Cross phase coherence11/29/2023 ![]() Indeed, Maxwell’s equations in the paraxial approximation lead to a model analogous to the Gross–Pitaievskii equation 22, which describes the mean-field dynamics of a three-dimensional Bose–Einstein condensate density (i.e., order parameter): the linear refractive index profile plays the role of a trapping potential, and cubic nonlinearity corresponds to boson–boson interactions 21. Our findings confirm the hydrodynamic picture of multimode beam propagation as a fluid of light. In this regime, the hydrodynamic features of light are well-known in guided wave optics: in the framework of nonlinear interactions within multidimensional systems such as MMFs, optical beams are often referred to as a “ fluids of light” 21. While photons do not interact in vacuum, the interplay between photons of a light beam is however possible in a nonlinear medium. In the latter case, the collective beam dynamics has a direct hydrodynamic analogy with the order parameter of a three-dimensional boson gas: multimode beam condensation is predicted to emerge from turbulent wave mixing 18, 19, 20. Interestingly, in multimode systems, the spontaneous emergence of beam cleanup has been observed, potentially mediated by photon interactions with optical 11 or acoustic 12 phonons, or by direct photon–photon interactions 13, 14, 15, 16, 17. Nonlinear multimode fibres (MMFs) permit orders of magnitude scaling of power from fibre lasers, the workhorse of industrial laser applications 7, 8, 9, and improved resolution for multiphoton microscopy and endoscopic imaging 2, 10. These fibres enable also the new frontier of spatial-division-multiplexed optical communications 2, 3, 4, 5, where nonlinearity remains the main limitation to system capacity 6. Interest in nonlinear multimode and multicore optical fibre systems has recently surged 1, 2. Our discovery may impact theoretical approaches on wave condensation, and open new opportunities for coherent beam combining. While directly related to the initial pump coherence, the emergence of nonlinear spatial coherence is achieved without additional noise, even for self-cleaning obtained on different modes, and in spite of the fibre structural disorder originating from intrinsic imperfections or external perturbations. We thus prove that the self-cleaning mechanism preserves the beams’ mutual coherence via a noise-free parametric process. The two beams are pumped by the same input laser, yet are self-cleaned into independent multimode fibres. Here, we reveal that we can generate two self-cleaned beams with a mutual coherence large enough to produce a clear stable fringe pattern at the output of a nonlinear interferometer. A low intensity light beam emerges from a graded-index, highly multimode optical fibre with a speckled shape, while at higher intensity the Kerr nonlinearity may induce a spontaneous spatial self-cleaning of the beam. ![]()
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