Multimode optical fibres are enjoying a renewed attention, boosted by the urgent need to overcome the current capacity crunch of single-mode fibre systems and by recent advances in multimode complex nonlinear optics [1][2][3][4][5][6][7][8][9][10][11][12][13]. In this work, we demonstrate that standard multimode fibres can be used as ultrafast all-optical tool for transverse beam manipulation of high power laser pulses. Our experimental data show that the Kerr effect in a graded-index multimode fibre is the driving mechanism for overcoming speckle distortions, leading to a somewhat counter-intuitive effect resulting in a spatially clean output beam robust against fibre bending. Our observations demonstrate that nonlinear beam reshaping into the fundamental mode of a multimode fibre can be achieved even in the absence of a dissipative process such as stimulated scattering (Raman or Brillouin) [14,15].Beam propagation in multimode fibres (MMFs) is subject to a complex interplay of spatio-temporal processes. However, only few studies addressed nonlinear pulse propagation in MMFs, leaving this field largely untapped for the past thirty years. Very recently, there has been a resurgence of interest in MMFs for both fundamental and applied research. MMFs could provide a solution to meet increasing demands of new breakthrough technologies for light control and manipulation in communications, high-power fibre lasers and metrology [1,2,16]. In fundamental physics, MMFs may provide a natural tool for investigating spatiotemporal soliton dynamics [5,6], and for unveiling new, exciting nonlinear phenomena [3,4,9,13].It is well known that light experiences an inherent randomization when propagating along MMFs, whereby input laser beams of high spatial quality fade into irregular granularities called speckles. Fibre stress or bending, as well as technological irregularities of the fibre, couple different guided modes and introduce supplementary randomization of the transmission features. For this reason, MMFs are not ideally suited for beam delivery and were replaced by single-mode fibres (SMFs) since the early days of optical communications. Recent works demonstrated that specific signal-processing algorithms could be used to predict or manage the beam shape at the output of a MMF by controlling its input field [17][18][19]. In particular, the application of multiple-input, multiple-output (MIMO) digital signal processing techniques enables the use of spatial-division multiplexing based on MMFs [2]. For high-power beam delivery applications, the spontaneous recovery of spatial beam quality in MMFs has so far been experimentally achieved exclusively through nonlinear dissipative processes such as stimulated Raman scattering (SRS) [14] or stimulated Brillouin scattering (SBS) [20]. However, these techniques do not lead to any self-cleaning of the input laser beam. It is now known that for powers above a critical level (few MWs) self-phase modulation (SPM) may overcome diffraction for any size of the beam, and this may in turn c...

Spatiotemporal mode coupling in highly multimode physical systems permits new routes for exploring complex instabilities and forming coherent wave structures. We present here the first experimental demonstration of multiple geometric parametric instability sidebands, generated in the frequency domain through resonant space-time coupling, owing to the natural periodic spatial self-imaging of a multimode quasi-continuous-wave beam in a standard graded-index multimode fiber. The input beam was launched in the fiber by means of an amplified microchip laser emitting sub-ns pulses at 1064 nm. The experimentally observed frequency spacing among sidebands agrees well with analytical predictions and numerical simulations. The first-order peaks are located at the considerably large detuning of 123.5 THz from the pump. These results open the remarkable possibility to convert a near-infrared laser directly into a broad spectral range spanning visible and infrared wavelengths, by means of a single resonant parametric nonlinear effect occurring in the normal dispersion regime. As further evidence of our strong space-time coupling regime, we observed the striking effect that all of the different sideband peaks were carried by a well-defined and stable bell-shaped spatial profile.

We provide a perspective overview of the emerging field of nonlinear optics in multimode optical fibers. These fibers enable new methods for the ultrafast light-activated control of temporal, spatial, and spectral degrees of freedom of intense, pulsed beams of light, for a range of different technological applications.

We experimentally demonstrate that pumping a gradedindex multimode fiber with sub-ns pulses from a microchip Nd:YAG laser leads to spectrally flat supercontinuum generation with a uniform bell-shaped spatial beam profile extending from the visible to the mid-infrared at 2500 nm. We study the development of the supercontinuum along the multimode fiber by the cut-back method, which permits us to analyze the competition between the Kerr-induced geometric parametric instability and stimulated Raman scattering. We also performed a spectrally resolved temporal analysis of the supercontinuum emission. The strong modal confinement and the versatile dispersion engineering of single-mode fibers (SMFs) have permitted to demonstrate efficient and spatially coherent supercontinuum (SC) sources spanning from the ultra-violet to the mid-infrared (MIR) [1]. However, the small mode area of SMFs limits the accepted energy to relatively low values (less than 20 μJ for subns pulses). For this reason, SC sources based on SMFs cannot be used for applications where high pulse energies are required. Although multimode fibers (MMFs), such as graded-index (GRIN) fibers, permit the propagation of high energy pulses, these are subject to mode beating and mixing, owing to the difference of modal propagation constants and linear mode coupling. Modal interference brings a speckled intensity pattern at the MMF output, which prevents the use of MMFs whenever the preservation of spatial beam quality is required [2].Recent experiments by Krupa et al. [3] led to the unexpected discovery that Kerr nonlinearity of glass fibers above a certain threshold pulse power may lead to the generation of a selfsustained bell-shaped nonlinear beam in a highly multimode GRIN fiber. This means that linear mode mixing can be effectively washed out by means of the Kerr effect, so that a cleaned multimode light beam remains effectively selfpreserved. Kerr self-cleaning (KSC) stems from nonlinear coupling among the fundamental mode and higher-order modes [3,4]. KSC occurs at power levels at least one order of magnitude lower than the critical power of catastrophic light self-focusing in a GRIN MMF [5]. Because it is a conservative process, KSC is fundamentally different from the well-known Raman beam cleanup that is observed at the Stokes wavelength [6]. In addition, KSC occurs before a substantial pump spectral broadening has occurred [3]. For powers above the KSC threshold, nonlinear spectral broadening in MMFs results from a complex interplay between the spatial and temporal degrees of freedom [7][8][9]. Because of the self-imaging of the multimode beams in a GRIN MMF, the Kerr effect leads to a long-period intensity grating which induces mode conversion [4] and quasi-phase-matched (QPM) four-wave mixing (FWM) [10]. For temporal multimode femtosecond solitons in the anomalous dispersion regime [11], the nonlinear index grating produces an effective periodic nonlinearity which, in turn, induces a series of dispersive wave sidebands [12,13]. On the other hand, for ...

Beam self-imaging in nonlinear graded-index multimode optical fibers is of interest for many applications, such as implementing a fast saturable absorber mechanism in fiber lasers via multimode interference. We obtain a new exact solution for the nonlinear evolution of first and second order moments of a laser beam of arbitrary transverse shape carried by a graded-index multimode fiber. We have experimentally directly visualized the longitudinal evolution of beam self-imaging by means of femtosecond laser pulse propagation in both the anomalous and the normal dispersion regime of a standard telecom graded-index multimode optical fiber. Light scattering out of the fiber core via visible photo-luminescence emission permits us to directly measure the self-imaging period and the beam dynamics. Spatial shift and splitting of the self-imaging process under the action of self-focusing are also revealed.

We experimentally demonstrate that Kerr spatial self-cleaning of a pulsed beam can be obtained in an amplifying multimode optical fiber. An input peak power of 500 W only was sufficient to produce a quasi-single-mode emission from the double-clad ytterbium doped multimode fiber (YMMF) with non-parabolic refractive index profile. We compare the self-cleaning behavior observed in the same fiber with loss and with gain. Laser gain introduces new opportunities to achieve spatial self-cleaning of light in multimode fibers at a relatively low power threshold.

This corrects the article DOI: 10.1103/PhysRevLett.116.183901.

We report the experimental observation of Kerr beam self-cleaning in a graded-index multimode fiber, leading to output beam profiles different from a bell shape, close to the LP01 mode. For specific coupling conditions, nonlinear coupling among the guided modes can reshape the output speckle pattern generated by a pulsed beam into the low order LP11 mode. This was observed in a few meters long multimode fiber with 750 ps pulses at 1064 nm in the normal dispersion regime. The power threshold for LP11 mode self-cleaning was about three times larger than that required for Kerr nonlinear selfcleaning into the LP01 mode.Multimode optical fibers (MMFs) are currently extensively revisited for communication applications, and because they provide a convenient experimental platform for the investigation of complex space-time nonlinear dynamics. Various nonlinear propagation phenomena have been theoretically predicted to occur in multimode fibers since the eighties [1-5], but it is not until recently that some of them were actually observed. Consider, for instance, multimode optical solitons [6] and geometric parametric instability (GPI) [7]. On the other hand, experiments on nonlinear propagation in multimode fibers have recently revealed an unexpected effect that was named Kerr beam self-cleaning. It consists in the reshaping, at high powers, of the speckled output intensity pattern into a bell-shaped beam close to the fundamental LP01 mode of a graded index (GRIN) MMF. Such nonlinear beam evolution was observed at power levels below the threshold for frequency conversion, as well as below the self-focusing threshold, with subnanosecond to femtosecond pulses propagating in the normal dispersion regime [7][8][9][10]. It is generally admitted today that Kerr self-cleaning results from a complex nonlinear coupling, or fourwave mixing (FWM) interaction among a large population of guided modes. Namely, the combination of spatial self-induced periodic imaging and Kerr nonlinearity creates a periodic longitudinal modulation of the refractive index of the fiber core. This permits quasi-phase matching and energy exchange between guided modes by means of FWM [11]. The nonlinear energy exchange between the fundamental mode and the high-order modes (HOMs) exhibits a nonreciprocal behavior, driven by self-phase modulation [8,12]. In these conditions, all the energy transferred in the fundamental mode remains definitively trapped, which explains the robust nature of the self-cleaning process. Besides that model, alternative concepts based on instability of the HOMs [10], or on modified wave turbulence theory [4] have been introduced, which could also explain the unconventional spatial dynamics observed in MMFs.In this Letter, we report the experimental demonstration of Kerr beam self-cleaning in favor of the LP11 mode of a gradient index (GRIN) MMF. This is quite unexpected, since all previous works on Kerr beam self-cleaning, based on either numerical investigations or experiments, reported self-cleaning of the output field into a smo...