Soliton-like Pulses Research Articles

Enhanced performance of all-PM Ho-doped fiber oscillator using NPE-SESAM hybrid mode-locking

We demonstrate a 2.08 µm all-polarization-maintaining (PM) holmium-doped fiber oscillator using a hybrid mode-locking technique with nonlinear polarization evolution (NPE) and a semiconductor saturable absorber mirror (SESAM). This oscillator features a linear structure with dual output ports. It initiates stable single-pulse mode-locking at a fundamental repetition rate of 57.86 MHz, requiring only about 400 mW of pump power. However, removing SESAM requires increasing the pump power to about 2.2 W—about a 5.8-fold increase—to initiate mode-locking, which starts in a multi-pulse state. Additionally, the oscillator can operate in two distinct states by adjusting the phase bias, ensuring that the main output port delivers high-quality, soliton-like femtosecond pulses. The other port, known as the rejection port, emits lower-quality pulses with different spectral and temporal characteristics. However, in one state, the pulse quality at the rejection port is significantly enhanced, approaching the high quality of the main output port. Theoretical analysis indicates that the pulse quality at the rejection port strongly relies on the energy distribution between the two orthogonally polarized pulses in the PM fiber. Another advantage of the hybrid mode-locking configuration is that it allows a pump power tuning range to maintain single-pulse operation as high as 220 mW. It is ∼4 times higher than that of the NPE-only configuration which is about 60 mW. These results indicate that oscillators using hybrid mode-locking exhibit much greater flexibility and reliability than those using PM-NPE alone. The hybrid mode-locking technique shows potential in addressing the self-starting challenges inherent in PM-NPE lasers, thereby advancing their applicability in practical scenarios.

Localized wave structures: Solitons and beyond

The review is concerned with solitary waves and other localized structures in the systems described by a variety of generalizations of the Korteweg–de Vries (KdV) equation. Among the topics we focus upon are “radiating solitons,” the generic structures made of soliton-like pulses, and oscillating tails. We also review the properties of solitary waves in the generalized KdV equations with the modular and “sublinear” nonlinearities. Such equations have an interesting class of solutions, called compactons, solitary waves defined on a finite spatial interval. Both the properties of single solitons and the interactions between them are discussed. We show that even minor non-elastic effects in the soliton–soliton collisions can accumulate and result in a qualitatively different asymptotic behavior. A statistical description of soliton ensembles (“soliton gas”), which emerges as a major theme, has been discussed for several models. We briefly outline the recent progress in studies of ring solitons and lumps within the framework of the cylindrical KdV equation and its two-dimensional extension. Ring solitons and lumps (2D solitons) are of particular interest since they have many features in common with classical solitons and yet are qualitatively different. Particular attention is paid to interactions between the objects of different geometries, such as the interaction of ring solitons and shear flows, ring solitons and lumps, and lumps and line solitons. We conclude our review with views of the future developments of the selected lines of studies of localized wave structures in the theory of weakly nonlinear, weakly dispersive waves.

Mode-locked large-mode-area Er/Yb-doped fiber oscillator via nonlinear polarization evolution with enhanced mode suppression

We report a mode-locked Er/Yb-doped large-mode-area (LMA) fiber oscillator based on nonlinear polarization evolution (NPE), which utilizes a linear cavity primarily composed of polarization-maintaining (PM) fibers. The oscillator operates at 1.56 µm with a fundamental repetition rate of 34.47 MHz and has two output ports. One port can deliver high-quality soliton-like pulses with a pulse duration of 325 fs and an average power of 39.5 mW (corresponding to a pulse energy of 1.15 nJ). In contrast, the other port not only generates lower-quality complex pulses but also exhibits poorer short-term and long-term stability, likely due to cross-phase modulation effects. To the best of our knowledge, this is the first implementation of the NPE mode-locked technology in a PM-LMA Er/Yb-doped fiber oscillator at 1.55 µm which often suffers from poor self-starting mode-locking capabilities. This achievement is primarily attributed to the use of endlessly single-mode photonic crystal fibers, which effectively suppress higher-order modes in PM-LMA fibers.

Generation of 583 fs optical pulses at 10 GHz from a regeneratively mode-locked fiber laser combining nonlinear polarization evolution

A regeneratively mode-locked erbium fiber laser was numerically investigated and experimentally demonstrated, which was able to generate a 583 fs pulse train at 10 GHz via intracavity pulse compression with nonlinear polarization evolution (NPE). To excite the NPE at such a high repetition rate, a dispersion map was intentionally introduced to obtain short pulses accompanied by high peaks through soliton-like pulse shaping. Numerical simulations indicated that steady-state oscillation with pulses below 1 ps can be successfully established using this laser configuration. Experimentally, we obtained a pulse duration of 583 fs and a 3 dB spectral width of 4.5 nm at an average output power of 15.6 mW. Simultaneously, supermode suppression of more than 80 dB was also obtained from the appropriate biased NPE.

Continuous-wave and SESAM mode-locked operation of a Yb:YSr3(PO4)3 laser.

We report on the continuous-wave (CW) and, for what we believe to be the first time, passively mode-locked (ML) laser operation of an Yb3+-doped YSr3(PO4)3 crystal. Utilizing a 976-nm spatially single-mode, fiber-coupled laser diode as pump source, the Yb:YSr3(PO4)3 laser delivers a maximum CW output power of 333 mW at 1045.8 nm with an optical efficiency of 55.7% and a slope efficiency of 60.9%. Employing a quartz-based Lyot filter, an impressive wavelength tuning range of 97 nm at the zero level was achieved in the CW regime, spanning from 1007 nm to 1104 nm. In the ML regime, incorporating a commercially available semiconductor saturable absorber mirror (SESAM) to initiate and maintain soliton-like pulse shaping, the Yb:YSr3(PO4)3 laser generated pulses as short as 61 fs at 1062.7 nm, with an average output power of 38 mW at a repetition rate of ∼66.7 MHz.

Phase transitions in 2D multistable mechanical metamaterials via collisions of soliton-like pulses

In recent years, mechanical metamaterials have been developed that support the propagation of an intriguing variety of nonlinear waves, including transition waves and vector solitons (solitons with coupling between multiple degrees of freedom). Here we report observations of phase transitions in 2D multistable mechanical metamaterials that are initiated by collisions of soliton-like pulses in the metamaterial. Analogous to first-order phase transitions in crystalline solids, we observe that the multistable metamaterials support phase transitions if the new phase meets or exceeds a critical nucleus size. If this criterion is met, the new phase subsequently propagates in the form of transition waves, converting the rest of the metamaterial to the new phase. More interestingly, we numerically show, using an experimentally validated model, that the critical nucleus can be formed via collisions of soliton-like pulses. Moreover, the rich direction-dependent behavior of the nonlinear pulses enables control of the location of nucleation and the spatio-temporal shape of the growing phase.

Nonlinear Scattering of 248 nm Wavelength Light in High-Pressure SF6 and CH4 Gases for the Temporal Compression of a 20 ns KrF Laser Pulse

The nonlinear compression of narrowband (Δν ≈ 0.2 cm−1) 20 ns KrF laser pulses in SF6 at 10 atm and in CH4 at 50 atm pressure was studied. Both SBS and SRS optically phase-conjugated backward-reflected radiation was registered with an energy reflectivity of 10–14% in SF6 and CH4. In SF6, the SBS pulses gradually shortened from 10 ns to 2–3 ns with a decrease in pumping to the SBS threshold of ~10 mJ, while the SRS pulse had the shortest length of 30–60 ps for the maximal pumping of 120 mJ and broadened near the SRS threshold of ~30 mJ. For the SRS pulse energy, the ~2 mJ peak power 5 × 107 W was tenfold higher than the pump power. The theoretical model predicted a soliton-like SRS pulse compression to a temporal length of the order of the vibrational relaxation time. There was no pulse compression of backward SBS and SRS radiation in CH4, while, in the forward direction, SRS pulses shortened to 3–4 ns at reduced pumping.

All-polarization-maintaining Ho-doped fiber oscillator mode-locked with nonlinear polarization evolution.

We report a self-starting mode-locked all-polarization-maintaining (PM) holmium (Ho)-doped fiber oscillator operating at ∼2.08 µm based on nonlinear polarization evolution (NPE). The oscillator is configured as a linear cavity structure with two output ports exhibiting completely different pulse characteristics. One output port of the oscillator can deliver a stable, clean soliton-like pulse with a pulse duration of 439 fs and an average power of 7.5 mW at a fundamental repetition rate of 61.67 MHz. In contrast, the other port delivers a low-quality pulse with a complex structure. Numerical simulations reveal that the pulse difference between the two ports is mainly caused by the nonlinear optical interactions between the slow-axis and fast-axis modes in the PM fibers. Furthermore, the obtained clean pulses show significant improvements in relative intensity noise and power stability compared to complex pulses. Our study can help researchers obtain high-quality, stable pulses from PM-NPE mode-locked fiber oscillators.

Exploring dynamic behaviors of soliton-like pulses in the lossy electrical transmission line model with fractional derivatives: A comparative study

This study aims to explore the intricate behavior of soliton-like pulses within a nonlinear and lossy electrical transmission line. The transmission line is described by a mathematical model called the “beta derivative”, which is specifically designed to characterize the propagation of electrical solitons in media with both nonlinearity and dispersion properties. To achieve this goal, the (G′/G2)-expansion method is applied to a periodically loaded nonlinear beta derivative lossy transmission line with symmetric voltage-dependent capacitances. Soliton-like pulses, including periodic singular, dark, bright, and singular waves, are obtained using the (G′/G2)-expansion method based on the voltage equation. Three-dimensional and two-dimensional graphs of some of the obtained novel solutions satisfying relevant equations are provided to understand the underlying mechanisms of the soliton family. In terms of fractionality, the profiles of dark or bright waveforms maintain their complete forms, but their smoothness increases as the fractional parameters increase. On the other hand, periodic wave solutions exhibit an increase in periodicity. By adjusting the parameters of the model, the characteristics of the waves can be modified to generate desired wave profiles. Additionally, the study involves a comprehensive comparison among solutions derived from models incorporating the beta, conformable, and M−truncated derivatives. It examines how the amplitude of the solitons is influenced by the fractional parameter, utilizing graphs to visualize this impact by assigning specific fractional parameter values. These pulse-like solitons offer promising potential for integration within telecommunication systems, where they can function as information carriers, facilitating heightened data bit rates. By leveraging the findings of this study, advancements in telecommunication technology can be pursued, leading to enhanced efficiency and improved performance.

Mathematical modeling of chirped modulated waves along a multi-coupled nonlinear electrical transmission line with dispersive elements

This work presents a mathematical modeling of chirped modulated waves propagating along a two-dimensional nonlinear electrical transmission line consisting of nonlinear dispersive and purely nonlinear capacitive elements. Combining the rotating-wave approximation technique with the perturbation method, we derive a two-dimensional extended nonlinear Schrödinger equation with self-steepening and self-frequency shift, that predicts the formation and propagation of a very rich variety of soliton-like waves including bright, dark, kink, and double-kink soliton-like waves with nonlinear chirp in a multi-coupled nonlinear electrical transmission network with dispersive elements. Using this model equation, parameter domains are delineated in which these modulated waves exist. The parameter domains are found to be strongly dependent on the dispersive elements of the network system. Through exact solutions of the amplitude equation, we investigate the dynamics of chirped modulated waves along the network system under consideration. Our results show that the nonlinear chirp associated with each of the found soliton-like pulses is directly proportional to the wave intensity and is saturated at some finite value as the propagation coordinate approaches its asymptotic value. Also, we show that increasing the number of the network lines decreases the propagating speed of the soliton-like pulses. Most importantly, theoretical analysis show that chirping of found network pulses can be controlled by varying the self-steepening term and self-frequency shift. The validity of analytical results and the robustness of these chirped soliton-like voltage signals which may have important applications in signal processing systems are confirmed by numerical simulations. The results of our study may be launched in long distance telecommunication lines involving higher-order nonlinearities of the fiber.

Modified Exp-Function Method to Find Exact Solutions of Microtubules Nonlinear Dynamics Models

In this paper, we use the modified exp−ψθ-function method to observe some of the solitary wave solutions for the microtubules (MTs). By treating the issues as nonlinear model partial differential equations describing microtubules, we were able to solve the problem. We then found specific solutions to the nonlinear evolution equation (NLEE) covering various parameters that are particularly significant in biophysics and nanobiosciences. In addition to the soliton-like pulse solutions, we also find the rational, trigonometric, hyperbolic, and exponential function characteristic solutions for this equation. The validity of the method we developed and the fact that it provides more solutions are demonstrated by comparison to other methods. We next use the software Mathematica 10 to generate 2D, 3D, and contour plots of the precise findings we observed using the suggested technique and the proper parameter values.

Soliton-like optical pulse in a gain medium with dissipation under conditions of intra-pulse Raman scattering

The propagation of an optical pulse in a nonresonant gain medium with the Raman nonlinearity is studied. A nonlinear integro-differential equation for the envelope of the pulse electric field is derived. The solution of this equation in the form of a superluminal soliton-like pulse is obtained and analyzed.

Localized Unipolar Shear Deformation Autowaves in a Nonequilibrium Paramagnet

It is shown that a nanosecond unipolar soliton-like pulse of the type of a localized shear deformation autowave propagating perpendicular to the magnetic field can be formed in a cubic paramagnetic crystal subjected to longitudinal static deformation in the direction of external magnetic field. The influx of the energy stored in paramagnetic ions into the pulse due to the nonequilibrium initial population of their stationary quantum states is compensated by irreversible losses caused by pulse damping due to its interaction with thermal lattice vibrations, defects, and microinhomogeneities.

Behaviors of multiple pulsing in high power saturable-absorber mode-locked Yb:KGW laser

By investigating the mode-locked pulse characteristics with varying pump power, we report on the soliton pulse breakup and multiple pulsing of a high power femtosecond Yb:KGW laser at a 10 W level of output power. The pulse breakup from single to double pulses at an output power of 6.3 W, exhibits a step-like abrupt change in the spectrum and temporal duration. Even under multiple pulsing operation, the mode-locked pulses follow the soliton-like pulse formation model such that the pulse duration is inversely proportional to the pulse energy and the time-bandwidth product is close to the transform limit. The multiple pulsing and breakup characterized in this study provide an efficient and reliable method to confirm the single pulse operation of high power mode-locked solid-state lasers.

Stimulated generation of deterministic platicon frequency microcombs

Dissipative Kerr soliton generation in chip-scale nonlinear resonators has recently observed remarkable advances, spanning from massively parallel communications, to self-referenced oscillators, and to dual-comb spectroscopy. Often working in the anomalous dispersion regime, unique driving protocols and dispersion in these nonlinear resonators have been examined to achieve the soliton and soliton-like temporal pulse shapes and coherent frequency comb generation. The normal dispersion regime provides a complementary approach to bridge the nonlinear dynamical studies, including the possibility of square pulse formation with flattop plateaus, or platicons. Here we report observations of square pulse formation in chip-scale frequency combs through stimulated pumping at one free spectral range and in silicon nitride rings with + 55 fs 2 / mm normal group velocity dispersion. Tuning of the platicon frequency comb via a varied sideband modulation frequency is examined in both spectral and temporal measurements. Determined by second-harmonic autocorrelation and cross correlation, we observe bright square platicon pulse of 17 ps pulse width on a 19 GHz flat frequency comb. With auxiliary-laser-assisted thermal stabilization, we surpass the thermal bistable dragging and extend the mode-locking access to narrower 2 ps platicon pulse states, supported by nonlinear dynamical modeling and boundary limit discussions.

Dual-dispersion-regime dual-comb mode-locked laser.

We report on the first, to the best of our knowledge, solid-state dual-comb mode-locked laser that simultaneously operates in different dispersion regimes. Due to the intrinsic polarization multiplexing in a birefringent Yb:Ca3NbGa3Si2O14 (Yb:CNGS) gain medium, the laser emits two cross-polarized pulse trains with a repetition rate offset of ∼ 4.8 kHz from a single cavity. We obtain dual pulse generation with a 20-fold difference in duration by setting the net cavity group delay dispersion to cross zero across the emission band of the employed gain medium. While the duration of the soliton-like pulses experiencing anomalous dispersion amounts to 117 fs, the second laser output, which is spectrally located in the normal dispersion region, is strongly chirped with a pulse duration of 2360 fs.

Nonlinear Transformation of Sine Wave within the Framework of Symmetric (2+4) KdV Equation

This paper considers the transformation of a sine wave in the framework of the extended modified Korteweg–de Vries equation or (2+4) KdV, which includes a combination of cubic and quintic nonlinearities. It describes the internal waves in a medium with symmetric vertical density stratification, and all the considerations in this study are produced for the reasonable combinations of the signs of the coefficients for nonlinear and dispersive terms, provided by this physical problem. The features of Riemann waves—solutions of the dispersionless limit of the model—are described in detail: The times and levels of breaking are derived in an implicit analytic form depending on the amplitude of the initial sine wave. It is demonstrated that the shock occurs at two (for small amplitudes) or four (for moderate and large amplitudes) levels per period of sine wave. Breaking at different levels occurs at different times. The symmetric (2+4) KdV equation is not integrable, but nevertheless it has stationary solutions in the form of traveling solitary waves of both polarities with a limiting amplitude. With the help of numerical calculations, the features of the processes of a sinusoidal wave evolution and formation of undular bores are demonstrated and analyzed. Qualitative features of multiple inelastic interactions of emerging soliton-like pulses are displayed.

Modified Exp-Function Method to Find Exact Solutions of Ionic Currents along Microtubules

A number of solitary wave solutions for microtubules (MTs) are observed in this article by using the modified exp-function approach. We tackle the problem by treating the results as nonlinear RLC transmission lines, and then finding exact solutions to Nonlinear Evolution Equation (NLEE) containing parameters of particular importance in biophysics and nanobiosciences. For this equation, we find trigonometric, hyperbolic, rational, and exponential function solutions, as well as soliton-like pulse solutions. A comparison with other approach indicates the legitimacy of the approach we devised as well as the fact that our method offers extra solutions. Finally, we plot 2D, 3D and contour visualizations of the exact results that we observed using our approach using appropriate parameter values with the help of software Mathematica 10.

Ultra-Short Pulse Generation From Optical Parametric Oscillators With a Cavity-Length Detuning

We report that the pulse compression mechanism in cavity-length-detuned optical parametric oscillators (OPOs) could be used to generate high-quality, soliton-like optical pulses with sub-100 fs duration. By numerical simulations, we illustrated the pulse and spectral evolution in an OPO with respect to cavity-length detuning, including central wavelength shift, spectral broadening and pulse compression. Experimentally, from an OPO pumped by 180 fs pulses, we obtained 42 fs signal pulses with a time-bandwidth product of 0.32. At elevated pump powers, the formation of multiple pulses was observed. Nonetheless, we demonstrated that the high-quality optical pulses could be obtained by simply slightly increasing the cavity-length detuning.

Spectrally combined three-diode-pumped compact femtosecond Ti:sapphire laser exceeding 1 W mode-locked power.

The achievement of a high average power exceeding 1 W remains a major challenge for direct-diode pumped and mode-locked femtosecond Ti:sapphire lasers. Herein, we demonstrate high-power soliton-like pulses from a direct spectrally combined three-diode-pumped and semiconductor saturable absorber mirror (SESAM)-based mode-locked Ti:sapphire laser. Its mode-locked output power of up to 1 W was obtained in correspondence with a 68.8 MHz repetition rate and 55 fs pulse duration; thus, the pulse energy and peak power are 14.5 nJ and 264 kW, respectively. To the best of our knowledge, this is the highest reported output power and pulse energy from a Ti:sapphire laser with three spectrally combined pump diodes (471 nm, 491 nm, and 525 nm) and a simple beam expander. For efficient pumping, the combined pump beam, directed into the lens (f = 60 mm), which comprised three aspheric lenses along the fast axis and a shared cylindrical beam telescope (8× magnification) along the slow axis, resulting in a circular-focused beam in the Ti:sapphire crystal. The beam waist was measured to be 39 μm ×38 μm along the slow and fast axes.