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Abstract
Synchronised ultrafast soliton lasers have attracted great research interest in recent decades. However, there is a lack of comprehensive understanding regarding the buildup mechanism of synchronised pulses. Here, we report a dynamic analysis of independent and synchronised solitons buildup mechanisms in synchronised ultrafast soliton lasers. The laser comprises an erbium-doped fibre cavity and a thulium-doped fibre cavity bridged with a common arm. Pulses operating at two different wavelengths formed in the cavities are synchronised by cross-phase modulation-induced soliton correlation in the common fibre arm. We find that the whole buildup process of the thulium-doped fibre laser successively undergoes five different stages: continuous wave, relaxation oscillation, quasi-mode-locking, continuous wave mode-locking and synchronised mode-locking. It is found that the starting time of the synchronised solitons is mainly determined by the meeting time of dual-color solitons. Our results will further deepen the understanding of dual-color synchronised lasers and enrich the study of complex nonlinear system dynamics.
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1. Introduction
Ultrafast fibre lasers, which usually appear in the form of soliton pulses, are widely deployed in a variety of applications due to their remarkable physical performances, e.g., large peak power, high repetition rate, and broad spectral coverage [1–4]. Ultrafast pulses in fibre lasers are usually generated by the phase-locking of intracavity longitudinal modes, where a modulator plays a key role in the establishment of mode-locking. Low-dimensional nanomaterials, like carbon nanotubes [5–7], graphene [8–10] and black phosphorus [11–13], have been demonstrated remarkable saturable absorbers (SAs) for passive mode-locking, which are promising for further exploration of various ultrafast dynamics of optical pulses.
In contrast to a single wavelength laser, dual-color synchronised soliton sources are particularly interesting in applications, such as pump-probe techniques [14], coherent pulse synthesis [15], precise timing distribution [16] and coherent anti-Stokes Raman imaging [17,18]. The generation of dual-color synchronised solitons is usually realised by two means, injection mechanism (also called master-slave cavity) [18–20] and coupling method [21–24]. In the injection mechanism, a repetition-rate tunable pulse signal (master laser) is inputted to a cavity-fixed mode-locked laser (slave laser) when their repetition rates are close. The cross-phase modulation (XPM) induced pulse correlation forces the slave laser pulses to the same repetition rate as the input master signal, which can be further tuned by the master signal. This method features the origin of an independent pulse operation in the slave laser but requires a higher pulse energy master source. The coupling method is based on the combination of two individual cavities through a common arm, where the solitons correlate and interact during the propagation along the same direction, and XPM plays a major role in the buildup of synchronised solitons through the pulse-pulse pulling effect. A number of works have demonstrated the passive synchronisation of dual-color solitons in composite fibre cavities where broadband SAs were utilised to start the mode-locking [22–24]. The evolution of solitons from their independent operation to correlated and synchronised operation is attributed to a comprehensive effect of XPM and optical nonlinearity (e.g., negative group velocity dispersion (GVD)) [25–27]. This allows a stable synchronisation frequency range (SFR) when the correlation balance is maintained in the two solitons.
Lately, various emerging measurement techniques have enabled the investigation of complex soliton dynamics in fibre lasers (e.g., soliton molecules [28,29], soliton rains [30], soliton explosions [31], soliton collisions [32] and rogue waves [33]). However, the dynamics of how single-color pulses interact during the pulse evolution from the independent operation to the synchronisation in a dual-color fibre laser has not been intensively investigated. Herein, we report a direct observation of the synchronised soliton buildup dynamics in a dual-color fibre laser mode-locked with a broadband double-walled carbon nanotube saturable absorber (DWCNT-SA). The erbium and thulium-doped fibre cavity modes of the synchronised lasers are locked at the central wavelengths of ∼1560.8 nm and 1922.6 nm, respectively. Assisted by a frequency tunable optical chopper, we observe the intracavity light oscillation transition in continuous wave (CW), relaxation oscillation (RO), quasi-mode-locking (QML), continuous wave mode-locking (CWML) and synchronised mode-locking (SYML). It is observed that the starting time of synchronised pulses is mainly determined by the meeting-time of the dual-color solitons, where the XPM has a major contribution. Our results also find that the soliton correlation induces a shift of the central wavelengths while the spectral and pulse width remains unchanged. This is attributed to XPM-induced instantaneous frequency shift in the nonlinear medium.
Note that recent works demonstrated two-color synchronisation solitons in a single laser cavity, where intracavity group delay modulation was employed to realise synchronisation of two/multi-wavelength solitons [34,35]. The phase modulation in these works is applied to the transversal modes in the spatial domain. Thus, both longitudinal and transversal modes are shaped by the saturable absorber and spatial phase modulator. However, the working principle limits the wavelength spacing in these synchronisation solitons. As a comparison, our master-slave cavity utilises a broadband saturable absorber and XPM mechanism to force the synchronisation of two individual solitons. Only longitudinal modes are modulated, and large wavelength spacing is allowed to synchronise.
2. Mechanism of soliton synchronisation
It is well known that XPM is a nonlinear optical effect where the shift of the optical phase in one pulse is caused by the interaction with another pulse at a different frequency (or wavelength) in a nonlinear medium [36]. The generation of synchronised solitons can be attributed to the XPM effect between two soliton pulses with negative GVD. Considering that the soliton pulses operate at different repetition rates before synchronisation (i.e., independent operation region), they meet in the nonlinear medium with instantaneous frequencies of ω1 and ω2 [26]:
3. Experimental setup
Figure 1 shows the schematic of our synchronised laser setup, which is comprised of a 1.55 µm erbium-doped fibre cavity and a 1.9 µm thulium-doped fibre cavity connected in a shared section, where two 1550/1950nm wavelength division multiplexers (WDMs) are utilised to combine and divide the intracavity light. The 1.55 µm laser cavity employs a 976 nm laser diode (LD) to pump a piece of 0.6 m erbium-doped fibre (nLight Liekki Er80-8/125) through a 980/1550 nm WDM. A variable optical delay line (VODL, HJ Optronics VODL-1550-500) changes the length of the 1.55 µm laser cavity. The 1.9 µm laser cavity employs a 1550 nm laser pre-amplified by an erbium-doped fibre amplifier to pump a 2 m thulium-doped fibre (OFS TmDF200) through a 1550/1950nm WDM. In both optical loops, 90/10 optical couplers are used to extract 10% of the laser signal out, polarisation controllers are placed to adjust the intra-cavity polarisation state, and polarisation-independent isolators are inserted to force the signal propagation counterclockwise and clockwise in the 1.55 µm and 1.9 µm lasers, respectively. A broadband DWCNT-SA [37] generates ultrafast pulse by passive mode-locking, which is placed in the common arm incorporated with a 7 m single-mode fibre, where the enhanced XPM effect becomes dominant in the synchronised pulse evolution. Here, we especially introduce a chopper to turn on or off the pump light for the 1.9 µm laser to study the pulse dynamics and the synchronisation process. Power meter (Thorlabs PM100D), optical spectrum analysers (Anritsu MS9740A for 1.55 µm, APE waveScan for 1.9 µm), autocorrelator (APE PulseCheck 150), digital oscilloscope (Siglent SDS5104X), spectrum analyser (Anritsu MS2692A) and ultrafast photodiode detector (EOT ET-5000F) are utilised to assess the laser performance.
Fig. 1. Schematic setup of the synchronised fibre laser. LD: laser diode; WDM: wavelength division multiplexer; EDF: erbium-doped fibre; ISO: polarisation-independent isolator; PC: polarisation controller; VODL: variable optical delay line; SMF: single-mode fibre; SA: saturable absorber; OC: optical coupler; TDF: thulium-doped fibre.
4. Results and discussion
Self-starting CWML of the 1.55 µm and the 1.9 µm lasers are observed at their pump powers of 60.2 mW and 132.6 mW, respectively. The measured optical spectra and corresponding autocorrelation traces are presented in Fig. S1 of the Supplement 1. The fundamental repetition rate of the 1.9 µm laser with a fixed cavity length is measured as 12.8731 MHz, and the same value is obtained in the 1.55 µm pulse sequence when the cavity length is adjusted to approach the cavity length of the 1.9 µm laser via the VODL, as shown in Fig. S2 of the Supplement 1. Further tuning the VODL in the 1.55 µm laser, synchronised solitons can be obtained, exhibiting stable pulse sequences without swinging displayed on the oscilloscope trace as depicted in Fig. S3 of the Supplement 1. It is observed that the 1.55 µm laser is mode-locked in good stability even when the 1.9 µm laser is turned off by blocking its pump light with the chopper blade. As a comparison, synchronised pulses are retrieved immediately (see Visualization 1, further description in Supplement 1) when an open aperture of the chopper is switched to the pump beam. Figure 2 shows the optical spectra and autocorrelation traces of the 1.55 µm laser while the 1.9 µm laser is turned on or off by the chopper (i.e., independent operation of the 1.55 µm laser or synchronised operation of the 1.55 µm laser and the 1.9 µm laser). It can be seen that the spectral bandwidth of the 1.55 µm laser remains unchanged while the central wavelength of the spectrum blue-shifts ∼0.25 nm as shown in Fig. 2(a). Combined with Eqs. (1) and (2), here the 1.55 µm laser (ω1) repetition rate is smaller than the 1.9 µm laser (ω2) when they are under the independent operation region. XPM effect between two lasers with negative GVD causes an increase of ω1, and the spectrum center of the 1.55 µm laser shifts to a shorter wavelength. The shift primarily depends on the optical length difference between the two laser cavities. The full range output spectra of independent and synchronised operations are shown in the inset of Fig. 2(a). The CW peak at ∼1551.15 nm in the soliton spectrum is from the residual pump light of the 1.9 µm laser. Figure 2(b) shows that the autocorrelation traces in the independent and synchronised operations are highly consistent, indicating an unchanged pulse width, which is in accordance with the observation of unchanged spectral bandwidth in Fig. 2(a).
Fig. 2. The measured (a) optical spectra and (b) autocorrelation traces of the 1.55 µm laser at the independent or synchronised operation. Inset of Fig. (a): Full range output spectra of independent and synchronised operations.
To investigate the real-time buildup process of the synchronised dual-color lasers, we chop the pump light of the 1.9 µm laser to dynamically analyse the evolution of intracavity light. We notice that the 1550/1950nm WDM can not filter out the two different wavelength signals completely. Part signal of the 1.9 µm laser can couple to the Er-doped cavity after passing through the common section and come out from the 1550 nm coupler together with the 1.55 µm laser, enabling the oscilloscope to detect stronger pulse signal of the 1.55 µm laser and weaker pulse signal of 1.9 µm laser simultaneously from the 1550 nm output (see Fig. 3(c)). Figure 3(a) shows a real-time observation of the pulse sequences on the oscilloscope when a 31 Hz chopper frequency is applied. The top and bottom panels are the measured signals from the 1550 nm output and 1950nm output, respectively. We define the zero position of the time axis when the pump is just completely unblocked by the chopper blade. It can be seen that an obvious amplitude increase caused by the superposition of dual-color solitons appears from E point at ∼13.7 ms in the top panel, indicating SYML is achieved. The amplitude variation of the 1.55 µm laser before and after synchronisation is clearly seen in Visualization 1. After blocking the pump beam, soliton pulses of the 1.9 µm laser can maintain for a short time before completely vanishing. Figure 3(b) is a zoom-in illustration of region A in Fig. 3(a), which shows the buildup process of the solitons in the 1.9 µm laser (bottom panel) and the corresponding soliton behavior in the 1.55 µm laser (top panel). It can be seen that the start-up process before SYML of solitons in the 1.9 µm laser includes CW, RO, QML, and CWML [38–40]. Here RO is defined as the duration from the first laser spike (at ∼0.809 ms) to the last spike (at 1.077 ms) prior to the formation of mode-locking. After a continuous QML period of ∼0.124 ms, CWML is achieved at ∼1.201 ms. For the solitons in the 1.55 µm laser, there is an obvious amplitude decrease since the first laser spike of the 1.9 µm laser appears from the CW laser (at ∼0.809 ms) due to XPM between the 1.55 µm laser and the 1.9 µm laser. Figure 3(c) shows the zoom-in pulse sequences outputted from the 1550 nm coupler around regions B, C, D and E (represented by short dot lines) in Fig. 3(a), which demonstrates the evolution process of the formation of dual-color soliton synchronisation since CWML is established in the 1.9 µm laser. Due to the slight cavity length difference between the 1.55 µm laser and the 1.9 µm laser cavities, the dual-color solitons move closer after certain roundtrips evolution and finally meet. Then, the dual-color solitons maintain synchronised propagation, which is a result of XPM induced pulling effect. The buildup time of synchronised solitons is mainly determined by the meeting time of dual-color solitons, which is mainly affected by the initial relative position of the dual-color solitons when CWML is just established in the 1.9 µm laser. The initial relative position is irregular at each chopping period. Figure 3(d) illustrates the chopper blade position to the pump laser beam corresponding to Fig. 3(c), where the chopper rotates counterclockwise, as indicated by the arrows.
Fig. 3. Real-time observation of the laser temporal dynamics. (a) Oscilloscope pulse sequences of the 1.55 µm and the 1.9 µm lasers in the time window when the 1.9 µm laser is on. (b) Buildup process of solitons in the 1.9 µm laser and corresponding soliton behavior in the 1.55 µm laser corresponding to region A in (a). (c) The pulse sequences of the dual-color solitons corresponding to regions B, C, D and E in (a), respectively. (d) Spacial position diagram of the chopper blades to the pump laser beam corresponding to (c).
To investigate the influence of the pump power on the starting time from CW to CWML of the solitons in the 1.9 µm laser when the 1.55 µm laser operates in CWML, we set the chopping period at ∼4.13 ms as shown in Fig. S4, indicating that the unblocked time interval of the 1.9 µm laser is ∼2.065 ms since the chopper frequency duty cycle is 50%. The pump power of the 1.55 µm laser is then fixed at 63.9 mW, and the pump power of the 1.9 µm laser increases from ∼132.6 mW to 152.6 mW. The starting time of RO, QML and CWML reduce from 1.212 ms to 0.861 ms, from 1.519 ms to 1.105 ms and from 1.635 ms to 1.232 ms (see Fig. 4(a)), respectively, which verifies that higher pump power of the 1.9 µm laser could speed up the generation of laser spikes and the buildup of QML and CWML. This result is mainly attributed to the faster saturation time of the DWCNT-SA under increased pump power. Furthermore, we fix the pump power of the 1.9 µm laser at 150 mW and increase the pump power of the 1.55 µm laser from ∼60.2 mW to 64.7 mW. The starting time of RO remains the same at ∼0.884 ms, but the starting time of QML and CWML reduces from ∼1.201 ms to 1.104 ms and from ∼1.331 ms to 1.233 ms (as shown in Fig. 4(b)) respectively, which indicates that the influence of the 1.55 µm solitons on the start of the 1.9 µm lasing is negligible before the generation of the first laser spike, whereas the solitons in the 1.55 µm laser with higher energy could promote the buildup of QML and CWML in the 1.9 µm laser. This may also be attributed to the XPM effect between the 1.55 µm laser and the 1.9 µm laser. Higher energy of the 1.55 µm laser leads to a stronger XPM effect and facilitates the buildup process in the 1.9 µm laser. The pump powers used here are limited by possible pulse splitting. The pump powers we used in our experiments aim to maintain stable mode-locking and avoid potential pulse splitting.
Fig. 4. Laser dynamics of the 1.9 µm laser versus the pump powers of (a) 1.9 µm laser while the 1.55 µm laser pump power is fixed at 63.9 mW and (b) 1.55 µm laser while the 1.9 µm laser pump power is fixed at 150 mW.
We further investigate the factors that affect the SFR in the distance and the maximum frequency difference (MFD) to obtain synchronisation in the dual-color soliton laser system. Visualization 2 and Visualization 3 in Supplement 1 show the synchronisation status displayed on a digital oscilloscope and a radio frequency (RF) spectrum analyser through finely tuning the VODL. The repetition rates of the 1.9 µm laser are set as f1 and f2 when the soliton synchronisation is obtained and detached. Then the SFR can be defined as |c/f1- c/f2|, where c is the speed of light in a vacuum. In Fig. 5(a), the SFR of the two solitons increases gradually from ∼1.402 mm to 1.699 mm when the 1.55 µm laser pump power increases from ∼60.2 mW to 64.7 mW, and the 1.9 µm laser pump power is fixed at 132.6 mW. On the contrary, with the pump power of the 1.9 µm laser increasing from ∼132.6 mW to 152.6 mW while the pump power of the 1.55 µm laser is fixed at 63.9 mW, the SFR decreases from ∼1.651 mm to 1.370 mm as shown in Fig. 5(b). These results reveal that the 1.55 µm laser behaves more like a master cavity, as it identifies a dominant position in the pulse-pulling effect, which can be attributed to its shorter pulse width (see Fig. S1 of the Supplement 1). Also, the higher pulse energy of the 1.55 µm laser and lower pulse energy of the 1.9 µm laser could enhance the pulling effect to make the synchronisation of the dual-color solitons more stable. In addition, the SFR could be affected by the length of the common fibre. Before the turning point, the SFR would increase with the fibre length. This is due to the stronger pulling effect between the dual-color solitons induced by the enhanced XPM effect in a longer fibre. Further increasing the common fibre length would decrease the SFR, because the walk-off effect between the dual-color solitons limits the effective interaction length.
Fig. 5. SFR versus pump power in (a) the 1.55 µm laser while the 1.9 µm laser pump power is fixed at 132.6 mW and (b) the 1.9 µm laser while the 1.55 µm laser pump power is fixed at 63.9 mW.
The initial repetition rate of the 1.9 µm laser is defined as f3 in the case of independent operation. Then, MFD can be expressed as |f3-f1|. Similar to the above results of SFR, it can be seen that the MFD of the dual-color laser pulses increases gradually from ∼30 Hz to 46 Hz as the increase of the 1.55 µm laser pump power, as shown in Fig. 6(a). On the contrary, the MFD decreases gradually from ∼43 Hz to 30 Hz as the increase of the 1.9 µm laser pump power, as plotted in Fig. 6(b). These results evidence that power-induced enhancement in the pulling effect is a key factor to enlarge the MFD of the synchronised solitons. Our research is helpful for synchronised dual-color fibre laser design. A higher pump power of the laser in the dominant position and a lower pump power of the laser in an affiliated position are preferred for designing a synchronised dual-color fibre laser with high stability.
Fig. 6. MFD to obtain the synchronised dual-color solitons versus pump power of (a) the 1.55 µm laser and (b) the 1.9 µm laser.
5. Conclusion
In conclusion, we demonstrate a dual-color synchronised fibre laser and observe the soliton buildup process directly. The synchronised pulses are mode-locked at central wavelengths of 1560.8 nm and 1922.6 nm with full width at half maximum of 4.37 nm and 3.4 nm, corresponding to the pulse width of 736 fs and 1.24 ps, respectively. By using an optical chopper to modulate the 1.9 µm laser pump light, we are able to investigate the real-time temporal dynamics of the solitons as a function of time and power. Our results indicate that the amounts of dual-color solitons meet in time, and the XPM-induced soliton pulling effect could shift the central wavelength of the solitons. Experimental observation of the pulse formation process in the 1.9 µm laser unveils that the time-dependent status evolution includes CW, RO, QML, CWML, and SYML. Further investigation suggests that pump power in both the 1.55 µm laser and the 1.9 µm laser can determine the starting time of the QML and CWML in a coupled laser configuration. In addition, our measurement also reveals that the SFR and the MFD in the dual-color soliton system are influenced by the strength of the pulling effect, which can be enhanced in the 1.55 µm laser when higher laser energy applies, and in the 1.9 µm laser when lower laser energy applies. Our work not only demonstrates a simple and compact approach for the realisation of broadband dual-color soliton synchronisation by self-start mode-locking, but also performs an insight understanding of the complicated soliton system when correlated in a nonlinear optical medium.
Funding
European Research Executive Agency (H2020-MSCA-RISE-872049 (IPN-Bio)); Academy of Finland (PREIN, 320167); Villum Fonden (Villum Investigator grant 00037822).
Acknowledgments
The authors thank Y. Zhang, X. Bai, B. Zhang and K. Y. Lau for valuable discussions.
Disclosures
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.
Data availability
Data will be available on reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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