Mode-locking transitions in nano-structured weakly disordered lasers

Abstract

We report on a statistical approach to mode-locking transitions of nano-structured laser cavities characterized by an enhanced density of states. We show that the equations for the interacting modes can be mapped onto a statistical model exhibiting a first order thermodynamic transition, with the average mode-energy playing the role of inverse temperature. The transition corresponds to a phase-locking of modes. Extended modes lead to a mean-field like model, while in presence of localized modes, as due to a small disorder, the model has short range interactions. We show that simple scaling arguments lead to observable differences between transitions involving extended modes and those involving localized modes. We also show that the dynamics of the light modes can be exactly solved, predicting a jump in the relaxation time of the coherence functions at the transition. Finally, we link the thermodynamic transition to a topological singularity of the phase space, as previously reported for similar models.

10 pages, 5 figures

References in corpus (19)

• Geometric approach to Hamiltonian dynamics and statistical mechanics
• Saddles in the energy landscape probed by supercooled liquids
• Spatial Extent of Random Laser Modes
• Geometry of dynamics, Lyapunov exponents and phase transitions
• A Theorem on the origin of Phase Transitions
• Glassy behavior of light
• Topological Signature of First Order Phase Transitions
• Phase transitions and topology changes in configuration space
• Glassy behavior of light in random lasers
• Topological Origin of the Phase Transition in a Model of DNA Denaturation
• Topology and phase transitions: from an exactly solvable model to a relation between topology and thermodynamics
• Unattainability of a purely topological criterion for the existence of a phase transition for non-confining potentials
• Complex dynamics and configurational entropy of spatial optical solitons in nonlocal media
• The topological hypothesis on phase transitions: the simplest case
• Complex light: Dynamic phase transitions of a light beam in a nonlinear non-local disordered medium
• Topological properties of the mean field phi^4 model
• On the relationship between phase transitions and topological changes in one dimensional models
• Dynamics and geometric properties of the k-Trigonometric model
• Saddles and dynamics in a solvable mean-field model

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• Improved Pseudolikelihood Regularization and Decimation methods on Non-linearly Interacting Systems with Continuous Variables
• Phase transitions and topology in 2+k XY mean-field models