Spatio-Temporal Pulsating Dissipative Solitons through Collective Variable Methods

A semi-analytical approach for the pulsating solutions of the 3D complex Cubic-quintic Ginzburg-Landau Equation (CGLE) is presented in this article. A collective variable approach is used to obtain a system of variational equations which give the evolution of the light pulses parameters as a function of the propagation distance. The collective coordinate approach is incomparably faster than the direct numerical simulation of the propagation equation. This allows us to obtain, efficiently, a global mapping of the 3D pulsating soliton. In addition it allows describing the influence of the parameters of the equation on the various physical parameters of the pulse and their dynamics.

Damped Kadomtsev–Petviashvili Equation for Weakly Dissipative Solitons in Dense Relativistic Degenerate Plasmas

We have investigated the properties of three-dimensional electrostatic ion solitary structures in highly dense collisional plasma composed of ultra-relativistically degenerate electrons and non-relativistic degenerate ions. In the limit of low ion-neutral collision rate, we have derived a damped Kadomtsev–Petviashvili(KP) equation using perturbation analysis. Supplemented by vanishing boundary conditions, the time varying solution of damped KP equation leads to a weakly dissipative compressive soliton. The real frequency behavior and linear damping of solitary pulse due to ion-neutral collisions is discussed. In the presence of weak transverse perturbations, soliton evolution with damping parameter and plasma density is delineated pointing out the extent of propagation using typical parameters of dense plasma in the interior of white dwarfs.

Diffusion-induced deflection and the effect of two-wave mixing gain on dissipative photovoltaic solitons

In an open-circuit dissipative photovoltaic （PV） crystal, by considering the diffusion effect, the deflection of bright dissipative photovoltaic （DPV） solitons has been investigated by employing numerical technique and perturbational procedure. The relevant results show that the centre of the optical beam moves along a parabolic trajectory, while the central spatial-frequency component shifts linearly with the propagation distance; furthermore, both the spatial deflection and the angular derivation are associated with the photovoltaic field. Such DPV solitons have a fixed deflection degree completely determined by the parameters of the dissipative system. The small bending cannot affect the formation of the DPV soliton via two-wave mixing.

Collision Dynamics of Dissipative Matter-Wave Solitons in a Perturbed Optical Lattice

We investigate the stability and collision dynamics of dissipative matter-wave solitons formed in a quasi-one- dimensional Bose-Einstein condensate with linear gain and three-body recombination loss perturbed by a weak optical lattice. It is shown that the linear gain can modify the stability of the single dissipative soliton moving in the optical lattice. The collision dynamics of two individual dissipative matter-wave solitons explicitly depend on the linear gain parameter, and they display different dynamical behaviors in both the in-phase and out-of-phase interaction regimes.

Dissipative Kerr solitons in optical microresonators with Raman effect and third-order dispersion

Using the mean-field normalized Lugiato-Lefever equation,we theoretically investigate the dynamics of cavity soliton and comb generation in the presence of Raman effect and the third-order dispersion.Both of them can induce the temporal drift and frequency shift.Based on the moment analysis method,we analytically obtain the temporal and frequency shift,and the results agree with the direct numerical simulation.Finally,the compensation and enhancement of the soliton spectral between the Raman-induced self-frequency shift and soliton recoil are predicted.Our results pave the way for further understanding the soliton dynamics and spectral characteristics,and providing an effective route to manipulate frequency comb.

Temperature effect on dissipative holographic screening-photovoltaic solitons in a biased dissipative system

In a biased dissipative photovoltaic-photorefractive system, this paper investigates the temperature effect on the evolution and the self-deflection of the dissipative holographic screening-photovoltaic （DHSP） solitons. The results reveal that, the evolution and the self-deflection of the bright and dark DHSP solitons are influenced by the system temperature. At a given temperature, for a stable DHSP soliton originally formed in the dissipative system, it attempts to evolve into another DHSP soliton when the temperature change is appropriately small, whereas it will become unstable or break down if the temperature departure is large enough. Moreover, the self-deflection degree of the solitary beam centre increases as temperature rises in some range, while it is decided by the system parameters and is slight under small-signal condition. The system temperature can be adjusted to change the formation and the self-deflection of the solitary beam in order to gain certain optical ends. In a word, the system temperature plays a role for the DHSP solitons in the dissipative system.

A cladding-pumping based power-scaled noise-like and dissipative soliton pulse fiber laser

We report a high-average-power noise-like pulse(NLP) and dissipative soliton(DS) pulse fiber laser. Average power as high as 4.8 W could be obtained at the fundamental mode-locked repetition rate. The NLP can also be transformed into a more powerful DS mode-locking state by optimizing the polarization and losses of intra-cavity pulses in the nonlinear polarization evolution regime. The operation mode between the NLP and DS can be switched, and the laser output performance in both modes has been studied. The main advantage of this work is switchable high-power operation between the NLP and DS. In comparison with conventional single-mode NLP fiber lasers, the multi-function high-power optical source will greatly push its application in supercontinuum generation, coherence tomography, and industrial processing.

Generation of multi-wavelength square pulses in the dissipative soliton resonance regime by a Yb-doped fiber laser

Multi-wavelength square pulses are generated in the dissipative soliton resonance(DSR) regime by a Yb-doped fiber laser(YDFL) with a long cavity configuration. The spectral filter effect provided by a passive fiber with low-stress birefringence facilitates the establishment of multi-wavelength operation. Through appropriate control of the cavity parameters,a multi-wavelength DSR pulse can be generated in single-and dual-waveband regions. When the multi-wavelength DSR works in the 1038 nm waveband, the pulse duration can broaden from 2 ns to 37.7 ns. The maximum intra-cavity pulse energy is 152.7 nJ. When the DSR works in the 1038 nm and 1080 nm wavebands, the pulse duration can be tuned from2.3 ns to 10.5 ns with rising pump power. The emergence of the 1080 nm waveband is attributed to the stimulated Raman scattering(SRS) effect. Our work might help a deeper insight to be gained into DSR pulses in all-normal-dispersion YDFLs.

Dual-wavelength dissipative soliton operation of an erbium-doped fibre laser using a nonlinear polarization rotation technique

We report on the generation of dual-wavelength dissipative solitons in a passively mode-locked fibre laser with a net normal dispersion using the nonlinear polarization rotation （NPR） technique. Taking the intrinsic advantage of the intracavity birefringence-induced spectral filtering effect in the NPR-based ring laser cavity, the dual-wavelength dissipative solitons are obtained. In addition, the wavelength separation and the lasing location of the dual-wavelength solitons can be flexibly tuned by changing the orientation of the polarization controller.

Interactions between optical bullets with different velocities in the three-dimensional cubic-quintic complex Ginzburg-Landau equation

By using the three-dimensional complex Ginzburg--Landau equation with cubic--quintic nonlinearity, this paper numerically investigates the interactions between optical bullets with different velocities in a dissipative system. The results reveal an abundance of interesting behaviours relating to the velocities of bullets： merging of the optical bullets into a single one at small velocities; periodic collisions at large velocities and disappearance of two bullets after several collisions in an intermediate region of velocity. Finally, it also reports that an extra bullet derives from the collision of optical bullets when optical bullets are at small velocities but with high energies.

Nonlinear optical properties of carboxyl-functionalized graphene oxide for dissipative soliton resonance pulse generation

Here,we investigated the nonlinear optical(NLO)characteristics of carboxyl-functionalized graphene oxide(GO-COOH)in the near-infrared(NIR)region.The results revealed that GO-COOH samples exhibit strong saturable absorption at low pump levels and a gradual transition to reverse saturable absorption(RSA)with increasing pump power.Then the saturable absorber(SA)by depositing the GO-COOH on the side-polished fiber(SPF)was employed in Yb-and Er-doped fiber lasers.Stable ultrashort pulses operating in the dissipative soliton(DS)and conventional soliton(CS)regimes were obtained with pulse widths of 26.6 ps and 968 fs,respectively.Besides,the dissipative soliton resonance(DSR)phenomenon caused by the RSA of GO-COOH was also observed with increasing pump power.The high-stable DSR mode-locked pulses with the maximum pulse energy of 1.91 nJ and 0.74 nJ were obtained in YDFL and EDFL respectively.These results not only reveal the potentiality of GO-COOH in ultrafast photonics applications but also open a new avenue to explore high-pulse-energy laser sources based on twodimensional materials.

Two-dimensionally controllable DSR generation from dumbbell-shaped mode-locked all-fiber laser

An all-fiber dumbbell-shaped dual-amplifier mode-locked Er-doped laser that can function in dissipative soliton resonance(DSR)regime is demonstrated.A nonlinear optical loop mirror(NOLM)and a nonlinear amplifying loop mirror(NALM)are employed to initiate the mode-locking pulses.Unlike conventional single-amplifier structure,the output peak power of which remains unchanged when pump power is varied,the proposed structure allows its output peak power to be tuned by changing the pump power of the two amplifiers while the pulse duration is directly determined by the amplifier of nonlinear amplifying loop mirror.The entire distribution maps of peak power and pulse duration clearly demonstrate that the two amplifiers are related to each other,and they supply directly a guideline for designing tunable peak power DSR fiber laser.Pulse width can change from 800 ps to 2.6 ns and peak power varies from 13 W to 27 W.To the best of our knowledge,the peak power tunable DSR pulse is observed for the first time in dumbbell-shaped Er-doped all-fiber mode-locked lasers.

The phase shift analysis of the colliding dissipative KdV solitons

In this work,the head-on collisions of the non-stationary dissipative soliton in ultracold neutral plasmas(UNPs)are investigated.The extended Poincare-Lighthill-Kuo(PLK)approach is adopted for reducing the fluid equations of the UNPs to two-counterpropagating damped Korteweg-de Vries(dKdV)equations.The dKdV equation is not an integrable Hamiltonian system,i.e.,does not have an exact solution.Thus,one of the main goal of this paper is to find a new general approximate analytical solution to the dKdV equation for investigating the mechanism of the propagation and interaction of the non-stationary dissipative solitons.The residual error is estimated for checking the accuracy of the new obtained solution.The approximate analytical soliton solutions are adopted for deriving the temporal phase shifts after the collision.The impact of physical parameters on the nonstationary dissipative soliton profile and the temporal phase shifts is discussed.The obtained results will contribute to understand the mechanism of propagation and interaction of many nonlinear phenomena in different nonlinear mediums such as ocean,sea,optical fiber,plasma physics,etc.

2.1 μm,high-energy dissipative soliton resonance from a holmium-doped fiber laser system

We propose a 2.1μm high-energy dissipative soliton resonant(DSR)fiber laser system based on a mode-locked seed laser and dual-stage amplifiers.In the seed laser,the nonlinear amplifying loop mirror technique is employed to realize mode-locking.The utilization of an in-band pump scheme and long gain fiber enables effectively exciting 2.1μm pulses.A section of ultra-high numerical aperture fiber(UHNAF)with normal dispersion and high nonlinearity and an output coupler with a large coupling ratio are used to achieve a high-energy DSR system.By optimizing the UHNAF length to55 m,a 2103.7 nm,88.1 nJ DSR laser with a 3-dB spectral bandwidth of 0.48 nm and a pulse width of 17.1 ns is obtained under a proper intracavity polarization state and pump power.The output power and conversion efficiency are 0.233W and 4.57%,respectively,both an order of magnitude higher than those of previously reported holmium-doped DSR seed lasers.Thanks to the high output power and nanosecond pulse width of the seed laser,the average power of the DSR laser is linearly scaled up to 50.4 W via a dual-stage master oscillator power amplifier system.The 3-dB spectral bandwidth broadens slightly to 0.52 nm,and no distortion occurs in the amplified pulse waveform.The corresponding pulse energy reaches 19.1μJ,which is the highest pulse energy in a holmium-doped mode-locked fiber laser system to the best of our knowledge.Such a 2.1μm,high-energy DSR laser with relatively wide pulse width has prospective applications in mid-infrared nonlinear frequency conversion.

Picosecond dissipative soliton generation from an ytterbium‑doped fber laser based on a BP/SnSe_(2)‑PVA mixture saturable absorber

Stable picosecond dissipative soliton pulses were observed in an ytterbium-doped fber laser employing a high-quality mixture of BP/SnSe_(2)-PVA saturable absorber(SA).The modulation depth,saturation intensity,and non-saturable loss of the mixture of BP/SnSe_(2)-PVA SA were measured with values of 5.98%,18.37 MW/cm2,and 33%,respectively.Within the pump power range of 150–270 mW,stable dissipative soliton pulses were obtained with an output power of 1.68–4 mW.When the minimum pulse duration is 1.28 ps,a repetition rate of 0.903 MHz,center wavelength of 1064.38 nm and 3 dB bandwidth of 2 nm were obtained.The maximum pulse energy of 4.43 nJ and the signal-to-noise ratio up to 72 dB were achieved at pump power of 270 mW.The results suggest that the BP/SnSe_(2)-PVA mixture SA has outstanding nonlinear saturable absorption characteristics and broad ultrafast laser applications.

Temporal-filtering dissipative soliton in an optical parametric oscillator

Dissipative solitons have been realized in mode-locked fiber lasers in the theoretical framework of the Ginzburg±Landau equation and have significantly improved the pulse energy and peak power levels of such lasers.It is interesting to explore whether dissipative solitons exist in optical parametric oscillators in the framework of three-wave coupling equations in order to substantially increase the performance of optical parametric oscillators.Here,we demonstrate a temporalfiltering dissipative soliton in a synchronously pumped optical parametric oscillator.The temporal-gain filtering of the pump pulse combined with strong cascading nonlinearity and dispersion in the optical parametric oscillator enables the generation of a broad spectrum with a nearly linear chirp;consequently,a significantly compressed pulse and high peak power can be realized after dechirping outside the cavity.Furthermore,we realized,for the first time,dissipative solitons in an optical system with a negative nonlinear phase shift and anomalous dispersion,extending the parameter region of dissipative solitons.The findings may open a new research block for dissipative solitons and provide new opportunities for mid-infrared ultrafast science.

Atom-referenced and stabilized soliton microcomb

For the applications of the frequency comb in microresonators,it is essential to obtain a fully frequency-stabilized microcomb laser source.In this study,we present a system for generating a fully atom-referenced stabilized soliton microcomb.The pump light around 1560.48 nm is locked to an ultra-low-expansion(ULE)cavity.This pump light is then frequency-doubled and referenced to the atomic transition of87Rb.The repetition rate of the soliton microcomb is injection-locked to an atomic-clockstabilized radio frequency(RF)source,leading to mHz stabilization at 1 s.As a result,all comb lines have been frequencystabilized based on the atomic reference and the ULE cavity,achieving a very high precision of approximately 18 Hz at 1 s,corresponding to the frequency stability of 9.5×10^(-14).Our approach provides a fully stabilized microcomb experiment scheme with no requirement of f-2f technique,which could be easily implemented and generalized to various photonic platforms,thus paving the way towards the ultraprecise optical sources for high precision spectroscopy.

Harmonic dissipative soliton resonance pulses in a fiber ring laser at different values of anomalous dispersion

The pulse dynamics of harmonic mode-locking in a dissipative soliton resonance(DSR) region in an erbiumdoped fiber ring laser is investigated at different values of anomalous dispersion. The fiber laser is mode-locked by a nonlinear polarization rotation technique. By inserting 0–200 m anomalous dispersion single-mode fiber in the laser cavity, the cavity length is changed from 17.3 to 217.3 m, and the corresponding dispersion of the cavity ranges from -0.27 to-4.67 ps^2. The observed results show that the tuning range of repetition rate under a harmonic DSR condition is highly influenced by the cavity dispersion. Furthermore, it is found that, by automatically adjusting their harmonic orders, the lasers can work at certain values of repetition rate, which are independent of the cavity length and dispersion. The pulses at the same repetition rate in different laser configurations have similar properties, demonstrating that each achievable repetition rate represents an operation regime of harmonic DSR lasers.

Power-scaled dissipative soliton using double-cladding-pumped Yb-doped all-fiber amplifier

We report on an all-fiber oscillator followed by an all-fiber amplifier to produce as short as 382 fs laser pulses with up to 0.9 W average power. The oscillator is an all-normal-dispersion all-fiber dissipative soliton laser operating at1030 nm, and operating in dissipative soliton mode. The amplifier stage is mainly based on a double-cladding20 μm radius ytterbium-doped fiber pumped by an up to 2.5 W CW laser source. The optical-to-optical conversion amplifier efficiency is around 40%. To our knowledge, this is the first report of an all-fiber mode-locked fiber laser oscillator amplified by an all-fiber amplifier.

Novel anlytical solution to the damped Kawahara equation and its application for modeling the dissipative nonlinear structures in a fluid medium

A novel approximate analytical solution to the linear damped Kawahara equation using a suitable hypothesis is reported for the first time.Based on the exact solutions(such as solitary waves,cnoidal waves,etc.)of the undamped Kawahara equation,the dissipative nonlinear structures like dissipative solitons and cnoidal waves are investigated.The obtained solution is considered a general solution,i.e.,it can be applied for studying the properties of all dissipative traveling waves described by the linear damped Kawahara equation.Our technique is not limited to solve the linear damped Kawahara equation only,but it can be used for solving a large number of non-integrable evolution equations related to the realistic natural phenomena.Moreover,the maximum global residual error in the whole space-time domain is estimated for checking the accuracy of the obtained solutions.The obtained solutions can help many researchers in explaining the ambiguities about the mechanisms of propagation of nonlinear waves in complex systems such as seas,oceans,plasma physics,and much more.