Soliton Trapping Research Articles

Thouless pumping and trapping of two-component gap solitons

We study Thouless pumping and arresting of gap solitons in a two-component Bose gas loaded into an optical superlattice. We show that, depending on the atomic interactions and chemical potentials, the two solitons can be simultaneously pumped or trapped, but we also identify regimes where one soliton is pumped and the other arrested. These behaviors can be understood by considering an effective model of the system based on a variational approach, which reveals that the soliton width is a suitable qualifier for the observed behaviors: solitons with a larger width get transported, while solitons with a smaller width get trapped. Since these widths can be controlled by tuning interactions, it should be possible to observe all behaviors experimentally. Published by the American Physical Society 2024

Vector pure-quartic soliton molecule fiber laser

Pure-quartic solitons (PQSs) balanced by the fourth-order dispersion (FOD) and nonlinearity in weakly birefringent optical fibers exhibit unique characteristics that differ from those of traditional solitons. Owing to the long oscillating tail of the PQS, soliton trapping can be easily promoted either between the sub pulses inside the molecule or along the two polarization axes of the birefringent fiber. Thus, observing the interaction and motion dynamics of vector PQS molecules promotes great opportunities for unveiling new mechanisms of soliton molecular complexity. In this work, we numerically explore the transient dynamics of vector PQS molecules by solving the coupled Ginzburg-Landau equations which are contributed by the FOD. Diverse real-time dynamics of vector PQS molecules are demonstrated for the first time, including stationary and pulsating, which originate from the multi-scale energy exchange inside the molecule and between the orthogonal axes depending on the nonlinear effect. In addition, we reveal that the buildup process of vector PQS molecules includes splitting, pulsating, and synchronization. The related dynamics of the pulse separation and phase difference that constitute the relevant internal degrees of freedom of the molecule are also mapped. These efforts may shed new insights into understanding the internal dynamics of soliton molecular complexes and decomposing the dynamics of complex nonlinear systems.

Co‐Generation of Orthogonal Soliton Pair in a Monolithic Fiber Resonator with Mechanical Tunability

AbstractSoliton frequency combs generated in microresonators offer powerful tools for optical metrology, due to the high time‐frequency resolution. Here, via exciting the intracavity Brillouin laser in a high Q monolithic fiber resonator, a pair of orthogonal Kerr soliton combs is generated, which share the same repetition (frep ≈ 1.001 GHz) due to the soliton trapping but different central wavelengths (≈ 9.278 GHz). They offer rich dual‐comb beat notes with minimum phase noise down to −166.5 dBc Hz−1@1 MHz. Thanks to the geometric flexibility of the monolithic fiber resonator, the orthogonal soliton pair is found to be mechanically controllable with high precision. Specifically, by applying external stress on the microcavity in a range of ≈ 0–7.33 mN, the difference of their carrier‐envelope‐offset frequencies (Δfceo) is linearly tunable with a response of 0.3 kHz µN−1, meanwhile, tunability of the frep reaches 0.4 kHz µN−1. Such an orthogonally polarized dual soliton with stress controllability combining Brillouin excitation and parametric oscillation can offer a miniature all‐in‐fiber tool for wide applications ranging from frequency‐adjustable photonic microwave sources to highly sensitive gyroscopes.

Dispersive waves generation in photonic crystal fibers: The role on supercontinuum generation and rogue waves manipulation

Based on photonic crystal fiber, the generation and behavior of dispersive waves in optical fiber system are presented. The individual soliton induced dispersive waves and collision-induced dispersive waves generation are introduced and compared, and the ways of dispersion wave generation are also given in terms of pumping conditions and fiber properties. The dispersion slope affects soliton trapping of dispersive waves and the role of soliton trapping of dispersive waves on supercontinuum is different in photonic crystal fibers with different zero dispersion wavelengths. From the point of view of the number of zero dispersion wavelength, we reveal the effect of dispersive waves on supercontinuum generation and the relationship between dispersive wave and zero dispersion wavelength. Rogue waves induced by dispersive waves are also discussed and how to control rogue waves by using dispersive waves is shown.

Anomalous soliton trapping in net-normal dispersion lasers.

In a nonlinear optical system with birefringence such as fiber lasers, soliton trapping can be achieved when the fast (slow) component experiences blueshift (redshift) at normal dispersion to compensate for polarization-mode dispersion (PMD). In this Letter, we demonstrate an anomalous vector soliton (VS) whose fast (slow) component shifts to the red (blue) sides, which is opposite to traditional soliton trapping. It is found that the repulsion between the two components is induced by net-normal dispersion and PMD, while the attraction is ascribed to linear mode coupling and saturable absorption. The equilibrium of attraction and repulsion permits the self-consistent evolution of VSs circulating in the cavity. Our results indicate that the stability and dynamics of VSs are worth revisiting and studying in-depth, especially in lasers with complex configurations, despite it being a well-known object in nonlinear optics.

Dual-state vector soliton in mode-locked fiber laser

Vector soliton originates from the soliton trapping dynamics via cross-phase modulation (XPM) which has been used to achieve supercontinuum, optical switching and optical analog of gravity-like potentials. Dual-state vector soliton (DSVS) is reported in mode-locked fiber laser under appropriate birefringence. Two vector soliton states emitted alternatively display double-peak and Lorentz-shaped spectral profile, respectively. The two orthogonally polarized components of the double-peak spectrum exhibit obvious redshift and blueshift, respectively, while the frequency shift for the other state is limited even with the reversed shift direction, which illustrates a unique vector soliton evolution dynamic. DSVS originates from the pulse trapping induced by XPM, as well as the periodical evolution and frequency shift induced by self-phase modulation under dispersion-managed condition. The vector period-doubling phenomenon will further enrich the understanding about soliton, and also guide the design of mode-locked laser.

120-fs single-pulse generation from stretched-pulse fiber Kerr resonators.

Fiber Kerr resonators are simple driven resonators with desirable wavelength and repetition rate flexibility for generating ultrashort pulses for applications including telecommunications, biomedicine, and materials processing. However, fiber Kerr resonators to date often generate longer pulses and require more complicated techniques for generating single pulses than would be desirable for applications. Here we address these limits by demonstrating robust single-pulse performance supporting 120-fs pulse durations in fiber Kerr resonators based on stretched-pulse solitons. Through matching numerical and experimental studies, stretched-pulse soliton performance is found to strongly depend on the total cavity length, and the optimum length is found to depend on the drive, Raman scattering, and the total pulse stretching. The bandwidth increases with decreasing net dispersion, enabled by shorter total cavity lengths. In a cavity with an optimized length and the described setup, stable stretched-pulse solitons corresponding to 120-fs duration are experimentally observed. In addition, soliton trapping is demonstrated with a pulsed drive source despite large intracavity breathing, and single-pulse performance is observed. Robust with high performance single-pulse generation is a critical step toward useful femtosecond pulse generation.

Soliton trapping and orthogonal Raman scattering in a birefringent photonic crystal fiber

We report on trapped pulse generation in birefringent photonic crystal fiber. Linearly polarized ultrashort pulses are injected into the fiber in an anomalous dispersion regime. We observed experimentally that a soliton pulse polarized along the fast fiber axis partially transfers its energy to the orthogonal polarization. The generated pulse is amplified through the orthogonal Raman gain. The two polarization components are located at group-velocity-matched wavelengths. The experimental works are in agreement with numerical simulations. The obtained results are important for applications of the light sources using self-frequency shifted solitons that demand high polarization purity.

Dark-Bright Soliton Bound States in a Microresonator.

Dissipative Kerr solitons in microresonators have facilitated the development of fully coherent, chip-scale frequency combs. In addition, dark soliton pulses have been observed in microresonators in the normal dispersion regime. Here, we report bound states of mutually trapped dark-bright soliton pairs in a microresonator. The soliton pairs are generated seeding two modes with opposite dispersion but with similar group velocities. One laser operating in the anomalous dispersion regime generates a bright soliton microcomb, while the other laser in the normal dispersion regime creates a dark soliton via Kerr-induced cross-phase modulation with the bright soliton. Numerical simulations agree well with experimental results and reveal a novel mechanism to generate dark soliton pulses. The trapping of dark and bright solitons can lead to light states with the intriguing property of constant output power while spectrally resembling a frequency comb. These results can be of interest for telecommunication systems, frequency comb applications, and ultrafast optics.

Coherent control of optical solitons interaction via external potential in electromagnetically induced transparency system

A scheme is proposed to realize coherent control of optical solitons propagation and interaction in a three level Λ type electromagnetically induced transparency (EIT) system with external potential. For single soliton propagation, we realize the transmission and trapping of optical soliton via external potential. For double solitons interaction, we realize the coherent control of attractive and repulsion interaction of two optical solitons, and design a XNOR logical operation. At last, for triple solitons incident case, we study the interaction properties of the three solitons depending on the initial phase difference, based on the coherent control of interaction between three solitons via external potential, we design a beam selector. The results obtained here are useful not only for the deep understanding of optical soliton interaction, but also for applications in all optical quantum information processing, etc.

Coherent control of optical soliton interaction via electromagnetically induced transparency with spatial modulation

We propose a scheme to realize the coherent control of optical soliton propagation and interaction in a three level Λ type electromagnetically induced transparency system with the control field being spatially modulated. We show that the spatial perturbation of the control field has no influence on the linear propagation properties and self-phase modulation of the probe field but can produce an equivalent external potential to affect the nonlinear propagation of the probe field. For single soliton propagation, we realize the transmission and trapping of optical solitons via external potential. For double soliton interaction, we realize the coherent control of attractive and repulsion interactions of two optical solitons and design an XNOR logical operation. Finally, for the triple soliton incident case, based on the coherent control of interaction between three solitons via external potential, we design a beam selector. The results obtained here are useful not only for the deep understanding of optical soliton interaction but also for applications in all optical quantum information processing.

Past and Present Trends in the Development of the Pattern-Formation Theory: Domain Walls and Quasicrystals

A condensed review is presented for two basic topics in the theory of pattern formation in nonlinear dissipative media: (i) domain walls (DWs, alias grain boundaries), which appear as transient layers between different states occupying semi-infinite regions, and (ii) two- and three-dimensional (2D and 3D) quasiperiodic (QP) patterns, which are built as a superposition of plane–wave modes with incommensurate spatial periodicities. These topics are selected for the present review, dedicated to the 70th birthday of Professor Michael I. Tribelsky, due to the impact made on them by papers of Prof. Tribelsky and his coauthors. Although some findings revealed in those works may now seem “old”, they keep their significance as fundamentally important results in the theory of nonlinear DW and QP patterns. Adding to the findings revealed in the original papers by M.I. Tribelsky et al., the present review also reports several new analytical results, obtained as exact solutions to systems of coupled real Ginzburg–Landau (GL) equations. These are a new solution for symmetric DWs in the bimodal system including linear mixing between its components; a solution for a strongly asymmetric DWs in the case when the diffusion (second-derivative) term is present only in one GL equation; a solution for a system of three real GL equations, for the symmetric DW with a trapped bright soliton in the third component; and an exact solution for DWs between counter-propagating waves governed by the GL equations with group-velocity terms. The significance of the “old” and new results, collected in this review, is enhanced by the fact that the systems of coupled equations for two- and multicomponent order parameters, addressed in this review, apply equally well to modeling thermal convection, multimode light propagation in nonlinear optics, and binary Bose–Einstein condensates.

Vector soliton dynamics in a high-repetition-rate fiber laser.

The existence of vector solitons that arise from the birefringence nature of optical fibers has been increasingly of interest for the stability of mode-locked fiber lasers, particularly for those operating in the high-fundamental-repetition-rate regime, where a large amount of fiber birefringence is required to restore the phase relation between the orthogonally polarized vector solitons, resulting in stable mode-locking free of polarization rotation. These vector solitons can exhibit diverse time-varying polarization dynamics, which prevent industrial and scientific applications requiring stable and uniform pulse trains at high fundamental repetition rates. This pressing issue, however, has so far been rarely studied. To this end, here we theoretically and experimentally dissect the formation of vector solitons in a GHz-repetition-rate fiber laser and investigate effective methods for suppressing roundtrip-to-roundtrip polarization dynamics. Our numerical model can predict both dynamic and stable regimes of high-repetition-rate mode-locking by varying the amount of fiber birefringence, resulting in the polarization rotation vector soliton (PRVS) and linearly polarized soliton (LPS), respectively. These dynamic behaviors are further studied by using an analytical approach. Interestingly, our theoretical results indicate a cavity-induced locking effect, which can be a complementary soliton trapping mechanism for the co-propagating solitons. Finally, these theoretical predications are experimentally verified, and we obtain both PRVS and LPS by adjusting the intracavity fiber birefringence.

Gain-switched semiconductor laser driven soliton microcombs

Dissipative Kerr soliton generation using self-injection-locked III-V lasers has enabled fully integrated hybrid microcombs that operate in turnkey mode and can access microwave repetition rates. Yet, continuous-wave-driven soliton microcombs exhibit low energy conversion efficiency and high optical power threshold, especially when the repetition frequencies are within the microwave range that is convenient for direct detection with off-the-shelf electronics. Here, by actively switching the bias current of injection-locked III-V semiconductor lasers with switching frequencies in the X-band and K-band microwave ranges, we pulse-pump both crystalline and integrated microresonators with picosecond laser pulses, generating soliton microcombs with stable repetition rates and lowering the required average pumping power by one order of magnitude to a record-setting level of a few milliwatts. In addition, we unveil the critical role of the phase profile of the pumping pulses, and implement phase engineering on the pulsed pumping scheme, which allows for the robust generation and the stable trapping of solitons on intracavity pulse pedestals. Our work leverages the advantages of the gain switching and the pulse pumping techniques, and establishes the merits of combining distinct compact comb platforms that enhance the potential of energy-efficient chipscale microcombs.

Long-Time Asymptotics for the Focusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions in the Presence of a Discrete Spectrum

The long-time asymptotic behavior of solutions to the focusing nonlinear Schrödinger (NLS) equation on the line with symmetric, nonzero boundary conditions at infinity is studied in the case of initial conditions that allow for the presence of discrete spectrum. The results of the analysis provide the first rigorous characterization of the nonlinear interactions between solitons and the coherent oscillating structures produced by localized perturbations in a modulationally unstable medium. The study makes crucial use of the inverse scattering transform for the focusing NLS equation with nonzero boundary conditions, as well as of the nonlinear steepest descent method of Deift and Zhou for oscillatory Riemann–Hilbert problems. Previously, it was shown that in the absence of discrete spectrum the xt-plane decomposes asymptotically in time into two types of regions: a left far-field region and a right far-field region, where to leading order the solution equals the condition at infinity up to a phase shift, and a central region where the asymptotic behavior is described by slowly modulated periodic oscillations. Here, it is shown that in the presence of a conjugate pair of discrete eigenvalues in the spectrum a similar coherent oscillatory structure emerges but, in addition, three different interaction outcomes can arise depending on the precise location of the eigenvalues: (i) soliton transmission, (ii) soliton trapping, and (iii) a mixed regime in which the soliton transmission or trapping is accompanied by the formation of an additional, nondispersive localized structure akin to a soliton-generated wake. The soliton-induced position and phase shifts of the oscillatory structure are computed, and the analytical results are validated by a set of accurate numerical simulations.

XPM‐Induced Vector Asymmetrical Soliton with Spectral Period Doubling in Mode‐Locked Fiber Laser

AbstractCross phase modulation (XPM) can induce soliton trapping in nonlinear medium, which has been employed to achieve vector soliton, optical switching, and optical analog of gravity‐like potentials. Here, the first observation of a novel soliton operation is reported whose wavelength exhibits redshift and blueshift periodically in a mode‐locked fiber laser under appropriate birefringence and dispersion map. XPM dominates the dynamics by inducing and sustaining the vector asymmetrical soliton (VAS) with spectral period doubling, and exhibits a unique trajectory of pulse trapping. The XPM‐induced VAS is an idiosyncratic steady state featured with asymmetry in the model based on the coupled Ginzburg–Landau equation, which depicts the distinct pulse features in comparison with vector soliton, soliton molecule, and traditional period‐doubling evolutions. The two orthogonal polarized directions of mode‐locked fiber laser can be regarded as the XPM‐coupled dissipative resonators guiding the further study of the optical nonlinear dynamics and chaos for soliton, which is helpful to laser design and brings useful insights into nonlinear science and applications.

Oscillatory motion of a counterpropagating Kerr soliton dimer

Both the group velocity and phase velocity of two solitons can be synchronized by a Kerr-effect mediated interaction, causing what is known as soliton trapping. Trapping can occur when solitons travel through single-pass optical fibers or when circulating in optical resonators. Here, we demonstrate and theoretically explain a new manifestation of soliton trapping that occurs between counter-propagating solitons in microresonators. When counter-pumping a microresonator using slightly detuned pump frequencies and in the presence of backscattering, the group velocities of clockwise and counter-clockwise solitons undergo periodic modulation instead of being locked to a constant velocity. Upon emission from the microcavity, the solitons feature a relative oscillatory motion having an amplitude that can be larger than the soliton pulse width. This relative motion introduces a sideband fine structure into the optical spectrum of the counter-propagating solitons. Our results highlight the significance of coherent pumping in determining soliton dynamics within microresonators and add a new dimension to the physics of soliton trapping.

Stationary and pulsating vector dissipative solitons in nonlinear multimode interference based fiber lasers.

Rapid progress in real-time spectroscopy uncovers the spatio-spectral scenarios of ultrashort pulses in dissipative systems. Varieties of transient soliton dynamics on different timescales have been revealed. Here, we report on an experimental observation of stationary and pulsating vector dissipative solitons in a nonlinear multimode interference (NL-MMI) based fiber laser with net normal dispersion. Polarization non-discrimination of the NL-MMI mode-locking facilitates the dissipative soliton trapping process. Two orthogonally polarized components are coupled together through oppositely shifting their central frequencies to form the group-velocity-locked vector dissipative solitons (GVLVDSs). Dispersive Fourier transform (DFT) based polarization resolved measurement enables insights into the transient polarization dynamics and the long-term evolution. Particularly, both stationary and pulsating GVLVDSs are obtained with appropriate parameter settings. It is found that the quasi-stationary pulsating manner is accompanied with recurrent spectral breathing and energy oscillation; the two orthogonally polarized components possess synchronous pulsating manners due to the cross-phase modulation induced trapping mechanism and the similar formation process. Additionally, chaotic pulsation is also captured in sense that the spectra cannot recover to their original profiles despite of the harmonic energy oscillation. All these findings can enhance our understanding towards soliton pulsation with the freedom of vectorial degree.

Study on the impact of high-order effects on the evolution of a trapped soliton pumped by a high-power pulse

We theoretically and numerically investigate the influence of high-order effects on a trapped soliton pumped by a high-power pulse during nonlinear propagation. According to the moment method, some evolution rules of a trapped soliton are found in the presence of high-order effects by theoretically analyzing five moment parameters. Further, the temporal and spectral evolutions of a trapped soliton are numerically studied in details. It is demonstrated that the third-order dispersion (TOD) only affects the center position of a trapped soliton, but it does not change the spectrum structure. The intrapulse Raman scattering (IRS) causes a trapped soliton to red-shift and modifies the spectrum structure, thus the asymmetric oscillation structure is generated in the lagging edge of a spectrum. The self-steepening (SS) mainly changes the distribution of red-shifted components, however, it has little effect on the blue-shifted spectrum. Moreover, suppression or enhancement of the Raman-induced frequency shift (RIFS) affected by TOD and SS is also discussed.

Theoretical Study on Dual-Comb Generation and Soliton Trapping in a Single Microresonator with Orthogonally Polarized Dual Pumping

Microresonator-based optical frequency combs (known as microcombs or Kerr combs) have a large repetition frequency ranging typically from 10 to 1000 GHz, which is compatible with fast-scanning applications, including dual-comb spectroscopy and LiDAR. In this research, we numerically study dual-comb generation and soliton trapping in a single microresonator, whose two transverse modes are excited with orthogonally polarized dual pumping. The simulation model is described by using coupled Lugiato-Lefever equations (LLEs), which take account of cross-phase modulation and the difference in repetition frequencies. The numerical simulation calculates the dual-comb formation in a microresonator, whose microcombs propagate as soliton pulses and cause soliton trapping depending on the parameters. In the simulation, a trapped soliton is seeded by one of the original solitons in two transverse modes. In addition, we introduce an analytical solution for trapped solitons in coupled LLEs using a Lagrangian perturbation approach and clarify the relation between the parameters. Revealing the conditions of dual-comb soliton generation and soliton trapping is helpful in terms of optimizing the conditions for causing or avoiding these phenomena.