Soliton Fission Research Articles

Rational, semi-rational solution and self-consistent sources extension of the variable-coefficient extended modified Kadomtsev-Petviashvili equation

In this paper, we apply Hirota bilinear method and determinant technique to derive the Nth-order rational solution expressed compactly in terms of Matsuno determinants for the variable-coefficient extended modified Kadomtsev-Petviashvili (mKP) equation. As a special case, we obtain the M-lump solution expressed in terms of 2M × 2M determinants for the mKPI equation and investigate the dynamical behaviors of 1- and 2-lump solutions. Furthermore, we present the Wronskian and Grammian solution for the variable-coefficient extended mKP equation. Based on the Grammian solution, we construct the line soliton, the line breather and the semi-rational solution on constant and periodic backgrounds for the mKPI equation. Through the asymptotic analysis, we show that the semi-rational solutions describe the fission and fusion of lumps and line solitons. In addition, we construct the variable-coefficient extended mKP equation with self-consistent sources via the source generation procedure and derive its N-soliton solution in the compact form of Grammian and Wronskian.

Experimental and numerical investigation of breaking bores in straight and meandering channels with different Froude numbers

ABSTRACT This study investigates the propagation characteristics of breaking bore in meandering channels focusing on the effects of Froude number (F) on the breaking bore. The experiments are conducted with different Froude number conditions of F = 3.99 for high F and F = 1.53 for low F in a straight and meandering channel. The experimental results are compared with calculated results by Shallow Water Equation (SWE) model and three-dimensional calculation model. In the low F condition, the oscillation of water level like a soliton fission was observed and it was amplified along both banks in the meandering channel. This was explained using the temporal variation of the transverse water surface gradient calculated by SWE model, that is not related with non-hydrostatic pressure component and vertical distribution of the velocity. The high F condition is characterized by the longitudinal gradient of bore head caused by large energy loss. In the meandering channel, the SWE model overestimated the wave height near the bore front along both banks. This is because the secondary flow in the meandering channel increases the velocity near the bed and the flow resistance compared with low F condition and reduces the wave height.

M -Lump Solution, Semirational Solution, and Self-Consistent Source Extension of a Novel 2 + 1 -Dimensional KdV Equation

In this paper, we derive the M -lump solution in terms of Matsuno determinant for the combined KP3 and KP4 (cKP3-4) equation by applying the double-sum identities for determinant and investigate the dynamical behaviors of 1- and 2-lump solutions. In addition, we derive the Grammian solution for the cKP3-4 equation and construct the semirational solutions from the Grammian solution. Through the asymptotic analysis, we show that the semirational solutions describe fusion and fission of lumps and line solitons and rogue lump phenomena. Furthermore, we construct the cKP3-4 equation with self-consistent sources via the source generation procedure and present its Grammian and Wronskian solution.

Galilean-transformed solitons and supercontinuum generation in dispersive media

The Galilean transformation is a universal operation connecting the coordinates of a dynamical system, which move relative to each other with a constant speed. In the context of exact solutions of the universal nonlinear Schrödinger equation (NLSE), inducing a Galilean velocity (GV) to the pulse involves a frequency shift to satisfy the symmetry of the wave equation. As such, the Galilean transformation has been deemed to be not applicable to wave groups in nonlinear dispersive media. In this paper, we demonstrate that in a wave tank generated Galilean-transformed envelope and Peregrine solitons show clear variations from their respective pure dynamics on the water surface. The type of deviations depends on the sign of the GV and can be captured by the modified NLSE or the Euler equations. Moreover, we show that positive Galilean-translated envelope soliton pulses exhibit self-modulation. While designated GV and wave steepness values expedite multi-soliton dynamics, the strong focusing of such higher-order coherent waves inevitably lead to the generation of supercontinua as a result of soliton fission. We anticipate that kindred experimental and numerical studies might be implemented in other dispersive wave guides governed by nonlinearity.

Validation of tsunami numerical simulation models for an idealized coastal industrial site

ABSTRACT Numerous tsunami numerical models have been proposed, but their prediction accuracies have not been directly compared. For quantifying the modeling uncertainties, the authors statistically analyzed the prediction results submitted by participants in the tsunami blind contest held at the 17th World Conference on Earthquake Engineering. The reproducibility of offshore water level generated due to the tsunami with soliton fission significantly decreased when the nonlinear shallow water equation models (NSWE) was used compared to three-dimensional (3D) models. The inundation depth was reproduced well in 3D models. However, the reproducibility of wave forces acting on the structure and velocities over land was lower in 3D models than that in NSWE models. For cases where the impulsive tsunami wave pressure generated could not be calculated based on the hydrostatic assumption, the prediction accuracy of the NSWE models was higher than that of the 3D models. The prediction accuracies of both models were not improved at small grid-cell sizes. The NSWE model cannot simulate the short-wave component and vertical pressure distribution. Therefore, further developments in 3D models and smoothed particle hydrodynamics methods (SPH) are needed. The presented results contribute to the future development of tsunami numerical simulation tools.

Two new integrable differential-difference hierarchies related to the relativistic Toda lattice equation and their soliton fusion or fission

Starting from a discrete spectral problem, two new integrable differential-difference hierarchies are presented and their Lax pairs are given, respectively. The first hierarchy is related to the relativistic Toda lattice equation. Darboux transformations for the first systems in the two hierarchies are derived, respectively, accordingly their explicit solutions are obtained. By selecting appropriate parameters, we can see the phenomena of soliton fission or soliton fusion.

Scaling of self-compression of near-IR femtosecond pulses in hollow-core fibers down to the single-cycle limit

We numerically investigate the scaling of self-compression processes with experimental parameters for near-infrared ultrashort pulses (30 fs) in gas-filled hollow-core fiber (HCF). These simulations over a wide-range of input pulse energies as well as filling gas pressures reveal a remarkable scaling of the self-compression process and dynamics. As a function of soliton order N, we identify the relation between the propagation distance after which self-compression in the HCF begins and the subsequent propagation length up to which the pulse remains maximally compressed; both these length scales decrease with an increase in N, the soliton order. Although previous investigations revealed pulse compression scaling laws which provide a good approximation for input pulse-widths ∼100 fs down to the limit where soliton fission begins to dominate the dynamics, these are not sufficiently accurate to describe the entire scaling dynamics. Instead, we identify a more generalized set of scaling laws by taking both third-order dispersion and the saturation of the compression factor due to soliton fission into account. These conclusions about scaling are robust: our simulations were carried out over a wide range of realistic input pulse energies and gas pressures as implemented in laboratories taking into account higher-order dispersive properties of the gaseous propagating medium. Therefore, given that these numerical investigations consider conditions typically applied in practice in laboratories, this work provides elegant design principles and guideposts relevant to realizing systems capable of achieving self-compression at substantially high pulse energies down to the few-cycle limit; they are of paramount importance in generating single as well as trains of attosecond pulses and acceleration strategies for electrons and ions in intense laser pulses.

Hamiltonian approach to modelling interfacial internal waves over variable bottom

We study the effects of an uneven bottom on the internal wave propagation in the presence of stratification and underlying non-uniform currents. Thus, the presented models incorporate vorticity (wave–current interactions), geophysical effects (Coriolis force) and a variable bathymetry. An example of the physical situation described above is well illustrated by the equatorial internal waves in the presence of the Equatorial Undercurrent (EUC). We find that the interface (physically coinciding with the thermocline and the pycnocline) satisfies in the long wave approximation a KdV–mKdV type equation with variable coefficients. The soliton propagation over variable depth leads to effects such as soliton fission, which is analysed and studied numerically as well.

Dispersive wave generation at 4 µm in a dispersion-engineered fluorotellurite fiber pumped by a 1.98 µm femtosecond fiber laser

We demonstrate dispersive wave generation at 4 µm in a dispersion-engineered fluorotellurite fiber pumped by a 1.98 µm femtosecond fiber laser. All-solid fluorotellurite fibers with a core diameter of ∼2.6 µm are fabricated by using a rod-in-tube method. The fluorotellurite fibers have two zero-dispersion wavelengths (ZDWs). The first ZDW is 1.328 µm and the second one is 3.551 µm. As the pump laser is launched into the fluorotellurite fiber, firstly, tunable mid-infrared Raman solitons are generated through higher order soliton compression, soliton fission and soliton self-frequency shift. Then, red-shifted dispersive wave at 4 µm is generated as those Raman solitons meet the second ZDW (∼3.551 µm) and soliton self-frequency shift cancellation occurs. Our results show that dispersion-engineered fluorotellurite fibers are promising nonlinear media for constructing all-fiber 4 µm light sources

Cadmium telluride waveguide for coherent MIR supercontinuum generation covering 3.5-20 µm.

The mid-infrared (MIR) wavelength coincides with various molecular resonances. In particular, a 13-20 µm wavelength window has fingerprints of unique groups such as organometallic, halogenated, and aromatic bonds. In this work, for the first time, to the best of our knowledge, an on-chip supercontinuum generation (SCG) source based on cadmium telluride (CdTe)/ cadmium sulfide (CdS)/ silicon heterostructure is proposed to extend the on-chip SCG beyond 13 µm (spanning 3.5 to 20 µm). CdTe has an ultra-broad transparent spectral range up to 25 µm, and almost the largest third-order nonlinear coefficient (n2∼ 5×10-17 m2/W at 1.55 µm, 1.3×10-17 m2/W at 9 µm, several times larger than that of silicon) among the MIR materials, making CdTe an excellent candidate for long-wavelength MIR on-chip SCG. The waveguide structure is designed with CdS as the intermediate cladding layer to achieve a low waveguide loss and high mode confinement. A large-core CdTe waveguide is tailored to generate a low and flat dispersion (< 30 ps/nm/km) in a spectral range spanning from 5 to 20 µm, while balancing the large effective nonlinearity and the convenience of coupling. The simulation results solved by the nonlinear Schrödinger equation manifest that the engineered large cross-section waveguide with only 2.5-mm propagation distance broadens the MIR spectrum covering 3.5 to 20 µm pumped by a 9 µm femtosecond laser. Moreover, it is found that good coherence is achieved from the designed MIR waveguide, before severe soliton fission breaks the temporal profile. 5-fold self-compression of the pump pulse down to 1.6 optical cycles is observed while propagating inside the CdTe waveguide. The detailed simulation of the CdTe/CdS/Si waveguide design with the various waveguide parameters, polarizations, pump wavelengths, and pump power are provided. With the SC spectrum covering almost the entire fingerprint regime and the excellent coherence generated from the designed CdTe waveguide, it provides abundant new opportunities for MIR microphotonics.

Supercontinuum generation with interference fringes through two-soliton bound state

We experimentally and numerically study the supercontinuum (SC) generation with dense interference fringes by two-soliton bound state picosecond lasers based on the soliton fission and self-phase modulation. The simulations are consistent with the experimental results. The bandwidth, flatness and modulation depth of SC can be improved through detailed dispersion optimization. The simulation results suggest that the interference fringes depend on the two-soliton bound state and their modulation period can be adjusted by changing its pulse separation. We found that a smaller pulse duration helps to strengthen the modulation depth of SC. Increasing the pulse duration and amplifier gain will cause the deterioration of the modulation depth and coherence of SC, which indicates the necessity of reducing noise in the system. This work provides an interesting and novel method to study the mechanism of SC generation.

730 mW, 2-8 μm supercontinuum generation and the precise estimation of multi-pulse spectral evolution in the soft-glass fibers cascaded nonlinear system

We experimentally demonstrate the 2-8 μm high-power supercontinuum generation and theoretically propose a statistical method for precise estimation of the multi-pulse spectral evolution in the ZBLAN and As2S3 fiber cascaded all-fiber structured nonlinear system. In the experiment, with the aid of the ultra-low loss fusion splice technology, high-efficiency fiber butt-coupling technology and precise thermal management technology, we obtained a record-breaking supercontinuum source with a spectrum spanning from 2 μm to 8 μm at a power of 730 mW. Considering the strong pulse splitting and soliton fission effects in fibers, to precisely estimate the multi-pulse spectral evolution in this system, we, for the first time, built a multi-pulse pump model with the Pearson product-moment correlation coefficient method based multi-pulse selection mechanism. In combination with the existing approaches and some new programmatic work, finally, we verified that the simulation results are in good agreement with the experimental one.

Soliton fusion and fission for the high-order coupled nonlinear Schrödinger system in fiber lasers

With the rapid development of communication technology, optical fiber communication has become a key research area in communications. When there are two signals in the optical fiber, the transmission of them can be abstracted as a high-order coupled nonlinear Schrödinger system. In this paper, by using the Hirota’s method, we construct the bilinear forms, and study the analytical solution of three solitons in the case of focusing interactions. In addition, by adjusting different wave numbers for phase control, we further discuss the influence of wave numbers on soliton transmissions. It is verified that wave numbers k 11, k 21, k 31, k 22, and k 32 can control the fusion and fission of solitons. The results are beneficial to the study of all-optical switches and fiber lasers in nonlinear optics.

Generation of mid-infrared supercontinuum by designing circular photonic crystal fiber

A circular photonic crystal fiber (C-PCF) based on As2Se3 is designed, which has three zero dispersion wavelengths and flat dispersion. Using this fiber, a wide mid-infrared supercontinuum (MIR-SC) can be generated by launching a femtosecond pulse in the first anomalous dispersion region. The simulation results show that the MIR-SC is formed by soliton self-frequency shift and direct soliton spectrum tunneling on the long wavelength side and self-phase modulation, soliton fission on the short wavelength side. Further, optical shocking and four-wave mixing (FWM) are not conducive to the long-wavelength extension of MIR-SC, while the number and intensity of fundamental solitons have a greater effect on the short-wavelength extension of MIR-SC. The generation of optical shocking waves, FWM waves and fundamental solitons can be obviously affected by changing the fiber length and input pulse parameters, so that the spectrum range and flatness can be adjusted with great freedom. Finally, under the conditions of 4000 W pulse peak power, 30 fs pulse width, 47 mm fiber length, and 0 initial chirp, a wide MIR-SC with a coverage range of 2.535 μm–16.6 μm is obtained. These numerical results are encouraging because they demonstrate that the spread of MIR-SC towards the red and blue ends can be manipulated by choosing the appropriate incident pulse and designing optimized fiber parameters, which contributes to applications in such diverse areas as spectroscopy, metrology and tomography.

A physical model of tsunami inundation and wave pressures for an idealized coastal industrial site

A series of physical model experiments of tsunami inundation over an idealized industrial site located in a coastal area were performed in this study. Two types of tsunami-like waves with markedly different characteristics were generated. The first was a single long wave and the second was a long wave with soliton fission (undular bore). This study measured the water surface elevation and velocity, as well as the pressures at several heights for some building and tank models that were installed over the coastal area. An experimental benchmark dataset for the tsunami inundations and impacts over a complex topography were produced. This investigation shows that a wide spatial variance of the maximum inundation depth was observed. This was caused by the effects of the surrounding structures, especially the blocking effects due to the structures. The location where the effects occurred depends on the blocking fraction as well as the Froude number of inflows. This study also investigates the relationship between the pressures and neighboring flow profiles. It was determined that under the inundation flow condition without soliton fissions and wave breaking, the maximum pressures can be predicted by the Asakura-type model from the neighboring flow profiles. On the other hand, for the bore condition, the Cross-type model is more appropriate for predicting the maximum pressures. The log-normal standard deviations of the differences between the measured maximum pressures and the predicted pressures are also shown. This information can be useful when performing a probabilistic damage analysis or analyzing the fragility of buildings.

Wideband Spectral Enhancement through On‐Chip Bragg‐Soliton Dynamics

Supercontinuum generation (SCG) through soliton fission provides high‐brightness, spectrally‐rich light needed for hyperspectral imaging, broadband spectroscopy, and fluorescence microscopy. The prospect of miniaturization has led to many demonstrations of this phenomenon in integrated platforms. However, due to the moderate dispersion and nonlinearity generally available in channel waveguides, femtosecond pulses have typically been required to date, as the use of picosecond pulses would require unpractically long devices to achieve soliton fission. Here, spectral bandwidth enhancement of the supercontinuum process through Bragg grating induced soliton‐effect compression and soliton fission is demonstrated. This approach uses picosecond pulses on a complementary metal oxide semiconductor (CMOS)‐compatible, millimeter‐scale platform, consisting of a monolithically integrated cladding‐modulated Bragg grating with a channel waveguide. The strong dispersion near the stopband of the grating enables compression and fission of picosecond higher‐order solitons, which enhances the spectral broadening in the channel waveguide. A 4.3 spectral bandwidth enhancement is reported, with respect to a reference waveguide of the same length. The output spectra are further studied both through simulations and experiments and determined to possess high spectral coherence. These results highlight a simple route to significantly augment the bandwidth of nonlinear processes such as SCG while maintaining low power and compact footprint.

General theory and observation of Cherenkov radiation induced by multimode solitons

Advancements in computational capabilities along with the possibility of accessing high power levels have stimulated a reconsideration of multimode fibers. Multimode fibers are nowadays intensely pursued in terms of addressing longstanding issues related to information bandwidth and implementing new classes of high-power laser sources. In addition, the multifaceted nature of this platform, arising from the complexity associated with hundreds and thousands of interacting modes, has provided a fertile ground for observing novel physical effects. However, this same complexity has introduced a formidable challenge in understanding these newly emerging physical phenomena. Here, we provide a comprehensive theory capable of explaining the distinct Cherenkov radiation lines produced during multimode soliton fission events taking place in nonlinear multimode optical fibers. Our analysis reveals that this broadband dispersive wave emission is a direct byproduct of the nonlinear merging of the constituent modes comprising the resulting multimode soliton entities, and is possible in both the normal and anomalous dispersive regions. These theoretical predictions are experimentally and numerically corroborated in both parabolic and step-index multimode silica waveguides. Effects arising from different soliton modal compositions can also be accounted for, using this model. At a more fundamental level, our results are expected to further facilitate our understanding of the underlying physics associated with these complex “many-body” nonlinear processes.

Supercontinuum generation in a carbon disulfide core microstructured optical fiber.

We demonstrate supercontinuum generation in a liquid-core microstructured optical fiber using carbon disulfide as the core material. The fiber provides a specific dispersion landscape with a zero-dispersion wavelength approaching the telecommunication domain where the corresponding capillary-type counterpart shows unsuitable dispersion properties for soliton fission. The experiments were conducted using two pump lasers with different pulse duration (30 fs and 90 fs) giving rise to different non-instantaneous contributions of carbon disulfide in each case. The presented results demonstrate an extraordinary high conversion efficiency from pump to soliton and to dispersive wave, overall defining a platform that enables studying the impact of non-instantaneous responses on ultrafast soliton dynamics and coherence using straightforward pump lasers and diagnostics.

Rogue waves and lumps on the nonzero background in the ‐symmetric nonlocal Maccari system

AbstractIn this paper, the ‐symmetric version of the Maccari system is introduced, which can be regarded as a two‐dimensional generalization of the defocusing nonlocal nonlinear Schrödinger equation. Various exact solutions of the nonlocal Maccari system are obtained by means of the Hirota bilinear method, long‐wave limit, and Kadomtsev–Petviashvili (KP) hierarchy method. Bilinear forms of the nonlocal Maccari system are derived for the first time. Simultaneously, a new nonlocal Davey‐Stewartson–type equation is derived. Solutions for breathers and breathers on top of periodic line waves are obtained through the bilinear form of the nonlocal Maccari system. Hyperbolic line rogue wave (RW) solutions and semirational ones, composed of hyperbolic line RW and periodic line waves are also derived in the long‐wave limit. The semirational solutions exhibit a unique dynamical behavior. Additionally, general line soliton solutions on constant background are generated by restricting different tau‐functions of the KP hierarchy, combined with the Hirota bilinear method. These solutions exhibit elastic collisions, some of which have never been reported before in nonlocal systems. Additionally, the semirational solutions, namely, (i) fusion of line solitons and lumps into line solitons and (ii) fission of line solitons into lumps and line solitons, are put forward in terms of the KP hierarchy. These novel semirational solutions reduce to ‐lump solutions of the nonlocal Maccari system with appropriate parameters. Finally, different characteristics of exact solutions for the nonlocal Maccari system are summarized. These new results enrich the structure of waves in nonlocal nonlinear systems, and help to understand new physical phenomena.

Embedded split-step methods optimized with a step size control for solving the femtosecond pulse propagation problem in the nonlinear fiber optics formalism

We present the suitability of two optimized split-step methods for validating the femtosecond pulse propagation problem in the nonlinear fiber optics formalism that is governed by an extended nonlinear Schrödinger equation. In particular, the embedded split-step Fourier method (embedded-SSFM) and the embedded symmetrized split-step Fourier method (embedded-SymSSFM), which are optimized by the implementation of a step size control algorithm, are tested in terms of the femtosecond soliton fission phenomenology to analyze the numerical stability. As a result, it is possible to validate that these numerical methods introduce the appropriate resolution as function of the accuracy order that is needed at different stages of the soliton fission dynamics, which involves very large spectral shifts driven by the interaction between the nonlinear response and the high-order dispersion contribution of the optical fiber. Thus, the presented numerical methods can be used to validate accurately complex processes such as the development of supercontinuum spectra in the current formalism.