Bright-dark Soliton Pairs Research Articles

Generation of dual-wavelength Q-switched pulses and bright-dark pulses pairs in an erbium-doped fiber laser with NbS2 as saturable absorber

In this experiment, stable dual-wavelength Q-switched pulses and bright-dark pulses pairs are achieved in an erbium-doped fiber laser based on NbS2 under saturable absorber. At pump powers of 172 mW–322 mW, stable dual-wavelength Q-switched pulses with center wavelengths of 1531.9 nm and 1557.05 nm were obtained with a signal-to-noise ratio (SNR) as high as 43 dB. The repetition frequency was increased from 14.3 kHz to 22.7 kHz as the pump power was increased. When the pump power was increased to 340 mW, we found stable bright-dark pulses with center wavelengths of 1559.7 nm and 1560.12 nm, respectively, and a repetition frequency of 3.44 MHz with an SNR of 52 dB. The experimental results show that NbS2 can be used as an excellent SA for fiber lasers and demonstrate that NbS2 can be used to study dual-wave Q-switched pulses and bright-dark soliton pairs.

Generation of Bright-Dark soliton pairs in mode-locked fiber laser based on WSe2/MoSe2 heterojunction

In this study, the WSe2/MoSe2 heterojunction was fabricated by liquid-phase exfoliation (LPE) method with a modulation depth of 11.39 % and saturable intensity of 0.246 GW/cm2. The WSe2/MoSe2 heterojunction was used as a saturable absorber (SA) to achieve bright-dark soliton pairs modulation in Er-doped fiber laser (EDFL)successfully. Stable bright-dark soliton pairs, with a repetition frequency of 4.459 MHz, were successfully generated using a pump power of 218.8 mW. The central wavelengths were found to be at 1564.16 nm and 1564.98 nm with the peak-to-peak spacing of 0.82 nm. The single-pulse energy was determined to be 0.7 nJ. The experimental results demonstrate the exceptional nonlinear saturable absorption characteristics of the WSe2/MoSe2 heterojunction. These findings offer valuable insights for future research on bright-dark soliton pairs utilizing this material.

Optical Nonlinearity of Violet Phosphorus and Applications in Fiber Lasers

A D-shaped fiber is coated with a new two-dimensional nanomaterial, violet phosphorus (VP), to create a saturable absorber (SA) with a modulation depth of 3.68%. Subsequently, the SA is inserted into a fiber laser, enabling successful generation of dark solitons and bright–dark soliton pairs through adjustment of the polarization state within the cavity. Through further study, mode-locked pulses are achieved, proving the existence of polarization-locked vector solitons. The results indicate that VP can be used as a polarization-independent SA.

Bright and Dark Soliton Pulse in Solid Core Photonic Crystal Fibers

The nonlinear Schrodinger (NLS) equation was utilized to conduct an analytical study on the soliton control in homogeneous photonic crystal fibers (PCFs) within both the normal and anomalous dispersion regimes. The split step Fourier method and MATLAB computation were used to generate the analytical soliton solutions for the NLS problem. The bright and dark soliton can be controlled by the group-velocity distribution (GVD). It is capable of demonstrating the fabrication of a fully coherent PCF. Moreover, dark soliton pulses have been seen in PCF in the typical dispersion domain. Here, we present the bound states of bright–dark soliton pairs that are mutually confined in a PCF. Solitons are produced when two modes with opposing dispersions are replanted. One laser operating in the anomalous dispersion domain produces the bright soliton, while the second laser running in the normal dispersion phase produces the dark soliton by normal dispersion cross-phase modulation with the light soliton. The results unequivocally point to a novel method of generating dark soliton pulses. Capturing both bright and dark solitons can produce light states that, interestingly, have a consistent power output and spectrally resemble a frequency comb. These results may have use in soliton states in atomic physics, ultrafast optics, frequency comb technologies, and telecommunications systems. A radically new approach to the stabilization of powerful wave packages in the negative and positive GVD regions of interacting waves is illustrated.

Conversion from Q-switched to bright-dark soliton pair mode-locked operation in an InSb based erbium-doped fiber laser

In this experiment, stable Q-switched pulses and bright-dark soliton pairs were realized in an InSb based erbium-doped fiber laser. Firstly, when the pump power was between 70 and 115 mW, a stable passive Q-switched operation with a central wavelength of 1565.38 nm was achieved, and the signal-to-noise ratio (SNR) was about 37 dB. As the pump power increased, the repetition frequency of the Q-switched pulse can be increased from 4.0145 to 10.623 kHz. When the pump power was increased to the range of 185 to 450 mW, stable bright-dark soliton pairs mode-locked operation was realized, and the two peaks of the spectrum were located at 1568.67 and 1569.34 nm, respectively. The pulse repetition rate was 3.419 MHz, and the SNR was about 59 dB. This research will broaden the application of InSb in ultrafast optics and nonlinear optics.

Vector combined cnoidal wave and soliton solutions for a 3D partially nonlocal CNLSE

A 3D distributed-coefficient coupled nonlinear Schrödinger equation(CNLSE) with the partially nonlocal nonlinearity(PNN) for locality in two transverse directions and non-locality in the longitudinal direction becomes the center of attention in this paper. A one-to-one corresponding expression from the distributed-coefficient CNLSE with the PNN to the constant-coefficient CNLSE is confirmed. By way of the Darboux transformation, combined vector solutions of cnoidal wave and soliton with different structures for double components are found. Evolutional behaviors of dark-bright soliton pair, dark-bright soliton pair traveling parallelly along the top of cnoidal wave, and soliton break-up are revealed when parameters of solutions are selected as different values.

Generation of mode-locked states of conventional solitons and bright-dark solitons in graphene mode-locked fiber laser

This paper proposes a mode-locked fiber laser based on graphene-coated microfiber. The total length of the fiber laser resonant cavity is 31.34 m. Under the condition of stable output of bright-dark soliton pairs from the fiber laser, dual-wavelength tuning is realized by adjusting the polarization controller (PC), and the wavelength tuning range is 11 nm. Furthermore, the effects of polarization states on bright-dark solitons are studied. It is demonstrated that the mode-locking state can be switched between conventional solitons and bright-dark solitons in the graphene mode-locked fiber laser. Bright-dark soliton pairs with different shapes and nanosecond pulse width can be obtained by adjusting the PC and pump power.Graphical

Temperature effects on soliton pairs in novel photorefractive crystals having both the linear and quadratic electro-optic effects

We investigate and formulate a detailed theory studying the temperature effects on bright-dark optical spatial soliton pair in the novel photorefractive crystals having both the nonlinearities i.e., the quadratic and linear electro-optic effects. The coupled modified Nonlinear Schrodinger (NLS) equations is solved exactly to obtain analytical solutions for both the components. There are few physical factors which are dependent on the temperature: the dielectric constant, dark irradiance and the diffusion current. We consider the variation of dielectric constant and dark irradiance to study the effect on the nonlinearity. Various FWHM curves are plotted which give us an idea of the self trapping nonlinearity’s dependence on the temperature

GeTe based modulator for the generation of soliton, soliton molecule and bright-dark soliton pair

We experimentally investigated GeTe as a modulator for generating conventional soliton, soliton molecule and bright-dark soliton pair in an Er-doped fiber laser (EDFL) for the first time. The GeTe exhibited typical saturable absorption properties with modulation depth and saturation intensity of about 9.5% and 8.2 MW/cm2. With the GeTe based saturable absorber, conventional soliton mode-locked EDFL was demonstrated with ultrashort pulse duration of 972 fs. Through controlling the pump power and polarization controller, the single soliton state can evolve into soliton molecule state. Furthermore, bright-dark soliton pair can also be obtained in this fiber laser at the appropriate pump power. This work demonstrated that the GeTe can be used as a potential candidate modulator for soliton fiber laser.

2D BP/InSe Heterostructures as a Nonlinear Optical Material for Ultrafast Photonics.

The BP/InSe heterojunction has attracted the attention of many fields in successful combined high hole mobility of black phosphorus (BP) and high electron mobility of indium selenide (InSe), and enhanced the environmental stability of BP. Nevertheless, photonics research on the BP/InSe heterostructure was insufficient, while both components are considered promising in the field. In this work, a two-dimensional (2D) BP/InSe heterostructure was fabricated using the liquid-phase exfoliation method. Its linear and non-linear optical (NLO) absorption was characterized by ultraviolet−visible−infrared and Open-aperture Z-scan technology. On account of the revealed superior NLO properties, an SA based on 2D BP/InSe was prepared and embedded into an erbium-doped fiber laser, traditional soliton pulses were observed at 1.5 μm with the pulse duration of 881 fs. Furthermore, harmonic mode locking of bound solitons and dark-bright soliton pairs were also obtained in the same laser cavity due to the cross-coupling effect. The stable mode-locked operation can be maintained for several days, which overcome the low air stability of BP. This contribution further proves the excellent optical properties of 2D BP/InSe heterostructure and provides new probability of developing nano-photonics devices for the applications of double pulses laser source and long-distance information transmission.

Generation of bright-dark soliton pairs based on a ferromagnetic insulator Cr2Si2Te6 as a modulator in an Er-doped fiber laser.

In this work, a saturable absorber (SA) based on Cr2Si2Te6 (CST), with a modulation depth of 14.90% and saturation intensity of 4.81MW/cm2, was prepared by a liquid phase stripping method. Its nonlinear optical properties and application in obtaining mode-locked pulse output of bright-dark solitons are studied. When the pump power was 1250 mW, the maximum output power was 26.60 mW; the energy of the single pulse was 15.02 nJ, and the repetition rate was 1.77 MHz. Our results provided evidence that CST can be used as an excellent SA for a mode-locked laser and demonstrated that ferromagnetic insulators can be used for the study of bright-dark soliton pairs.

Dark-Bright Soliton Bound States in a Microresonator.

Dissipative Kerr solitons in microresonators have facilitated the development of fully coherent, chip-scale frequency combs. In addition, dark soliton pulses have been observed in microresonators in the normal dispersion regime. Here, we report bound states of mutually trapped dark-bright soliton pairs in a microresonator. The soliton pairs are generated seeding two modes with opposite dispersion but with similar group velocities. One laser operating in the anomalous dispersion regime generates a bright soliton microcomb, while the other laser in the normal dispersion regime creates a dark soliton via Kerr-induced cross-phase modulation with the bright soliton. Numerical simulations agree well with experimental results and reveal a novel mechanism to generate dark soliton pulses. The trapping of dark and bright solitons can lead to light states with the intriguing property of constant output power while spectrally resembling a frequency comb. These results can be of interest for telecommunication systems, frequency comb applications, and ultrafast optics.

Bright Soliton and Bright–Dark Soliton Pair in an Er-Doped Fiber Laser Mode-Locked Based on In2Se3 Saturable Absorber

The output power in ultrafast fiber lasers is usually limited due to the lack of a versatile saturable absorber with high damage threshold and large modulation depth. Here we proposed a more efficient strategy to improve the output energy of erbium-doped fiber laser based on indium selenide (In2Se3) prepared by using the physical vapor deposition (PVD) method. Finally, stable mode-locked bright pulses and triple-wavelength dark–bright pulse pair generation were obtained successfully by adjusting the polarization state. The average output power and pulse energy were 172.4 mW/101 nJ and 171.3 mW/100 nJ, which are significantly improved compared with the previous work. These data demonstrate that the PVD-In2Se3 can be a feasible nonlinear photonic material for high-power fiber lasers, which will pave a fresh avenue for the high-power fiber laser.

Parameter regulation for periodic wave pair and photovoltaic soliton pair excitations in the bias photovoltaic-photorefractive crystal

In the bias photovoltaic-photorefractive crystal, the two-component nonlinear Schrödinger equation can portray the dynamics of periodic wave pair and photovoltaic soliton pair. These excitations are analytically revealed including the Jacobian sn-cn type and sn-dn type periodic wave pair and their related dark-bright soliton pair, the mixed elliptic function pair excitation and their related bi-peaked soliton and bright soliton pair. In view of these results, the formation conditions of these periodic wave and soliton pairs are related to parameters of the photovoltaic field, the space charge electric field, irradiance and nonlinearity. Moreover, the excitation regulation of soliton pairs including amplitudes, widths and the change of propagation constants based on the parameter related to the photovoltaic field and space charge electric field is investigated in the bias photovoltaic-photorefractive LiNbO3 crystal.

Dissipative Kerr solitons in a photonic dimer on both sides of exceptional point

Exceptional points are a ubiquitous concept widely present in driven-dissipative coupled systems described by a non-Hermitian Hamiltonian. To date, exceptional points have been extensively examined in the systems supporting only a few optical modes, thereby leaving the observation of collective (multimode) effects outside of the scope of the study. In the present paper, we analyze the role of exceptional points in nonlinear multimode photonics. Specifically, we provide insights into the complex nonlinear dynamics arising in a continuous wave-driven pair of strongly coupled microresonators. Investigating this system, we demonstrate mechanisms of dissipative Kerr soliton formation in two fundamentally different regimes separated by a line of exceptional points. Highlighting the diversity of emergent nonlinear effects, we describe the on-demand generation of single-solitons, perfect soliton crystals and bright-dark soliton pairs on either side of exceptional points.

Multiple double-pole bright-bright and bright-dark solitons and energy-exchanging collision in the M-component nonlinear Schrödinger equations.

Multiple double-pole bright-bright and bright-dark soliton solutions for the multicomponent nonlinear Schrödinger (MCNLS) system comprising three types of nonlinearities, namely, focusing, defocusing, and mixed (focusing-defocusing) nonlinearities, arising in different physical settings are constructed. An interesting type of energy-exchanging phenomenon during collision of these double-pole solitons is unraveled. To explore the objectives, we consider the general solutions of a set of generalized MCNLS equations and by taking the long-wavelength limit with proper parameter choices of single-pole bright-bright and bright-dark soliton pairs, the multiple double-pole bright-bright and bright-dark soliton solutions are constructed in terms of determinants. The regular double-pole bright-bright solitons exist in the focusing and focusing-defocusing MCNLS equations and undergo a particular type of energy-sharing collision for M≥2 in addition to the usual elastic collisions. A striking feature observed in the process of energy-sharing collisions is that the double-pole two-soliton possessing unequal intensities before collision indeed exactly exchange their intensities after collision. Further, the existence of double-pole bright-dark solitons in the MCNLS equations with focusing, defocusing, and mixed (focusing-defocusing) nonlinearities is analyzed by constructing explicit determinant form solutions, where the double-pole bright solitons exhibit elastic and energy-exchanging collisions while the double-pole dark solitons undergo mere elastic collision. The double-pole bright-dark solitons possess much richer localized coherent patterns than their counterpart double-pole bright-bright solitons. For particular choices of parameters, we demonstrate that the solitons would degenerate into the background, resulting in a lower number of solitons. Another important observation is the formation of doubly localized rogue waves with extreme amplitude, in the case of double-pole bright-dark four-solitons. Our results should stimulate interest in such special multipole localized structures and are expected to have ramifications in nonlinear optics.

TaSe2-based mode-locked fiber laser with four switchable operating states

Transition metal dichalcogenides (TMDs) have attracted considerable attention in electronics and photonics. Tantalum diselenides (TaSe2) as a member of TMDs has been employed for field effect transistors and all-optical switching, and its nonlinear optical response has also been investigated. However, the applications of TaSe2 in ultrafast fiber lasers have not been exploited. Here, TaSe2 deposited on D-shaped fiber is used as saturable absorber (SA) in Er-doped fiber laser, and four switchable operating states (bright solitons, dark solitons, bright-dark soliton pairs and their HML counterparts, as well as bright-dark-bright soliton pairs) are realized successfully. To the best of our knowledge, this is the first presentation of a mode-locked fiber laser with the TaSe2-based SA, and also the first study of bright and dark soliton properties of a TaSe2-based fiber laser. It is foreseeable that TaSe2 will become an appealing candidate for bright and dark soliton fiber lasers.

Coupled spatial periodic waves and solitons in the photovoltaic photorefractive crystals

The evolution of spatial solitons in the photovoltaic photorefractive crystal can be governed by the specific coupled nonlinear Schrodinger equations. Under the photovoltaic field with the external bias field, the coupled cn–sn-type periodic wave solution and the corresponding photorefractive bright–dark soliton pair were constructed to describe the evolution of beam. The influence of the external bias field on solitonic dynamics is analyzed. In the photovoltaic crystal, coupled sn–cn-type, sn–dn-type periodic wave solutions, solution constructed by products of elliptic functions and the corresponding dark–bright soliton pair and coupled double-peaked soliton solutions are found to describe the evolution of a spatial-phase-modulated photovoltaic soliton and a non-phase-modulated beam.

Photovoltaic spatial solitons and periodic waves in a photovoltaic crystal

A coupled nonlinear Schrödinger equation describes the propagation of a spatial-phase-modulated photovoltaic soliton and a non-phase-modulated beam in a photovoltaic crystal. With the help of the Jacobian elliptic function method and the leading term analysis, three kinds of Jacobian elliptic function solutions including coupled sn–cn type solution, coupled sn–dn type solution and solution constructed by products of elliptic functions are reported. In the long wave limit, these solutions become dark-bright soliton pair solution and coupled twin-peaked type solution. From these solutions, the amplitude, width and frequencies of solitons are determined by the Glass constants of the spatial-phase-modulated, non-phase-modulated and background beams.

Pulse shaping of bright-dark vector soliton pair**Project supported by the National Key Research and Development Program of China (Grant No. 2018YFB0504500) and the National Natural Science Foundation of China (Grant No. 51672177).

We simulate pulse shaping of bright–dark vector soliton pair in an optical fiber system. Through changing input pulse parameters (amplitude ratio, projection angle, time delay, and phase difference), different kinds of pulse shapes and spectra can be generated. For input bright–dark vector soliton pair with the same central wavelength, “2+1”- and “2+2”-type pseudo-high-order bright–dark vector soliton pairs are achieved. While for the case of different central wavelengths, bright–dark vector soliton pairs with multiple pulse peaks/dips are demonstrated with appropriate pulse parameter setting.