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Abstract Optical pulses traveling through multimode optical fibers encounter the influence of both linear disturbances and nonlinearity, resulting in a complex and chaotic redistribution of power among different modes. In our research, we explore the phenomenon where multimode fibers reach stable states marked by the concentration of energy into both single and multiple sub-systems. We introduce a weighted Bose-Einstein law, demonstrating its suitability in describing thermalized modal power distributions in the nonlinear regime, as well as steady-state distributions in the linear regime. We apply the law to experimental results and numerical simulations. Our findings reveal that, at power levels situated between the linear and soliton regimes, energy concentration occurs locally within higher-order modal groups before transitioning to global concentration in the fundamental mode within the soliton regime. This research broadens the application of thermodynamic principles to multimode fibers, uncovering previously unexplored optical states that exhibit characteristics akin to optical glass.

Abstract Novel fundamental notions helping in the interpretation of the complex dynamics of nonlinear systems are essential to our understanding and ability to exploit them. In this work we predict and demonstrate experimentally a fundamental property of Kerr-nonlinear media, which we name mode rejection and takes place when two intense counter-propagating beams interact in a multimode waveguide. In stark contrast to mode attraction phenomena, mode rejection leads to the selective suppression of a spatial mode in the forward beam, which is controlled via the counter-propagating backward beam. Starting from this observation we generalise the ideas of attraction and rejection in nonlinear multimode systems of arbitrary dimension, which paves the way towards a more general idea of all-optical mode control. These ideas represent universal tools to explore novel dynamics and applications in a variety of optical and non-optical nonlinear systems. Coherent beam combination in polarisation-maintaining multicore fibres is demonstrated as example.

ABSTRACTThe input power-induced transformation of the transverse intensity profile at the output of graded-index multimode optical fibers from speckles into a bell-shaped beam sitting on a low intensity background is known as spatial beam self-cleaning. Its remarkable properties are the output beam brightness improvement and robustness to fiber bending and squeezing. These properties permit to overcome the limitations of multimode fibers in terms of low output beam quality, which is very promising for a host of technological applications. In this review, we outline recent progress in the understanding of spatial beam self-cleaning, which can be seen as a state of thermal equilibrium in the complex process of modal four-wave mixing. In other words, the associated nonlinear redistribution of the mode powers which ultimately favors the fundamental mode of the fiber can be described in the framework of statistical mechanics applied to the gas of photons populating the fiber modes. This description has been corroborated by a series of experiments by different groups. However, some open issues still remain, and we offer a perspective for future studies in this emerging and controversial field of research.

Abstract Phase-matching of the third-harmonic generation process can be used to extend the emission of radiation from Kerr microresonators into new spectral regions far from the pump wavelength. Here, we present a theoretical mean-field model for optical frequency combs in a dissipative and nonlinear χ (3)-based cavity system with parametric coupling between fundamental and third-harmonic waves. We investigate temporally dispersive dual-comb generation of phase-matched combs with broad bandwidth and anomalous dispersion of the fundamental field, individuating conditions for accessing a multistable regime that simultaneously supports two types of coupled bright cavity solitons. These bistable cavity solitons coexist for the same pump power and frequency detuning, while featuring dissimilar amplitudes of their individual field components. Third-harmonic generation frequency combs grant telecom pump laser sources a simultaneous and direct access to both the near-infrared and the visible regions, which may prove advantageous for the development of optical clocks and sensing applications.

The beam self-cleaning effect in graded-index multimode optical fibers has several interesting potential applications, such as high-resolution nonlinear imaging and mode-locked fiber lasers. Most experimental and theoretical studies of beam self-cleaning have neglected the role of the state of polarization of light. In this work, we fill this gap by reporting extensive experimental investigations of beam self-cleaning in multimode fibers, for beams with different input states of light polarization. We found that the state of polarization undergoes a complex evolution, which may lead either to full conservation of the input state of polarization, or to nearly complete light depolarization at the fiber output. The former outcome is compelling for applications based on the beam self-cleaning effect, such as multimode mode-locked fiber lasers for micromachining, and multimode devices for microscopy and endoscopy. The latter result, instead, permits to test the limits of validity of current purely scalar theoretical approaches for describing nonlinear propagation in multimode fibers.

This research investigates the visible upconversion luminescence which is induced by multiphoton absorption of soft glass fiber defects. The study of this phenomenon has thus far been restricted to standard silica fibers. We observed the emission of green and cyan light as a consequence of fiber material ionization. We investigate both the commercial ZBLAN step index and in-house-made tellurite nanostructured graded-index fibers. For the latter, the analysis of the luminescence signal permits us to determine the core and cladding refractive index difference. Upconversion luminescence is a powerful tool for characterizing soft glass fibers and a promising platform for innovative photonic technologies and mid-IR applications.

Optical rogue waves are the optical counterpart of sudden and dramatic oceanic wave formations the underlying physics of which are thought to be connected with solitons. Here, the authors report the observation of a 2D spatial twin spotlight beam in anisotropic crystals with quadratic nonlinearity, that spontaneously appears and disappears as a function of laser beam in intensity.

In this article, we review recent advances in the technology of writing fiber Bragg gratings (FBGs) in selected cores of multicore fibers (MCFs) by using femtosecond laser pulses. The writing technology of such a key element as the FBG opens up wide opportunities for the creation of next generation fiber lasers and sensors based on MCFs. The advantages of the technology are shown by using the examples of 3D shape sensors, acoustic emission sensors with spatially multiplexed channels, as well as multicore fiber Raman lasers.

Abstract Multimode fibres provide a promising platform for boosting the capacity of fibre links and the output power of fibre lasers. The complex spatiotemporal dynamics of multimode beams may be controlled in spatial and temporal domains via the interplay of nonlinear, dispersive and dissipative effects. Raman nonlinearity induces beam cleanup in long graded-index fibres within a laser cavity, even for CW Stokes beams pumped by highly-multimode laser diodes (LDs). This leads to a breakthrough approach for wavelength-agile high-power lasers. However, current understanding of Raman beam cleanup is restricted to a small-signal gain regime, being not applicable to describing realistic laser operation. We solved this challenge by experimentally and theoretically studying pump-to-Stokes beam conversion in a graded-index fibre cavity. We show that random mode coupling, intracavity filtering and Kerr self-cleaning all play a decisive role for the spatio-spectral control of CW Stokes beams. Whereas the depleted LD pump radiation remains insensitive to them.

Abstract Beam self-cleaning (BSC) in graded-index (GRIN) multimode fibers (MMFs) has been recently reported by different research groups. Driven by the interplay between Kerr effect and beam self-imaging, BSC counteracts random mode coupling, and forces laser beams to recover a quasi-single mode profile at the output of GRIN fibers. Here we show that the associated self-induced spatiotemporal reshaping allows for improving the performances of nonlinear fluorescence (NF) microscopy and endoscopy using multimode optical fibers. We experimentally demonstrate that the beam brightness increase, induced by self-cleaning, enables two and three-photon imaging of biological samples with high spatial resolution. Temporal pulse shortening accompanying spatial beam clean-up enhances the output peak power, hence the efficiency of nonlinear imaging. We also show that spatiotemporal supercontinuum (SC) generation is well-suited for large-band NF imaging in visible and infrared domains. We substantiated our findings by multiphoton fluorescence imaging in both microscopy and endoscopy configurations.

Controlling the generation of solitons in multimode photonic systems may boost the performance of optical communication networks. Here, the conditions under which an experimentally observed walk-off multimode soliton is generated are revealed.

Abstract 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. 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. The two beams are pumped by the same input laser, yet are self-cleaned into independent multimode fibres. We thus prove that the self-cleaning mechanism preserves the beams’ mutual coherence via a noise-free parametric process. 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. Our discovery may impact theoretical approaches on wave condensation, and open new opportunities for coherent beam combining.

We experimentally demonstrate spatial beam self-cleaning in an Yb-doped graded-index multimode fiber taper, both in passive and active configurations. The input laser beam at 1064 nm was injected for propagation from the small to the large core side of the taper, with laser diode pumping in a counterdirectional configuration. The Kerr effect permits to obtain high-beam quality amplification with no accompanying frequency conversions. As a result, our nonlinear taper amplifier may provide an important building block for multimode fiber lasers and amplifiers.

Modulation instability is a universal phenomenon that can be found in a wide variety of nonlinear systems where, in the presence of a noise seed, peaks of random intensities can be generated. Several dynamical systems admit exact solutions in the form of breathers or solitons on a finite background. The vast majority of soliton studies has been restricted so far to one-dimensional systems. In contrast, the occurrences of localized structures in fully spatiotemporal systems has been only sporadically explored. In this work, we experimentally study the conditions for the wave-breaking of spatially extended optical beams in the process of second harmonic generation. Whenever the pump energy of the picosecond-long fundamental beam reaches a critical level, the beam shape at the second harmonic in a KTP crystal breaks into small filaments. These filaments exhibit extreme local intensity peaks, and their statistical distribution can be modified by the input energy of the fundamental beam. Moreover, by analyzing similar wave-breaking dynamics in a PPLN crystal in the presence of a higher nonlinear quadratic response, we observe that the spatial beam breaking may even gradually vanish as the laser intensity grows larger, leading to a spatial reshaping into a smooth and wider beam, accompanied by a substantial broadening of its temporal spectrum.

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.

Optical frequency combs are one of the most remarkable inventions in recent decades. Originally conceived as the spectral counterpart of the train of short pulses emitted by mode-locked lasers, frequency combs have also been subsequently generated in continuously pumped microresonators, through third-order parametric processes. Quite recently, direct generation of optical frequency combs has been demonstrated in continuous-wave laser-pumped optical resonators with a second-order nonlinear medium inside. Here, we present a concise introduction to such quadratic combs and the physical mechanism that underlies their formation. We mainly review our recent experimental and theoretical work on formation and dynamics of quadratic frequency combs. We experimentally demonstrated comb generation in two configurations: a cavity for second harmonic generation, where combs are generated both around the pump frequency and its second harmonic and a degenerate optical parametric oscillator, where combs are generated around the pump frequency and its subharmonic. The experiments have been supported by a thorough theoretical analysis, aimed at modelling the dynamics of quadratic combs, both in frequency and time domains, providing useful insights into the physics of this new class of optical frequency comb synthesizers. Quadratic combs establish a new class of efficient frequency comb synthesizers, with unique features, which could enable straightforward access to new spectral regions and stimulate novel applications.

Supercontinuum generation in a multicore fiber in which several uncoupled cores were doped with dissimilar concentrations of germanium was studied experimentally. Germanium doping provided control over the separation between the zero-dispersion wavelength and the 1064-nm wavelength of a Q-switched Nd:YAG pump laser. Supercontinua generated independently in each core of the same piece of fiber displayed clear and repeatable differences due to the influence of germanium doping on refractive index and four-wave mixing. The spectral evolution of the subnanosecond pump pulses injected into the different cores was accurately reproduced by numerical simulations.

We experimentally study four-wave mixing in highly nonlinear fibers using two independent and partially coherent laser pumps and a third coherent signal. We focus our attention on the Bragg-scattering frequency conversion. The two pumps were obtained by amplifying two Intracavity frequency-shifted feedback lasers working in a continuous wave regime.