Soliton States Research Articles

Dynamics of twin pulse propagation and dual-optical switching in a Λ + Ξ atomic medium

Optical bistability (OB) and optical multistability (OM) as well as optical soliton and all-optical switching have been successfully established in a lambda + cascade-type five-level atomic medium under electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) regimes. For this configuration, three laser fields are required to excite atomic transitions. The probe laser field with two circularly left- and right-polarized components excites atoms in a lambda-type configuration. Meanwhile, two coupling laser fields excite atoms in a ladder-type configuration. In this way, the above optical phenomena can occur with two frequency channels corresponding to the circularly left- and right-polarized light components. By adjusting the strength/direction of the static magnetic field in the presence of the driving field, the EIT and EIA effects can be swapped, at the same time, OB and OM effects can also be converted. In the EIT regime, the propagation of the probe pulse easily achieves the soliton state, whereas it can be completely extinguished in the EIA regime. This makes it easy to create an all-optical switching mechanism. Especially, both components of the probe field (cw) can be modulated into a synchronous or asynchronous square pulse according to the modulation of the driving field. The results obtained from the investigated model may provide merits of the applications for optical storage and all-optical switching for multi-channel optical communications.

Scattering amplitudes of fermions on monopoles

We consider scattering processes involving massless fermions and ’t Hooft-Polyakov magnetic monopoles in a minimal SU(2) model and in the Grand Unified SU(5) theory. We construct expressions for on-shell amplitudes for these processes in the J = 0 partial wave using the spinor helicity basis consisting of single-particle and pairwise helicities. These processes are unsuppressed and are relevant for the monopole catalysis of proton decay. The amplitudes for the minimal processes involving a single fermion scattering on a monopole in the initial state and half-fermion solitons in the final state are presented for the first time and are used to obtain the amplitudes for processes involving more fermions in the initial state and integer fermion numbers in the final state. A number of such anomalous and non-anomalous processes, along with their amplitude expressions, are written down for the SU(5) GUT model.

Multisoliton complex systems with explicit superpotential interactions

We consider scalar field theories in dimensions with N fields which interact through a potential , which is defined in terms of an explicit superpotential W. We construct W for any N in terms of a known superpotential w for a single-scalar model, such as that for the sine-Gordon equation or the ϕ 4 model, leading to an expression for V which has multiple minima that supports solitons. Static solitons which minimize the total energy in each soliton sector appear as solutions of first-order Bogomolny equations, which have a gradient structure. These are identical in form to equations which arise in the context of synchronization phenomena in complex systems, with the space and time variables interchanged. The sine-Gordon superpotential, for example, leads to an explicit periodic superpotential W for N scalar fields, with associated Bogomolny equations that are equivalent to the well-known Kuramoto equations which describe the synchronization of identical phase oscillators on the unit circle. The known asymptotic properties of the Kuramoto system, for both positive and negative coupling constants, ensure that finite-energy solitons exist for any given set of intermediate values imposed at the origin. Besides the models derived from the sine-Gordon equation, we investigate ϕ 4 and ϕ 6 models with N scalar fields and show numerically that solitons again exist over a wide range of parameters. We also derive general properties of the elementary meson excitations of the system, in particular we show that meson-soliton bound states exist over a restricted range of mass parameters with respect to an exact solution of the ϕ 6 system for N = 3.

Routes from stationary dissipative solitons to chaos in a Mamyshev oscillator

Mamyshev oscillators (MOs), a new type of femtosecond fiber laser, can produce not only high-performance stationary dissipative solitons (SDSs), but also exhibit chaotic dynamics. Since chaotic behavior may lead to dramatic degradation of the performance, it is particularly important to investigate chaotic dynamics in MOs. Here, using numerical simulation and experimental research methods, we systematically investigate different routes from SDSs to chaos in an MO. Specifically, by simply increasing the gain saturation energy under different polarization states, we obtained different routes from SDSs to chaos, including via a cascade of period-doubling bifurcations (CPDB), via a quasi-cascade of period-doubling bifurcations, and via a double CPDB. In addition, the evolution from dissipative soliton molecules to chaos via CPDB was also observed by increasing the gain saturation energy with a small filter wavelength separation. This finding shows that the evolution from SDSs to chaos is a generic property of laser systems and can appear in various pulse patterns such as single pulse, dissipative soliton molecules, and harmonic mode-locking pulses, which may be beneficial for better understanding chaotic dynamics in MOs.

Bright and Dark Soliton Pulse in Solid Core Photonic Crystal Fibers

The nonlinear Schrodinger (NLS) equation was utilized to conduct an analytical study on the soliton control in homogeneous photonic crystal fibers (PCFs) within both the normal and anomalous dispersion regimes. The split step Fourier method and MATLAB computation were used to generate the analytical soliton solutions for the NLS problem. The bright and dark soliton can be controlled by the group-velocity distribution (GVD). It is capable of demonstrating the fabrication of a fully coherent PCF. Moreover, dark soliton pulses have been seen in PCF in the typical dispersion domain. Here, we present the bound states of bright–dark soliton pairs that are mutually confined in a PCF. Solitons are produced when two modes with opposing dispersions are replanted. One laser operating in the anomalous dispersion domain produces the bright soliton, while the second laser running in the normal dispersion phase produces the dark soliton by normal dispersion cross-phase modulation with the light soliton. The results unequivocally point to a novel method of generating dark soliton pulses. Capturing both bright and dark solitons can produce light states that, interestingly, have a consistent power output and spectrally resemble a frequency comb. These results may have use in soliton states in atomic physics, ultrafast optics, frequency comb technologies, and telecommunications systems. A radically new approach to the stabilization of powerful wave packages in the negative and positive GVD regions of interacting waves is illustrated.

Transformation of rotating dipole and vortex solitons in an anharmonic potential

We investigate the basic properties of dipole and vortex solitons, both quiescent and rotating, supported by the axially symmetric anharmonic potential in a medium with cubic-quintic nonlinearity. The static solitons exhibit nonmonotonous behavior in terms of propagation constant as a function, and feature bistability regions. In the rotating frame, the dipole solitons transform into vortex solitons and the topological charge increases gradually with the growth of rotation frequency. Linear stability analysis and direct simulations reveal that rotating dipole solitons with higher charges are more stable than those with lower charges. Meanwhile, dipole solitons can rotate persistently during propagation and preserve their shape over multiple rotation periods. Our findings provide an alternative way for the transformation to achieve dipole and vortex solitons with higher topological charges.

Noisy soliton pulsation and its dynamics in a mid-infrared ultrafast fiber laser

We demonstrate the real-time dynamics of a unique pulsating soliton state featuring noisy behaviors in a mid-infrared ultrafast fiber laser at 2 μm. By virtue of the time-stretch dispersive Fourier transform method, the pulsating behaviors of the noisy solitons are investigated. We find that the noisy pulsating solitons are characterized by a special optical spectrum. The shot-to-shot spectra and pulse energy of these pulsating noisy pulses can evolve periodically with the roundtrips. Besides, the real-time optical spectra within a single period exhibit irregular fluctuations in terms of the spectral profile and intensity, suggesting that the pulsating solitons are made up of noisy wave packets with chaotic features. These results can further enrich the pulsating soliton dynamics and also give new insights into the nonlinear pulse dynamics of mid-infrared ultrafast fiber lasers.

Controllable and abundant soliton states from an all-fiber laser based on a ZrGeTe4 saturable absorber

With many applications increasing expectations for the tunability of coherent pulses, the demand for tunable soliton fiber lasers (TSFLs) is growing. Two-dimensional ternary zirconium germanium telluride (ZrGeTe4) nanomaterials provide an opportunity to obtain high-performance TSFLs. In this research, we developed a TSFL with ZrGeTe4-based saturable absorber (SA). Employing a strategy of constant pump power, tunable soliton states were acquired. The 1st to 5th order harmonic mode-locking were obtained sequentially. The shortest pulse able to obtain was 1.05 ps. Furthermore, the soliton molecule was also obtained. The results suggest that ZrGeTe4-SA may provide an effective route for photonics research.

Using dark solitons from a Bose–Einstein condensate necklace to imprint soliton states in the spectral memory of a free boson gas

A possible use of matter-wave dark-soliton crystal produced by a Bose–Einstein condensate (BEC) with ring geometry, to store soliton states in the quantum memory of a free boson gas, is explored. A self-defocusing nonlinearity combined with dispersion and the finite size of the BEC, favor the creation of dark-soliton crystals that imprint quantum states with Jacobi elliptic-type soliton wavefunctions in the spectrum of the free boson gas. The problem is formulated by considering the Gross–Pitaevskii equation with a positive scattering length, coupled to a linear Schrödinger equation for the free boson gas. With the help of the matter-wave dark soliton-crystal solution, the spectrum of bound states created in the free boson gas is shown to be determined by the Lamé eigenvalue problem. This spectrum consists of quantum states whose wave functions and energy eigenvalues can be unambiguously identified. Among these eigenstates some have their wave functions that are replicas of the generating dark soliton crystal.

Symmetry-breaking bifurcations and excitations of solitons in linearly coupled NLS equations with PT-symmetric potentials

We address symmetry-breaking bifurcations (SBBs) in the ground state (GS) and dipole-mode (DM) solitons of the one-dimensional linearly coupled NLS equations, modelling the propagation of light in a dual-core planar waveguide with the Kerr nonlinearity and two types of P T -symmetric potentials. The P T -symmetric potential is employed to obtain different types of solutions. A supercritical pitchfork bifurcation occurs in families of symmetric solutions of both the GS and DM types. A novel feature of the system is interplay between breakings of the P T and inter-core symmetries. Stability of symmetric GS and DM modes and their asymmetric counterparts, produced by SBBs of both types, is explored via the linear-stability analysis and simulations. It is found that the instability of P T -symmetric solutions takes place prior to the inter-core symmetry breaking. Surprisingly, stable inter-core-symmetric GS solutions may remain stable while the P T symmetry is broken. Fully asymmetric GS and DM solitons are only partially stable. Moreover, we construct symmetric and asymmetric GS solitons under the action of a pure imaginary localized potential, for which the SBB is subcritical. These results exhibit that stable solitons can still be found in dissipative systems. Finally, excitations of symmetric and asymmetric GS solitons are investigated by making the potential’s parameters or the system’s coupling constant functions, showing that GS solitons can be converted from an asymmetric shape onto a symmetric one under certain conditions. These results may pave the way for the study of linear and nonlinear phenomena in a dual-core planar waveguide with P T potential and related experimental designs.

Reproduction of mode-locked pulses by spectrotemporal domain-informed deep learning.

The accurate reproduction of unique pulse states in a mode-locked fiber laser is an important scientific issue and has wide applications in the laser industry. We present what we believe to be a novel method for automatically and precisely reproducing targeted soliton states in a mode-locked fiber laser by spectrotemporal domain-informed deep learning. Targeted solitons are experimentally reproduced via a superior matching process with a spectrotemporal mean square error (MSE) of 3.99 × 10-5. The outstanding feature of our reproduction algorithm is that the pulse information in both the spectral and temporal domains is jointly adopted for reconstructing targeted soliton states from white noise, rather than establishing arbitrary mode-locked pulse states, as described in previous studies. Additionally, a single-layer perceptron model is proposed to retrieve the phase distribution of a mode-locked pulse, validating the physical completeness of our reproduction approach. Our approach advances ultrafast laser technology, enabling the precise control of pulse dynamics in applications such as optical communication and nonlinear optics.

Versatile octave-spanning soliton crystals with high conversion efficiency in a Si3N4 microresonator.

Microresonator-based soliton crystals are a key recent advancement in the study of the rich nonlinear dynamics of soliton states. The soliton crystals are self-organized temporal pulses filling the microresonator cavity and have strong comb lines with wide spacing making them of great interest in many potential applications such as communication and meteorology. However, achieving a broad spectrum, tunable repetition rates, and high conversion efficiency are still a challenge. Here, we report the deterministic generation of versatile octave-spanning soliton crystals with various repetition rates via avoided mode crossings. In addition, we investigate the conversion efficiency of the obtained soliton crystals and achieved above ∼50% in one of the devices with a suitable coupling. Our results pave the way for accessing coherent broad and tunable on-chip soliton crystals, thus requiring a rigorous and viable microcavity design to engineer the desired mode coupling position.

A solvable model for symmetry-breaking phase transitions

Analytically solvable models are benchmarks in studies of phase transitions and pattern-forming bifurcations. Such models are known for phase transitions of the second kind in uniform media, but not for localized states (solitons), as integrable equations which produce solitons do not admit intrinsic transitions in them. We introduce a solvable model for symmetry-breaking phase transitions of both the first and second kinds (alias sub- and supercritical bifurcations) for solitons pinned to a combined linear-nonlinear double-well potential, represented by a symmetric pair of delta-functions. Both self-focusing and defocusing signs of the nonlinearity are considered. In the former case, exact solutions are produced for symmetric and asymmetric solitons. The solutions explicitly demonstrate a switch between the symmetry-breaking transitions of the first and second kinds (i.e., sub- and supercritical bifurcations, respectively). In the self-defocusing model, the solution demonstrates the transition of the second kind which breaks antisymmetry of the first excited state.

Nonlinear-Fourier-Transform-Based Dynamic Analyses on the Multiple Cavity Solitons in Kerr Microresonators

The Kerr microresonators have aroused widespread interests for their ultrahigh integration, compatible fabrication and ultralow energy consumption. Similar to the traditional mode-locked fiber lasers, the microresontors can sustain the generation of dissipative solitons called cavity solitons relying on the double balance of gain and loss as well as nonlinearity and dispersion. The state of multiple solitons is common in the microresonator with anomalous dispersion. In particular, an ideal state named as soliton crystals is obtained when the multiple solitons have a equidistant arrangement. And recent experiments have successfullly observed soliton crystals in the Kerr microresonators. To intuitively reveal the formation and evolution dynamics of the multiple solitons and get insight into the underlying physical mechanisms of soliton crystals, we applied the nonlinear Fourier transform to project these states into nonlinear discrete spectrum. The discrete spectra of single soliton with different modulated background waves have been displayed, which can help distinguish different optical components. Then, the nonlinear spectrum evolution of normal multiple solitons state shows the typical nonlinear states of the intracavity field. And the equidistant solitons have the effects of power enhancement, whose spectral intensity is several times that of a single soliton state. Comparing with the discrete spectrum of the equidistant solitons, the solitons inside the soliton crystals interact with each other by the modulated background. Our results suggest that the nonlinear Fourier transform is a powerful technique to characterize soliton dynamics in the Kerr microresonator, which provides a new perspective to understand the interactions of cavity solitons.

Soliton Interactions with Different Dispersion Curve Functions in Heterogeneous Systems

In practical optical communication systems, there are some factors that can affect transmission quality of optical solitons. The constant coefficient nonlinear Schrödinger (NLS) equation has been unable to meet the actual research needs. We need to use the variable coefficient NLS equation to simulate an actual system, so as to explore its potential application value. Based on the variable coefficient NLS equation, six dispersion decreasing fibers (DDFs) with different dispersion curve functions are used as transmission media to study generation and interaction of two solitons in an optical communication system. The two soliton interaction phenomena, such as the bound state solitons, are theoretically obtained. Moreover, the output characteristics of bound state solitons in different DDFs are discussed, which enriches the transmission phenomenon of two solitons in the optical communication system. This study has great application value in fields such as optical information processing devices, condensed matter physics, and plasma, and provides an indispensable theoretical basis for development of new optical devices.

Multiple Bound State Soliton Pulses in the All Polarization Maintaining Fiber Laser.

The bound state soliton pulse, a novel mode-locked output state of fiber lasers, has been studied extensively to gain a better understanding of soliton interactions and to explain the mechanism behind the generation of mode-locked pulses. In this particular research, we utilized a self-made saturable absorber (SA) consisting of single-walled carbon nanotubes (SWCNT) in a fully polarization maintaining (PM) erbium-doped fiber optical path. Through this setup, we observed various bound state pulse phenomena, including the double bound state with different phase differences, the bound state formed by two double pulse bound states, the multi-pulse bound state, etc. The abundant bound soliton pulse states demonstrated the excellent nonlinear absorption characteristics of the SA as well as the excellent optical properties of the all-PM fiber laser. It contributed to exploring the relationship between sub pulses and mode-locked pulses in the future. Additionally, due to the strong interaction between bound state solitons and the inherent stability of the PM optical path, there was potential for utilizing this setup as a seed source to enhance the stability of high-power fiber lasers.

Delayed feedback control on wave dynamics in a nonlinear optical cavity with third-order chromatic dispersion

By taking into account third-order dispersion effects in the presence of feedback, we investigate the stability and nonlinear dynamic movements of waves created in microcavities and fiber cavities from numerical simulations of the extended Lugiato–Lefever equation. The current analysis emphasizes that third-order scattering, feedback strength, and feedback local and global components allow for the numerical observation of dissipative bound states of solitons and chaos with extended and antisymmetric interaction domains. In this regard, we demonstrate how the symmetry of the localized structural interactions is broken by the radiation that results from third-order dispersion.

Real-time evolution dynamics during transitions between different dissipative soliton states in a single fiber laser.

Various dissipative soliton solutions exist in the parameter space of mode-locked fiber lasers, including both coherent and incoherent pulses. Novel ultrafast laser designs can lead to distinctive dissipative soliton solutions formed by unique pulse shaping dynamics in the same cavity. However, transitionary states in between steady-state mode-locked regimes remain largely unexplored. Here, we investigate the intermediate transition dynamics in a versatile Tm-doped fiber laser capable of emitting both dissipative solitons with anomalous-dispersion and normal-dispersion pulse-shaping mechanisms by adjusting an intracavity polarization controller. Real-time pulse dynamics during mode-locking transitions are analyzed with a modified dispersive Fourier transform setup, illustrating characteristic pulse shaping mechanisms typically reserved for different dispersion regimes. Combined with a spectral intensity correlation analysis, the coherence evolution between two distinct mode-locked states is fully resolved for the first time.

Noise-like pulses in dispersion-controlled fiber lasers

Noise-like pulse generation in ring lasers in which the anomalous dispersion of the cavity fiber is partially compensated by using a normal-dispersion fiber has been studied by numerical simulation. Solitons moving in this cavity are periodically subjected to temporal compression in the anomalous-dispersion fiber and expansion in the normal-dispersion fiber. It has been found that in these lasers, stationary solitons become unstable and passive mode locking occurs through the emission of bunched noise-like pulses consisting of chaotically evolving solitons. The results are relevant to the development of noise-like pulse generation and methods for controlling lasing regimes.

Real-time observation of stationary and pulsating noise-like vector pulses in a fiber laser.

Rapid progress in real-time measurement technology has uncovered varieties of transient pulse dynamics. Here, we report the vector nature of noise-like pulse (NLP) in a passive fiber laser based on the nonlinear optical loop mirror (NOLM) as the polarization independent saturable absorber. After achieving the basic operation regime of NLP, various types of vector pulses, namely, the polarization locked noise-like vector pulse (PLNLVP), the group velocity locked noise-like vector pulse (GVLNLVP), and the transitional state of combined characteristics of GVLNLVP and polarization rotation noise-like vector pulse (PRNLVP) are also obtained in the cavity. Besides, by utilizing the Dispersive Fourier transform (DFT) technique, the spectral evolution and the energy vibration of pulsating PLNLVP, GVLNLVP, and the transitional state of combined characteristics of GVLNLVP and PRNLVP are also analyzed in real time. Particularly, the coexisting pulsation vector state of NLP and soliton is also captured. All these findings will help to complement our understanding of noise-like vector pulses (NLVPs) in a fiber laser.