Transcription 29 January 2016accepted: 15 June 2016Published: 06 July 2016Polarization domain wall pulsesin a microfiber-based topologicalinsulator fiber laserJingmin Liu1, Xingliang Li1, Shumin Zhang1, Han Zhang2, Peiguang Yan3, Mengmeng Han1,Zhaoguang Pang1 & Zhenjun Yang1Topological insulators (TIs), are novel two-dimension materials, which can act as effective saturableabsorbers (SAs) in a fiber laser. Moreover, based on the evanescent wave interaction, deposition ofthe TI on microfiber would create an effective SA, which has combined advantages from the strongnonlinear optical response in TI material together with the sufficiently-long-range interaction lengthin 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 orthogonaldegenerate 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, polarizationlocked noise-like pulses and their harmonic mode locked counterparts, incoherently coupledpolarization domain wall pulses, including bright square pulses, bright-dark pulse pairs, dark pulsesand bright square pulse-dark pulse pairs are all observed with different pump powers and polarizationstates.Ultrafast pulses have been widely used in material processing, optical communications, medicine, and opticalsensing1–4. Passively mode-locked fiber lasers have also been demonstrated to be an excellent method for generating ultrafast pulses. In order to realize mode locked pulses, a saturable absorber (SA) is usually placed inthe resonant cavity. In general, lasers that use nonlinear polarization rotation (NPR) as SAs are unstable. Whilelaser based on nonlinear optical loop mirrors (NOLMs) or nonlinear amplifying loop mirrors (NALMs) withentirely polarization-maintaining cavity were demonstrated to be self-starting and stable5. Apart from NOLM orNALM, a material-based SA can also be used to generate stable mode-locked pulses. One type of material-basedSA, the semiconductor saturable absorber mirror, however, always has a narrow transmission bandwidth andrequires complex fabrication and packaging6,7. Another material-based SA, based on single-walled carbon nanotubes (SWCNTs) though easier to fabricate and cost effective, has working wavelengths that are connected withthe diameter of the nanotubes8. A third material-based SA, graphene, has a higher optical damage threshold,lower loss and better wavelength-independence than SWCNTs. However, monolayer graphene always has a smallabsorption at 1550 nm9–11. Recently, several new and intensively investigated nanomaterials, including transitionmetal dichalcogenides (TMDCs), black phosphorus (BP) and topological insulators (TIs), have been used as SAs.However, TMDCs have sizeable bandgaps corresponding to only the visible and near-infrared spectrum ranges12,while BP is very sensitive to the environment because of the high reactivity of BP with air, and this might limittheir applications in real devices13. Compared with above two nanomaterials, TIs have been found to have narrowtopologically non-trivial energy gaps, and corresponding to a broadband saturable absorption. They have alsobeen found to have a low saturable optical intensity, high damage threshold and large modulation depth14,15. SinceBernard et al. first demonstrated a TI-based SA in 2012, passive mode-locking or Q-switching operation has beenachieved experimentally in different wavebands16–20. In addition, TIs also possess giant third order nonlinearityand have attracted much attention for their ability to generate short and high-energy laser pulses17,21. The TInano-materials can composite with polymer to form thin films, and then were transferred to fiber end face to1College of Physics Science and Information Engineering, Hebei Advanced Thin Films Laboratory, Hebei NormalUniversity, Shijiazhuang 050024, China. 2Key Laboratory of Optoelectronic Devices and Systems of Ministry ofEducation and Guangdong Province, Shenzhen University, Shenzhen, 518060, China. 3Shenzhen key laboratoryof laser engineering, College of Optoelectronic Engineering, Shenzhen University, Shenzhen, 518060, China.Correspondence and requests for materials should be addressed to S.Z. (email: zhangsm [email protected])Scientific Reports 6:29128 DOI: 10.1038/srep291281 1. Schematic of Er-doped vector fiber laser. WDM: wavelength-division multiplexer; HCEDF: highconcentration erbium-doped fiber; PC: polarization controller; PI-ISO: polarization-independent isolator;TI SA: topological insulator saturable absorber; OC1: 90:10 optical coupler; OC2: 50:50 optical coupler; PBS:polarization beam splitter.act as a SA22,23. Unfortunately, thermal effects can damage the fiber end surface as well as the TI SA. In order toovercome the above drawbacks, two types of TI SAs, made by depositing the TI directly onto the microfiber orside-polished fiber (D-shaped fiber) have been proposed24,25. Since only a part of optical intensity interacts withthe TI in the cavity, these types of TI SAs can alleviate the thermal load on the fiber. In addition, the controllablelength of the deposited material helps to increase the interaction length between the light and the TI. Note however, that compared with the microfiber, the insertion loss of the D-shaped fiber itself will increase dramatically ifthe single mode fiber (SMF) is polished to the core26.By using a microfiber-based TI SA, harmonic mode-locked pulses, stable Q-switched pulses and multi-solitonpulses have all be obtained in fiber lasers24,27,28. However, in all these cases, only scalar solitons were obtained.Since there exists asymmetries in the fiber waveguide caused during manufacturing, externally applied stress,or bending, a SMF always exhibits random birefringence, and hence can support two degenerate modes thatare polarized in orthogonal directions. If the laser cavity does not include a polarizer, cross coupling betweenthese two modes occurs, which results in different polarization dynamic states dependent on the different propagation velocities along the fiber. These states include group velocity locked polarization domains (PDs), andpolarization locked (PL) pulses. Zakharov and Mikhailov first theoretically predicted the formation of PDs innonlinear optics29. Malomed theoretically studied the polarization domain wall (PDW) between traveling wavesby solving the coupled Ginzburg-Landau equations, and pointed out that PDWs might be realized as a boundary produced in two dimensions by a collision of waves traveling in different directions30. This prediction wasconfirmed experimentally by Pitois et al.31. Wabnitz and Daino theoretically studied the possibility of generatingPD solitary waves in nonlinear optical fibers32, and Haelterman and Sheppard showed theoretically the existenceof polarization domain wall soliton (PDWS) in a dispersive Kerr medium33,34. Williams and Roy observed PDsin a unidirectional erbium-doped fiber ring laser, and obtained square-wave pulses and irregular temporal patterns as operating parameters were changed35,36. Lecaplain presented a simple theoretical model to explain thedifferent PDW complexes formed in fiber ring lasers operating with either a normal path-averaged dispersion oran average anomalous dispersion37,38. Tang et al. observed polarization resolved operation of a quasi-isotropiccavity, erbium-doped fiber laser and demonstrated the formation of PD39. Subsequently, Zhang et al. observedexperimentally two types of phase-locked vector solitons in erbium-doped fiber lasers with weakly birefringentcavities40,41. Tang’s group experimentally observed soliton-dark pulse pair formation in a birefringent cavity fiberlaser42. Recently, our group obtained group velocity locked PDs in an Yb-doped fiber laser with a quasi-square PDalong one axis but with a chaotic-state PD along the other in the time domain43. A common feature of the abovelasers was that they had no mode locker in the cavity. On the other hand, dark solitons in a fiber laser based on anNPR SA, or carbon nanotube SA have been observed44,45.As mentioned above, a TI is a new type of SA, and a microfiber-based TI SA could effectively increasethe interaction length between the light and the TI. Therefore, the question arises as to whether lasers with amicrofiber-based TI SA can emit different PDs, or dark pulses. This was the initial motivation for our work.In this paper, we experimentally investigated a net normal dispersion vector Er-doped fiber laser using amicrofiber-based TI as the SA. This kind of SA can increase the length over which the light and the TI interact,and possess high nonlinearity. By adjusting the pump power and the PCs, various PDs with different widths andshapes, PL dark pulses and their harmonic mode locked counterparts, PL noise-like pulses and their harmonicmode locked counterparts could all be obtained.ResultsExperimental set-up and sample characterization. A schematic diagram of the experimental set-up isshown in Fig. 1. The laser cavity contained a 4.6-m long high concentration erbium-doped fiber (HCEDF) with agroup velocity dispersion (GVD) of 66.3 ps2 km 1 at 1550 nm, and a 13-m SMF with a GVD of 2 2 ps2 km 1. Thenet cavity dispersion was 0.019 ps2. A 976-nm laser diode was used to pump the HCEDF through a 980/1550 nmwavelength-division multiplexer (WDM). Two intra-cavity polarization controller (PC1) and PC2 were used tochange the polarization state of the cavity. A polarization independent isolator (PI-ISO), whose polarizationdependent loss was lower than 0.2 dB, was used to ensure the unidirectional operation of the ring cavity. A 90:10output coupler (OC1) was used to output 10% of the cavity light. Passive mode locking was realized by usingScientific Reports 6:29128 DOI: 10.1038/srep291282 2. Characterization and measurement. (a) Measured XRD pattern of Bi2Te3. (b) Low-magnificationSEM image of Bi2Te3 nanosheets. (c) High-magnification SEM image of Bi2Te3 nanosheets. (d) Microscopeimage of microfiber-based TI SA. (e) Microscope image of the evanescent field of the microfiber-based TIobserved using visible light.a microfiber-based TI SA. To observe the vector characteristics of the pulses, another extra-cavity PC3 and afiber-based polarization beam splitter (PBS) were connected to OC2. An optical spectrum analyzer (YokogawaAQ6317C) with a maximum resolution of 0.01 nm, a 1 GHz real-time oscilloscope (Yokogawa DL9140) with three3-GHz photo-detectors and a commercial optical autocorrelator (FP-103XL) were used to observe the opticalspectrum, temporal domain shape and pulse width.In experiment, the TI was made of bismuth telluride (Bi2Te3), which was prepared as follows: Bi2Te3 bulk crystals were placed into a autoclave filled with an ethylene glycol solution of lithium hydroxide. The autoclave wasthen oven-heated to achieve intercalation of Bi2Te3 by the lithium ions dissolved in the solution. The dispersionsin the solution were collected by filtration and rinsed with acetone. Colloidal suspensions of Bi2Te3 could be readily prepared by exfoliating the lithiated powder in deionized water. By filtering through porous polyvinylidenefluoride membranes, Bi2Te3 nanosheet membranes were obtained after drying18,46.In order to characterize the TI, we measured the X-ray diffraction (XRD) pattern of the prepared Bi2Te3 nanosheets using a X-ray diffractometer (X’pert PRO MPD), as shown in Fig. 2a. Several distinct diffraction peaks,which correspond to the [006], [015], [1010], and [0015] crystal planes (JCPDS NO. 15-0863) can be indexed toBi2Te3 (space group: R-3m) with lattice constants a   b  0.438 nm, and c  3.05 nm. In order to check the morphology of the Bi2Te3, we blended the powder with an ethanol solution and then ultrasonically processed it forhalf an hour at a power of 100 W. The suspension produced was then deposited on a silicon wafer using a pipette,and dried in vacuum. The resulting sample was observed using a scanning electron microscope (SEM). The lowermagnification SEM image in Fig. 2b shows that the nanosheets were randomly dispersed on the silicon wafer.A higher magnification SEM image shown in Fig. 2c indicates that the Bi2Te3 had a clear hexagonal structure.An aqueous suspension of Bi2Te3 produced as described above was also deposited on the surface of the microfibers constituting the SA. Figure 2d shows a highly enlarged microscope image of the fabricated microfiber-basedTI SA measured by a ternary inverted metallurgical microscope (Jiangnan MR5000). The microscope image ofthe fabricated microfiber shown in Fig. 2d was used to measure the tapered fiber. The tapered fiber had a waistdiameter of 30 μ m and a core diameter of 2.16 μ m. Assuming the refractive index of the core nco and cladding nclwere 1.454 and 1.45 respectively, one can calculate that the normalized frequency, V, was about 0.5 by using theequation:Scientific Reports 6:29128 DOI: 10.1038/srep291283 3. (a) Experimental setup for measurement of the nonlinear absorption of the microfiber-based TI; (b)measured transmission curve and the corresponding fitting curve.V 2πr(n2co n2cl )λ(1)where r is the core radius, and λ     1.56 μ m is the wavelength. As Bilodeau pointed out, for a tapered fiber, whenV is smaller than 0.84, the fundamental LP01 mode is no longer confined to the core but instead is guided bythe cladding-air interface, which results in a mode field with the same diameter as the tapered fiber47–49.Consequently, we can deduce that the mode field diameter was also 30 μ m in our experiment. We also observedthe evanescent field of the microfiber-based TI by injecting visible light into the SA, as shown in Fig. 2e. The interaction between the evanescent field and the TI occurs only in an elongated area on one side of the optical fiber.To further investigate the characteristics of the TI, we measured its nonlinear absorption, using a femtosecondlaser source with center wavelength of 1551.6 nm, repetition rate of 50 MHz, and a tunable pulse width (CalmarOpt-com FPL-04TTYSU11). The experimental setup is shown in Fig. 3a. Since the femtosecond pulse widthdecreased as the pump power increased, an optical autocorrelator was used to monitor the pulse width at thesame time. Figure 3b shows the transmission curve of the microfiber-based TI transmission curve. By using thefitted equation of the nonlinear saturable absorption curve, T(I)   1   T   exp( I/Isat)   Tns, where T(I) is thetransmission, T is the modulation depth, I is the input peak power intensity, Isat is the saturable intensity, andTns is the nonsaturable loss50, one can calculate that the modulation depth was 5.5%, the nonsaturable loss Tns was57.4%, and the saturable intensity was 27.2 MW/cm2.In the experiment, we have also measured the polarization dependent loss (PDL) of the microfiber before andafter deposing the TI. They were found to be 0.04 dB and 0.4 dB at 1550 nm, respectively. Since these PDLs valueare small, we may conclude that the pulse operations described below were not caused by the NPR51.Experimental ObservationsDifferent interactions between the orthogonal linearly polarized eigenmodes. Since there wereno polarizers in the cavity, the laser always simultaneously oscillated with two orthogonal linear polarizationeigenmodes, and these two eigenmodes could interact along the fiber. By adjusting the intra-cavity PCs, the cavitybirefringence could be altered and a rich set of PDW pulses could be obtained, including bright square pulses,bright-dark pulse pairs, uniformly distributed dark pulses, unevenly distributed dark pulses and bright squarepulse-dark pulse pairs.When the pump power was increased to 255 mW and the intra-cavity PCs were carefully adjusted, two orthogonal modes oscillating simultaneously were easily formed. Though these orthogonal polarization componentspropagate with different group velocities in the fiber, they can trap one another through cross-phase modulation,thus enabling them to propagate as a single entity39,52. In addition, within one cavity round-trip period, the laseremission would switch from one polarization to the other, forming two PDs, which showed a wide width in x axis,while displayed a narrow width in y axis. As a result, a bright square pulse was formed in the total laser intensityoutput (Initial) of Fig. 4a. The spectra of the two linear polarization components (x axis and y axis) had differentcentral wavelengths of 1560.02 nm and 1560.25 nm, as shown in Fig. 4b. Since the two PDs had a wavelength separation, the coupling was incoherent. Also, since there was only a small wavelength difference of 0.23 nm betweenthe two orthogonal polarization components, the two orthogonal polarization components had only a small timedelay as they propagated in the cavity. We may conclude that the net cavity birefringence was small in this state.Careful adjustment of the PCs away from the conditions for the bright square pulses, which corresponded toScientific Reports 6:29128 DOI: 10.1038/srep291284 4. Bright square pulses. (a) Pulse traces before (Initial) and after (x axis and y axis) passing through thePBS; (b) optical spectra before (Initial) and after (x axis and y axis) passing through the PBS.Figure 5. Bright-dark pulse pairs. (a) Pulse traces before (Initial) and after (x axis and y axis) passing throughthe PBS; (b) optical spectra before (Initial) and after (x axis and y axis) passing through the PBS.changing the net linear cavity birefringence, resulted in changing the widths and the shapes of the PDs. Figure 5shows another manifestation of the PDs. The time domain graph shows that unlike the x axis of Fig. 4a, where thePDs have a square top, the PDs on the x axis of Fig. 5a have a slightly oblique top. Through incoherent couplingbetween the orthogonal linear polarization modes, the total emission shows a periodic bright-dark pulse pair, asshown in Fig. 5a (Initial). The corresponding polarization resolved spectra are shown in Fig. 5b. The 3-dB bandwidths were 0.32 nm for the x axis and 0.16 nm for the y axis and the corresponding central wavelengths were1560.15 nm and 1560.23 nm, respectively. The separation of the wavelengths between the two parts was slight,which again indicates a small value of the average cavity birefringence.When we decreased the pump power to 230 mW and adjusted PC1 and PC2, a dark pulse was observed beforethe PBS as shown in Fig. 6a. Since this dark pulse appeared at a polarization switching position of the total laseroutput intensity, and separated two PDs in a period, it was identified as a dark PDWS34. Figure 6a shows regularlydistributed dark PDWS, for which the round trip time was 88 ns, which corresponds to the cavity length. It isobvious that the intensity of the pulses at the center of the dip did not fall to zero. These dark pulses are called“gray” pulses, and have been studied by our group, as reported in ref. 53. The central wavelengths of the twomodes were 1560.16 nm and 1560.2 nm, and their spectral widths were 0.34 nm and 0.29 nm, as shown in Fig. 6b.When the pump power was slightly increased to 248 mW, splitting of the PDs occurred. As an example, Fig. 7ashows one of the split states, in which four PDs were formed in the cavity. Correspondingly, irregularly distributed PDWSs were also obtained (see Fig. 7a initial trace). That is to say, depending on the cavity parameters, thePDWSs could have different forms. In addition, the PDWSs had different depths in the time domain. The polarization resolved spectra are shown in Fig. 7b. We found that the separation of the central wavelengths of the twocomponents was still small. The 3-dB bandwidths were 0.33 nm and 0.32 nm.Very interestingly, by further adjusting the intra-cavity PCs, another PDWS form consisting of bright squarepulse-dark pulse pairs was also obtained in the total laser intensity output, as shown in Fig. 8a (Initial). The timedomain graph shows that like the domain for the x axis of Fig. 5a, the PDs for the x axis of Fig. 8a also have aScientific Reports 6:29128 DOI: 10.1038/srep291285 6. Fundamental dark pulses. (a) Pulse traces before (Initial) and after (x axis and y axis) passingthrough the PBS; (b) optical spectra before (Initial) and after (x axis and y axis) passing through the PBS.Figure 7. Unevenly distributed dark PDW pulses. (a) Pulse traces before (Initial) and after (x axis and y axis)passing through the PBS; (b) optical spectra before (Initial) and after (x axis and y axis) passing through thePBS.Figure 8. Bright square pulse-dark pulse pairs. (a) Pulse traces before (Initial) and after (x axis and y axis)passing through the PBS; (b) optical spectra before (Initial) and after (x axis and y axis) passing through thePBS.Scientific Reports 6:29128 DOI: 10.1038/srep291286 9. PL vector dark pulses. (a) Pulse traces of fundamental vector dark pulses before (Initial) and after(x axis and y axis) passing through the PBS and (b) corresponding optical spectra; (c) pulse traces of high orderharmonic mode-locked vector dark pulses and (d) corresponding optical spectra.slightly oblique top. The total emission then showed a periodic bright square pulse-dark pulse pair. The spectra ofthe two modes on the x axis and y axis have slightly different central wavelengths of 1560.18 nm and 1560.22 nm,and the spectral widths are 0.36 nm and 0.35 nm, as shown in Fig. 8b.Polarization-locked vector dark pulses. Through increasing the pump power and carefully adjustingintra-cavity PCs, we obtained vector dark pulses. Further adjusting the PCs, which corresponded to tuning thewavelengths of the laser oscillations, the wavelength separation between the two orthogonal vector dark pulsescould be tuned to zero. In this case, the group velocity difference could be assumed to be negligible. Then theorthogonal vector dark pulses maintained their temporal and polarization state profiles during propagationwithin the birefringent environment. Such dark pulses could be referred to as phase- or PL vector dark pulses54–56.With a pump power of 265 mW, we first obtained PL fundamental dark pulses as shown in Fig. 9a. The twocomponents shared the same repetition rate of 11.4 MHz, which was consistent with the cavity length. Figure 9bshows that the two polarization components have same central wavelength of 1560.10 nm.With a further increase in the pump power, we also obtained PL high order harmonic mode-locked (HML)dark pulses. In order to protect the laser pump source, the highest order we obtained was 11, which had a repetition rate of 125.4 MHz, as shown in Fig. 9c. The two polarization components had the same central wavelength of1560.16 nm as shown in Fig. 9d. We also found that the spectral intensity difference between the two orthogonalpolarization components was less than 3 dB. These observations further confirmed that they were PL HML darkpulses.Polarization-locked noise-like pulses.By further rotating the PCs while holding the pump power at248 mW, we also obtained noise-like pulses, as shown in Fig. 10. The inset in Fig. 10b shows the autocorrelationtrace of a single pulse before passing through the PBS, and we can see that there is a coherent peak riding on awide shoulder that extends over the entire scanning time window, which indicates that a noise-like pulse wasformed. We also found that the two parts had the same central wavelength of 1560.12 nm (see Fig. 10b) and thatthe pulse trains were uniform in spacing both before and after passing through the PBS (see Fig. 10a), whichshowed that they were PL fundamental noise-like pulses.As the pump power was further increased to 270 mW, the fundamental noise-like pulses began to split, andhigh order HML noise-like pulses were formed. The highest order obtained was 28, as shown in Fig. 10c. TheScientific Reports 6:29128 DOI: 10.1038/srep291287 10. PL noise-like pulses. (a) Pulse traces of fundamental noise-like pulses before (Initial) and after (xaxis and y axis) passing through the PBS and (b) corresponding optical spectra (Inset: autocorrelation trace ofthe total pulse); (c) pulse traces of high order harmonic mode-locked noise-like pulses and (d) correspondingoptical spectra.spectra in Fig. 10d shows that the two orthogonal polarization components had the same central wavelength of1560.04 nm, which indicates that they were PL high order HML noise-like pulses.It has previously been found experimentally that noise-like pulses are generated in a cavity with mode lockingmechanisms such as NPR, SWCNTs, figure-eight, etc.57–59. Therefore, the observation of the PL noise-like pulsescan be attributed to the microfiber-based TI SA.DiscussionIn conclusion, we have demonstrated an Er-doped mode locked vector fiber laser that used a microfiber-basedtopological insulator as a saturable absorber. The experimental results showed that the formation of bright squarepulses, bright-dark pulse pairs, uniformly distributed dark pulses, unevenly distributed dark pulses and brightsquare pulse-dark pulse pairs all resulted from the existence of PDs and that the high nonlinearity provided by themicrofiber-base TI SA is favorable for the splitting of the PDs. Since neither the formation of the PDs nor the highnonlinearity are unique properties of the TI used in this work, we may infer that the different pulse generationregimes seen here are possible using other nanomaterial based SA with high nonlinearity. In fact, Gao et al. havedemonstrated PDs in a mode-locked fiber laser based on reduced graphene oxide60. 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in a unidirectional erbium-doped fiber ring laser, and obtained square-wave pulses and irregular temporal pat - terns as operating parameters were changed 35,36. Lecaplain presented a simple theoretical model to explain the different PDW complexes formed in fiber ring lasers operating with either a normal path-averaged dispersion or