Hydrodynamic 2D Turbulence and Spatial Beam Condensation in Multimode Optical Fibers.

E V Podivilov,S Turitsyn,V A Gonta,K Krupa,M P Fedoruk,S Wabnitz,O S Sidelnikov,D S Kharenko,S A Babin

doi:10.1103/physrevlett.122.103902

Abstract

We show that Kerr beam self-cleaning results from parametric mode mixing instabilities that generate a number of nonlinearly interacting modes with randomized phases-optical wave turbulence, followed by a direct and inverse cascade towards high mode numbers and condensation into the fundamental mode, respectively. This optical self-organization effect is an analogue to wave condensation that is well known in hydrodynamic 2D turbulence.

Highlights

We show that Kerr beam self-cleaning results from parametric mode mixing instabilities that generate a number of nonlinearly interacting modes with randomized phases—optical wave turbulence, followed by a direct and inverse cascade towards high mode numbers and condensation into the fundamental mode, respectively
It is well known that linear wave propagation in MMFs is affected by random mode coupling, which leads to highly irregular speckled intensity patterns at the fiber output, even when the fiber is excited with a high quality, diffraction limited input beam
Recent experiments [6,7,8,9] have surprisingly discovered that the intensity dependent contribution to the refractive index, or Kerr effect, has the capacity to counteract such random mode coupling in a graded index (GRIN) MMF, leading to the formation of a highly robust nonlinear beam

Summary

Published by the American Physical Society

To that of transverse nonlinear optics in multimode fibers, we provide a fascinating connection that will be of special appeal to a wide physics community. Cross fertilization from the hydrodynamic approach and complex transverse spatial pattern formation in multimode optical fibers will pave the way for substantial progress in this emerging field of research, and could shed new light on other phenomena, such as spatial mode cleaning of beam filamentation in air [17,18]. The equation for the field amplitude E 1⁄4 Aðz; r⃗ Þ × expðiωt − ikpzÞffiffiffiffiiffinffiffiffiffiffiffiaffiffiffiffiGffiffi RIN fiber [with refractive index nðz; r⃗ Þ 1⁄4 n0 1 − Δ2r2 þ n2I þ δnðz; r⃗ Þ] reads as. Terms in the right-hand side denote nonlinearity, angular dispersion, and random refractive index fluctuations. The equation for the normalized envelope Ψ reads as. Xmþm11⁄4m2þm pþp11⁄4p2þp þ Cnm;m1 ðζÞBp1;m1 δð2p1 þ jm1j − 2p − jmjÞ: ð4Þ m1 ;p1

An important physical insight into the mechanism for

Findings

Raman threshold