Transitional and steady mode-lockingevolution of dissipative solitons

Leiran Wang, Xueming Liu,* Yongkang Gong, Dong Mao, and Xiaohui LiState Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Opticsand Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, China

*Corresponding author: liuxueming72@yahoo.com

Received 26 January 2010; accepted 1 April 2010;posted 14 April 2010 (Doc. ID 123331); published 5 May 2010

We have experimentally observed the transitional and steady mode-locking (ML) evolution of dissipativesolitons (DSs). It is found that pulses with different energies can coexist in the cavity during the evolu-tion. When an additional pulse is generated from the laser, it initially exhibits weak intensity, and thengradually develops into the fully grown pulse with the increase of pump power. Meanwhile, the spectralprofile of pulses is modulated at its top. The dynamic processes occur stage by stage, and can be regardedas the transitional states between the two nearby steady ML states. To our best knowledge, this is thefirst report on experimental observations for the detailed dynamic evolutions of pulse shaping in a DSlaser. © 2010 Optical Society of America

OCIS codes: 140.3510, 140.4050, 190.5530.

1. Introduction

Fiber lasers are very attractive because they have anumberofpotential applications [1–4].Traditional so-litons with the pulse duration of sub-ps are achievedby setting the net cavity dispersion as slightly nega-tive [3]. Recently, passive mode locking has been suc-cessfully realized in the cavity with largely positive oreven all-normal dispersion [5–7]. The newly gener-ated pulses, named dissipative solitons (DSs) [8,9],show quite different characteristics from traditionalsolitons existing in negative dispersion cavities. Thepulse-shaping mechanism of DSs includes laser gain,loss, normal group-velocity-dispersion, nonlinear po-larization (NPR) effect, spectrum filtering, and othernonlinear Kerr effects [6,7]. In contrast to traditionalsolitons in conservative systems, DSs exist in noncon-servative systems,where thegainand loss coexist andplay an essential role in the generation of pulses [8].

Various operating states involving multiple pulseshave been reported in net-anomalous-dispersionfiber lasers [4] and DS laser cavities [10]. Each ofthe multiple pulses shares the same physical param-

eters (e.g., the spectrum profile and the pulse en-ergy). The effects of energy quantization and pulsecompetition uniform the pulses [4]. Therefore, itbecomes rather a challenge to achieve mode-lockedpulses with different energies in practical experi-ments. Especially, when the pulses are close enoughto each other in temporal domain, the so-calledbound solitons are generated, where they combinetogether and seem like a single strong pulse ratherthan separated multiple pulses [11]. However, eachcomponential pulse still holds the same physicalcharacteristics indeed.

In our previous work [12], multiple DSs with theidentical physical characteristics were achieved ina net-normal-dispersion mode-locked fiber laser.We experimentally and theoretically demonstratedthat DSs could exhibit various spectral and temporalproperties [13,14]. However, the additional DSs werealways formed approximately instantaneously, sothat we were not able to identify the detailed pulse-shaping processes in our previous reports [12–14].Abdelalim et al. demonstrated that pulses withdifferent energies can coexist in a laser cavity withnormal dispersion by numerical investigations [15].Unfortunately, the corresponding experimental

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results for the detailed pulsating dynamics have notbeen observed so far.

In this report, we have experimentally observedthe detailed pulse-shaping and evolving processesfor the first time, to the best of our knowledge. TheDS laser cavity alternately operates on the steadyand transitional mode-locking (ML) states, and itis found that pulses with different duration and en-ergy can coexist in the cavity during the evolution.With the increase of pump power, an additionalDS is initially generated with weak energy, and gra-dually evolves into fully grown pulses. The dynamicprocesses occur stage by stage and, thus, can be re-garded as the transitional states that connect the twonearby steady ML states. The additional subpulsesupplements the existing strong solitons and contri-butes to the modulation of the spectral profile. Ourexperimental results reveal the behavior of transi-tional evolution of DSs, which is quite differentfrom the characteristics observed on conventionalsolitons.

2. Experimental Setup

The configuration of the DS fiber laser is schemati-cally shown in Fig. 1. The length of the erbium-dopedfiber is 19:9m, and the dispersion parameter D at1550nm is about −42ps=nm=km. Other fibers inthe cavity are the standard single-mode fiber with alength of 3:7m, and D is about 17 ps=nm=km. So thetotal length of the laser cavity is ∼23:6m, and thenet cavity dispersion is estimated as∼1ps2. The fun-damental frequency of the cavity is ∼8:7MHz, corre-sponding to the pulse separation of∼115ns. A 980nmlaser diode works as the pump source. A wavelength-division-multiplexed (WDM) and a 10% fused coupler(OC) work as the input and output port of the cavity,respectively. An optical spectrum analyzer (OSA), an11GHz digital storage oscilloscope (DSO) togetherwith a 12GHz photodetector (PD), and an autocorre-lator (AC) are used to monitor the laser output. Thepolarization states can be controlled by adjustingthe two polarization controllers (PCs), and the NPRtechnique is utilized to mode lock the laser.

3. Experimental Results

With the appropriate adjustment of the two PCs, self-started ML can be achieved when the pump power Pis beyond a threshold value (e.g., P ¼ 62mW). Thefiber laser operates on the stable ML state fromthe continuous-wave (CW) state. The typical pulsespectrum for this situation when P ¼ 62mW isshown in Fig. 2(a), where the profile is almost a rec-tangular shape with a 3dB width of ∼16nm. Thespectrum exhibits the typical characteristics of nor-mal-dispersion pulses (e.g., the steep spectral edges)[6–9]. The spectrum profile with a rigid limited band-width indicates the effect of gain spectral filtering[7], because no additional active spectral filters areemployed here. The corresponding pulse sequence,the radio-frequency (RF) spectrum, and the autocor-

relation trace for P ¼ 62mW are shown in Figs. 2(b)–2(d), respectively.

From Figs. 2(b) and 2(c) we can see that a single-pulse sequence is emitted from the laser cavity, andthe stable fundamental-frequency ML state isconfirmed with a supermode suppression of ∼70dB.As shown in Fig. 2(d), the autocorrelation trace has afull width at half-maximum (FWHM) of∼24:4ps. If aGaussian pulse profile is assumed, the pulse FWHMduration is estimated as ∼17:3ps, which gives atime–bandwidth product of ∼33:9. Therefore, thepulse is highly chirped, and the mechanism can beunderstood as follows. The self-phase modulation(SPM) and other Kerr nonlinear effects can inducea positive frequency chirp to the pulse [3]. Whenthe radiation wave travels along the cavity withstrong normal dispersion, the redshifted frequencycomponents near the leading edge of the pulse pro-pagate much faster than the blueshifted frequencycomponents near the trailing edge. This will leadto the broadening of pulse duration, as well as theaccumulation of the pulse chirp [7,12].

While maintaining the PCs’ operation state and in-creasing P, the pulse spectrum widens to both sidesbecause the SPM effect is enhanced with the pumpstrengthening. Because of the strong normal cavitydispersion together with the SPM effect, the pulseskeep stretching and the chirp accumulates to a largerdegree. While the P reaches as high as 90mW, thepulse spectrum exhibits a CW breakthrough, as

Fig. 1. (Color online) Schematic diagram of the DS laser cavity.

Fig. 2. (Color online) (a) Optical spectrum, (b) oscilloscope trace,(c) RF spectrum, and (d) autocorrelation trace for P ¼ 62mW.

2666 APPLIED OPTICS / Vol. 49, No. 14 / 10 May 2010

shown in Fig. 3(a), and now the 3dB spectrum widthenlarges to ∼20nm.

Further increasing the P and keeping the othercavity parameters fixed, an interesting phenomenonhappens, i.e., the CW breakthrough broadens to bothsides, and gradually develops into an approximatelyrectangular shape, which is similar to the mainspectrum profile. The detailed spectra versus P areshown in Figs. 3(b)–3(d). Meanwhile, the correspond-ing oscilloscope traces indicate that an additionalsubpulse is gradually generated from the cavity,despite the relatively weak intensity, as shown inFigs. 4(a)–4(d). It is worth noting that these statesare not steady because the weaker subpulses oscil-late in the temporal domain. The instantaneousseparations between the main and the additivepulses are variable. However, the intensities of theweaker pulses are constant at a fixed P value. Thesestates are quite the contrary of those in Ref. [15],where the two pulses have a fixed separation inthe temporal domain, while their intensities keepvarying through the interaction. Furthermore, fromFig. 4 we can see that the typical temporal separa-tions among the stronger and the weaker pulsesare about several nanoseconds. According to thetheory in [11], such a large separation cannot sup-port the bound-soliton operation, which generallyemerges with a pulse separation of several ps. More-over, because the pulse duration is 2 orders of mag-nitude less than the pulse separation (∼17ps versusseveral nanoseconds), the DSs cannot interact di-rectly through their tails and they do not exchangeenergy [15]. So the individual DSs are well sepa-rated, and the autocorrelation traces will maintainthe Gaussian profile without modulated sidebands.Therefore, the autocorrelation traces are omittedfor the purpose of conciseness, and, here, we will con-centrate on the pulse characteristics in the spectraland temporal domains.

The mechanism of the subpulse shaping can be un-derstood as follows. When the pump power is toostrong for a steady single DS to sustain, the excesspower will create a CW breakthrough on top of the

spectrum, as shown in Fig. 3(a), and the DS exhibitsa mixed state of the CW and steady ML regimes[10,16]. Meanwhile, no additive subpulses areformed at this stage, which can be confirmed byFig. 4(a). Further enlarging the P, the CW mostlytends to destabilize the ML operation, and leads tochaotic or pure CW regimes [10]. However, takingmodulation instability (MI) into consideration, whichgenerally results in the breakup of a CWor quasi-CWstate into a periodic pulse train [17], it is reasonableto assume that in some special cases, partially MLstates can arise from the CW. In our case, incompleteML can be realized from the additive CW componentthrough theMI effect, as shown in Figs. 3(b)–3(d) and4(b)–4(d). Because of the intrinsic non-fully growncharacteristics, the initially formed small subpulsesare so weak that the global and local soliton interac-tion is not strong enough to organize the pulses withinvariable distributions [18]. Thus the small pulsesoscillate continuously in the temporal domain.Meanwhile, the total spectra show the combinedstates of the two DSs [Figs. 3(b)–3(d)], where the ad-ditive sub-DS creates modulation on top of the spec-trum, while the main spectrum width is determinedby the stronger DS.

Further increasing the P, the additive DSs becomestronger, as shown in Fig. 5. The modulated top ofthe spectrum broadens to both sides and almost cov-ers the whole spectrum as the P reaches 102mW[Fig. 5(a)]. The corresponding pulse sequence inthe temporal domain, as depicted in Fig. 5(b), revealsthat the additive sub-DS in this stage is much stron-ger and begins to oscillate together with the mainDS. When the P is enlarged to 115mW, steadydual-pulse ML can be achieved. The correspondingoptical spectrum and oscilloscope trace are shown inFigs. 5(c) and 5(d), respectively. In this stage, thespectrum turns back to a typical rectangular profile,just similar to the steady single-pulse operation statefor P ¼ 62mW. Meanwhile, the two DSs exhibit al-most the same intensities, as shown in Fig. 5(d).The relative height difference of the two pulse se-quences is less than 5%, and it is attributed to the

Fig. 3. (Color online) Optical spectrum when P is (a) 90mW, (b)92mW, (c) 95mW, and (d) 98mW.

Fig. 4. (Color online) Oscilloscope traces when P is (a) 90mW, (b)92mW, (c) 95mW, and (d) 98mW.

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practical measurement precision. Considering thewhole evolving processes mentioned above, it be-comes obvious that the non-fully grown DS regimescan be regarded as the transitional states and con-nect the two nearby steady ML states.

More pulse operation states can be achieved by in-creasing P to a larger degree and maintaining theother cavity parameters. As depicted in Figs. 6(a)and 6(b), transitional states of triple pulse can alsobe achieved, where the intensities of additive DSs in-crease asP enlarges from 234mWto 244mW.WhenPreaches 260mW, steady triple-pulse ML can be rea-lized, as shown in Fig. 6(c). The spectrum evolvingprocesses are quite similar to that of the dual-pulsestates, and thus we do not demonstrate them in thispaper for the purpose of conciseness. Figure 6(d)shows the quadruple-pulse sequence forP ¼ 375mW.Because of the practical measurement error, the tran-sitional states for large-number pulses are not asobvious as the low-count DSs.

4. Comparisons and Analysis

Although we have investigated multiple pulses inour previous reports [12–14], the pulses were formedapproximately instantaneously. Our previous works

did not involve the detailed pulse-shaping and evol-ving processes. Contrarily, in this report (here thecavity parameters are quite different from those inRefs. [12–14], e.g., the pump power and the polariza-tion states), we obtain very different results andsuccessfully observe the detailed pulse-forming dy-namics. For example, in our previous work [12],the experimental results showed that there existedalternately stable and unstable ML states with re-spect to the pump power. The stable ML operationtended to be limited by the accumulation of excessivepulse chirps. When the pump power and the pulseenergy are beyond a certain value, the laser becomesso unstable that we can hardly get a steady snapshotof the optical spectrum. The typical spectral profileand the corresponding autocorrelation trace for theunstable states of Ref. [12] are shown in Figs. 7(a)and 7(b), respectively. However, in this report, the ex-cessive energy beyond the capability of a stable pulseis now transferred to the newly generated subpulse.Thus the main pulse can maintain stable operation,and the unstable ML states mentioned in Ref. [12]are avoided. Because the intensities of the mainpulse and the subpulse keep almost fixed at a certainP value, we can obtain a clear optical spectrum. Thetypical spectrum and autocorrelation trace for thetransitional state of this report are depicted inFigs. 7(e) and 7(f), respectively.

Furthermore, we had demonstrated that DSs couldexhibit various properties in Refs. [13,14]. By increas-ing the pump power, the spectral profiles of DSsevolved initially from a rectangular shape, then totheunstable operationwith strong fluctuations on theedges of spectral profile, and finally to the trapezoidprofile. The corresponding spectral profile and auto-correlation trace are shown in Figs. 7(c) and 7(d),respectively. So the laserwas operated on three differ-ent statuses and emitted DSs with different types.However, in this report, the spectral profiles of pulsesapproximately keep the rectangular shape, whichindicates that the main pulse and the additionalsubpulse are with the same type during evolutions.

Fig. 5. (Color online) Optical spectra and oscilloscope traces: (a),(b) for P ¼ 102mW and (c), (d) for P ¼ 115mW.

Fig. 6. (Color online) Oscilloscope traces for the transitional stateof the triple pulse at (a) P ¼ 234mW and (b) P ¼ 244mW. Oscillo-scope traces for (c) stable states of the triple pulse at P ¼ 260mWand (d) steady states of the quadruple pulse at P ¼ 375mW.

Fig. 7. (Color online) Comparisons with unstable states in Refs.[12–14] and transitional states of this report: optical spectra (top)correlation traces (bottom).

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So the results in this report are quite distinct fromthose in Refs. [13,14], and the detailed pulse-shapingand evolving processes are reported for the first timeto the best of our knowledge.

5. Conclusions

In this manuscript we report on the experimental ob-servations for multiple DSs operating on the ultra-large normal cavity-dispersion regime. The opticalspectra and the intensities of pulses vary with thepump power and polarization states. The dynamicevolution of multiple DSs is demonstrated. Pulseswith different energies are achieved, and we findthat they can coexist in the cavity during the evolu-tion. With the increase of pump power, the newlygenerated DSs are initially formed with weak inten-sities and finally develop into fully grown pulses. Theadditional weak pulse oscillates in the temporal do-main, while it maintains its intensity and creates themodulation in spectral profile. These processes occurstage by stage and, thus, can be regarded as the tran-sitional states connecting the two nearby steady MLstates. This work brings the possibility of investi-gating the detailed pulse-shaping and evolving pro-cesses of DSs.

This work was supported by the “Hundreds ofTalents Programs” of the Chinese Academy ofSciences and by the National Natural Science Foun-dation of China (NSFC) under grants 10874239 and10604066.

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