Energy and wave-action flows underlying Rayleigh-Jeans thermalization of optical waves propagating in a multimode fiber ^(a)

Abstract

The wave turbulence theory predicts that a conservative system of nonlinear waves can exhibit a process of condensation, which originates in the singularity of the Rayleigh-Jeans equilibrium distribution of classical waves. Considering light propagation in a multimode fiber, we show that light condensation is driven by an energy flow toward the higher-order modes, and a bi-directional redistribution of the wave-action (or power) to the fundamental mode and to higher-order modes. The analysis of the near-field intensity distribution provides experimental evidence of this mechanism. The kinetic equation also shows that the wave-action and energy flows can be inverted through a thermalization toward a negative temperature equilibrium state, in which the high-order modes are more populated than low-order modes. In addition, a Bogoliubov stability analysis reveals that the condensate state is stable.

Interplay of thermalization and strong disorder: Wave turbulence theory, numerical simulations, and experiments in multimode optical fibers

“…By adjusting the applied stress, we can tune the strength of mode coupling (i.e., σ). In the absence of an applied stress, polarization coupling and random coupling among degenerate modes take place: In this weak random coupling regime the energy E = j β j w j is conserved during light propagation in the MMF [23,25], as confirmed by direct experimental measurements [24,[29][30][31][32]. Here, we apply stress on the MMF to induce a random coupling among non-degenerate modes [45][46][47][48]53].…”

“…This phenomenon received a recent renewed interest with the discovery of spatial beam cleaning in multimode optical fibers (MMFs) [19][20][21]. Along this line, RJ thermalization and light condensation in MMFs have been discussed [22][23][24][25][26][27][28] and recently observed experimentally [29][30][31][32][33].…”

“…[29] for details. Here, the originality with respect to all previous experiments on beam cleaning condensation and thermalization [19][20][21][29][30][31][32], is that we introduce strong disorder in the experiment. Strong mode coupling is obtained by applying a stress to the MMF with clamps [49].…”

Weak Langmuir turbulence in disordered multimode optical fibers

“…At variance with an apparently similar phenomenon driven by the dissipative Raman effect in MMFs, known as Raman beam cleanup [27], this self-organization process is due to a purely conservative Kerr nonlinearity [26]. While the detailed understanding of spatial beam cleaning is still debated, different works indicate that certain regimes of beam selfcleaning can be described as a natural process of optical wave thermalization to thermal equilibrium [28][29][30][31][32], a feature that has been recently demonstrated experimentally [33][34][35]. This has motivated the development of a wave turbulence formalism that takes into account the structural disorder inherent to light propagation in MMFs.…”

Feynman rules for forced wave turbulence

“…A 3. This includes: elastic plate wave turbulence[8][9][10][11][12][13][14], turbulence in surface gravity waves[15][16][17][18][19], in gravitational waves[20][21][22][23], acoustic turbulence[24], planetary Rossby waves[25], waves on bubbles[26], emergent hydrodynamics[27], in a diatomic chain[28], in plasmas[29,30], optical waves[31][32][33], and rotating waves[34,35], and in FPUT chains[36].…”