Vector dark domain wall solitons in a fiber ring laser

Impact of stimulated Raman scattering on dark soliton generation in a silica microresonator

Generating a coherent optical frequency comb at an arbitrary wavelength is important for fields such as precision spectroscopy and optical communications. Dark solitons which are coherent states of optical frequency combs in normal dispersion microresonators can extend the operating wavelength range of these combs. While the existence and dynamics of dark solitons has been examined extensively, requirements for the modal interaction for accessing the soliton state in the presence of a strong Raman interaction at near visible wavelengths has been less explored. Here, analysis on the parametric and Raman gain in a silica microresonator is performed, revealing that four-wave mixing parametric gain which can be created by a modal-interaction-aided additional frequency shift is able to exceed the Raman gain. The existence range of the dark soliton is analyzed as a function of pump power and detuning for given modal coupling conditions. We anticipate these results will benefit fields requiring optical frequency combs with high efficiency and selectable wavelength such as biosensing applications using silica microcavities that have a strong Raman gain in the normal dispersion regime.

Formation of color solitons and domains in fiber lasers

Using numerical simulation, we have investigated the generation of color solitons consisting of two radiation fragments with different carrier frequencies in a dual-wavelength laser. The proposed mechanism for the formation of such solitons involves nonlinear losses that increase with increasing intensity, the dispersion of the refractive index, spectral gain inhomogeneity, and the generation of a doublet radiation spectrum, owing to the corresponding spectral-dependent losses in the laser. The proposed theory explains the main features of the experimentally observed formation of color domains in fiber lasers and has the potential for further development of methods for controlling the nonlinear dynamics of laser radiation.

Pulse evolution and multi-pulse state of coherently coupled polarization domain walls in a fiber ring laser

Pulse evolution and multi-pulse state of coherently coupled polarization domain walls (PDW) is experimentally demonstrated in a novel fiber ring laser. Versatile pulse shapes benefit by wide range moving of PDW in the weakly birefringent fiber. The 8.6 m short-cavity structure is more compact and accessible based on a 976 nm pump with nearly zero negative dispersion (-0.0002 ps²). Besides, multi-pulse patterns such as PDW splitting, harmonic mode-locking, and periodic soliton collision are also observed under larger net negative dispersion (-3.09 ps²) and 151m-longer cavity. This is the first demonstration of coherently coupled PDW in a fiber laser using a bandpass filter and the formation of coherently coupled PDW is ascribed to the BPF's force filtering.

Self-starting triple-wavelength vector dark soliton with a bismuth-doped fiber saturable absorber

We report on the generation of a triple-wavelength vector dark soliton in an all-fiber ring cavity of erbium-doped fiber laser mode-locked with a bismuth-doped fiber saturable absorber. The formation of the triple-wavelength vector dark soliton is due to the cross-phase coupling derived from the cavity birefringence. The mode-locked laser operated at a 1.89 MHz repetition rate with a 335 ns pulse width, and its robustness is confirmed.

Collision between soliton and polarization domain walls in fiber lasers

We report on the experimental observation of coexistence of solitons and polarization domains, as well as features of soliton collision with polarization domain walls (or kink solitons) in a single mode fiber laser. Depending on the sign of cavity dispersion, either bright or dark solitons have been formed in our fiber laser. Under suitable laser operation conditions, they could even coexist with polarization domains and collide with the domain walls. We show experimental evidence of both the elastic and inelastic soliton collisions with the domain wall solitons. Some interesting features of soliton interaction with polarization domains in a fiber laser are also firstly revealed.

The Influence of Signal Polarization on Quantum Bit Error Rate for Subcarrier Wave Quantum Key Distribution Protocol

In this paper, we consider the influence of a divergence of polarization of a quantum signal transmitted through an optical fiber channel on the quantum bit error rate of the subcarrier wave quantum key distribution protocol. Firstly, we investigate the dependence of the optical power of the signal on the modulation indices' difference after the second phase modulation of the signal. Then we consider the Liouville equation with regard to relaxation in order to develop expressions of the dynamics of the Stokes parameters. As a result, we propose a model that describes quantum bit error rate for the subcarrier wave quantum key distribution depending on the characteristics of the optical fiber. Finally, we propose several methods for minimizing quantum bit error rate.

Nondegenerate solitons and their collisions in Manakov systems

Recently, we have shown that the Manakov equation can admit a more general class of nondegenerate vector solitons, which can undergo collision without any intensity redistribution in general among the modes, associated with distinct wave numbers, besides the already-known energy exchanging solitons corresponding to identical wave numbers. In the present comprehensive paper, we discuss in detail the various special features of the reported nondegenerate vector solitons. To bring out these details, we derive the exact forms of such vector one-, two-, and three-soliton solutions through Hirota bilinear method and they are rewritten in more compact forms using Gram determinants. The presence of distinct wave numbers allows the nondegenerate fundamental soliton to admit various profiles such as double-hump, flat-top, and single-hump structures. We explain the formation of double-hump structure in the fundamental soliton when the relative velocity of the two modes tends to zero. More critical analysis shows that the nondegenerate fundamental solitons can undergo shape-preserving as well as shape-altering collisions under appropriate conditions. The shape-changing collision occurs between the modes of nondegenerate solitons when the parameters are fixed suitably. Then we observe the coexistence of degenerate and nondegenerate solitons when the wave numbers are restricted appropriately in the obtained two-soliton solution. In such a situation we find the degenerate soliton induces shape-changing behavior of nondegenerate soliton during the collision process. By performing suitable asymptotic analysis we analyze the consequences that occur in each of the collision scenario. Finally, we point out that the previously known class of energy-exchanging vector bright solitons, with identical wave numbers, turns out to be a special case of nondegenerate solitons.

Recent advances in real-time spectrum measurement of soliton dynamics by dispersive Fourier transformation

Mode-locking lasers have not only produced huge economic benefits in industrial fields and scientific research, but also provided an excellent platform to study diverse soliton phenomena. However, the real-time characterization of the ultrafast soliton dynamics remains challenging for traditional electronic instruments due to their relatively low response bandwidth and slow scan rate. Consequently, it is urgent for researchers to directly observe these ultrafast evolution processes, rather than just indirectly understand them from numerical simulations or averaged measurement data. Fortunately, dispersive Fourier transformation (DFT) provides a powerful real-time measurement technique to overcome the speed limitations of traditional electronic measurement devices by mapping the frequency spectrum onto the temporal waveform. In this review, the operation principle of DFT is discussed and the recent progress in characterizing the ultrafast transient soliton dynamics of mode-locking lasers is summarized, including soliton explosions, soliton molecules, noise-like pulses, rogue waves, and mode-locking buildup processes.

Dark solitons in the exploding pulsation of the bright dissipative soliton in ultrafast fiber lasers

Soliton explosion is an extremely pulsating behavior of the bright dissipative soliton (DS) in ultrafast lasers. By numerical simulation, we find that the dark soliton (DAS) can coexist with the bright soliton during the exploding process. The collapsed temporal structure of the exploding soliton is induced by the DASs. We reveal the birthing, evolving, and decaying of the DASs inside the bright DS. The time-frequency analysis of the exploding soliton helps us better understand the temporal and spectral structures of the exploding soliton, which might be useful for real-time spectroscopy of the coexisting dark and bright solitons during the soliton explosion.

Stable dark pulses produced by a graphite oxide saturable absorber in a fiber laser cavity

In this paper, we report for the first time, to the best of our knowledge, the experimental generation of dark pulses in the 1.5 µm band from a passively $Q$Q-switched fiber laser employing graphite oxide as the saturable absorber, generating tunable microsecond pulses with kHz repetition rates. The graphite oxide samples were obtained by recycling the graphite present in Li-ion batteries used in cell phones through a chemical separation and oxidation process. Sample characterization employing x-ray diffraction, solid-state $ ^{{13}}{\rm C} $¹³C nuclear magnetic resonance, and Raman spectroscopy showed that the produced graphite oxide exhibited a homogeneously oxidized structure. Dark pulse emission could be observed at a relatively low pump threshold of 35 mW in a short 20 m laser cavity, indicating that the graphite oxide acted as a saturable absorber, significantly enhancing the nonlinearity of the laser cavity. Additionally, dark pulse operation was demonstrated at a high stability with a signal-to-noise ratio of 56 dB and a pulse-to-pulse timing jitter of 159.84 fs.

Bidirectional dark-soliton fiber lasers for high-sensitivity gyroscopic application

Bidirectional mode-locked lasers are very useful in laser sensing and optical communications. Here we report a bidirectional domain wall soliton (DWS) fiber laser with an anomalous dispersion cavity. Two mode-locked dark pulse trains propagating in the opposite directions have been generated. Moreover, the specific application as a gyroscopic effect has been demonstrated by mounting this DWS laser on a rotating platform. The beat frequency of the two dark pulse DWS beams is measured as a linear function of the rotation velocity. The rotation sensitivity reaches 3.31 kHz/(deg/s), which are comparable with the one in a bright pulse laser gyroscope. Without the limit of using tunable delay lines, the DWS laser gyroscope has the advantages of simple structure, high sensitivity, and low cost, while possessing the entire superiority of a mode-locked laser gyroscope. It is more promising for the applications in modern inertia navigation systems.

Memristive devices based on emerging two-dimensional materials beyond graphene

With the explosion of data in the information universe and the approaching of fundamental limits in silicon-based flash memories, the exploration of new device architectures and alternative materials is necessary for next-generation memory technology. Accordingly, emerging two-dimensional (2D) material-based memristive devices have attracted increasing attention due to their unique properties and great potential in flexible and wearable devices, and even neuromorphic computing systems. Herein, we provide an overview of the recent progress on memristive devices based on 2D materials beyond graphene. The device structures and choice of active materials and electrodes materials are summarized for various types of 2D material-based memristive devices. Following the discussion and classification on the device performances and mechanisms, the challenges and perspectives on future research based on 2D materials are also presented.

Bi2Te3 Topological Insulator for Domain-Wall Dark Pulse Generation from Thulium-Doped Fiber Laser

We have experimentally demonstrated domain-wall (DW) dark pulses from a thulium-doped fiber laser incorporating a topological insulator saturable absorber (SA). The bulk-structured Bi2Te3 was used as the SA, which was constructed on a fiber ferrule platform through the deposition of the Bi2Te3 mixed with distilled water. The DW dark pulses were generated from the thulium-doped fiber laser cavity with a dual wavelength at 1956 nm and 1958 nm. The dark pulse width and the repetition rate were measured as ~10.3 ns and ~20.7 MHz over the pump power of ~80 mW, respectively. To the best of our knowledge, this work is the first demonstrated generation of the DW dark pulse from a thulium-doped fiber laser using nanomaterial-based SA.

Multiple-soliton in spatiotemporal mode-locked multimode fiber lasers

Experimental observations of spatiotemporal mode-locked multiple-soliton, including harmonic mode locking and multiple pulses, in multimode fiber (MMF) lasers are reported. Numerical simulations are conducted to investigate the nonlinear dynamics of multi-pulsing. The influences of cavity parameters on the spatiotemporal outputs are analyzed by simulations, which agree with the experimental observations qualitatively. This work would contribute to understanding the complex spatiotemporal nonlinear dynamics in MMF lasers.

Nondegenerate Solitons in Manakov System

It is known that the Manakov equation which describes wave propagation in two mode optical fibers, photorefractive materials, etc., can admit solitons which allow energy redistribution between the modes on collision that also leads to logical computing. In this Letter, we point out that the Manakov system can admit a more general type of nondegenerate fundamental solitons corresponding to different wave numbers, which undergo collisions without any energy redistribution. The previously known class of solitons which allows energy redistribution among the modes turns out to be a special case corresponding to solitary waves with identical wave numbers in both the modes and traveling with the same velocity. We trace out the reason behind such a possibility and analyze the physical consequences.

Various large-energy soliton operations within an Er-doped fiber laser with bismuth selenide as a saturable absorber

Different large-energy mode-locked operations were successfully obtained within a Bi₂Se₃-based Er-doped fiber laser. First, mode-locked operation with maximum pulse energy of 17.2 nJ and pulse width of 187 ns under a pulse repetition rate of 537.6 kHz was obtained under the pump power of 680 mW. In addition, the characteristics of dark solitons and soliton rains, which also exhibit large pulse energies, have been investigated experimentally. Our results fully proved that Bi₂Se₃ was an excellent candidate for investigating various mode-locked operations with large pulse energy due to its high nonlinear effect and high damage threshold.

Color domains in fiber lasers

We report on the experimental observation of a color domain (CD) phenomenon in a dissipative soliton fiber laser. The CDs are constituted by a wavelength-dependent condensed phase of pulses in motion. Single CD, dual CD, and tricolor domain that occupy all the cavity space are observed. The CDs have flexible tunability of duty cycle, amplitude, wavelength, and wavelength spacing. The CDs derive from the wavelength-dependent slow evolution of gain, and the formation mechanism of multiple CDs can be explained by cross gain saturation.

Pulse dynamics of dual-wavelength dissipative soliton resonances and domain wall solitons in a Tm fiber laser with fiber-based Lyot filter

We report on the first demonstration of dual-wavelength square-wave pulses in a thulium-doped fiber laser. Under appropriate cavity parameters, dual-wavelength dissipative soliton resonances (DSRs) and domain wall solitons (DWSs) are successively obtained. Meanwhile, dark pulses generation is achieved at the dual-wavelength DWSs region due to the overlap of the two domain wall pulses. The fiber-based Lyot filter, conducted by inserting PMF between an in-line PBS and a PD-ISO, facilitates the generation of dual-wavelength operation. The polarization-resolved investigation suggests that the cross coupling between two orthogonal polarization components in the high nonlinear fiber plays an important role in the square-wave pulses formation. The investigation may be helpful for further understanding the square-wave pulse formation and has potential in application filed of multi-wavelength pulsed fiber lasers.

Generation of vector dissipative and conventional solitons in large normal dispersion regime

We report the generation of both polarization-locked vector dissipative soliton and group velocity-locked vector conventional soliton in a nanotube-mode-locked fiber ring laser with large normal dispersion, for the first time to our best knowledge. Depending on the polarization-depended extinction ratio of the fiber-based Lyot filter, the two types of vector solitons can be switched by simply tuning the polarization controller. In the case of low filter extinction ratio, the output vector dissipative soliton exhibits steep spectral edges and strong frequency chirp, which presents a typical pulse duration of ~23.4 ps, and can be further compressed to ~0.9 ps. In the contrastive case of high filter extinction ratio, the vector conventional soliton has clear Kelly sidebands with transform-limited pulse duration of ~1.8 ps. Our study provides a new and simple method to achieve two different vector soliton sources, which is attractive for potential applications requiring different pulse profiles.

Motion of dissipative optical fronts under the action of an oscillating pump

The dynamics of domain walls in optical bistable systems with pump and loss is considered. It is shown that an oscillating component of the pump affects the average drift velocity of the domain walls. The cases of harmonic and biharmonic pumps are considered. It is demonstrated that in the case of biharmonic pulse the velocity of the domain wall can be controlled by the mutual phase of the harmonics. The analogy between this phenomenon and the ratchet effect is drawn. Synchronization of the moving domain walls by the oscillating pump in discrete systems is studied and discussed.

Polarization domain wall pulses in a microfiber-based topological insulator fiber laser

Topological insulators (TIs), are novel two-dimension materials, which can act as effective saturable absorbers (SAs) in a fiber laser. Moreover, based on the evanescent wave interaction, deposition of the TI on microfiber would create an effective SA, which has combined advantages from the strong nonlinear optical response in TI material together with the sufficiently-long-range interaction length in fiber taper. By using this type of TI SA, various scalar solitons have been obtained in fiber lasers. However, a single mode fiber always exhibits birefringence, and hence can support two orthogonal degenerate modes. Here we investigate experimentally the vector characters of a TI SA fiber laser. Using the saturated absorption and the high nonlinearity of the TI SA, a rich variety of dynamic states, including polarization-locked dark pulses and their harmonic mode locked counterparts, polarization-locked noise-like pulses and their harmonic mode locked counterparts, incoherently coupled polarization domain wall pulses, including bright square pulses, bright-dark pulse pairs, dark pulses and bright square pulse-dark pulse pairs are all observed with different pump powers and polarization states.

Generation of dark solitons in erbium-doped fiber lasers based Sb(2)Te(3) saturable absorbers

Dark solitons, which have better stability in the presence of noise, have potential applications in optical communication and ultrafast optics. In this paper, the dark soliton formation in erbium-doped fiber lasers based Sb(2)Te(3) saturable absorber (SA) is first experimentally demonstrated. The Sb(2)Te(3) SA is fabricated by using the pulsed laser deposition method. The generated dark solitons are centered at the wavelength of 1530 nm and repetition rate of 94 MHz. Analytic solutions for dark solitons are also obtained theoretically.

Initial conditions for dark soliton generation in normal-dispersion fiber lasers

We report results of numerical simulations on the various initial conditions for dark soliton generation in an all-normal-dispersion fiber laser. All the dark solitons generated are odd dark solitons. Differently from the dark soliton generation in fibers, where an arbitrary dip could evolve into a dark soliton, it is found that the dark soliton can originate only from an initial dip with a certain parameter requirement. A bright pulse with either a hyperbolic secant square, Gaussian, or Lorentz profile can be developed into a dark soliton, provided that the parameters of the initial bright pulse are selected. Dark solitons can be generated in fiber lasers only if there is a phase jump, and this phase jump can be maintained and evolve to π during the pulse evolution.

Vector rectangular-shape laser based on reduced graphene oxide interacting with a long fiber taper

A vector dual-wavelength rectangular-shape laser (RSL) based on a long fiber taper deposited with reduced graphene oxide is proposed, where nonlinearity is enhanced due to a large evanescent-field-interacting length and strong field confinement of an 8 mm fiber taper with a waist diameter of 4 μm. Graphene flakes are deposited uniformly on the taper waist with light pressure effect, so this structure guarantees both excellent saturable absorption and high nonlinearity. The RSL with a repetition rate of 7.9 MHz shows fast polarization switching in two orthogonal polarization directions, and temporal and spectral characteristics are investigated.

Experimental observation of different soliton types in a net-normal group-dispersion fiber laser

Different soliton types are observed in a net-normal group-dispersion fiber laser based on nonlinear polarization rotation for passive mode locking. The proposed laser can deliver a dispersion-managed soliton, typical dissipation solitons, and a quasi-harmonic mode-locked pulse, a soliton bundle, and especially a dark pulse by only appropriately adjusting the linear cavity phase delay bias using one polarization controller at the fixed pump power. These nonlinear waves show different features, including the spectral shapes and time traces. The experimental observations show that the five soliton types could exist in the same laser cavity, which implies that integrable systems, dissipative systems, and dark pulse regimes can transfer and be switched in a passively mode-locked laser. Our studies not only verify the numeral simulation of the different soliton-types formation in a net-normal group-dispersion operation but also provide insight into Ginzburg-Landau equation systems.

Observations of three types of pulses in an erbium-doped fiber laser by incorporating a graphene saturable absorber

We experimentally observed three types of pulses generated in an erbium-doped fiber laser by incorporating a homemade graphene saturable absorber (GSA). The generated pulses from the laser oscillator include dual-wavelength dark pulses, fundamentally step-like pulses, and non-soliton second-harmonic pulses. These operation regimes are first reported by using graphene as the saturable absorber. Our results will further indicate that the GSA can function well for obtaining various ultrafast pulse phenomena, highlighting the practical potential of graphene in ultrafast photonics technologies.

Experimental observation of vector solitons in a highly birefringent cavity of ytterbium-doped fiber laser

We report on the first experimental observation of dark-bright and dark-dark vector solitons in a highly birefringent cavity of all-normal-dispersion ytterbium-doped fiber laser. With the usage of different length of polarization maintaining fibers in the cavity, totally four types of vector solitons with different features were observed.

Controllable double tunneling induced transparency and solitons formation in a quantum dot molecule

We consider the coupling effect between interdot tunneling coupling and external optical control field to study the linear optical property and the formation of temporal optical solitons in a quantum dot molecules system, analytically. The results show that the double tunneling induced transparency (TIT) windows are appeared in the absorption curve of probe field because of the formation of dynamic Stark splitting and quantum destructive interference effect from the two upper levels. Interestingly, the width of the TIT window becomes wider with the increasing intensity of the optical control field. We also find that the Kerr nonlinear effect of the probe field can be modulated effectively through coherent control both the control field and the interdot tunneling coupling in this system. Meanwhile, we demonstrate that the formation of dark or bright solitons can be practical regulated by varying the intensity of the optical control field.

Harmonic mode locking counterparts of dark pulse and dark-bright pulse pairs

We have investigated experimentally different operational states of an all-normal-dispersion ytterbium-doped fiber (YDF) ring laser with a long cavity. Various operational states were obtained by adjusting a polarization controller (PC) and the pump power. Self-pulsing, bright pulses, dark-bright pulse pairs and their harmonic mode locking (HML) counterparts, as well as dark pulses and their HML counterparts have all been obtained. Numerical simulations reproduce well the formation processes of dark pulses and dark-bright pulse pairs.

Domain walls and vortices in linearly coupled systems

We investigate one- and two-dimensional radial domain-wall (DW) states in the system of two nonlinear-Schrödinger (NLS) or Gross-Pitaevskii (GP) equations, which are couple by linear mixing and by nonlinear XPM (cross-phase-modulation). The system has straightforward applications to two-component Bose-Einstein condensates, and to bimodal light propagation in nonlinear optics. In the former case the two components represent different hyperfine atomic states, while in the latter setting they correspond to orthogonal polarizations of light. Conditions guaranteeing the stability of flat continuous wave (CW) asymmetric bimodal states are established, followed by the study of families of the corresponding DW patterns. Approximate analytical solutions for the DWs are found near the point of the symmetry-breaking bifurcation of the CW states. An exact DW solution is produced for ratio 3:1 of the XPM and SPM (self-phase modulation) coefficients. The DWs between flat asymmetric states, which are mirror images of each other, are completely stable, and all other species of the DWs, with zero crossings in one or two components, are fully unstable. Interactions between two DWs are considered too, and an effective potential accounting for the attraction between them is derived analytically. Direct simulations demonstrate merger and annihilation of the interacting DWs. The analysis is extended for the system including single- and double-peak external potentials. Generic solutions for trapped DWs are obtained in a numerical form, and their stability is investigated. An exact stable solution is found for the DW trapped by a single-peak potential. In the 2D geometry, stable two-component vortices are found, with topological charges s=1,2,3. Radial oscillations of annular DW-shaped pulsons, with s=0,1,2, are studied too. A linear relation between the period of the oscillations and the mean radius of the DW ring is derived analytically.

Dual-wavelength domain wall solitons in a fiber ring laser

We report on the first experimental observation of dual wavelength domain wall type of dark solitons in a fiber laser made of all normal group velocity dispersion fibers. It was shown that this solitary wave is formed due to the cross coupling between two different wavelength laser beams and consists of localized dip structures separating the two different wavelength laser emissions.

Dark and bright pulse passive mode-locked laser with in-cavity pulse-shaper

We demonstrate the integration of a spectral pulse-shaper into a passive mode-locked laser cavity for direct control of the output pulse-shape of the laser. Depending on the dispersion filter applied with the pulse-shaper we either observe a bright or dark "soliton-like" pulse train. The results demonstrate the strong potential of an in-cavity spectral pulse-shaper as an experimental tool for controlling the dynamics of passively mode-locked lasers.