General Phase Diagram of Multimodal Ordered and Disordered Lasers in Closed and Open Cavities

Abstract

We present a unified approach to the theory of multimodal laser cavities including a variable amount of structural disorder. A general mean-field theory is studied for waves in media with variable nonlinearity and randomness. Phase diagrams are reported in terms of optical power, degree of disorder, and degree of nonlinearity, tuning between closed and open cavity scenarios. In the thermodynamic limit of infinitely many modes, the theory predicts four distinct regimes: a continuous wave behavior for low power, a standard mode-locking laser regime for high power and weak disorder, a random laser for high pumped power and large disorder, and a novel intermediate regime of phase locking occurring in the presence of disorder but below the lasing threshold.

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

“…Subsequent demonstrations of RSB appeared in 1D erbium-doped random fiber laser [4,5] and 3D functionalized TiO 2 particle-based dye-colloidal [3] and neodymium-doped YBO 3 solid-state [2] RLs. In these cavityless systems, the manifestation of RSB concurs with the settlement of a glassy phase of light -a photonic spin-glass phase, in which the modes are nontrivially correlated though displaying incoherent oscillation [6][7][8][9][10][11][12][13]. The threshold separating the prelasing regime with amplified spontaneous emission (ASE) and the RL behavior thus…”

“…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.…”