Search Results (81)

Tellurene has a wide bandwidth and low propagation loss at near-infrared wavelengths due to its nonlinear absorption coefficient. Therefore, we prepared tellurene–polyvinyl alcohol (Te-PVA) film as a saturable absorber in an Er-doped fiber laser by liquid phase exfoliation and spin-coating. The modulation depth was 5.25% and the saturation intensity was 17.02 MW/cm. The nonlinear optical properties of the film and its application in high-stability mode-locked operation were studied. A mode-locked pulse with a fundamental frequency of 8.48 MHz and a central wavelength of 1560.10 nm was obtained, with a signal-to-noise ratio which was greater than 75 dB. A traditional soliton mode-locked operation with a pulse width of 1.41 ps was achieved. In addition, eighth- and 19^th-harmonic mode-locked operations were obtained by adjusting the pump power and polarization controller. Our results show that Te-PVA film functioned as a saturable absorber which enabled harmonic mode-locking with an SNR of 75 dB in an Er-doped fiber laser. It is thus an excellent ultra-fast photonics material. Full article

This paper presents a four-component integrable extension of the derivative nonlinear Schrödinger (DNLS) soliton hierarchy, namely, the Kaup–Newell hierarchy of soliton equations. Motivated by a general extension idea for the Kaup–Newell spectral matrix, we propose a specially constructed 4th-order matrix-valued eigenvalue problem involving four potentials and derive the corresponding integrable Hamiltonian hierarchy via the Lax pair framework. A recursion operator and a bi-Hamiltonian structure are established to demonstrate the Liouville integrability of the resulting hierarchy. As an illustrative example, we derive an integrable system of four DNLS equations, each containing two linear dispersion terms, which differs from standard integrable systems. Full article

This paper aims to introduce a real four-component integrable extension of the complex Kaup–Newell soliton hierarchy. Following a general idea for extending the standard Kaup–Newell spectral matrix, we propose a specific matrix eigenvalue problem involving four real potentials and construct the corresponding integrable Hamiltonian hierarchy via the zero-curvature formulation. A recursion operator and a bi-Hamiltonian structure are presented to demonstrate the Liouville integrability of the resulting hierarchy. As an illustrative example, we derive an integrable system of four real derivative nonlinear Schrödinger equations, each containing two linear dispersion terms and generalizing the standard complex derivative nonlinear Schrödinger equations. Full article

This work extends the analytical operation of the Riemann–RHPHilbert approach (RHA) for fractional-order nonlinear integrable systems under the solvable meaning of inverse scattering transform (IST) to variable-coefficient fractional-order nonlinear models. Firstly, based on the matrix spectral problem proposed by Ablowitz, Kaup, Newell, and Segur, this article derives an integer-order integrable system, which is abbreviated as the AKNS hierarchy. Secondly, by taking specific values of the operator in the derived AKNS hierarchy, a variable-coefficient fractional higher-order NLS hierarchy (vfhNLSH) is obtained, and its anomalous dispersion relation (ADR) is derived via formal solution. Significantly, the reductions of the vfhNLSH include three variable-coefficient fractional-order integrable models: the Hirota equation (vfHE), the Lakshmanan–Porsezian–Daniel equation (vfLPDE), and the fifth-order NLS equation (vffNLSE). Finally, we conduct a detailed study on the representative vfHE as an example rather than a special case and construct its explicit N-fold analytical solution based on the extension of the RHA. At the same time, numerical visualization simulations are conducted to demonstrate the waveform structure characteristics of the solutions under $N=1$ and $N=2$ conditions, including solitons, breathers, and their coupled nonlinear waves. The same process is fully applicable to the other two reduced models, with only some differences in the related results and the dynamic behavior of the solutions. It is shown that the temporal part of the Lax pair associated with the vfHE cannot yet be explicitly determined. Therefore, the fractional-order extension of the RHA presented in this article constitutes a formal or RHA-inspired construction, rather than a fully rigorous fractional-order RHA extension. Full article

We propose and analyze a new class of photonic neurons based on spatial solitons generated in photorefractive media. They are designed to operate entirely within the optical domain. By engineering single-node and multi-node multichannel architectures, we demonstrate the feasibility of constructing balanced, scalable, and reconfigurable structures capable of emulating neural behaviors such as symmetric signal splitting, plasticity, and dynamic adaptation. The optimization of geometric parameters—including soliton waveguides features, input distances, and incidence angles—proves crucial for ensuring the stability of solitonic propagation and the proper functioning of interaction nodes. The results lay the groundwork for the development of high-performance optical neural circuits, with potential applications in distributed signal processing, neuromorphic artificial intelligence, and reconfigurable optical memories. Full article

The chiral quark soliton model (CQSM) is an effective quark model of baryons maximally taking account of the most important feature of low-energy QCD, i.e., the spontaneous chiral symmetry breaking of the QCD vacuum and the associated appearance of Nambu–Goldstone pions. It shares many common features with the famous Skyrme model in that the baryons are viewed as rotating hedgehog objects in both models. Despite many similarities, it turned out that the CQSM can give more realistic predictions on most baryon observables. Above all, a decisive advantage of the CQSM over the Skyrme-like models is that it can handle non-local quark–quark correlations in baryons, which is absolutely impossible within the framework of effective meson theories. This feature is decisively important for making theoretical predictions on the quark distribution functions inside the nucleon, which are defined as nucleon matrix elements of bilinear quark operators with light-cone separation. In the present paper, we try to elucidate why and how the CQSM can give successful predictions for a variety of types of nucleon quark distribution functions, especially for the flavor asymmetry of the unpolarized and longitudinally polarized sea-quark (anti-quark) distribution functions in the nucleon. Full article

This article proposes a novel time-space two-grid high-order compact difference scheme for the one-dimensional nonlinear Schrödinger equation subject to Dirichlet boundary conditions. In comparison with the fully nonlinear compact difference scheme, the proposed methodology combines a small-scale nonlinear fourth-order compact difference algorithm on a time-space coarse grid and a large-scale linearized correction compact difference algorithm on a fine grid. In contrast to the time two-grid compact difference method, the proposed scheme applies the two-grid technique in both the spatial and temporal domains, thereby further improving computational efficiency. Solutions from the coarse grid are projected onto the fine grid via a temporally linear and spatially cubic Lagrange interpolation operator. Unconditional stability and optimal convergence rates, which are fourth-order in space and second-order in time, are proven in both the discrete $L^2$ and $L^{\infty }$ norms, without any constraints on the grid ratio. In addition to the standard techniques of the energy method, a discrete Sobolev inequality and an a priori error estimate are employed to demonstrate stability and high-order convergence. Finally, the theoretical results are validated through numerical experiments, which confirm the robustness and reliability of the proposed approach. A single-soliton experiment demonstrates that, compared with the fully nonlinear compact difference scheme, the proposed method achieves a significant reduction in CPU time while maintaining a comparable level of accuracy. Additional experiments further illustrate the algorithm’s effectiveness in simulating two-soliton interactions and soliton birth. These findings establish the proposed scheme as a highly efficient alternative to conventional nonlinear approaches. Full article

We report on sub-50 fs pulse generation from a diode-pumped mode-locked laser based on an ytterbium-doped monoclinic potassium yttrium double tungstate crystal operating in the 1 μm spectral region. Pumping by a low-power, spatially single-mode, fiber-coupled laser diode at 976 nm, a maximum continuous-wave output power of 433 mW at 1066.1 nm was obtained. Using a quartz-based intracavity Lyot filter, an exceptionally broad continuous-wavelength tuning range of 98 nm was achieved. In the mode-locked regime, the diode-pumped Yb:KY(WO₄)₂ laser delivered soliton pulses as short as 46 fs at a central wavelength of 1069.2 nm by employing a SEmiconductor Saturable Absorber Mirror. To the best of our knowledge, these results represent the broadest continuous-wave tuning range and the shortest pulse duration ever reported for lasers based on ytterbium-doped monoclinic double tungstate crystals. Full article

The present work is devoted to the analysis of a time-fractional Gardner equation arising in the modeling of nonlinear plasma waves in media endowed with memory and anomalous transport effects. Building on a physically motivated soliton profile, we construct a finite-time fractional ansatz in which the integer-order time variable is replaced by a fractional reparametrization that encodes the Caputo memory kernel. Within this framework, the governing evolution equation is not treated via a formal infinite expansion but rather via a finite approximation, whose quality is assessed directly via the associated residual. The Caputo fractional derivative is evaluated by a strong finite-difference formula that is second-order accurate in time and preserves the nonlocal convolution structure of the fractional operator. This combination of a finite fractional ansatz and a strong Caputo discretization allows us to compute the residual of the time analytically fractional Gardner equation and to use it as a quantitative diagnostic of accuracy and consistency. Two representative classes of nonlinear structures supported by the Gardner equation are examined in detail: a smooth solitary-wave profile and a cnoidal-wave configuration. For each example, the approximate fractional solution is generated, the corresponding residual is evaluated in space–time, and global and final-time residual norms are determined to quantify the influence of the fractional order on the wave dynamics and on the quality of the approximation. The numerical results show that the proposed residual-controlled approach yields residual magnitudes that remain one to two orders of magnitude smaller than those associated with truncated residual power-series approximations constructed from the same data, while preserving the expected qualitative features of fractional solitary and cnoidal waves in non-Markovian plasma environments. Full article

We demonstrate an all-polarization-maintaining (PM) mode-locked thulium-doped fiber laser operating in the net-normal-dispersion regime based on a figure-9 nonlinear amplifying loop mirror (NALM) configuration. A chirped fiber Bragg grating (CFBG) and a commercial PM dispersion-compensating fiber (PM-DCF) are incorporated into the figure-9 cavity, providing a large normal net dispersion and enabling stable dissipative-soliton mode-locking. Under stable dissipative-soliton operation, the laser delivers a maximum output power of 53.6 mW at a repetition rate of 12.31 MHz, corresponding to a pulse energy of 4.3 nJ. The output spectrum has a central wavelength of ~1952 nm with a 3 dB bandwidth of ~11 nm. The all-PM laser oscillator directly generates a fs pulse without extra-cavity compression, achieving a pulse duration of 545 fs at the CFBG arm. Moreover, stable fundamental mode-locking is verified by a high radio-frequency signal-to-noise ratio (SNR) exceeding 82 dB and a long-term root-mean-square (RMS) power fluctuation of 0.45% over two hours. To the best of our knowledge, this represents the highest output power generated from an all-PM-fiber figure-9 laser oscillator in the 2 μm band, alongside fs-pulse operation. This high-power, compact, stable and environment-insensitive fs-pulsed laser source shows great potential as an ideal seed for biomedical imaging and mid-infrared frequency combs. Full article

Colloidal PbSe quantum dots are promising candidates as saturable absorbers for ultrafast fiber lasers, but their performance is often limited by surface-related defects and chemical instability, leading to aggregation under optical pumping. In this study, we present a freestanding PbSe/PbS quantum dot-polystyrene composite saturable absorber film, with PbS overcoating on PbSe to enhance surface passivation and oxidation resistance. The composite exhibits a saturation intensity of 5.76 kW·cm⁻², a modulation depth of 33%, and an optical damage threshold of 13.6 mJ·cm⁻². When integrated into a bidirectionally pumped erbium-doped fiber laser in the anomalous-dispersion regime, the device demonstrates self-starting soliton mode locking at an ultralow pump threshold of 6 mW, generating 1.06 ps pulses with a radio-frequency signal-to-noise ratio of approximately 65 dB. The spectra remain stable over an 8-month period, showing excellent environmental and operational durability. These findings confirm that PbSe/PbS quantum dots in a polymer matrix offer a robust, low-threshold saturable absorber platform for ultrafast fiber lasers. Full article

In this study, a novel (2+1)-dimensional generalized Sawada-Kotera (gSK) equation is first proposed, followed by the derivation of its corresponding Hirota bilinear form (bgSK). Utilizing the Hirota direct method and the “long-wave” limit of its N-soliton solutions, we obtain M-lump solutions that decay to a uniform background state in all spatial directions. Furthermore, we construct hybrid solutions consisting of M-lump and line-soliton (stripe-soliton) interactions. Finally, the dynamic properties and evolutionary behavior of these solutions are illustrated through detailed numerical simulations and graphical analysis. Full article

We demonstrate Kerr-lens mode-locked operation of a Tm,Ho:Ca(Gd,Y)AlO₄ laser pumped by a narrow-linewidth, continuous-wave Ti:sapphire laser at 797 nm. Soliton pulses as short as 145 fs are generated at 2087.8 nm in σ-polarization via soft-aperture Kerr-lens mode-locking, with an average output power of 203 mW (0.5% output coupler) at ~80.5 MHz. To the best of our knowledge, this result represents the first demonstration of a Kerr-lens mode-locked laser based on a Tm,Ho:Ca(Gd,Y)AlO₄ crystal exhibiting both structural and compositional disorder. Full article

The objective of this study is to investigate $\rho$-Einstein solitons on submanifolds of a para-Sasakian manifold under certain curvature conditions. The novelty of this work lies in the characterization of $\rho$-Einstein solitons on anti-invariant submanifolds of a para-Sasakian manifold equipped with a semi-symmetric non-metric connection, where the structure vector field is taken as the potential vector field. We establish several significant results concerning the classification of $\rho$-Einstein solitons with respect to the $W_3$-curvature tensor and the semi-symmetric non-metric connection. Moreover, we construct a non-trivial example of an anti-invariant submanifold of a five-dimensional para-Sasakian manifold by solving an associated system of partial differential equations. Full article

An overview on the study of nonlinear evolution equations of soliton type is provided. In addition, 5th-order nonlinear evolution equations are shown to be connected to the Caudrey–Dodd–Gibbon–Sawada–Kotera (CDGSK) equation via Bäcklund transformations. The links are depicted in a wide net of links which we term a Bäcklund Chart. The links obtained previously by Rogers and Carillo and by Carillo and Fuchssteiner are revisited, and new results are obtained. A 5th-order nonlinear evolution equation, which does not seem to appear in any list of integrable equations, is provided. All the connected equations exhibit a very interesting symmetry structure enjoyed by the corresponding full hierarchies. Indeed, they all admit a hereditary recursion operator. Hence, each one of the mentioned equations represents the base member of a corresponding hierarchy of equations. These hierarchies are constructed via the recursive application of the respective recursion operators. The symmetry properties of such equations are recalled. Finally, we compare the net of links, derived via Bäcklund transformations, in the case of the fifth-order nonlinear evolution equations with an analog net of links connecting third-order Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations. Analogies and discrepancies between the connections established in the case of fifth-order equations with respect to those established in the case of third-order equations are analyzed. This study aims to open the way for the construction of corresponding non-Abelian equations of the fifth order. Full article