Wave condensation with weak disorder versus beam self-cleaning in multimode fibers

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

“…Recent works suggested that this phenomenon of beam self-cleaning can be interpreted as a consequence of a wave thermalization and condensation process [38][39][40][41][42]. In particular, a wave turbulence kinetic equation (KE) describing this effect has been derived in [38,39]. This process has been experimentally demonstrated in a recent work [43], where the condensate fraction across the transition to condensation has been found in agreement with the RJ equilibrium theory.…”

“…2 plausible experimental values ℓ c = 0.3m and 2π/σ = 2.14m [49]. For these parameters disorder no longer dominates nonlinear effects (L d ∼ L nl ), and strictly speaking the KE ( 2) is no longer valid [39]. However, the scaling predicted by the KE, namely that thermalization is accelerated by decreasing the disorder (see the parameter ∆β in the denominator of ( 2)) is responsible for a fast process of condensation for the small disorder considered in Fig.…”

“…In its most general form that conserves the wave-action N = p |a p | 2 , the Hermitian matrices D p (z) are expanded into the Pauli matrices σ j , D p (z) = 3 j=0 ν p,j (z)σ j , where σ 0 is the identity matrix and ν p,j (z) are independent and identically distributed real-valued random processes, with variance σ 2 and correlation length ℓ c . Introducing the parameter ∆β = σ 2 ℓ c , the characteristic length scale of disorder is L d = 1/∆β [39]. Finally note that since the disorder is ("time") z dependent, our system is of different nature than those studying the interplay of thermalization and Anderson localization [24].…”

“…Kinetic equation.-It is important to recall that our experiments are carried out in the weakly nonlinear regime L lin ∼ 1/β 0 ≪ L nl ∼ 1/(γN ) [43], and that linear propagation effects dominate disorder effects, L lin ≪ L d (or ∆β ≪ β 0 ). According to this latter separation of spatial scales, turbulence in MMFs is described by a discrete wave turbulence approach [38,39], which means that only exact resonances contribute to the KE, while quasiresonances can be neglected [8]. Indeed, assuming that disorder effects dominate nonlinear effects L d ≪ L nl , we have derived a discrete wave turbulence KE that describes the nonequilibrium evolution of the averaged modal components n p (z) = |a p | 2 (z) during the propagation through the fiber [38,39]:…”

Two octave supercontinuum generation in a non-silica graded-index multimode fiber

“…Understanding the physics of complex nonlinear optical systems has been the focus of intense research in recent years and, in this context, the generation of broadband supercontinuum in graded-index multimode fibers (GRIN MMFs) has attracted particular attention [1][2][3][4][5][6][7][8]. In addition to multimode fibers providing additional degrees of freedom to optimize supercontinuum for specific applications, the spatio-temporal propagation in such fibers reveals a rich landscape of nonlinear dynamics, with close links to universal phenomena such as wave turbulence [9][10][11][12].…”