Regular ArticlesEvolutions of versatile wavelength-dependent bound solitons
Introduction
Passively mode-locked fiber lasers have been employed as ideal platforms for investigating nonlinear dynamic process and generate ultrashort pulses for many years [1]. According to the net dispersion of the laser cavity, different kinds of pulses including conventional solitons, dispersion managed solitons and dissipative solitons were widely studied in previous reports [2], [3]. Since a soliton can hardly maintain stable when excessive nonlinearity exists in the laser cavity, pulse splitting phenomenon would occur due to the peak-power-clamping effect [2]. Multipulse operations such as soliton bunches, harmonic mode locking, noise like pulse and bound state are observed and verified as intrinsic states of the laser emission [4], [5], [6], [7]. Based on these regimes, the generation of multiple solitons and soliton interactions are of great importance in exploring complex pulse behaviors. Normally, soliton interactions in the fiber laser can be divided into three types: direct soliton interaction, dispersion-wave mediated soliton interaction and continuous wave soliton interaction [8]. Researches focusing on direct soliton interaction and dispersive-wave mediated soliton interaction have been extensively proposed [9], [10], [11]. As a typical form of multiple pulses, bound state is originated from the repulsions and attractions between closely spaced solitons resulted from nonlinear and dispersive effects [12]. Specifically, for a bound-state soliton pair, two solitons assemble together and co-propagate with fixed temporal separation and phase difference. The bound solitons whose separation is less than 5 times of the soliton width (full width at half maximum) are considered as tightly bound state. Otherwise, they are regarded as loosely bound state. Additionally, based on the phase relationship of the soliton pair, four types of bound state composing of in-phase, out-of-phase, phase-difference and phase-difference soliton pairs can be classified. As a dissipative process, investigations about the formation and evolution mechanism of bound state have significant values in nonlinear optics. The formation of bound state was first predicted by Malomed based on the nonlinear Schrödinger equation and complex Ginzburg Landau equation [13]. Heretofore, diverse-structure bound states have been generated by distinct mode-locking schemes including nonlinear polarization rotation (NPR), figure-of-eight structure and nonlinear multimodal interference as artificial saturable absorbers (SAs) and carbon nanotube, graphene, topological insulators (TIs), black phosphorus as real SAs [14], [15], [16], [17], [18], [19]. In the meantime, combined with advanced modulation formats, bound state also plays an important role in extending the coding alphabet to give an expansion of the propagation capacity in high speed fiber communication systems [20].
It has been verified that the managements of cavity parameters have a deep influence on characteristics of bound state [21]. Adjusting the pump power and intra-cavity polarization state are common ways to manipulate the number, temporal separation, and relative phase difference of bound solitons [22], [23], [24], [25]. Researches revealed crucial roles of intra-cavity birefringence and gain for bound solitons [26], [27]. However, discussions about the relationship between the bound state and the lasing wavelength are rarely reported. Taking this factor into consideration, evolutions of bound state in different lasing wavelengths are worthy to be investigated.
In this paper, varying the operating wavelength and the intra-cavity polarization state artificially, different types of bound states are obtained in an anomalous-dispersion passively mode-locked fiber laser. Confirmed by the typical spectra and autocorrelation traces, the laser output transforms from a conventional soliton to loosely bound-state soliton pairs with the soliton separation from 13.62 ps to 31.36 ps. Under the same pump power, versatile structures of multiple-soliton bound states are also achieved after carefully adjusting the tunable filter and the orientation of the polarization controller. These results might serve as a new approach to obtain structure-controllable bound states and would be beneficial to further revealing the complex nonlinear interactions between solitons in fiber lasers.
Section snippets
Experimental setup
As displayed in Fig. 1, NPR mode-locked technique is adopted in the ring cavity configuration. A segment of 2.6-m erbium-doped fiber (EDF) pumped by a 976 nm laser diode (LD) is employed as the gain medium. The pump light is injected into the laser oscillator via a 980/1550 nm wavelength division multiplexer (WDM). An optical coupler (OC) extracts ~ 10% optical power from the laser oscillator. A tunable bandpass filter (tuning range: 1480 nm to 1560 nm; 3 dB bandwidth: 2.00 nm; group delay:
Experimental results and discussion
To begin with, the operating wavelength of the tunable filter is fixed at 1516.0 nm and continuous wave emission is observed when the pump power is set as 21 mW. After the orientation of PC is precisely adjusted, mode locking is initiated when the pump power exceeds 169 mW. In order to optimize the output performance and facilitate the pulse splitting, the pump power is elevated to 279 mW. The pulse train monitored by a 1 GHz bandwidth oscilloscope (Tektronix MDO3104) with a 12.5 GHz bandwidth
Conclusions
In conclusion, evolutions of wavelength-dependent bound solitons are obtained and studied experimentally. Fixing the pump power at 279 mW and tuning the operating wavelength of the optical filter from 1525.2 nm to 1557.7 nm continuously, the laser output evolves from a conventional soliton to loosely bound-state soliton pairs whose separation switches from 13.62 ps to 31.36 ps. Meanwhile, soliton interaction varies with the change of soliton separation. Through managing initial mode-locking
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work was supported by the Science and Technology Planning Project of Shenzhen Municipality (JCYJ20180306171923592, JSGG20190819175801678).
References (37)
- et al.
Bound states of solitons in a fiber laser mode locked with carbon nanotube saturable absorber
Opt. Commun.
(2011) - et al.
Dissipative soliton interactions inside a fiber laser cavity
Opt. Fiber Technol.
(2005) - et al.
Observation of dissipative soliton bound states in a nonlinear multimodal interference based all-fiber all-normal-dispersion mode-locking laser
Opt. Laser Technol.
(2019) - et al.
Dissipative solitons for mode-locked lasers
Nat. Photonics
(2012) - et al.
Ultrashort-pulse fiber ring lasers
Appl. Phys. B
(1997) - et al.
Ömer Ilday, Soliton-similariton fibre laser
Nat. Photonics
(2010) - et al.
L-Band GHz Femtosecond Passively Harmonic Mode-Locked Er-Doped Fiber Laser Based on Nonlinear Polarization Rotation
IEEE Photonics J.
(2019) - et al.
Noise-like pulse generation around 1.3-µm based on cascaded Raman scattering
Opt. Express
(2020) - et al.
Observation of diverse structural bound-state patterns in a passively mode-locked fiber laser
Appl. Phys Express
(2020) - et al.
Dissipative solitons compounds in a fiber laser. Analogy with the states of the matter
Appl. Phys. B
(2010)
Soliton interaction in a fiber ring laser
Phys. Rev. E
Interaction forces among solitons ina optical fibers
Opt. Lett.
Experimental observation of soliton interaction over long fiber paths: discovery of a long-range interaction
Opt. Lett.
Long-range soliton interactions in periodically amplified fiber links
J. Opt. Soc. Am. B
Origin of the bound states of pulses in the stretched-pulse fiber laser
Opt. Express
Bound solitons in the nonlinear Schrödinger-Ginzburg Landau equation
Phys. Rev. A
Formation of Various Soliton Molecules in a 2- $\mu$ m Anomalous-Dispersion Mode-Locked Fiber Laser
IEEE Photon. Technol. Lett.
Observation of Wavelength Tuning and Bound States in Fiber Lasers
Sci. Rep.
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