Search Results (105)

This study focuses on the analysis of soliton solutions within the framework of the time-fractional cubic–quintic nonlinear Schrödinger equation (TFCQ-NLSE), a powerful model with broad applications in complex physical phenomena such as fiber optic communications, nonlinear optics, optical signal processing, and laser–tissue interactions in medical science. The nonlinear effects exhibited by the model—such as self-focusing, self-phase modulation, and wave mixing—are influenced by the combined impact of the cubic and quintic nonlinear terms. To explore the dynamics of this model, we apply a robust analytical technique known as the sub-ODE method, which reveals a diverse range of soliton structures and offers deep insight into laser pulse interactions. The investigation yields a rich set of explicit soliton solutions, including hyperbolic, rational, singular, bright, Jacobian elliptic, Weierstrass elliptic, and periodic solutions. These waveforms have significant real-world relevance: bright solitons are employed in fiber optic communications for distortion-free long-distance data transmission, while both bright and dark solitons are used in nonlinear optics to study light behavior in media with intensity-dependent refractive indices. Solitons also contribute to advancements in quantum technologies, precision measurement, and fiber laser systems, where hyperbolic and periodic solitons facilitate stable, high-intensity pulse generation. Additionally, in nonlinear acoustics, solitons describe wave propagation in media where amplitude influences wave speed. Overall, this work highlights the theoretical depth and practical utility of soliton dynamics in fractional nonlinear systems. Full article

The objective of the present study is to detect chirped optical solitons of the perturbed Chen–Lee–Liu equation with full nonlinearity. By virtue of the traveling wave hypothesis, the discussed model is reduced to a simple form known as an elliptic equation. The latter equation, which is a second-order ordinary differential equation, is handled by the undetermined coefficient method of two forms expressed in terms of the hyperbolic secant and tangent functions. Additionally, the auxiliary equation method is applied to derive several miscellaneous solutions. Various types of chirped solitons are revealed such as W-shaped, bright, dark, gray, kink and anti-kink waves. Taking into consideration the existence conditions, the dynamical behaviors of optical solitons and their corresponding chirp are illustrated. The modulation instability of the perturbed CLL equation is examined by means of the linear stability analysis. It is found that all solutions are stable against small perturbations. These entirely new results, compared to previous works, can be employed to understand pulse propagation in optical fiber mediums and dynamic characteristics of waves in plasma. Full article

This paper consists of various kinds of wave solitons to the mathematical model known as the truncated M-fractional FitzHugh–Nagumo model. This model explains the transmission of the electromechanical pulses in nerves. Through the application of the modified extended tanh function technique and the modified $(G^{\prime }/G^2)$-expansion technique, we are able to achieve the series of exact solitons. The results differ from the current solutions because of the fractional derivative. These solutions could be helpful in the telecommunication and bioscience domains. Contour plots, in two and three dimensions, are used to describe the results. Stability analysis is used to check the stability of the obtained solutions. Moreover, the stationary solutions of the focusing equation are studied through modulation instability. Future research on the focused model in question will benefit from the findings. The techniques used are simple and effective. Full article

This study explores analytical soliton solutions for the cubic–quintic time-fractional nonlinear non-paraxial pulse transmission model. This versatile model finds numerous uses in fiber optic communication, nonlinear optics, and optical signal processing. The strength of the quintic and cubic nonlinear components plays a crucial role in nonlinear processes, such as self-phase modulation, self-focusing, and wave combining. The fractional nonlinear Schrödinger equation (FNLSE) facilitates precise control over the dynamic properties of optical solitons. Exact and methodical solutions include those involving trigonometric functions, Jacobian elliptical functions (JEFs), and the transformation of JEFs into solitary wave (SW) solutions. This study reveals that various soliton solutions, such as periodic, rational, kink, and SW solitons, are identified using the complete discrimination polynomial methods (CDSPM). The concepts of chaos and bifurcation serve as the framework for investigating the system qualitatively. We explore various techniques for detecting chaos, including three-dimensional and two-dimensional graphs, time-series analysis, and Poincarè maps. A sensitivity analysis is performed utilizing a variety of initial conditions. Full article

In this work, we report the formation of multiple mode-locking states in an Erbium/Ytterbium co-doped fiber laser, such as domain-wall (DW) dark pulses, high-order dark harmonic pulses, dissipative soliton resonance (DSR) pulses, and dual-wavelength h-shaped pulses. By increasing the pump power and adjusting the quarter-wave retarder (QWR) plates, we experimentally achieve 310th-order harmonic dark pulses. DSR pulses emerge at a pump power of 1.01 W and remain stable up to 9.07 W, reaching a maximum pulse width of 676 ns and a pulse energy of 1.608 µJ, while Dual-wavelength h-shaped pulses have a threshold of 1.42 W and maintain stability up to 9.07 W. Using a monochromator, we confirm that these h-shaped pulses result from the superposition of a soliton-like pulse and a DSR-like pulse, emitting at different wavelengths but locked in time. The fundamental repetition rate for dark pulsing, DSR, and h-shaped pulses is 321.34 kHz. This study provides new insights into complex pulse dynamics in fiber lasers and demonstrates the versatile emission regimes achievable through precise pump and polarization control. Full article

The concept of space–time duality in optics was originally based on the mathematical connection between the diffraction of beams in space and the dispersion of pulses in time. This concept has been extended in recent years from the temporal analog of reflection for optical pulses to photonic time crystals in a medium where refractive index varies with time in a periodic fashion. In this review, I discuss how the concept of space–time duality and the use of nonlinear optics has led to many advances in recent years. Starting from the historical origin of space–time duality, time lenses and their applications are reviewed first. Later sections cover phenomena such as soliton-induced temporal reflection, time-domain waveguiding, and the formation of spatiotemporal Bragg gratings. Full article

In this research, we investigate the phenomenon of multistability and complex dynamic behaviors in plasma waves by utilizing advanced mathematical techniques. We examine how fractional-order derivatives influence plasma wave stability by applying the fractional diffusion–reaction model, the framework of nonlinear dynamical systems, and the $\left({\displaystyle \frac{G^{\prime }}{G^2}}\right)$ method. The principal direction of our work is associated with different forms of oscillations in the plasma wave: non-linear periodic, solitons, and kink waves. This leads to the study of small amplitude pulses and solitary waves, which are significant in plasma activities. Using bifurcation analysis, we discuss how these waves appear and develop under different conditions, as well as determine which conditions generate the chaotic behavior or highly complex patterns of waves. We study the details of transitions between waves and their chaotic behavior to characterize the laws that govern their plasma environment. Moreover, we have used non-linear modeling and numerical simulations to understand in detail the complex patterns and the factors of stability underlying the phenomena of plasma waves. In addition, our study also investigates the correspondence between non-linearity, multi-stability, and the birth of complex structures such as solitons and kink waves. The solutions of the dynamical system produced by the proposed nonlinear model generate different patterns of response based on system parameter variation. These patterns include oscillations and decay behaviors. Research results about system stability and solution convergence under various parameter settings provide an extended performance evaluation of the proposed method through a better understanding of system dynamics. They increase our understanding of chaotic behavior in plasma systems and pave the way for applications in plasma physics and energy systems, as well as advanced technologies. Full article

We conducted a comprehensive comparative study of numerical solvers for the generalized Korteweg–de Vries (gKdV) equation, focusing on classical Fourier-based Crank–Nicolson methods and physics-informed neural networks (PINNs). Our work benchmarks these approaches across nonlinear regimes—including the cubic case ($\nu =3$)—and diverse initial conditions such as solitons, smooth pulses, discontinuities, and noisy profiles. In addition to pure PINN and spectral models, we propose a novel hybrid PINN–spectral method incorporating a regularization term based on Fourier reference solutions, leading to improved accuracy and stability. Numerical experiments show that while spectral methods achieve superior efficiency in structured domains, PINNs provide flexible, mesh-free alternatives for data-driven and irregular setups. The hybrid model achieves lower relative $L^2$ error and better captures soliton interactions. Our results demonstrate the complementary strengths of spectral and machine learning methods for nonlinear dispersive PDEs. Full article

In this paper, we investigate the dynamics of the generalized Chen–Lee–Liu (gCLL) equation utilizing the Riemann–Hilbert method to derive its $\mathit{N}$-soliton solution. We incorporate a self-steepening term and a Kerr nonlinear term to characterize nonlinear light propagation in optical fibers based on the Chen–Lee–Liu (CLL) equation more accurately. The Riemann–Hilbert problem is addressed through spectral analysis derived from the Lax pair formulation, resulting in an $\mathit{N}$-soliton solution for a reflectance-less system. We also present explicit formulas for solutions involving one and two solitons, thereby providing theoretical support for stable long-distance signal transmission in optical fiber communication. Furthermore, by adjusting parameters and conducting comparative analyses, we generate three-dimensional soliton images that warrant further exploration. The stability of soliton solutions in optical fibers offers novel insights into the intricate propagation behavior of light pulses, and it is crucial for maintaining the integrity of communication signals. Full article

A polarization-maintaining all-fiber laser source based on a nonlinear amplifying loop mirror with broadband operation (64 nm) around 1920 nm is demonstrated. The oscillator can generate 66 pJ up-chirped dissipative soliton pulses at a repetition rate of 22.8 MHz with a high polarization extinction ratio of 17 dB. By adding a polarization controller to the polarization-maintaining dispersion-compensating fiber, the filter behavior can be adjusted allowing for the tuning of the emission to a center wavelength of 1878 nm, 1907 nm, and 1926 nm. Using an all-polarization-maintaining single-mode fiber amplifier with anomalous dispersion, the pulses are amplified to 0.9 nJ and compressed to a near Fourier-limited pulse duration of 170 fs with a peak power of 4.3 kW. Such all-fiber-based sources are attractive due to their compact size, high beam quality, and good environment stability. Full article

Femtosecond fiber lasers are widely utilized across various fields and also serve as an ideal platform for studying soliton dynamics. Bound-state solitons, as a significant soliton dynamic phenomenon, attract widespread attention and research interest because of their potential applications in high-speed optical communication, all-optical information storage, quantum computing, optical switching, and high-resolution spectroscopy. We investigate the effects of pump power variations on the formation of mode-locked solitons and bound-state solitons in a femtosecond fiber laser with a Cr₂S₃ saturable absorber (SA) through numerical simulations while observing the transition, formation, and break-up process of bound soliton pulses. By optimizing the cavity structure and adjusting the net dispersion, the mode-locked soliton is obtained based on this SA. This is the narrowest solitons produced by this SA to date, exhibiting the smallest time-bandwidth product. Moreover, stable double-bound solitons and unique (2 + 1) triple-bound solitons are successfully obtained. The diverse bound-state solitons not only demonstrate the excellent nonlinear absorption properties of Cr₂S₃ as a saturable absorber but also expand the scope of applications for Cr₂S₃ saturable absorbers in fiber lasers. Full article

In the near-zero negative dispersion region of highly nonlinear fiber, the process of wavelength conversion based on the mechanism of intra-pulse stimulated Raman scattering is sensitive to the parameters of pumping pulse and fiber length under the combined effects of nonlinearity and dispersion. Therefore, we experimentally demonstrate the process in detail by using conventional soliton pulses with three sets of pulse parameters and two highly nonlinear fiber lengths of 400 m and 500 m. The experimental results show that, under the combined action of dispersion and several types of nonlinear mechanisms, the wavelength conversion processes are apparently different when using pulses with different parameters to pump different lengths of highly nonlinear fibers. Specifically, the separation degree of the frequency-shifted pulse spectrum and pumping pulse spectrum, and the corresponding redshift rate and pump power consumption all show significantly different results. The experimental results can guide the selection of more suitable parameters for the pumping pulse and the length of highly nonlinear fiber to achieve a better effect of wavelength redshift or spectrum broadening for various practical applications. Full article

In this work, we theoretically simulate the modulation of a soliton molecule that has an initial chirped Gaussian pulse shape in a 1 μm extra-cavity optical fiber modulation system. Different soliton parameters in orthogonal polarizations are applied to achieve controllable optical solitons’ output with specific properties in the time/frequency domain. For instance, when the phase difference is changed, both pulse shapes’ and corresponding optical spectra’s peak intensities will have a sudden change when the orthogonal phase difference is π/2. These simulation results provide a beneficial reference value for extra-cavity shaping of different solitons that come from nonlinear optical systems. Optimally, the reported results could pave the groundwork for industrial growth in ultrafast laser design. Full article

The synchronization of a soliton frequency comb in a Kerr cavity with pulsed laser injection is studied numerically. The neutral delay differential equation is used to model the light dynamics in the cavity. This model allows for the investigation of both cases where the pulse repetition period is close to the cavity round-trip time and where the repetition period of the injection pulses is close to a rational fraction $M/N$ of the round-trip time. It is demonstrated that solitons can exist in this latter case, provided that the injection pulses are of a higher amplitude, which is directly proportional to the number M. Furthermore, it is shown that the synchronization range of the solitons is also proportional to the number M. The solitons excited by pulses with a period slightly different from the M:N-resonance can be destabilized by the Andronov–Hopf bifurcation, which occurs when the injection level at the soliton position decreases to M times the injection amplitude corresponding to the saddle-node bifurcation in a model equation with uniform injection. Full article

A wavelength-switchable ytterbium-doped mode-locked fiber laser is reported in this article. Two Mach–Zehnder interferometers (MZIs, denoted as MZI1, MZI2) with close free spectral ranges (FSRs) are connected in series to form a Vernier effect sensor. By utilizing the filtering effect of the Vernier effect sensor, the wavelength-switchable output of an ytterbium-doped mode-locked fiber laser is realized. When the 3 dB bandwidth of the Vernier effect filter is set to be 5.31 nm around 1073.42 nm, stable dissipative solitons are obtained. Stretching MZI1 horizontally, the central wavelengths of the pulses can be switched among 1073.42 nm, 1055.38 nm, and 1036.22 nm, with a total tunable central wavelength range of 37.2 nm. When the 3 dB bandwidth of the Vernier effect filter is set to be 4.07 nm, stable amplifier similaritons are obtained. Stretching MZI1 horizontally, the central wavelengths of the pulses are switchable among 1072.71 nm, 1060.15 nm, 1048.92 nm, and 1037.26 nm, with a total tunable central wavelength range of 35.15 nm. Compared with traditional fiber interference filters, the Vernier effect filter has a higher sensitivity, making wavelength switching more convenient and providing a wider tuning range for the ytterbium-doped mode-locked fiber laser. Full article