Thermalization and condensation in an incoherently pumped passive optical cavity

Abstract

We study theoretically and numerically the condensation and the thermalization of classical optical waves in an incoherently pumped passive Kerr cavity. We show that the dynamics of the cavity exhibits a turbulent behavior that can be described by the wave turbulence theory. A mean-field kinetic equation is derived, which reveals that, in its high finesse regime, the cavity behaves essentially as a conservative Hamiltonian system. In particular, the intracavity turbulent field is shown to relax adiabatically toward a thermodynamic equilibrium state of energy equipartition. As a consequence of this effect of wave thermalization, the incoherent optical field undergoes a process of condensation, characterized by the spontaneous emergence of a plane wave from the incoherently pumped cavity. The condensation process is an equilibrium phase transition that occurs below a critical value of the (kinetic) energy of the incoherent pump. In spite of the dissipative nature of the cavity dynamics, the condensate fraction of the high-finesse cavity field is found in quantitative agreement with the theory inherited from the purely conservative (Hamiltonian) nonlinear Schrödinger equation.

Non-locality and collective emission in disordered lasing resonators

“…We stress that recently, the problem of light condensation has been discussed by several authors, either with reference to dissipative systems (as lasers) 17,34 or Hamiltonian dynamics; [36][37][38] ; the validity of a GP-like (or purely real Ginzburg-Landau) equation to describe the spatial distribution of energy in experiments casts new light on the investigation of these effects, for which further theoretical work is needed and will be reported elsewhere.…”

Weak Langmuir optical turbulence in a fiber cavity

“…The analysis reveals that the system exhibits, as a general rule, a turbulent dynamics. The main difference with respect to the previous works [42,53], is that we consider here a highly incoherent pump wave, in such a way that the Raman effect can no longer be neglected. The causality condition inherent to the Raman response function fundamentally changes the nature of the turbulent dynamics considered previously [42,53].…”

“…The main difference with respect to the previous works [42,53], is that we consider here a highly incoherent pump wave, in such a way that the Raman effect can no longer be neglected. The causality condition inherent to the Raman response function fundamentally changes the nature of the turbulent dynamics considered previously [42,53]. More specifically, the analysis reveals that the turbulent behavior is exclusively dominated by the Raman effect, whose kinetic description is found to be formally analogous to that used to describe weak Langmuir turbulence in plasmas [56][57][58] (also see [59,60]).…”

“…In this work we consider a passive optical fiber ring cavity pumped by an incoherent optical wave, whose coherence time, t c , is much smaller than the round-trip time, t c ≪ t R [42,52,53]. In this way, the optical beams from different cycles are mutually incoherent with one another, which makes the optical cavity non-resonant.…”

“…This irreversible process of thermalization is described in detail by the wave turbulence (WT) theory, which is inherently a nonequilibrium theory formally based on irreversible kinetic equations, as expressed by a H−theorem of entropy growth [40,41]. In particular, the WT formalism describes a process of wave condensation that can occur in an incoherently pumped passive optical cavity [42].…”