multimode lasing in open and disordered cavities is discussed and the derivation of the general statistical models in this framework is presented. When light is propagating in a disordered medium, the system can be analyzed via the replica method. For high degrees of disorder and nonlinearity, a glassy behavior is expected at the lasing threshold, providing a suggestive link between glasses and photonics. We describe in details the results for the general Hamiltonian model in mean field approximation and mention an available test for replica symmetry breaking from intensity spectra measurements. Finally, we summary some perspectives still opened for such approaches.Comment: 16 pages, 7 figure

Lévy Statistics and Glassy Behavior of Light in Random Fiber Lasers

“…On the other hand, in the RL regime above the threshold the modes acquire phase coherence and nontrivial correlations (see below), similarly to the spin-glass phase at low temperatures in disordered magnets. Moreover, as also reported for spin-glass systems [84], the RL regime presents the property of RSB [73][74][75][76][77][78][79][80].…”

“…A great advance in the theoretical understanding of the combined effect of amplification, nonlinearity, and disorder in RL systems was put forward in a series of articles [73][74][75][76][77][78][79][80][81][82] published along the last decade. We start by reviewing the theoretical background [73][74][75][76][77][78][79][80] underlying the variety of photonic behaviors displayed by RLs, which relies its basis on the Langevin equations that drive the dynamics of the complex slow-amplitudes modes ( ),…”

“…We start by reviewing the theoretical background [73][74][75][76][77][78][79][80] underlying the variety of photonic behaviors displayed by RLs, which relies its basis on the Langevin equations that drive the dynamics of the complex slow-amplitudes modes ( ),…”

Replica Symmetry Breaking in the Photonic Ferromagneticlike Spontaneous Mode-Locking Phase of a Multimode Nd:YAG Laser

“…Consequently, identical systems prepared under identical conditions (system replicas) can reach different states with different measures of observable quantities and nontrivial correlation patterns in a replica symmetry breaking scenario. Later on, the scope of this concept was much extended to reach other complex systems [14], including neural networks and structural glasses.In the photonic context, theoretical predictions of RSB behavior emerged in the last decade [6][7][8][9][10][11][12][13], mainly related to the properties of multimode random lasers (RLs). In the photonic-to-magnetic analogy, the mode amplitudes play the role of the spins and the excitation pumping energy acts as the inverse temperature.…”

“…In the photonic context, theoretical predictions of RSB behavior emerged in the last decade [6][7][8][9][10][11][12][13], mainly related to the properties of multimode random lasers (RLs). In the photonic-to-magnetic analogy, the mode amplitudes play the role of the spins and the excitation pumping energy acts as the inverse temperature.…”