This letter is to pave the way towards the demonstration of spatiotemporal similariton pulses evolution in passive multimode fibers with Raman amplification. We present numerically these issues in a graded-index and step-index multimode fibers and provide a first look at the complex spatiotemporal dynamics of similariton pulses. The results showed that the similariton pulses can be generated in both multimode fibers. The temporal and the spectral evolution of the pulses can be characterized as parabolic shapes with linear chirp and kW peak power. By compressed these, high energy femtoseconds pulses can be obtained starting initial picoseconds pulses. Spatial beam profile could be preserved in both multimode fibers under the predominantly excitation of the fundamental mode. Specifically, Raman amplification and similariton pulses generation in graded-index multimode fiber improves the spatial beam cleaning process under the different initial condition.
Spatiotemporal mode-locking in a laser with anomalous dispersion is investigated. Mode-locked states with varying modal content can be observed, but we find it difficult to observe highly multimode states. We describe the properties of these mode-locked states and compare them to the results of numerical simulations. Prospects for the generation of highly-multimode states and lasers based on multimode soliton formation are discussed.
Experimental and numerical studies of spatiotemporal femtosecond soliton propagation over up to 1 km spans of parabolic graded-index (GRIN) fibers reveal that initial multimode soliton pulses naturally and irreversibly evolve into a singlemode soliton. This is carried by the fundamental mode of the fiber, which acts as a dynamical attractor of the multimode system for up to the record value (for multimode fibers) of 5600 chromatic dispersion distances. This experimental evidence invalidates the use of variational approaches, which intrinsically require that the initial multimode propagation of…
In this Letter, we demonstrate, to the best of our knowledge, the first spatiotemporally mode-locked fiber laser with self-similar pulse evolution. The multimode fiber oscillator generates parabolic amplifier similaritons at 1030 nm with 90 mW average power, 2.3 ps duration, and 37.9 MHz repetition rate. Remarkably, we observe experimentally a near-Gaussian beam quality (M^2<1.4) at the output of the highly multimode fiber. The output pulses are compressed to 192 fs via an external grating compressor. Numerical simulations are performed to investigate the cavity dynamics which confirm experime…
We demonstrate an all-fiber spatiotemporal mode-locked laser based on graded-index multimode fiber. Due to the high damage threshold of graded-index multimode fiber devices, the output single-pulse energy reach up to 11.67 nJ. The beam quality at mode-locked state is significantly improved compared with continuous wave state as a result of the self-cleaning effect. By amplifying the pulse in the multimode fiber amplifier, high power pulses with high beam quality can be obtained in the all-fiber system based on graded-index MMFs.
We shape fs optical pulses and deliver them in a single spatial mode to the input of a multimode fiber. The pulse is shaped in time such that at the output of the multimode fiber an ultrashort pulse appears at a predefined focus. Our result shows how to raster scan an ultrashort pulse at the output of a stiff piece of square-core step-index multimode fiber and in this way the potential for making a nonlinear fluorescent image of the scene behind the fiber, while the connection to the multimode fiber can be established via a thin and flexible single-mode fiber. The experimental results match ou…
We experimentally demonstrate that pumping a graded-index 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 emissi…
We experimentally isolate and directly observe multimode solitons in few-mode graded-index fiber. By varying the input energy and modal composition of the launched pulse, we observe a continuous variation of multimode solitons with different spatiotemporal properties. They exhibit an energy-volume relation that is distinct from those of single-mode and fully spatiotemporal solitons.
Spatiotemporal nonlinear interactions in multimode fibers are of interest for beam shaping and frequency conversion by exploiting the nonlinear propagation of different pump regimes from quasi-continuous wave to ultrashort pulses centered around visible to infrared pump wavelengths. The nonlinear effects in multi-mode fibers depend strongly on the excitation condition, however relatively little work has been reported on this subject. Here, we present the first machine learning approach to learn and control the nonlinear frequency conversion inside multimode fibers by tailoring the excitation c…
We demonstrate the first multimode fiber interference-based filtering in an all-fiber spatiotemporally mode-locked laser. The oscillator generates dissipative soliton pulses at 1036 nm with 12 mW average power, 6.24 ps duration and 24.3 MHz repetition rate. The reported pulse energy (0.5 nJ) represents ~4 times improvement over the previously reported single-mode all-normal dispersion mode-locked lasers with multimode interference-based filtering. Numerical simulations are performed to reveal cavity and spatiotemporal mode-locking dynamics. The proposed oscillator presents an alternative appro…
In this contribution a numerical model is developed to study the time dynamics of photoluminescence emitted by Tb3+ doped multimode chalcogenide-selenide glass fibers pumped by laser light at approximately 2 microns. The model consists of a set of partial differential equations (PDEs), which describe the temporal and spatial evolution of the photon density and level populations within the fiber. In order to solve numerically the PDEs a Method of Lines is applied. The modeling parameters are extracted from measurements and from data available in the literature. The numerical results obtained su…
Spatiotemporal solitons (STSs) are localized solitary waves in both space and time that involve complex linear and nonlinear processes. Optical STSs have been observed in various media, but they are difficult to be realized in multimode fibers due to their large modal dispersion. Here, we report STS mode-locking and spatiotemporal nonlinear dynamics in a step-index multimode fiber mediated by gain. Gain competition and energy redistribution among different spatial modes help nonlinearity effectively cancel both temporal splitting and spatial diffracting of the entire pulse (multicomponent soli…
Despite the abundance and importance of three-dimensional systems, relatively little progress has been made on spatiotemporal nonlinear optical waves compared to time-only or space-only systems. Here we study radiation emitted by three-dimensionally evolving nonlinear optical waves in multimode fiber. Spatiotemporal oscillations of solitons in the fiber generate multimode dispersive wave sidebands over an ultrabroadband spectral range. This work suggests routes to multipurpose sources of coherent electromagnetic waves, with unprecedented wavelength coverage.
We develop a spatiotemporal mode decomposition technique to study the mode power distribution of ultrashort pulses emerging from long spans of graded-index multimode fiber, for different input laser conditions. We find that beam mode power content in the dispersive pulse propagation regime can be described by the Bose-Einstein law, as a result of the process of power diffusion from linear and nonlinear mode coupling among nondegenerate mode groups. In the soliton regime, the output mode power distribution approaches the Rayleigh-Jeans law
In this paper, we investigate for the first time, the spatiotemporal dynamics of self-similar parabolic pulse evolution in multimode fibers (MMFs). We present numerical predictions of the existence of parabolic pulse in a graded and step index MMFs and demonstrate that the parabolic pulse formation process could have a prominent effect on the spatiotemporal behavior in both fibers. We study the effect of the input pulse energy and its initial modal composition on the resulting parabolic pulse and the corresponding spatial beam profile. When the fundamental mode is mostly excited, the pulse evo…
Period-doubling bifurcation is a universal dynamic of nonlinear systems, which has been extensively investigated in laser systems with a single transverse mode. This study presents an experimental observation and theoretical investigation of the period-doubling bifurcation in spatiotemporal mode-locked (STML) multimode fiber lasers. In the period-doubling state, it is observed that the pulse train modulation varies with the transverse-mode, and the output beam profile fluctuates rapidly and periodically. The numerical simulations conducted in this study are in good agreement with the experimen…
We present a spatiotemporally mode-locked Mamyshev oscillator. A wide variety of multimode mode-locked states, with varying degrees of spatiotemporal coupling, are observed. We find that some control of the modal content of the output beam is possible through the cavity design. Comparison of simulations to experiments indicates that spatiotemporal mode-locking is enabled by nonlinear intermodal interactions and spatial filtering, along with the Mamyshev mechanism. This work represents a first exploration of spatiotemporal mode-locking in an oscillator with the Mamyshev saturable absorber.
In this work, we introduce a method for stabilizing spatiotemporal solitons. These solitons correspond to light bullets in multimode optical fiber lasers, energy-scalable waveguide oscillators and amplifiers, localized coherent patterns in Bose-Einstein condensates, etc. We show that a three-dimensional confinement potential, formed by a spatial transverse (radial) parabolic graded refractive index and dissipation profile, combined with quadratic temporal phase modulation, may permit the generation of stable spatiotemporal dissipative solitons. This corresponds to combining phase mode-locking …
We introduce a mechanism of stable spatiotemporal soliton formation in a multimode fiber laser. This is based on spatially graded dissipation, leading to distributed Kerr-lens mode-locking. Our analysis involves solutions of a generalized dissipative Gross-Pitaevskii equation. This equation has a broad range of applications in nonlinear physics, including nonlinear optics, spatiotemporal patterns formation, plasma dynamics, and Bose-Einstein condensates. We demonstrate that careful control of dissipative and non-dissipative physical mechanisms results in the self-emergence of stable (2+1)-dime…
The performance of fiber mode-locked lasers is limited due to the high nonlinearity induced by the spatial confinement of the single-mode fiber core. To massively increase the pulse energy of the femtosecond pulses, amplification is obtained outside the oscillator. Recently, spatiotemporal mode-locking has been proposed as a new path to fiber lasers. However, the beam quality was either highly multimode and/or with low pulse energy. Here we present an approach to reach high energy per pulse directly in the mode-locked multimode fiber oscillator with a near single-mode output beam. Our approach…
Beam self-cleaning (BSC) in graded-index (GRIN) multimode fibres (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 fibres. Here we show that the associated self-induced spatiotemporal reshaping allows for improving the performances of nonlinear fluorescence microscopy and endoscopy using multimode optical fibres. We experimentally demonstrate that the beam brightness increase, induced by self-c…
A laser is based on the electromagnetic modes of its resonator, which provides the feedback required for oscillation. Enormous progress has been made in controlling the interactions of longitudinal modes in lasers with a single transverse mode. For example, the field of ultrafast science has been built on lasers that lock many longitudinal modes together to form ultrashort light pulses. However, coherent superposition of many longitudinal and transverse modes in a laser has received little attention. The multitude of disparate frequency spacings, strong dispersions, and complex nonlinear inter…
We develop the scheme of dispersion management (DM) for three-dimensional (3D) solitons in a multimode optical fiber. It is modeled by the parabolic confining potential acting in the transverse plane in combination with the cubic self-focusing. The DM map is adopted in the form of alternating segments with anomalous and normal group-velocity dispersion. Previously, temporal DM solitons were studied in detail in single-mode fibers, and some solutions for 2D spatiotemporal "light bullets", stabilized by DM, were found in the model of a planar waveguide. By means of numerical methods, we demonstr…
We experimentally demonstrate simultaneous spatial and temporal compression in the propagation of light pulses in multimode nonlinear optical fibers. We reveal that the spatial beam self-cleaning recently discovered in graded-index multimode fibers is accompanied by significant temporal reshaping and up to four-fold shortening of the injected sub-nanosecond laser pulses. Since the nonlinear coupling among the modes strongly depends on the instantaneous power, we explore the entire range of the nonlinear dynamics with a single optical pulse, where the optical power is continuously varied across…
Multimode optical fibers has emerged as the platform that will bridge the gap between nonlinear optics in bulk media and in single-mode fibers. However, the understanding of the transition between these two research fields still remains incomplete despite numerous investigations of intermodal nonlinear phenomena and spatiotemporal coupling. Some of the striking phenomena observed in bulk media with ultrashort and ultra-intense pulses (i.e., conical emission, harmonic generation and light bullets) require a deeper insight to be possibly unveiled in multimode fibers. Here we generalize the conce…
Dissipative Kerr soliton (DKS) frequency combs - also known as microcombs - have arguably created a new field in cavity nonlinear photonics, with a strong cross-fertilization between theoretical, experimental, and technological research. Spatiotemporal mode-locking (STML) not only add new degrees of freedom to ultrafast laser technology, but also provide new insights for implementing analogue computers and heuristic optimizers with photonics. Here, we combine the principles of DKS and STML for the first time to demonstrate the STML DKS by developing an unexplored ultrahigh-quality-factor Fabry…
The characterization of the complex spatiotemporal dynamics of optical beam propagation in nonlinear multimode fibers requires the development of advanced measurement methods, capable of capturing the real-time evolution of beam images. We present a new space-time mapping technique, permitting the direct detection, with picosecond temporal resolution, of the intensity from repetitive laser pulses over a grid of spatial samples from a magnified image of the output beam. By using this time-resolved mapping, we provide the first unambiguous experimental observation of instantaneous intrapulse non…
We demonstrate the stabilization of two-dimensional nonlinear wave patterns by means of a dissipative confinement potential. Our analytical and numerical analysis, based on the generalized dissipative Gross-Pitaevskii equation, makes use of the close analogy between the dynamics of a Bose-Einstein condensate and that of mode-locked fiber laser, operating in the anomalous dispersion regime. In the last case, the formation of stable two-dimensional patterns corresponds to spatiotemporal mode-locking, using dissipation-enhanced mode cleaning. We analyze the main scenarios of pattern destabilizati…
We overview recent advances in the research on spatiotemporal beam shaping in nonlinear multimode optical fibers. An intense light beam coupled to a graded index (GRIN) highly multimode fiber undergoes a series of complex nonlinear processes when its power grows larger. Among them, the lowest threshold effect is the Kerr-induced beam self-cleaning, that redistributes most of the beam energy into a robust bell-shaped beam close to the fundamental mode. At higher powers a series of spectral sidebands is generated, thanks to the phase matching induced by the long period grating due to the periodi…
Multimode fibres (MMFs) are attracting interest for complex spatiotemporal dynamics, and for ultrafast fibre sources, imaging and telecommunications. This new interest is based on three key properties: their high spatiotemporal complexity (information capacity), the important role of disorder, and complex intermodal interactions. To date, phenomena in MMFs have been studied only in limiting cases where one or more of these properties can be neglected. Here we study MMFs in a regime in which all these elements are integral. We observe a spatial beam-cleaning process preceding spatiotemporal mod…
Real-Time Visualization of the Spatiotemporal Dynamics of 3D Solitons
State Key Laboratory of Information Photonics and Optical Communications, School of Electronic Engineering, Beijing University of Posts and Telecommunications（北京邮电大学电子工程学院信息光子学与光通信国家重点实验室）
Multimode fibers (MMFs) support abundant spatial modes and involve rich spatiotemporal dynamics, yielding many promising applications. Here, we investigate the influences of the number and initial energy of high-order modes (HOMs) on the energy flow from the intermediate modes (IMs) to the fundamental mode (FM) and HOMs. It is quite surprising that random distribution of high-order modes evolves to a stationary one, indicating the asymptotic behavior of orbits in the same attraction domain. By employing the Lyapunov exponent, we prove that the threshold of the HOMs-attractor is consistent with…
We present a theoretical and numerical study of light propagation in graded-index (GRIN) multimode fibers where the core diameter has been periodically modulated along the propagation direction. The additional degree of freedom represented by the modulation permits to modify the intrinsic spatiotemporal dynamics which appears in multimode fibers. More precisely, we show that modulating the core diameter at a periodicity close to the self-imaging distance allows to induce a Moiré-like pattern, which modifies the geometric parametric instability gain observed in homogeneous GRIN fibers.
We report the spatial beam self-cleaning in bi-tapered conventional multimode fibers (MMFs) with different tapered lengths. Through the introduction of the bi-tapered structure in MMFs, the input beam with poor beam quality from a high-power fiber laser can be converted to a centered, bell-shaped beam in a short length, due to the strengthened nonlinear modes coupling. It is found that the bi-tapered MMF with longer tapered length at the same waist diameter shows better beam self-cleaning effect and larger spectral broadening. The obtained results offer a new method to improve the beam quality…
We develop a model for the description of nonlinear pulse propagation in multimode optical fibers with a parabolic refractive index profile. It consists in a 1+1D generalized nonlinear Schrödinger equation with a periodic nonlinear coefficient, which can be solved in an extremely fast and efficient way. The model is able to quantitatively reproduce recently observed phenomena like geometric parametric instability and broadband dispersive wave emission. We envisage that our equation will represent a valuable tool for the study of spatiotemporal nonlinear dynamics in the growing field of multimo…
Multimode fibers are widely explored for optical communication, imaging and sensing applications. The interference of fiber guided modes generates a speckle pattern, which has been used for high-precision spectroscopy, temperature, and strain sensing. Here we demonstrate a single-shot full-field temporal measurement technique based on a multimode fiber. The complex spatiotemporal speckle field is created by a reference pulse propagating through the fiber, and it interferes with a signal pulse. From the time-integrated interference pattern, both the amplitude and the phase of the signal are ret…
Nonlinear propagation of signals in single-mode fiber is well understood, and is typically observed by measuring the temporal profile or optical spectrum of an emerging signal. In multimode fibers, the nonlinearity has both a spatial and a temporal element, and a complete investigation of the interactions between propagating modes requires resolving the output in both space and time. We report here spatiotemporal measurements of two nonlinear interacting LP$_{0m}$ modes of a step-index few-mode fiber (FMF). We describe a method to selectively excite two propagating modes through the use of a p…
We introduce a model for spatiotemporal modelocking in multimode fiber lasers, which is based on the (3+1)-dimensional cubic-quintic complex Ginzburg-Landau equation (cGLE) with conservative and dissipative nonlinearities and a 2-dimensional transverse trapping potential. Systematic numerical analysis reveals a variety of stable nonlinear modes, including stable fundamental solitons and breathers, as well as solitary vortices with winding number $n=1$, while vortices with $n=2$ are unstable, splitting into persistently rotating bound states of two unitary vortices. A characteristic feature of …
Recent remarkable progress in wave-front shaping has enabled control of light propagation inside linear media to focus and image through scattering objects. In particular, light propagation in multimode fibers comprises complex intermodal interactions and rich spatiotemporal dynamics. Control of physical phenomena in multimode fibers and its applications is in its infancy, opening opportunities to take advantage of complex mode interactions. In this work, we demonstrate a wave-front shaping approach for controlling nonlinear phenomena in multimode fibers. Using a spatial light modulator at the…
Ultrashort high-energy pulses at wavelengths longer than 1 $μ$m are nowadays desired for a vast variety of applications in ultrafast and strong-field physics. To date, the main answer to the wavelength tunability for energetic, broadband pulses still relies on optical parametric amplification (OPA), which often requires multiple and complex stages, may feature imperfect beam quality and has limited conversion efficiency into one of the amplified waves. In this work, we present a completely different strategy to realize an energy-efficient and scalable laser frequency shifter. This relies on th…
