Dispersion-less Kerr solitons in spectrally confined optical cavities.

Solitons are self-reinforcing localized wave packets that manifest in the major areas of nonlinear science, from optics to biology and Bose-Einstein condensates. Recently, optically driven dissipative solitons have attracted great attention for the implementation of the chip-scale frequency combs that are decisive for communications, spectroscopy, neural computing, and quantum information processing. In the current understanding, the generation of temporal solitons involves the chromatic dispersion as a key enabling physical effect, acting either globally or locally on the cavity dynamics in a decisive way. Here, we report on a novel class of solitons, both theoretically and experimentally, which builds up in spectrally confined optical cavities when dispersion is practically absent, both globally and locally. Precisely, the interplay between the Kerr nonlinearity and spectral filtering results in an infinite hierarchy of eigenfunctions which, combined with optical gain, allow for the generation of stable dispersion-less dissipative solitons in a previously unexplored regime. When the filter order tends to infinity, we find an unexpected link between dissipative and conservative solitons, in the form of Nyquist-pulse-like solitons endowed with an ultra-flat spectrum. In contrast to the conventional dispersion-enabled nonlinear Schrödinger solitons, these dispersion-less Nyquist solitons build on a fully confined spectrum and their energy scaling is not constrained by the pulse duration. Dispersion-less soliton molecules and their deterministic transitioning to single solitons are also evidenced. These findings broaden the fundamental scope of the dissipative soliton paradigm and open new avenues for generating soliton pulses and frequency combs endowed with unprecedented temporal and spectral features.

Superlocalization Reveals Long-Range Synchronization of Vibrating Soliton Molecules.

We implement a superlocalization method in the time domain that allows the observation of the external motion of soliton molecules in a fiber ring cavity laser with unprecedented accuracy. In particular, we demonstrate the synchronization of two oscillating soliton molecules separated by several nanoseconds, with intermolecular oscillations following the same pattern as the intramolecular motion of the individual molecules. These experimental findings indicate an interplay between the different interaction mechanisms that coexist inside the laser cavity, despite their very different characteristic ranges, timescales, strengths, and physical origins.

Smart lasers tame complex spatiotemporal cavity dynamics.

By associating multimode fibers, optical wavefront manipulation, and a feedback loop controlled by a genetic algorithm, researchers have demonstrated that nonlinear spatiotemporal dynamics can be flexed within the laser cavity to achieve a user-specified objective, such as the lasing wavelength, output power, beam profile or pulsed operation.

Fundamental Peregrine Solitons of Ultrastrong Amplitude Enhancement through Self-Steepening in Vector Nonlinear Systems.

We report the universal emergence of anomalous fundamental Peregrine solitons, which can exhibit an unprecedentedly ultrahigh peak amplitude comparable to any higher-order rogue wave events, in the vector derivative nonlinear Schrödinger system involving the self-steepening effect. We present the exact explicit rational solutions on either a continuous-wave or a periodical-wave background, for a broad range of parameters. We numerically confirm the buildup of anomalous Peregrine solitons from strong initial harmonic perturbations, despite the onset of competing modulation instability. Our results may stimulate the experimental study of such Peregrine soliton anomaly in birefringent crystals or other similar vector systems.

Saturable plasmonic metasurfaces for laser mode locking.

Metamaterials are artificial materials made of subwavelength elementary cells that give rise to unexpected wave properties that do not exist naturally. However, these properties are generally achieved due to 3D patterning, which is hardly feasible at short wavelengths in the visible and near-infrared regions targeted by most photonic applications. To overcome this limitation, metasurfaces, which are the 2D counterparts of metamaterials, have emerged as promising platforms that are compatible with planar nanotechnologies and thus mass production, which platforms the properties of a metamaterial into a 2D sheet. In the linear regime, wavefront manipulation for lensing, holography, and polarization control has been achieved recently. Interest in metasurfaces operating in the nonlinear regime has also increased due to the ability of metasurfaces to efficiently convert incident light into harmonic frequencies with unusual polarization properties. However, to date, the nonlinear absorption of metasurfaces has been mostly ignored. Here, we demonstrate that plasmonic metasurfaces behave as saturable absorbers with modulation performances superior to the modulation performance of other 2D materials and exhibit unusual polarimetric nonlinear transfer functions. We quantify the link between saturable absorption, the plasmonic resonances of the unit cell and their distribution in a 2D metasurface, and finally provide a practical implementation by integrating the metasurfaces into a fiber laser cavity operating in pulsed regimes driven by the metasurface properties. As such, this work provides new perspectives on ultrathin nonlinear saturable absorbers for applications where tunable nonlinear transfer functions are needed, such as in ultrafast lasers or neuromorphic circuits.

General rogue wave solutions of the coupled Fokas-Lenells equations and non-recursive Darboux transformation.

We formulate a non-recursive Darboux transformation technique to obtain the general nth-order rational rogue wave solutions to the coupled Fokas-Lenells system, which is an integrable extension of the noted Manakov system, by considering both the double-root and triple-root situations of the spectral characteristic equation. Based on the explicit fundamental and second-order rogue wave solutions, we demonstrate several interesting rogue wave dynamics, among which are coexisting rogue waves and anomalous Peregrine solitons. Our solutions are generalized to include the complete background-field parameters and therefore helpful for future experimental study.

Bidirectional Soliton Rain Dynamics Induced by Casimir-Like Interactions in a Graphene Mode-Locked Fiber Laser.

We study experimentally and theoretically the interactions among ultrashort optical pulses in the soliton rain multiple-pulse dynamics of a fiber laser. The laser is mode locked by a graphene saturable absorber fabricated using the mechanical transfer technique. Dissipative optical solitons aggregate into pulse bunches that exhibit complex behavior, which includes acceleration and bidirectional motion in the moving reference frame. The drift speed and direction depend on the bunch size and relative location in the cavity, punctuated by abrupt changes under bunch collisions. We model the main effects using the recently proposed noise-mediated pulse interaction mechanism, and obtain a good agreement with experiments. This highlights the major role of long-range Casimir-like interactions over dynamical pattern formations within ultrafast lasers.

Peregrine Solitons Beyond the Threefold Limit and Their Two-Soliton Interactions.

Within the coupled Fokas-Lenells equations framework, we show explicitly that, in contrast to the expected threefold-amplitude magnification, Peregrine solitons can reach a peak amplitude as high as 5 times the background level. Besides, the interaction of two such anomalous Peregrine solitons can generate a spikelike rogue wave of extremely high peak amplitude, depending on the parameters used. We numerically confirm that the Peregrine soliton beyond the threefold limit can be reproduced from either a deterministic initial profile or a chaotic background field, hence anticipating the feasibility of its experimental observation.

Optical Peregrine rogue waves of self-induced transparency in a resonant erbium-doped fiber.

The resonant interaction of an optical field with two-level doping ions in a cryogenic optical fiber is investigated within the framework of nonlinear Schrödinger and Maxwell-Bloch equations. We present explicit fundamental rational rogue wave solutions in the context of self-induced transparency for the coupled optical and matter waves. It is exhibited that the optical wave component always features a typical Peregrine-like structure, while the matter waves involve more complicated yet spatiotemporally balanced amplitude distribution. The existence and stability of these rogue waves is then confirmed by numerical simulations, and they are shown to be excited amid the onset of modulation instability. These solutions can also be extended, using the same analytical framework, to include higher-order dispersive and nonlinear effects, highlighting their universality.

Real-Time Observation of Internal Motion within Ultrafast Dissipative Optical Soliton Molecules.

Real-time access to the internal ultrafast dynamics of complex dissipative optical systems opens new explorations of pulse-pulse interactions and dynamic patterns. We present the first direct experimental evidence of the internal motion of a dissipative optical soliton molecule generated in a passively mode-locked erbium-doped fiber laser. We map the internal motion of a soliton pair molecule by using a dispersive Fourier-transform imaging technique, revealing different categories of internal pulsations, including vibrationlike and phase drifting dynamics. Our experiments agree well with numerical predictions and bring insights to the analogy between self-organized states of lights and states of the matter.

Chirped Peregrine solitons in a class of cubic-quintic nonlinear Schrödinger equations.

We shed light on the fundamental form of the Peregrine soliton as well as on its frequency chirping property by virtue of a pertinent cubic-quintic nonlinear Schrödinger equation. An exact generic Peregrine soliton solution is obtained via a simple gauge transformation, which unifies the recently-most-studied fundamental rogue-wave species. We discover that this type of Peregrine soliton, viable for both the focusing and defocusing Kerr nonlinearities, could exhibit an extra doubly localized chirp while keeping the characteristic intensity features of the original Peregrine soliton, hence the term chirped Peregrine soliton. The existence of chirped Peregrine solitons in a self-defocusing nonlinear medium may be attributed to the presence of self-steepening effect when the latter is not balanced out by the third-order dispersion. We numerically confirm the robustness of such chirped Peregrine solitons in spite of the onset of modulation instability.

Rogue-wave bullets in a composite (2+1)D nonlinear medium.

We show that nonlinear wave packets localized in two dimensions with characteristic rogue wave profiles can propagate in a third dimension with significant stability. This unique behavior makes these waves analogous to light bullets, with the additional feature that they propagate on a finite background. Bulletlike rogue-wave singlet and triplet are derived analytically from a composite (2+1)D nonlinear wave equation. The latter can be interpreted as the combination of two integrable (1+1)D models expressed in different dimensions, namely, the Hirota equation and the complex modified Korteweg-de Vries equation. Numerical simulations confirm that the generation of rogue-wave bullets can be observed in the presence of spontaneous modulation instability activated by quantum noise.

Complementary optical rogue waves in parametric three-wave mixing.

We investigate the resonant interaction of two optical pulses of the same group velocity with a pump pulse of different velocity in a weakly dispersive quadratic medium and report on the complementary rogue wave dynamics which are unique to such a parametric three-wave mixing. Analytic rogue wave solutions up to the second order are explicitly presented and their robustness is confirmed by numerical simulations, in spite of the onset of modulation instability activated by quantum noise.

Generation of wavelength-tunable soliton molecules in a 2-µm ultrafast all-fiber laser based on nonlinear polarization evolution.

We report on the experimental observation of stable single solitons and soliton molecules in a 2-µm thulium-holmium-doped fiber laser mode-locked through the nonlinear polarization evolution technique within an anomalously dispersive cavity. Single 0.65 nJ solitons feature a 7.3 nm spectral FWHM and 540 fs temporal duration, yielding a time-bandwidth product close to the Fourier-transform limitation. Under the same pumping power of 740 mW, stable out-of-phase twin-soliton molecules, featuring a temporal separation of 2.5 ps between the two ∼700 fs pulses, are generated in a deterministic way, while the central wavelength of the soliton molecules can be tuned from 1920 to 1940 nm. Finally, we present strong experimental evidence of vibrating soliton molecules.

Watch-hand-like optical rogue waves in three-wave interactions.

We investigate the resonant interaction of three optical pulses of different group velocity in quadratic media and report on the novel watch-hand-like super rogue wave patterns. In addition to having a giant wall-like hump, each rogue-wave hand involves a peak amplitude more than five times its background height. We attribute such peculiar structures to the nonlinear superposition of six Peregrine-type solitons. The robustness has been confirmed by numerical simulations. This stability along with the non-overlapping distribution property may facilitate the experimental diagnostics and observation of these super rogue waves.

Dark three-sister rogue waves in normally dispersive optical fibers with random birefringence.

We investigate dark rogue wave dynamics in normally dispersive birefringent optical fibers, based on the exact rational solutions of the coupled nonlinear Schrödinger equations. Analytical solutions are derived up to the second order via a nonrecursive Darboux transformation method. Vector dark "three-sister" rogue waves as well as their existence conditions are demonstrated. The robustness against small perturbations is numerically confirmed in spite of the onset of modulational instability, offering the possibility to observe such extreme events in normal optical fibers with random birefringence, or in other Manakov-type vector nonlinear media.

Coexisting rogue waves within the (2+1)-component long-wave-short-wave resonance.

The coexistence of two different types of fundamental rogue waves is unveiled, based on the coupled equations describing the (2+1)-component long-wave-short-wave resonance. For a wide range of asymptotic background fields, each family of three rogue wave components can be triggered by using a slight deterministic alteration to the otherwise identical background field. The ability to trigger markedly different rogue wave profiles from similar initial conditions is confirmed by numerical simulations. This remarkable feature, which is absent in the scalar nonlinear Schrödinger equation, is attributed to the specific three-wave interaction process and may be universal for a variety of multicomponent wave dynamics spanning from oceanography to nonlinear optics.

Dark- and bright-rogue-wave solutions for media with long-wave-short-wave resonance.

Exact explicit rogue-wave solutions of intricate structures are presented for the long-wave-short-wave resonance equation. These vector parametric solutions feature coupled dark- and bright-field counterparts of the Peregrine soliton. Numerical simulations show the robustness of dark and bright rogue waves in spite of the onset of modulational instability. Dark fields originate from the complex interplay between anomalous dispersion and the nonlinearity driven by the coupled long wave. This unusual mechanism, not available in scalar nonlinear wave equation models, can provide a route to the experimental realization of dark rogue waves in, for instance, negative index media or with capillary-gravity waves.

Cross-phase modulational instability induced by Raman scattering in highly birefringent fiber.

We report experimental and theoretical studies of Raman-induced cross-phase modulational instabilities (XPMI) in a high-birefringence, normally dispersive optical fiber. Experimental results reveal that the Raman-Stokes wave, generated by a quasi-CW pump beam, interacts with the latter to create a novel type of XPMI sidebands. These sidebands are characterized by a narrow gain bandwidth. The sideband frequencies are well reproduced by a linear stability analysis as well as by full numerical solutions of the coupled generalized nonlinear Schrödinger equations.

Multi-gigahertz repetition-rate-selectable passive harmonic mode locking of a fiber laser.

We demonstrate a passive harmonically mode-locked erbium-doped fiber laser that operates at selectable harmonics spanning from the 6th to the 928th, which corresponds to repetition rates ranging from 153 MHz to 22.2 GHz. The noteworthy laser output stability is attested by supermode suppression levels as large as 41 dB. The influence of a continuous wave background on harmonics stability is tested.