Nonlinear beam self-imaging and self-focusing dynamics in a GRIN multimode optical fiber: theory and experiments

Spatiotemporal mode-locking and dissipative solitons in multimode fiber lasers

Multimode fiber (MMF) lasers are emerging as a remarkable testbed to study nonlinear spatiotemporal physics with potential applications spanning from high energy pulse generation, precision measurement to nonlinear microscopy. The underlying mechanism for the generation of ultrashort pulses, which can be understood as a spatiotempoal dissipative soliton (STDS), in the nonlinear multimode resonators is the spatiotemporal mode-locking (STML) with simultaneous synchronization of temporal and spatial modes. In this review, we first introduce the general principles of STML, with an emphasize on the STML dynamics with large intermode dispersion. Then, we present the recent progress of STML, including measurement techniques for STML, exotic nonlinear dynamics of STDS, and mode field engineering in MMF lasers. We conclude by outlining some perspectives that may advance STML in the near future.

Robust Three-Dimensional High-Order Solitons and Breathers in Driven Dissipative Systems: A Kerr Cavity Realization

We present a general approach to excite robust dissipative three-dimensional and high-order solitons and breathers in passively driven nonlinear cavities. Our findings are illustrated in the paradigmatic example provided by an optical Kerr cavity with diffraction and anomalous dispersion, with the addition of an attractive three-dimensional parabolic potential. The potential breaks the translational symmetry along all directions, and impacts the system in a qualitatively unexpected manner: three-dimensional solitons, or light bullets, are the only existing and stable states for a given set of parameters. This property is extremely rare, if not unknown, in passive nonlinear systems. As a result, the excitation of the cavity with any input field leads to the deterministic formation of a target soliton or breather, with a spatiotemporal profile that unambiguously corresponds to the given cavity and pumping conditions. In addition, the tuning of the potential width along the temporal direction results in the existence of a plethora of stable asymmetric solitons. Our results may provide a solid route toward the observation of dissipative light bullets and three-dimensional breathers.

Spatiotemporal analysis of an all-fiber multimode interference-based saturable absorber via a mode-resolved nonlinear Schrodinger equation

This paper presents an approach that combines the generalized multimode nonlinear Schrodinger equation with a transmission model to analyze spatiotemporal characteristics of multimode interference in single mode/large mode area fiber-graded-index multimode fiber-single mode fiber (SMF/LMA-GIMF-SMF) structures for the first time. Approximated self-imaging (ASIM) behavior in GIMF and the study of the latter structure used in spatiotemporal mode-locked fiber lasers are first demonstrated. Simulations show that these structures can work as saturable absorbers enabling high-energy pulse output due to nonlinear intermodal interactions and intensity-dependent multimode interference. Otherwise, underlying ASIM is proven that it can perturb the transmission of SMF/LMA-GIMF-SMF, causing instability of their saturable-absorption characteristics. This paper provides a theoretical guide for many applications, such as beam shaping, mode conversion, and high-energy ultrafast fiber laser.

Multimode soliton collisions in graded-index optical fibers

In this work, we unveil the unique complex dynamics of multimode soliton interactions in graded-index optical fibers through simulations and experiments. By generating two multimode solitons from the fission of an input femtosecond pulse, we examine the evolution of their Raman-induced red-shift when the input pulse energy grows larger. Remarkably, we find that the output red-shift of the trailing multimode soliton may be reduced, so that it accelerates until it collides with the leading multimode soliton. As a result of the inelastic collision, a significant energy transfer occurs between the two multimode solitons: the trailing soliton captures energy from the leading soliton, which ultimately enhances its red-shift, thus increasing temporal separation between the two multimode solitons.

Continuous spatial self-cleaning in GRIN multimode fiber for self-referenced multiplex CARS imaging

We demonstrate how spatial beam self-cleaning and supercontinuum generation in graded-index multimode optical fibers can be directly applied in multiplex coherent anti-Stokes Raman Scattering (M-CARS) spectroscopy. Although supercontinuum generation causes pump depletion mainly in the center of the beam, the partial recovery of the pump brightness due to self-cleaning may enable self-referenced M-CARS, with no additional delay lines to synchronize pump and Stokes waves. As a proof-of-principle, we report examples of imaging of single chemical compounds and polystyrene beads. The new scheme paves the way towards simpler M-CARS systems based on multimode fiber sources.

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

The generation of a two-octave supercontinuum from the visible to mid-infrared (700-2800 nm) in a non-silica graded-index multimode fiber is reported. The fiber design is based on a nanostructured core comprised of two types of drawn lead-bismuth-gallate glass rods with different refractive indices. This yields an effective parabolic index profile and ten times increased nonlinearity when compared to silica fibers. Using femtosecond pulse pumping at wavelengths in both normal and anomalous dispersion regimes, a detailed study is carried out into the supercontinuum generating mechanisms and instabilities seeded by periodic self-imaging. Significantly, suitable injection conditions in the high power regime are found to result in the output beam profile showing clear signatures of beam self-cleaning from nonlinear mode mixing. Experimental observations are interpreted using spatio-temporal 3+1D numerical simulations of the generalized nonlinear Schrödinger equation, and simulated spectra are in excellent agreement with experiment over the full two-octave spectral bandwidth. Experimental comparison with the generation of supercontinuum in a silica graded-index multimode fiber shows that the enhanced nonlinear refractive index of the lead-bismuth-gallate fiber yields a spectrum with a significantly larger bandwidth. These results demonstrate a new pathway towards the generation of bright, ultrabroadband light sources in the mid-infrared.

Variation of self-imaging length in multimode waveguides beyond the paraxial approximation

We demonstrate the precise variation of self-imaging distance with width of a Gaussian input, centrally fed into a symmetric dielectric slab waveguide of width ∼20λ₀. The width of the Gaussian is varied from the paraxial to completely nonparaxial domain. Unlike the paraxial case, the self-imaging distance is found to depend on the beam width and change with the number of excited modes in the waveguide. These features should be useful in designing devices that exploit self-imaging for improved efficiency, especially in nanophotonic circuits.

Statistical mechanics of beam self-cleaning in GRIN multimode optical fibers

Since its first demonstration in graded-index multimode fibers, spatial beam self-cleaning has attracted a growing research interest. It allows for the propagation of beams with a bell-shaped spatial profile, thus enabling the use of multimode fibers for several applications, from biomedical imaging to high-power beam delivery. So far, beam self-cleaning has been experimentally studied under several different experimental conditions. Whereas it has been theoretically described as the irreversible energy transfer from high-order modes towards the fundamental mode, in analogy with a beam condensation mechanism. Here, we provide a comprehensive theoretical description of beam self-cleaning, by means of a semi-classical statistical mechanics model of wave thermalization. This approach is confirmed by an extensive experimental characterization, based on a holographic mode decomposition technique, employing laser pulses with temporal durations ranging from femtoseconds up to nanoseconds. An excellent agreement between theory and experiments is found, which demonstrates that beam self-cleaning can be fully described in terms of the basic conservation laws of statistical mechanics.

Multimode solitons in step-index fibers

We experimentally generate multimode solitons in step-index fibers, where nonlinearity compensates for both chromatic and modal dispersion. These solitons are subject to Raman self-frequency shift, and their energy is gradually transfered to the fundamental fiber mode. We compare multimode soliton dynamics in both step-index and graded index fibers, in excellent agreement with numerical predictions.

Helical plasma filaments from the self-channeling of intense femtosecond laser pulses in optical fibers

We experimentally and numerically study the ignition of helical-shaped plasma filaments in standard optical fibers. Femtosecond pulses with megawatt peak power with proper off-axis and tilted coupling in the fiber core produce plasma skew rays. These last for distances as long as 1000 wavelengths thanks to a combination of linear waveguiding and the self-channeling effect. Peculiar is the case of graded-index multimode fibers; here the spatial self-imaging places constraints on the helix pitch. These results may find applications for fabricating fibers with helical-shaped core micro-structuration as well as for designing laser components and three-dimensional optical memories.

Rainbow Archimedean spiral emission from optical fibres

We demonstrate a new practical approach for generating multicolour spiral-shaped beams. It makes use of a standard silica optical fibre, combined with a tilted input laser beam. The resulting breaking of the fibre axial symmetry leads to the propagation of a helical beam. The associated output far-field has a spiral shape, independently of the input laser power value. Whereas, with a high-power near-infrared femtosecond laser, a visible supercontinuum spiral emission is generated. With appropriate control of the input laser coupling conditions, the colours of the spiral spatially self-organize in a rainbow distribution. Our method is independent of the laser source wavelength and polarization. Therefore, standard optical fibres may be used for generating spiral beams in many applications, ranging from communications to optical tweezers and quantum optics.

Depolarization of Light in Optical Fibers: Effects of Diffraction and Spin-Orbit Interaction

Polarization is measured very often to study the interaction of light and matter, so the description of the polarization of light beams is of both practical and fundamental interest. This review discusses the polarization properties of structured light in multimode graded-index optical fibers, with an emphasis on the recent advances in the area of spin-orbit interactions. The basic physical principles and properties of twisted light propagating in a graded index fiber are described: rotation of the polarization plane, Laguerre–Gauss vector beams with polarization-orbital angular momentum entanglement, splitting of degenerate modes due to spin-orbit interaction, depolarization of light beams, Berry phase and 2D and 3D degrees of polarizations, etc. Special attention is paid to analytical methods for solving the Maxwell equations of a three-component field using perturbation analysis and quantum mechanical approaches. Vector and tensor polarization degrees for the description of strongly focused light beams and their geometrical interpretation are also discussed.

Experimental observation of self-imaging in SMF-28 optical fibers

Spatial self-imaging, consisting of the periodic replication of the optical transverse beam profile along the propagation direction, can be achieved in guided wave systems when all excited modes interfere in phase. We exploited material defects photoluminescence for directly visualizing self-imaging in a few-mode, nominal singlemode SMF-28 optical fiber. Visible luminescence was excited by intense femtosecond infrared pulses via multiphoton absorption processes. Our method permits us to determine the mode propagation constants and the cutoff wavelength of transverse fiber modes.

Complex colloidal structures with non-linear optical properties formed in an optical trap

Illumination of a colloidal suspension of dielectric nanoparticles (50 nm in radius) with counter-propagating non-interfering laser beams of sufficient power leads to spatial redistribution of particles due to associated optical forces and formation of colloidal structures composed of thousands of nanoparticles along the beams. We employ a weak probe beam propagating through the colloidal structure and demonstrate that the colloidal structure acts effectively as a non-linear optical medium, similar to a gradient index lens, with optical transformation properties externally tunable by trapping laser power. With an increasing number of nanoparticles we observe the formation of a more complex colloidal structure axially and even laterally and we explain the origin of this process.