Pure-quartic Solitons Research Articles

Pure-quartic solitons with PT-symmetric nonlinearity

We propose a new, to the best of our knowledge, class of soliton based on the interaction of parity-time (PT) symmetric nonlinearity and quartic dispersion or diffraction. This novel kind of soliton is related to the recently discovered pure-quartic solitons (PQS), which arise from the balance of the Kerr nonlinearity and quartic dispersion, through a complex coordinate shift. We find that the PT-symmetric pure-quartic soliton presents important differences with respect to its Hermitian (Kerr) counterpart, including a nontrivial phase structure, a skewed spectral intensity, and a higher power for the same propagation constant. Further analysis reveals these solitons are linearly stable.

Symmetry-breaking bifurcations of pure-quartic solitons in dual-core couplers.

We investigate spontaneous symmetry- and antisymmetry-breaking bifurcations of solitons in a nonlinear dual-core waveguide with the pure-quartic dispersion and Kerr nonlinearity. Symmetric, antisymmetric, and asymmetric pure-quartic solitons (PQSs) are found, and their stability domains are identified. The bifurcations for both the symmetric and antisymmetric PQSs are of the supercritical type (alias phase transitions of the second kind). Direct simulations of the perturbed evolution of PQSs corroborate their stability boundaries predicted by the analysis of small perturbations.

Investigating innovative optical solitons for a (3+1)- dimensional nonlinear Schrödinger’s equation under the influences of 4th-order dispersive and parabolic law of nonlinearities

This study tackles a nonlinear Schrödinger’s equation in three dimensions, using three dispersive components of fourth order, often resulting in pure-quartic solitons. Pure-quartic bullets are known to deviate from conventional solitons due to their balance of fourth-order dispersion and nonlinearity. As bright and dark optically modulated bullets, we derive many solutions. Experiments on bullet transmission using optical nanofibers can benefit from the solutions found. Our creative solutions are produced by implementing the well-known scheme which is the improved modified extended tanh-function scheme. We find novel kinds of solutions (dark, bright, singular solitons, exponential, singular periodic, Weierstrass elliptic doubly periodic solutions, and Jacobi elliptic functions) that make their originality for the problem at hand evident by using the previously described approach. Contour plots and 2D and 3D visualizations in Wolfram Mathematica software are used to show how the well-furnished results propagate for various values of the necessary free parameters. The results demonstrate the computational processes’ precise, well-informed, and efficient nature. Through their integration with representational computations, they may be applied to increasingly complex phenomena. This work constitutes a major advancement in our comprehension of the intricate and erratic behavior of this mathematical model.

Pure-quartic soliton self-frequency shift in a mode-locked fiber laser

The pure-quartic soliton (PQS) offers the advantage of a wide spectrum and approximately Gaussian temporal profile, which has the potential to obtain high-energy ultrafast laser pulses. Thus, exploring the role of stimulated Raman scattering in the formation and propagation of PQSs in fiber lasers is crucial, especially considering the greater propensity for highpower and short PQS pulses compared to traditional solitons. Here, we present the modeling of a self-frequency shift (SFS) fiber laser based on the PQS, emphasizing the impact of fourth-order dispersion and the Raman effect. The significant red-shift in wavelength is discovered as the pump energy increases, revealing that the emergence of SFS is a universal attractor in mode-locked PQS fiber laser systems. Our simulations demonstrate that such wavelength tunability is a direct byproduct of the gain bandwidth limit and the stimulated Raman scattering for PQSs inside the fiber cavity, while the evolution dynamics in the gain and passive fiber show obvious differences. However, we find that the effect of SFS in a PQS fiber laser is compromised by a trade-off with the degradation of pulse quality, such as reshaping the oscillating tail and destroying the symmetry of the emission pulse. This Raman-induced nonlinear process under high pump energy facilitates the discovery of the comprehensive complexity of science for PQSs suffering from higher-dimensional forms of nonlinear effects in fiber lasers.

Pure-quartic soliton attracted state and multi-soliton molecules in mode-locked fiber lasers

This article explores the dynamic model of pure-quartic solitons (PQSs) in mode-locked fiber lasers. Firstly, the formation and dynamic behavior of the PQS attracted state in fiber lasers are investigated to demonstrate their exceptional stability, robustness, and predictability. Next, the transmission characteristics of single PQS in mode-locked fiber lasers is subsequently analyzed and compared to those of solitons generated while considering the effect of second-order dispersion. Finally, the evolution of multi-PQS molecules is explored, and a stability analysis method for these soliton molecules is proposed. The findings of this research are not only significant for a deeper understanding of nonlinear interaction mechanisms but also contribute to the development of ultrafast optical devices and offer new insights into the understanding and application of complex nonlinear systems.

Dark solitons and their bound states in a nonlinear fiber with second- and fourth-order dispersion

We study the excitations of dark solitons in a nonlinear optical fiber with the second- and fourth-order dispersion, and find the emergence of striped dark solitons (SDSs) and some multi-dark-soliton bound states. The SDSs can exhibit time-domain oscillating structures on a plane wave, and they have two types: the ones with or without the total phase step, while the multi-dark-soliton bound states exhibit different numbers of amplitude humps. By the modified linear stability analysis, we regard the SDSs as the results of the competition between periodicity and localization, and analytically give their existence condition, oscillation frequency, and propagation stability, which show good agreements with numerical results. We also provide a possible interpretation of the formation of the existing striped bright solitons (SBSs), and find that SBS will become the pure-quartic soliton when its periodicity and localization carry equal weight. Our results provide the theoretical support for the experimental observation of striped solitons in nonlinear fibers, and our method can also guide the discovery of striped solitons in other physical systems.

Pure-quartic soliton in a birefringence-managed fiber laser

Pure-quartic soliton (PQS) fiber lasers with a great variety of operating regimes have aroused considerable interest in high-energy ultrashort pulses and novel soliton patterns. Here, we numerically investigate the generation and dynamic properties of birefringence-managed pure-quartic soliton (BMPQS) in a positive fourth-order dispersion (FOD) fiber laser consisting of single-mode fibers and a section of polarization-maintaining fiber. The formation mechanism of the chirp-free BMPQS is dominated by the phase-matching effect, which arises from the co-actions of the birefringence, positive FOD, and nonlinear effects. It is observed that a higher FOD coefficient leads to energy transfer between the spectral sidebands inside the BMPQS. Moreover, the evolution of the BMPQS with the increase of the pump power confirms the phase-matching theory. Finally, the BMPQS molecule can be obtained with further increasing the pump power. This work offers a new avenue to create chirp-free pulses in positive FOD fiber lasers and enriches the sub-families of PQSs.

Buildup and synchronization regimes of a vector pure-quartic soliton molecule in a fiber laser cavity.

Pure-quartic solitons (PQSs) have recently received increasing attention due to their energy-width scaling over the traditional soliton, which has expanded our understanding of soliton dynamics with high-order dispersion in nonlinear systems. Here, we numerically reveal the asynchronization and synchronization processes of the sub-pulse within the vector PQS molecule in a mode-locked fiber laser by solving the coupled Ginzburg-Landau equations. During the establishment of a vector PQS molecule, the repulsion, attraction, and finally stabilization processes have been observed. Specifically, sub-pulse disappearance, regeneration, and finally synchronization with the other pulses are also investigated. Our analysis of the pulse energy, time interval, and relative phase evolution dynamics with the round trip indicates that the asynchronization and synchronization within the vector PQS molecule associate tightly with the gain competition and the cross-phase modulation. Our findings provide insights into the internal mutual dynamics within the vector soliton molecule and offer guidance for the applications of PQS.

Frequency-tunable quartic soliton in nonlinear negative-index metamaterials

An exact quartic soliton solution along with its constraint conditions in metamaterials (MMs) is presented on the basis of the nonlinear Schrödinger equation (NLSE) with second-, third- and fourth-order diffraction. Through analyzing the parameter relations based on the Drude model, it is demonstrated that the quartic soliton can only exist in the negative-index region (NIR) of self-focusing nonlinear MMs. With insight into the underlying parameter relations of quartic soliton, it is found that by selecting suitable frequency of incident wave, the quartic soliton in negative-index MMs (NIMs) exhibits frequency tunability or frequency stability. Particularly, the quartic solitons with different frequencies can propagate in an identical velocity, which provides a theoretical basis for realizing frequency division multiplexing (FDM) technology in nonlinear MMs. Different from pure-quartic soliton (PQS) in ordinary materials exhibiting oscillatory decaying tails in spatial domain and a flat top in frequency domain on logarithmic scale, the quartic soliton reported here possesses triangular distributions in both spatial and frequency domains. The presented results contribute to a fundamental theoretical support for future application of quartic soliton and are beneficial for exploring new solitary waves in MMs.

Pure-quartic Bragg solitons in chip-scale nonlinear integrated circuits

Pure-quartic solitons have gained significant attention recently due to their ability to achieve higher energy than classical solitons for short pulse durations, leveraging the interaction between self-phase modulation and anomalous fourth-order dispersion. However, challenges in generating the required dispersion profile and the scarcity of sufficiently low-loss devices with high nonlinearity and negligible nonlinear loss have restricted experimental progress. In this paper, we report a class of pure-quartic Bragg solitons that balances self-phase modulation and the ultra-strong Bragg-grating-induced negative fourth-order dispersion in combination with negligible group velocity dispersion and negligible third-order dispersion. We demonstrate pure-quartic Bragg soliton-effect compression of 2.4× in a compact millimeter-scale integrated low-loss and highly nonlinear waveguide circuit. Our findings show the potential of exploiting the exceptional dispersion profile of nonlinear Bragg gratings for advanced soliton generation and pulse shaping, particularly the advantageous energy scaling and associated compression of pure-quartic solitons.

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.

Internal motion within pulsating pure-quartic soliton molecules in a fiber laser

Various striking nonlinear evolution dynamics have been observed in mode-locked fiber lasers owing to the high peak power of the solitons. Herein, we numerically demonstrate the dynamical generation of dispersion-dependent pure-quartic solitons (PQS) molecules in a fiber laser. We discover the evolution from a single-pulse initial condition to different types of pulsating PQS molecules with enhanced net fourth-order dispersion, indicating that the internal motion and energy exchange can be both quasi-periodical and periodical. Furthermore, we reveal that the generation of these two types of pulsating PQS molecules is associated with a gain competition effect between the two sub pulses during mode-locking. Finally, we propose a new method that can achieve the transition between a loose PQS molecule and a tight PQS molecule. Enlightened by the numerical results, we speculate that more internal motion within the PQS molecule will be discovered, which will promote a deep insight into the physical mechanism behind.

Dissipative pure-quartic soliton resonance in an Er-doped fiber laser

Dissipative pure-quartic soliton (DPQS) that arises from the balance of positive fourth-order dispersion (FOD), nonlinearity, gain and loss has been proposed to generate high-energy pulse. Herein, we numerically investigate the generation of dissipative pure-quartic soliton resonance (DPQSR) in an Er-doped mode-locked fiber laser with all positive FOD. Our findings indicate that the formation of DPQSR depends on the reverse saturable absorption (RSA) effect of real saturable absorber. Then, the impacts of pump power, RSA coefficient and positive FOD in generating DPQSR pulse are investigated. With the increase of pulse energy, the asymmetrical temporal profile of DPQS transforms into a rectangular one. This work can be utilized to comprehend the dissipative pure-quartic soliton resonance as well as the development of an all positive FOD Er-doped fiber laser. In addition, it lays the way for the development of highly stable, high-energy pulsed lasers.

Nonlocal cubic and quintic nonlinear wave patterns in pure-quartic media

In this work, pure-quartic soliton (PQS)formation is investigated in the framework of a nonlinear Schrödinger equation with competing Kerr (cubic) and non-Kerr (quintic) nonlocal nonlinearities and quartic dispersion. In the process, the modulational instability (MI) phenomenon is activated under a suitable balance between the nonlocal nonlinearities and the quartic dispersion, both for exponential and rectangular nonlocal nonlinear responses. Interestingly, the maximum MI growth rate and bandwidth are reduced or can completely be suppressed for some specific values of the cubic and quintic nonlocality parameters, depending on the type of nonlocal response. The analytical results are confirmed via direct numerical simulations, where the instability supports the signature of pure-quartic dark and bright solitons. These results may provide a better understanding of PQS structures for their potential applications in the next generation of nonlinear optical devices.

Comprehensive analysis of pure-quartic soliton dynamics in a passively mode-locked fiber laser

The understanding of soliton dynamics promotes the development of ultrafast laser technology. High-energy pure-quartic solitons (PQSs) have gradually become a hotspot in recent years. Herein, we numerically study the influence of the gain bandwidth, saturation power, small-signal gain, and output coupler on PQS dynamics in passively mode-locked fiber lasers. The results show that the above four parameters can affect PQS dynamics. Pulsating PQSs occur as we alter the other three parameters when the gain bandwidth is 50 nm. Meanwhile, PQSs evolve from pulsating to erupting and then to splitting as the other three parameters are altered when the gain bandwidth is 10 nm, which can be attributed to the existence of the spectral filtering effect and intra-cavity fourth-order dispersion. These findings provide new insights into PQS dynamics in passively mode-locked fiber lasers.

Creeping and erupting dynamics in a pure-quartic soliton fiber laser.

Pure-quartic solitons (PQSs) are gradually becoming a hotspot in recent years due to their potential advantage to achieve high energy. Meanwhile, the fundamental research of PQSs is still in the fancy stage, and exploring soliton dynamics can promote the development of PQSs. Herein, we comprehensively and numerically investigate the impact of saturation power, small-signal gain, and output coupler on PQS dynamics in passively mode-locked fiber lasers. The result indicates that altering the above parameters makes PQSs exhibit pulsating or creeping dynamics similar to traditional solitons. Moreover, introducing an intra-cavity filter combined with intra-cavity large fourth-order dispersion makes PQSs go through stationary, pulsating to erupting. That is, the intra-cavity filter changes PQS dynamics. These findings provide new insights into PQS dynamics in fiber lasers.

Research progress of pure quartic soliton fiber laser

The pure-quartic soliton fiber laser is an innovative ultra-short pulse laser that can maintain a stable pulse shape through a balance between fourth-order dispersion effect and self-phase modulation effect. Comparing with traditional soliton laser that is dominated by second-order dispersion, the mode-locked pulse energy of pure-quartic soliton laser can be 1–2 orders of magnitude higher. This provides researchers with new ideas for developing high-energy and high-peak-power fiber lasers. Here, the generation and transmission characteristics of pure-quartic solitons in nonlinear optical systems such as fiber lasers in recent years are systematically reviewed. It also explores some special transient dynamic phenomena. Furthermore, in this article, the latest achievements of our research group in this area are also presented. Finally, the application prospect and development trend of pure-quartic soliton fiber lasers are prospected. These results will contribute to a more comprehensive understanding of the basic physical properties of pure-quartic soliton fiber lasers.

Pure-quartic solitons in presence of weak nonlocality

In this paper, we study the characteristics of pure-quartic optical solitons in a nonlinear medium having a weakly nonlocal response. We propose an nonlinear Schrödinger equation incorporating pure fourth-order diffraction, Kerr nonlinearity and weak nonlocality to describe the transmission of solitons in the system. We obtain analytic pure-quartic soliton solutions to this model in a variety of shapes and forms, unlike the case of the model without taking into account the weak nonlocal contribution. Besides, we find that the obtained localized structures have both bright and dark type waveforms in the transmission system. Interestingly, the functional forms of these solitons are expressed in terms of sech and tanh functions which do not possess oscillating tails, markedly different from the conventional pure-quartic solitons in the absence of weak nonlocality. These structures exist for both positive and negative quartic diffraction coefficient whereas pure-quartic solitons in the absence of nonlocality occur only for negative fourth-order dispersion. The numerical examples are presented for illustrating the soliton evolution dynamics in the optical waveguide.

The bound states of pure-quartic solitons

In this paper, we quantitatively study the equilibrium bound state and the oscillating bound state of pure-quartic solitons (PQSs). Based on the Lagrangian of the system, we obtain the analytic expression of the effective interaction potential, which makes it convenient to predict the critical separation between the interacting PQSs in the equilibrium bound state. Furthermore, we study the oscillation period of PQSs in the oscillating bound state by making an analogy between the evolution of PQS pair and the motion of the Newtonian particle in a potential well. The effective mass and the effective force are derived, and thereby the semianalytic expression of the oscillation period is obtained. The results are useful for gaining a physical insight into the evolution of the interacting PQSs in the two types of bound states.

Solitons in media with mixed, high-order dispersion and cubic nonlinearity

Although most soliton research has traditionally considered dominant quadratic dispersion, the recent discovery of pure-quartic solitons has inspired analysis of soliton solutions with large higher orders of dispersion. Here we present analytic expressions for families of bright soliton solutions at arbitrary dispersion orders and practical methods to obtain the associated dispersion relations. These results provide a framework for considering higher order dispersion solitons and show the potential for further investigation of solitons in higher order dispersion systems.