The nonlinear propagation of light pulses in liquid-filled photonic crystal fibers is considered. Due to the slow reorientational nonlinearity of some molecular liquids, the nonlinear modes propagating inside such structures can be approximated, for pulse durations much shorter than the molecular relaxation time, by temporally highly-nonlocal solitons, analytical solutions of a linear Schroedinger equation. The physical relevance of these novel solitary structures, which may have a broad range of applications, is discussed and supported by detailed numerical simulations.
We report on the experimental observation of stable dark solitons in an all normal dispersion fiber laser. We found experimentally that dark soliton formation is a generic feature of the fiber laser under strong continuous wave (CW) emission. However, only under appropriate pump strength and negative cavity feedback, stable single or multiple dark soliton could be achieved. Furthermore, we show that the features of the observed dark solitons could be well understood based on the nonlinear Schrodinger equation (NLSE).
We show that gap-acoustic solitons, i.e., optical gap solitons with electrostrictive coupling to sound modes, can be produced with velocities down to less than 2.5% of the speed of light using a fiber Bragg grating that is linearly coupled to a non-Bragg fiber over a finite domain. Forward- and backward-moving light pulses in the non-Bragg fiber that reach the coupling region simultaneously couple into the Bragg fiber and form a moving soliton, which then propagates beyond the coupling region.
The process of high-energy soliton fission is experimentally and numerically investigated in a graded-index multimode fiber. Fission dynamics is analyzed by comparing numerical observations and simulations. A novel regime is observed, where solitons produced by the fission have a nearly constant Raman wavelength shift and same pulse width over a wide range of soliton energies.
We report experimental observation of incoherently coupled dark-bright vector solitons in single-mode fibers. Properties of the vector solitons agree well with those predicted by the respective systems of incoherently coupled nonlinear Schroedinger equations. To the best of our knowledge, this is the first experimental observation of temporal incoherently coupled dark-bright solitons in single-mode fibers.
We have developed an analytical model based on the perturbation theory in order to study the optical propagation of two successive intense solitons in hollow-core photonic crystal fibers filled with Raman-active gases. Based on the time delay between the two solitons, we have found that the trailing soliton dynamics can experience unusual nonlinear phenomena such as spectral and temporal soliton oscillations and transport towards the leading soliton. The overall dynamics can lead to a spatiotemporal modulation of the refractive index with a uniform temporal period and a uniform or chirped spat…
We report on the observation of dispersion-managed (DM) dark soliton emission in a net-normal dispersion erbium-doped fiber laser. We found experimentally that dispersion management could not only reduce the pump threshold for the dark soliton formation in a fiber laser, but also stabilize the single dark soliton evolution in the cavity. Numerical simulations have also confirmed the DM dark soliton formation in a fiber laser.
We predict that a photonic crystal fiber whose strands are filled with a defocusing nonlinear medium can support stable bright and also vortex solitons if the strength of the defocusing nonlinearity grows toward the periphery of the fiber. The domains of soliton existence depend on the transverse growth rate of the filling nonlinearity and nonlinearity of the core. Remarkably, solitons exist even when the core material is linear.
We report the experimental observation of multiple dispersive waves emitted in the anomalous dispersion region of an optical fiber from a train of dark solitons. Each individual dispersive wave can be associated to one particular dark soliton of the train, using phase-matching arguments involving higher-order dispersion and soliton velocity. For a large number of dark solitons (>10), we observe the formation of a continuum associated with the efficient emission of dispersive waves.
Gas-filled hollow-core photonic crystal fibers offer unprecedented opportunities to observe novel nonlinear phenomena. The various properties of gases that can be used to fill these fibers give additional degrees of freedom for investigating nonlinear pulse propagation in a wide range of different media. In this review, we will consider some of the the new nonlinear interactions that have been discovered in recent years, in particular those which are based on soliton dynamics.
Dissipative solitons are non-dispersive localized waves that exhibit intriguing dynamics. In optical systems, the discovery of new soliton dynamics and how to accurately manipulate dissipative solitons are still largely unexplored and challenging in the ultrafast fiber laser community. Herein, we unveil a new type of dissipative soliton behavior in a net-normal-dispersion bidirectional ultrafast fiber laser. That is, the bidirectional dissipative solitons will always reveal similar spectral and temporal characteristics through common gain and loss modulation, even if the transient instability …
New resonant emission of dispersive waves by oscillating solitary structures is considered analytically and numerically. The resonance condition for the radiation is derived and it is demonstrated that the predicted resonances match the spectral lines observed in numerical simulations perfectly. The complex recoil of the radiation on the soliton dynamics is discussed.
We show that solitons undergo a strong blue shift in fibers with a dispersion landscape that varies along the direction of propagation. The experiments are based on a small-core photonic crystal fiber, tapered to have a core diameter that varies continuously along its length, resulting in a zero-dispersion wavelength that moves from 731 nm to 640 nm over the transition. The central wavelength of a soliton translates over 400 nm towards shorter wavelength. This accompanied by strong emission of radiation into the UV and IR spectral region. The experimental results are confirmed by numerical sim…
Vector soliton operation of erbium-doped fiber lasers mode locked with atomic layer graphene was experimentally investigated. Either the polarization rotation or polarization locked vector dissipative solitons were experimentally obtained in a dispersion-managed cavity fiber laser with large net cavity dispersion, while in the anomalous dispersion cavity fiber laser, the phase locked NLSE solitons and induced NLSE soliton were experimentally observed. The vector soliton operation of the fiber lasers unambiguously confirms the polarization insensitive saturable absorption of the atomic layer gr…
We report on the experimental observation of a new type of dark soliton in a fiber laser made of all normal group velocity dispersion fibers. It was shown that the soliton is formed due to the cross coupling between two different wavelength laser beams and has the characteristic of separating the two different wavelength laser emissions. Moreover, we show experimentally that the dual-wavelength dark solitons have a much lower pump threshold than that of the nonlinear Schrödinger equation dark solitons formed in the same laser.
A modified physics-informed neural network is used to predict the dynamics of optical pulses including one-soliton, two-soliton, and rogue wave based on the coupled nonlinear Schrödinger equation in birefringent fibers. At the same time, the elastic collision process of the mixed bright-dark soliton is predicted. Compared the predicted results with the exact solution, the modified physics-informed neural network method is proven to be effective to solve the coupled nonlinear Schrödinger equation. Moreover, the dispersion coefficients and nonlinearity coefficients of the coupled nonlinear Schro…
Optimization of the compression of input N-solitons into robust ultra-narrow fundamental solitons, with a tunable up- or downshifted frequency, is proposed in photonic crystal fibers (PCF) free of the Raman effect. Due to the absence of the Raman self-frequency shift, these fundamental solitons continue propagation maintaining the acquired frequency, once separated from the input N-soliton's temporal slot. A universal optimal value of the relative strength of the third-order-dispersion (TOD) is found, providing the strongest compression of the fundamental soliton, is found. It depends only the…
We present a theory describing trapping of the normally dispersive radiation by the Raman solitons in optical fibers. Frequency of the radiation component is continuously blue shifting, while the soliton is red shifting. Underlying physics of the trapping effect is in the existence of the inertial gravity-like force acting on light in the accelerating frame of reference. We present analytical calculations of the rate of the opposing frequency shifts of the soliton and trapped radiation and find it to be greater than the rate of the red shift of the bare Raman soliton. Our findings are essentia…
Solitons, as stable localized wave packets that can propagate long distance in dispersive media without changing their shapes, are ubiquitous in nonlinear physical systems. Since the first experimental realization of optical bright solitons in the anomalous dispersion single mode fibers (SMF) by Mollenauer et al. in 1980 and optical dark solitons in the normal dispersion SMFs by P. Emplit et al. in 1987, optical solitons in SMFs had been extensively investigated. In reality a SMF always supports two orthogonal polarization modes. Taking fiber birefringence into account, it was later theoretica…
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…
We derive the fundamental equations describing nonlinear propagation in multi-mode fibers in the presence of random mode coupling within quasi-degenerate groups of modes. Our result generalizes the Manakov equation describing mode coupling between polarizations in single-mode fibers. Nonlinear compensation of the modal dispersion is predicted and tested via computer simulations.
Solitons are non-dispersing localized waves that occur in diverse physical settings. A variety of optical solitons have been observed, but versions that involve both spatial and temporal degrees of freedom are rare. Optical fibers designed to support multiple transverse modes offer opportunities to study wave propagation in a setting that is intermediate between single-mode fiber and free-space propagation. Here we report the observation of optical solitons and soliton self-frequency shifting in graded-index multimode fiber. These wave packets can be modeled as multi-component solitons, or as …
We present experimental and numerical data on the supercontinuum generation in an optical fiber pumped in the normal dispersion range where the seeded dark and the spontaneously generated bright solitons contribute to the spectral broadening. We report the dispersive radiation arising from the interaction of the bright and dark solitons. This radiation consists of the two weak dispersing pulses that continuously shift their frequencies and shape the short and long wavelength wings of the supercontinuum spectrum.
We report on the existence of a novel kind of squeezing in photonic crystal fibers which is conceptually intermediate between the four-wave mixing induced squeezing, in which all the participant waves are monochromatic waves, and the self-phase modulation induced squeezing for a single pulse in a coherent state. This hybrid squeezing occurs when an arbitrary short soliton emits quasi-monochromatic resonant radiation near a zero group velocity dispersion point of the fiber. Photons around the resonant frequency become strongly correlated due to the presence of the classical soliton, and a reduc…
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…
We demonstrate that crossed arrays of optical fibers support the double-discrete linear and nonlinear propagation of light beams, in which not only the transverse coordinate (the fiber's number) is discrete, but also the longitudinal (propagation) coordinate, i.e., the number of the fiber-crossing site, is effectively discrete too. In the linear limit, this transmission regime features double-discrete self-collimation. The nonlinear fishnet arrays with both focusing and defocusing nonlinearities give rise to double-discrete spatial solitons. Solitons bifurcating from two different branches of …
We show theoretically that the photoionization process in a hollow-core photonic crystal fiber filled with a Raman-inactive noble gas leads to a constant acceleration of solitons in the time domain with a continuous shift to higher frequencies, limited only by ionization loss. This phenomenon is opposite to the well-known Raman self-frequency red-shift of solitons in solid-core glass fibers. We also predict the existence of unconventional long-range non-local soliton interactions leading to spectral and temporal soliton clustering. Furthermore, if the core is filled with a Raman-active molecul…
We report on the observation of various bound states of dispersion-managed (DM) solitons in a passively mode-locked Erbium-doped fiber ring laser at near zero net cavity group velocity dispersion (GVD). The generated DM solitons are characterized by their Gaussian-like spectral profile with no sidebands, which is distinct from those of the conventional solitons generated in fiber lasers with large net negative cavity GVD, of the parabolic pulses generated in fiber lasers with positive cavity GVD and negligible gain saturation and bandwidth limiting, and of the gain-guided solitons generated in…
The article provides a survey of (chiefly, theoretical) results obtained for self-trapped modes (solitons) in various models of one-dimensional optical waveguides based on a pair of parallel guiding cores, which combine the linear inter-core coupling with the intrinsic cubic (Kerr) nonlinearity, anomalous group-velocity dispersion, and, possibly, intrinsic loss and gain in each core. The survey is focused on three main topics: spontaneous breaking of the inter-core symmetry and the formation of asymmetric temporal solitons in dual-core fibers; stabilization of dissipative temporal solitons (es…
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 …
Soliton-soliton collisions have a crucial role in enhancing the spectrum of dispersive waves in optical fibers and collisions among in-phase solitons lead to a dramatic enhancement of the dispersive wave power, as well as to its significant spectral reshaping. We obtained a simple analytical model to estimate the spectral position, width and amplitude of the dispersive waves induced by a collision of two in-phase solitons. We tested our theory in the case of a dual concentric core microstructured fiber.
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 report on the experimental observation of two types of phase-locked vector soliton in weakly birefringent cavity erbium-doped fiber lasers. While a phase-locked dark-dark vector soliton was only observed in fiber lasers of positive dispersion, a phase-locked dark-bright vector soliton was obtained in fiber lasers of either positive or negative dispersion. Numerical simulations confirmed the experimental observations, and further showed that the observed vector solitons are the two types of phase-locked polarization domain-wall solitons theoretically predicted.
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.
Experimental study on the soliton dynamics of a passively mode locked fiber ring laser firstly revealed a state of bound soliton operation in the laser, where two solitons bind together tightly with fixed pulse separation. We further report on the properties of the bound-soliton emission of the laser. In particular, we demonstrate both experimentally and numerically that, like the single pulse soliton operation of the laser, the bound soliton emission is another intrinsic feature of the laser.
We report on the experimental observation of a novel type of polarization locked vector soliton in a passively mode-locked fiber laser. The vector soliton is characterized by that not only the two orthogonally polarized soliton components are phase locked, but also one of the components has a double-humped intensity profile. Multiple such phase-locked high order vector solitons with identical soliton parameters and harmonic mode-locking of the vector solitons were also obtained in the laser. Numerical simulations confirmed the existence of stable high-order vector solitons in fiber lasers.
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 …
The propagation of soliton waves is simulated through splices in optical fibers, in which fluctuations of dielectric parameters occur. The mathematical modeling of these local fluctuations of dielectric properties of fibers was performed by Gaussian functions. By simulating soliton wave propagation in optical fibers with Gaussian fluctuations in their dielectric properties, it was observed that the perturbed soliton numerical solution presented higher sensitivity to fluctuations in the dielectric parameter $β$, a measure of the intensity of nonlinearity in the fiber. In order to verify whether…
Rapid progress in passively mode-locked fiber lasers is currently driven by the recent discovery of vector feature of mode-locking pulses, namely, the group velocity-locked vector solitons, the phase locked vector solitons, and the high-order vector solitons. Those vector solitons are fundamentally different from the previously known scalar solitons. Here, we report a fiber laser where the mode-locked pulse evolves as a vector soliton in the strong birefringent segment and is transformed into a regular scalar soliton after the polarizer within the laser cavity. The existence of solutions in a …
Optical frequency combs in microresonators (microcombs) have a wide range of applications in science and technology, due to its compact size and access to considerably larger comb spacing. Despite recent successes, the problems of self-starting, high mode efficiency as well as high output power have not been fully addressed for conventional soliton microcombs. Recent demonstration of laser cavity soliton microcombs by nesting a microresonator into a fiber cavity, shows great potential to solve the problems. Here we comprehensively study the dissipative soliton generation and interaction dynami…
We experimentally observe soliton self-organization and pulsation in a passively mode-locked fiber laser. The optomechanical interaction in the optical fiber is key to the formation of equidistant soliton bunches. These solitons simultaneously undergo a pulsation process with a period corresponding to tens of the cavity round trip time. Using the dispersive Fourier transformation technique, we find that the Kelly sidebands in the shot-to-shot spectra appear periodically, synchronizing with the pulsation.
Pure solitons are for the first time distilled from the resonant continuous wave (CW) background in a fiber laser by utilizing nonlinear Fourier transform (NFT). It is identified that the soliton and the resonant CW background have different eigenvalue distributions in the nonlinear frequency domain. Similar to water distillation, we propose the approach of soliton distillation, by making NFT on a steady pulse generated from a fiber laser, then filtering out the eigenvalues of the resonant CW background in the nonlinear frequency domain, and finally recovering the soliton by inverse NFT (INFT)…
We report on the experimental observation of temporal cavity soliton destabilization via spatiotemporal chaos in a coherently-driven optical fiber ring resonator. Numerical simulations and theoretical analyses are in good agreement with experimental observations.
We study resonant radiation generated by bound solitons in a twin-core fiber near zero-dispersion wavelength, in the presence of higher order dispersion terms. We propose a theoretical description of dispersive wave generation mechanism and derive resonance conditions. The presence of third order dispersion term leads to generation of polychromatic dispersive radiation and transition from the regime of center of mass oscillations to the regime of amplitude oscillations. Such a transition is not reproduced in the case of symmetric fourth order dispersion.
An equation is derived for analyzing the self-action of a wave packets with few optical cycles in multicore fibers (MCF). A new class of stable out-of-phase spatio-temporal solitons with few cycle durations in the MCF with cores located in a ring is found and analyzed. The stability boundary of the obtained solutions is determined. As an example of using such solitons, we considered the problem of their self-compression in the process of multisoliton dynamics in the MCF. The formation of laser pulses with a duration of few optical cycles at the output of a ten-core MCF is shown.
We report results of numerical simulations on the multiple soliton generation and soliton energy quantization in a soliton fiber ring laser passively mode-locked by using the nonlinear polarization rotation technique. We found numerically that the formation of multiple solitons in the laser is caused by a peak power limiting effect of the laser cavity. It is also the same effect that suppresses the soliton pulse collapse, an intrinsic feature of solitons propagating in the gain media, and makes the solitons stable in the laser. Furthermore, we show that the soliton energy quantization observed…
The strongly-constrained physics-informed neural network (SCPINN) is proposed by adding the information of compound derivative embedded into the soft-constraint of physics-informed neural network(PINN). It is used to predict nonlinear dynamics and the formation process of bright and dark picosecond optical solitons, and femtosecond soliton molecule in the single-mode fiber, and reveal the variation of physical quantities including the energy, amplitude, spectrum and phase of pulses during the soliton transmission. The adaptive weight is introduced to accelerate the convergence of loss function…
The red shifted solitonic resonant radiation is a fascinating phase matching phenomenon that occurs when an optical pulse, launched in the normal dispersion regime of photonic crystal fiber, radiates across the zero dispersion wavelength. The formation of such phase-matched radiation is independent of the generation of any optical soliton and mainly governed by the leading edge of input pump which forms a shock front. The radiation is generated at the anomalous dispersion regime and found to be confined both in time and frequency domain. We experimentally investigate the formation of such radi…
We have experimentally investigated the soliton interaction in a passively mode-locked fiber ring laser and revealed the existence of three types of strong soliton interaction: a global type of soliton interaction caused by the existence of unstable CW components; a local type of soliton interaction mediated through the radiative dispersive waves; and the direct soliton interaction. We found that the appearance of the various soliton operation modes observed in the passively mode locked fiber soliton lasers are the direct consequences of these three types of soliton interaction. The soliton in…
Physics phenomena of multi-soliton complexes have enriched the life of dissipative solitons in fiber lasers. By developing a birefringence-enhanced fiber laser, we report the first experimental observation of group-velocity-locked vector soliton (GVLVS) molecules. The birefringence-enhanced fiber laser facilitates the generation of GVLVSs, where the two orthogonally polarized components are coupled together to form a multi-soliton complex. Moreover, the interaction of repulsive and attractive forces between multiple pulses binds the particle-like GVLVSs together in time domain to further form …
We report on the experimental observation of incoherently coupled dark vector soliton trapping in a fiber laser. Dark vector solitons along the two orthogonal polarization directions though with large difference in central frequency, energy and darkness could be still synchronously trapped as a group velocity locked dark vector soliton in virtue of the incoherent interactions. Our numerical simulation could well rebirth the experimental observations and confirm the existence of incoherently coupled dark vector soliton under certain conditions.
