Stable Single Soliton Research Articles

Generation of soliton molecules in a 1.5-μm ultrafast fiber laser based on Zinc 2,5-dihydroxyterephthalate saturable absorber

Two-dimensional (2D) Zinc 2,5-dihydroxyterephthalate (Zn-MOF-74) is a kind of metal–organic framework (MOF), which has been intensively studied in gas adsorption, gas storage, and catalysis. However, the potential applications of Zn-MOF-74 in the fields of optics, especially in the areas of nonlinear optical response and ultrafast optics need further exploration. Here, the nonlinear optical properties of Zn-MOF-74 are systematically investigated. In this work, we demonstrate that it gradually becomes saturated with the increase of the intensity of the incident pulse, which makes Zn-MOF-74 an effective saturable absorber in a mode-locked Er-doped fiber laser for ultrashort pulse generation. Our experiments yield stable single solitons as well as soliton molecules with tunable characteristics. When the pump power is 126 mW, conventional solitons with an output power of 2.35 mW and a pulse width of 0.93 ps are obtained. The generated pulses characterize a central wavelength of 1554.84 nm and a 3-dB bandwidth of 3.07 nm. By adjusting the pump power and polarization appropriately, the center wavelength of the soliton molecules is tunable from 1532.76 nm to 1554.24 nm. The experimental observations further proves that Zn-MOF-74 has great potential in ultrafast optics.

Real-time measurements of breathing dissipative soliton pairs in mode-locked fiber lasers

The emergence of breathing solitons, as well as the breathing soliton molecules undergoing periodic evolution in peak power and spectral width has attracted growing research attentions in dissipative systems. Beyond the intense pulse interactions within tightly-bound states with picoseconds interval, the long-range interplay between pulses separated by nanosecond-scale starts to be investigated in recent years, thus filling the long-standing academic gap between the bound solitons and independent multiple pulses. In this work, we report on the real-time observations of breathing dissipative soliton pairs with nanoseconds’ separations in a fiber laser operating under the threshold of stationary mode locking. Compared with conventional soliton counterpart, here the breathing soliton pair exhibit even more fascinating inter-pulse nonlinear dynamics due to the intriguing self-excited periodic evolutions. The shot-to-shot measurements of pulse intensity profiles, associated with dispersive Fourier transform clearly uncover not only the different breathing phase synchronization and pulse separations among different pulses but also the hysteresis behaviors of the breathing ratio by continuously varying the laser parameters. Moreover, we observed various transient stages in this unstable lasing regime, including the transition between stable single soliton and breathing soliton pair, as well as their long-range breather interaction. These results reveal the breathing multi-pulse state and the instantaneous non-equilibrium dynamics involving the breather pairs, enriching the framework of breathing solitons and opening a novel possibility to explore the internal motions of breathing soliton complex in nonlinear systems.

Generation of controllable bound solitons from a thulium–holmium co-doped mode-locked fiber laser

The characteristics of wavelength tuning and pulse separation changing of soliton pairs at 2 μm are still largely unexploited although they are helpful for the application of bound states in the field of high-capacity soliton fiber communication systems. We report on the experimental observations of stable bound solitons in a thulium–holmium co-doped passively mode-locked fiber laser by using the nonlinear polarization rotation technology. At a fixed pump power, the stable single soliton operation is converted to the soliton pair operation by cautiously adjusting the polarization controllers. Tightly bound soliton pairs with continuously tunable wavelengths from 1960.48 nm to 1989.45 nm, with a soliton separation of ∼4 ps, are observed. Meanwhile, several different pulse separations from 5.2 ps to 11.2 ps of soliton pairs are also realized. With the increasing pump power, a triple-soliton bound state is also observed. The results help in understanding the nonlinear dynamics of fiber lasers.

Pulsating dynamics in a pure-quartic soliton fiber laser.

We numerically investigate the pulsating dynamics of pure-quartic solitons (PQSs) in a passively mode-locked fiber laser. The bifurcation diagrams show that the PQS can alternate between the stable single soliton and pulsating regimes multiple times before transiting into the chaotic state. This multi-alternation behavior can be attributed to energy redistribution across the central part and the oscillating tails of the PQS, which is caused by an imperfect counterbalance between self-phase modulation (SPM)-induced and fourth-order dispersion (FOD)-induced phase shifts. Soliton creeping behavior can be observed during the pulsating process, accompanied by periodic asymmetric temporal profiles and central wavelength shifts of the PQS. These findings give new insights into the dynamics of PQSs in fiber lasers.

Detuning regulation of temporal solitons in a CaF2 microcavity

Detuning regulation based on the scanning pump wavelength plays an important role in the generation of temporal solitons in an optical microcavity. Field evolution inside a CaF2 microcavity during the detuning regulation process is demonstrated. It is found that a stable single soliton can be excited when modulation instability dominates in the microcavity during frequency tuning with an appropriate scanning speed and operational parameters. However, due to the excessive loss caused by tuning, the soliton eventually evolves into a DC distribution. The influence of different parameters on the light field after formation of the soliton is also studied. Other different parameters lead to different distributional forms of soliton evolution. For maintenance of the single soliton, the appropriate detuning parameter and pump power are changed suddenly after the soliton is generated, causing the soliton to remain stable. Moreover, in the single soliton region, a path within the parameter space of detuning and pump power is planned in order to compress the pulse width of the soliton, and the comb spectrum is broadened. The results of theoretical analysis are important for studying field and spectral characteristics during frequency detuning and for maintaining the temporal soliton in the microcavity.

Observation of various bound states based on a graded index multimode fiber saturable absorber

The formation of stable single solitons and various bound states based on a graded index multimode fiber (GIMF) is investigated experimentally for the first time. Taking advantage of the principle of nonlinear multimode interference, a 143.5 cm length of GIMF is bent and two polarization controllers are used to achieve stable passive mode-locking. The spectrum of single solitons centers on 1590.5 nm with a spectral bandwidth of 3.2 nm. 976 fs of pulse duration is obtained at the repetition rate of 14.31 MHz. The maximum output power of 14.572 mW with a corresponding single-pulse energy of 1 nJ is achieved. Meanwhile, all kinds of bound states, including soliton pairs, soliton triplets, soliton quartets, and multiple-pulse bound states with different pulse separations are realized. The bound soliton with two pulses obtained has a fixed pulse interval as the incident pump power is increased. Our results suggest that a GIMF might be employed as an effective saturable absorber for ultrafast photonics applications.

Generation of dispersion-managed solitons with sidebands in a 2-μm mode-locked fiber laser

We have experimentally obtained dispersion-managed solitons with sidebands in a passively mode-locked thulium-doped fiber laser. The stable single soliton with sidebands can be converted into two soliton pulses at the pump power of 867 mW with appropriate settings of the polarization controllers (PCs). By increasing the pump power and cautiously adjusting the PCs, the three, four, and five soliton pulses with nonuniform intensity operate with stability in the cavity due to the global soliton interaction caused by unstable continuous waves. Furthermore, the soliton bunch can be observed at the pump power of 1 W. The position of solitons in the soliton bunch is random with a fixed separation that is controllable by changing the linear phase delay. Our work gives insight into the dynamics of multipulse dispersion-managed solitons in a 2-μm mode-locked fiber laser.

L-Band Tunable and Dual-Wavelength Mode-Locked Fiber Laser With NCF-GIMF-Based SA

A hybrid structure of no-core fiber and graded-index multimode fiber (NCF-GIMF) is demonstrated, which can be used as both the saturable absorber (SA) and the wavelength selective element. By employing such a device, an L-band wavelength tunable Er-doped mode-locked laser is realized and stable single solitons of ~1.7 ps, with continuously tunable wavelengths from 1574 to 1601.1 nm, are generated. Moreover, dual-wavelength mode-locked laser operation at 1575.4 and 1603 nm is achieved, with a pulse duration of 1.2 and 1.7 ps, respectively. The proposed device is simple and compact and represents an effective approach for tunable and dual-wavelength mode-locked fiber laser operation.

Formation of Various Soliton Molecules in a 2-<inline-formula> <tex-math notation="LaTeX">$\mu$ </tex-math> </inline-formula>m Anomalous-Dispersion Mode-Locked Fiber Laser

We report on the experimental observations of stable single soliton and soliton molecules in an anomalous-dispersion thulium-doped passively mode-locked fiber laser by using the nonlinear polarization rotation technology. The stable single soliton operation can convert to the soliton pair operation by cautiously adjusting the PCs, at the pump power of 350 mW. It is experimentally demonstrated that the formation of stationary soliton pairs is related to the interaction between solitons and dispersive waves. By appropriately adjusting the cavity parameters, more complex soliton molecules composed of three, four, and five bound solitons can be observed. Meanwhile, we experimentally analyze complex nonlinear dynamics of soliton molecules around 2- ${\mu }\text{m}$ .

Self-consistent large-N analytical solutions of inhomogeneous condensates in quantum \u2102PN\u2009\u2212\u20091 model

We give, for the first time, self-consistent large-N analytical solutions of inhomogeneous condensates in the quantum ℂPN − 1 model in the large-N limit. We find a map from a set of gap equations of the ℂPN − 1 model to those of the Gross-Neveu (GN) model (or the gap equation and the Bogoliubov-de Gennes equation), which enables us to find the self-consistent solutions. We find that the Higgs field of the ℂPN − 1 model is given as a zero mode of solutions of the GN model, and consequently only topologically non-trivial solutions of the GN model yield nontrivial solutions of the ℂPN − 1 model. A stable single soliton is constructed from an anti-kink of the GN model and has a broken (Higgs) phase inside its core, in which ℂPN − 1 modes are localized, with a symmetric (confining) phase outside. We further find a stable periodic soliton lattice constructed from a real kink crystal in the GN model, while the Ablowitz-Kaup-Newell-Segur hierarchy yields multiple solitons at arbitrary separations.

Generation of wavelength-tunable soliton molecules in a 2-μm ultrafast all-fiber laser based on nonlinear polarization evolution

We report on the experimental observation of stable single solitons and soliton molecules in a 2-μm thulium-holmium-doped fiber laser mode-locked through the nonlinear polarization evolution technique within an anomalously dispersive cavity. Single 0.65nJ solitons feature a 7.3nm spectral FWHM and 540fs temporal duration, yielding a time-bandwidth product close to the Fourier-transform limitation. Under the same pumping power of 740mW, stable out-of-phase twin-soliton molecules, featuring a temporal separation of 2.5ps between the two ∼700 fs pulses, are generated in a deterministic way, while the central wavelength of the soliton molecules can be tuned from 1920 to 1940nm. Finally, we present strong experimental evidence of vibrating soliton molecules.

Self-Started Mode-Locking With Dispersion-Imbalanced Nonlinear Amplifier Loop

Self-started mode-locking in a polarization-maintaining figure-eight Er-doped fiber laser was demonstrated by optimizing the dispersion and the nonlinearity in the nonlinear amplifier loop mirror. Experimental results indicate that the build-up time of soliton pulse is directly linked to the available pump power and net dispersion. Three laser diodes, one in a linear loop and the others in a nonlinear loop, were applied to provide enough pump power for the start-up of the nonlinear evolution. As long as 8-min build-up time was observed as the net dispersion approaches to −0.115 and −0.043 ps2, it dramatically decreased to approximately millisecond order of magnitude as the net dispersion was optimized to −0.062 ps2. Stable single soliton could be obtained by reducing the hysteresis pump power.

Interaction length of DM solitons in the presence of third order dispersion with loss and amplification

We present an analysis of the interaction properties of time-division multiplexed dispersion-managed solitons in the strong management regime. The study is based on an ordinary differential equations model, obtained by means of the variational method, which takes into account third order dispersion, loss and periodic amplification. The validity of the model is assessed by comparing the variational results with direct simulations of the underlying partial differential equations, finding excellent agreement. We first study the conditions for stable single soliton pulse propagation as the amplifier position is varied in the dispersion map. Interactions between adjacent pulses are then investigated for both lossless and lossy systems and the effect of third-order dispersion is addressed. We find that the increase found in the interaction distance can be explained by an asymmetric effective shift of the average dispersion of each of the soliton pulses induced in the interaction process.

Bisoliton propagating in dispersion-managed system and its application to high-speed and long-haul optical transmission

We show that, in addition to a stable single soliton, a dispersion-managed (DM) system can also support stable bisolitons. The system parameters in which the bisolitons can exist are also studied. In addition, we propose novel error preventable line-coding schemes in which binary data are assigned to bisolitons and single DM solitons. By using the schemes, impairments arising from intrachannel interactions can be drastically reduced compared with the conventional scheme for the same bit rate. The compatibility of bisoliton to wavelength-division-multiplexed system is also discussed.

Symmetric bi-soliton solution in dispersion-managedsystem

It is shown that, in addition to a stable single soliton, a dispersion-managed system can also support a stable symmetric bi-soliton. The system parameters in which the symmetric bisoliton can exist are also studied.