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Abstract
We have demonstrated the generation of multicolor noise-like pulse complex in a passively Yb-doped mode-locked fiber laser based on a single mode-graded index multimode-single mode fiber (SMF-GIMF-SMF) device as the saturable absorber (SA). The stimulated Raman scattering (SRS) effect leads to the cascaded generation of the main noise-like pulse (NLP) at 1028.8 nm together with the noise like Raman pulse (RP) at 1076.1 nm. The generated dual wavelength pulses demonstrate the unique properties of mutually synchronization and coherence. The autocorrelation traces show that each of the synchronously mode-locked pulses exhibits a double-scale structure with a narrow peak which consists of a train of quasi-periodic beat pulses with a 35.7 fs pulse width and a pulse separation of about 77.2 fs. The total output power reaches 102.5 mW with 34% of it belonging to the RP. And furthermore, by separating the two pulses with spectral filters, the modulation fringes cannot be observed anymore. These results indicate that the Raman component participates in the mode-locking operation as a ‘signal’ instead of ‘noise’. Such a coherent Raman pulse source provides a novel platform for numerous applications, such as frequency comb spectroscopy and so on.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As a simple and economic ultrafast pulse source, passively mode-locked fiber lasers (MLFLs) have been extensively investigated as an ideal platform for studying new fields of soliton nonlinear dynamics [1], under the impetus of various applications, such as material processing [2], optical metrology [3], precision spectroscopy [4], and optical sensing [5]. Various kinds of solitons have been widely reported in the fiber laser system [6–9], such as conventional soliton, dissipative soliton (DS), bound state soliton, dark soliton, and so on. Besides these diverse dynamics, the ultrashort MLFLs can also provide a suitable platform for research on the nonlinear Raman soliton dynamics which is induced by the intracavity stimulated Raman scattering (SRS) process.
In the rare-earth (RE)-doped mode-locked fiber lasers, the SRS has a significant effect on the soliton dynamics as a parasitic phenomenon. In 2013, Aguergaray et al. report that the emergence of a strong Stokes signal generated from the SRS effect destabilizes the mode-locking operation and finally, leading to the operation in the noise-like regime [10]. Besides, the SRS process is also capable of producing other phenomena such as the rouge waves, the supercontinuum spectrum, and so on. In 2014, Runge et al. report that intracavity Raman conversion could lead to spectral fluctuations which is named as Raman rogue waves in an all-normal dispersion fiber laser [11]. However, in the above studies [10–13], the SRS effect is always considered as an induced noise influence, acting on the main pulse during propagation. By reinjection of the Raman pulse into the laser cavity, stable chirped Raman dissipative solitons (RDSs) are generated in the SRS process and form a multicolor complex with the main DSs [14]. In a relatively short all-normal-dispersion Yb-doped fiber laser mode-locked by the nonlinear polarization rotation (NPR) technique, benefiting from the small group velocity difference and the short propagation length, the RPs travel together with the DSs, and eventually, a broadband NLP with the bandwidth of 61.4 nm is generated [15]. The cascaded generation of coherent RDSs up to second order in a laser cavity is also demonstrated [16]. From these, the SRS effect can provide an ideal solution to generate the multi-color synchronous and coherent solitons, which can be applied for coherent pulse synthesis, frequency comb generation, and many other fields. More efforts are still required in further prospective research on the coherent parabolic pulses in the RE-doped mode-locked fiber lasers.
Several methods have been applied to the fiber lasers to achieve mode-locking pulses and the critical component that determines the performance of mode-locking is the saturable absorber (SA). Since the single mode-graded index multimode-single mode fiber (SMF-GIMF-SMF) geometry as an SA was theoretically proposed by Elham Nazemosadat and Arash Mafi in 2013 [17], the research on passively mode-locked fiber lasers with graded-index multimode fiber (GIMF) as SA is booming [18–20]. Such an all-fiber structured GIMF-based SA demonstrates the advantages of small insertion loss, high-damage-threshold, and excellent nonlinear properties, which promote itself suitable for studying soliton phenomena in the mode-locked fiber laser system. Furthermore, benefiting from the low modal dispersion and periodic self-imaging, diverse interesting nonlinear effects can be observed, including the self-phase modulation (SPM), SRS, and so on [21–23]. Meanwhile, spatiotemporal mode-locking of both longitudinal and transverse modes has been achieved in the GIMF [24–26], leading to the possibility of realizing the optical sources with unprecedented performances in temporal and frequency domains. Hence, the GIMF system has been proved to be not only physically interesting but also a unique platform for the investigation of nonlinear science.
Here, we report the generation of multicolor pulses in a linear cavity Yb-doped fiber laser mode-locked by a GIMF-based SA. The GIMF-based SA demonstrates a large modulation depth of 23.99% and a small saturation fluence of ∼ 6.82 µJ/cm2. A stable NLP + RP bound complex is achieved, benefiting from the strong SRS in the cavity. Both the dual pulses operate in the NLP regime. An interference pattern is observed in the coherent peak of the autocorrelation trace for the first time, which indicates the mutual coherence and synchronization of the dual-wavelength pulses. As the pump power changes, both the intensity of the Raman component and the interaction between the two components change as well. The coherence of the NLP + RP complex is further confirmed by investigating the separated pulses.
2. Experimental setup
The setup of the proposed passively mode-locked Yb-doped fiber laser is schematically illustrated in Fig. 1. As is depicted, double-end-pumped linear laser cavity is designed. Two 980 nm laser diodes (LD1 and LD2) are used to provide bidirectional pump power and two 980 nm polarization-independent optical isolators (PI-ISO1 and PI-ISO2) are inserted between the LD and the WDM to suppress the possible backward reflection light. The linear cavity configuration is constructed by using two reflection mirrors (RM1 and RM2) at both ends of the cavity. The linear cavity consists of the following devices: two 980/1030 nm wavelength division multiplexers (WDM1 and WDM2), a segment of 1.2 m ytterbium-doped fiber (YDF, Nufern SM-6/125, with absorption of 250 dB/m at 976 nm) serves as the gain medium, a polarization controller (PC) is employed to adjust the polarization state as well as the intracavity birefringence of the light, the SMF-GIMF-SMF SA element contains two sections of SMF (HI-1060) and a 40 cm section of GIMF (Corning) with core/cladding diameters of 62.5/125 µm used as SA which guarantees the mode-locking operation and an optical coupler (OC) with 60% output is used to direct the laser pulses out from the cavity. Additionally, a piece of ∼ 10 m SMF is added into the cavity for enhancing the nonlinear effect and the total length of the laser cavity is estimated to be ∼ 19 m. Compared with the ring-shaped laser cavity, the linear cavity has a shorter laser cavity length and it does not need to be equipped with an optical circulator or an optical isolator, which can simplify the structure of the cavity.
Fig. 1. Schematic diagram of the passively mode-locked Yb-doped fiber laser. LD: laser diode; PI-ISO: polarization-independent optical isolator; WDM: wavelength division multiplexer; YDF: ytterbium-doped fiber; PC: polarization controller; OC: optical coupler; RM: reflection mirror.
For the sake of taking further insight into the proposed SA device, the nonlinear optical properties need to be measured. The nonlinear transmission curve of the SA device is measured by using a 1064 nm nonlinear polarization rotation (NPR)-based mode-locked fiber laser with a repetition rate of 11 MHz and a pulse width of ∼ 45 ps. From Fig. 2, the nonlinear saturable absorption curve exhibits typical characteristics of saturable absorption and the measured data are fitted with a commonly used formula [27]:
Fig. 2. Nonlinear saturable absorption curve of the GIMF-based device, the black dots correspond to experimental data, and the red line is their fitting curve.
3. Results and discussions
The characteristics of output pulses are recorded by using an optical spectrum analyzer (OSA) (Yokogawa, AQ6370D) with a resolution of 0.02 nm, a 1.5 GHz oscilloscope (Keysight, DSOX4154A) combined with a 5 GHz photodetector (Thorlabs, DET08CFC/M), a radio frequency (RF) spectrum analyzer (Siglent, SSA3032X), and a second-harmonic autocorrelator (APE, Pulse Check 150). By properly adjusting the state of the PC in the laser cavity, the self-started mode-locking operation of the multi-pulse complex state can be realized within in a large range of the pump power between 202 and 827 mW. The corresponding output characteristics at the maximum pump power of 827 mW are illustrated in Fig. 3.
Fig. 3. Characteristics of the output mode-locking pulses: (a) optical spectrum on LOG SCALE at 1028.8/1076.1 nm; (b) optical spectrum on LIN SCALE at 1028.8/1076.1 nm; (c) the zoom-in of the coherent peak, (Inset) AC trace in a range of 150 ps; (d) the single pulse profile.
Figure 3(a) demonstrates the optical spectrum on a logarithmic scale where two central peaks simultaneously coexist. The main spectral peak is centered at 1028.8 nm, and a secondary spectral peak appears at 1076.1 nm. Indeed, the separation of ∼ 47.3 nm (corresponding to the frequency difference of 13.7 THz) is consistent with the downshifted ∼ 13 THz offset from an SRS process, conforming that the secondary peak originates from the intracavity Raman conversion. The substantially broad and smooth spectral shape of the dual wavelengths indicates that the fiber laser operates in the NL regime. The 3-dB bandwidth for the main NLP and the NL-RP are of 10 and 7 nm, respectively. Figure 3(b) demonstrates the optical spectrum in the linear scale where it can be estimated that the Raman contribution amounts to ∼ 34% of the total pulse energy, indicating the intensity of the Raman component is relatively comparable with that for the main NLP at this time.
Figure 3(c) shows the autocorrelation (AC) trace of the output mode-locking pulse. As depicted in the inset with a delay time of 150 ps, the trace exhibits a double-scale structure with a narrow coherent peak on the top of a relatively broad pedestal. In fact, such property is another representative characteristic of the NLPs. Substantially different from a classical Raman pulse [12–13], the zoom-in of the AC trace characterized by a periodic profile with strong modulations, which is attributed to the coherent beating of the main NLP and the RP. The synthesized pulse has a whole pulse duration of 233 fs with a pulse separation of about 77.2 fs. The fringe separation is defined by the frequency difference of dual wavelengths and can be calculated by the relation: Δν (the frequency difference of dual wavelengths) × T (the pulse separation) =1. In our experiment, the frequency difference of the NLPs and RPs is ∼13.7 THz, and thus, it agrees well with the above relation. In terms of the cosine-like pulse shape, the effective pulse duration of the optical pulse beating is as short as 35.7 fs, which is defined by the whole spectral range of the NLP + NL-RP complex. As the output intensities of the dual wavelengths are very close, the modulation depth of the quasi-periodic optically beating is of high-quality. Based on the above experimental results, it can be believed that the Raman component participates in the mode-locking operation as an independent ‘signal’ instead of ‘noise’, and furthermore, the NLPs and the RPs at two different carrier frequencies are temporally synchronous.
The RP is generated and amplified from the noise through SRS pumped by the main pulse. Different spectral parts of the NL-RP originate from the different parts of the main NLP through the Stoke-shifted process. The difference in the group velocities between main NLP and RP is compensated by the modal dispersion of the GIMF. In this process, the main NLP serve as the synchronous pump for the Raman component and then co- propagate together as one stable two-color complex in the common cavity. The main NLP and the NL-RP continuously interact with each other, resulting in the mutual coherence at a high level between the two pulses. As the NL-RP is bound with the main NLP via the nonlinear Raman process, they are different from the bound solitons or the dual-wavelength solitons. In our case, the DS and RDS form a stable two-wavelength complex with high coherence and synchronization, which is confirmed by the fringe pattern of the AC trace in Fig. 3(c).
In order to further identify the pulse width of the NLPs, the temporal profiles of the pulses are acquired with an oscilloscope, as shown in Fig. 3(d). Owing to the large normal dispersion and nonlinearity introduced by the SMF, the output multi-pulse complex breaks into a bunch of four pulses with a whole pulse duration of 4.9 ns.
The pulse train achieved at the maximum pump power of 827 mW is shown in Fig. 4(a). The interval between the multi-pulse complex is about 18.63 ns, corresponding to the repetition of 5.3680 MHz, indicating the fundamental frequency operation. In one cavity period scale, only one mode-locked pulse train is observed. The corresponding radio frequency (RF) spectrum with a scanning range of 1 MHz and the resolution bandwidth (RBW) of 10 Hz is measured, as demonstrated in Fig. 4(b). The fundamental peak is located at 5.3680 MHz with a signal-to-noise ratio (SNR) of about 64 dB, indicating low amplitude fluctuations and excellent pulse stability of the mode-locking operation. The inset of the Fig. 4(b) illustrates a periodically damped modulated RF spectrum with a broad scanning range of 0.8 GHz and the RBW of 3 kHz. There is a modulation-frequency of ${f_m} = $ 0.2 GHz exerting on the measured RF spectral distribution, which agrees well with the produced native pulse duration of $\tau = $4.99 ns and satisfies a reciprocal relation of ${f_m} = 1/\tau $ [28]. It can be seen again that the NLPs and the RPs are operating in a reliable and perfect synchronization status.
Fig. 4. (a) pulse train; (b) RF spectrum measured at the fundamental repetition rate of 5.3680 MHz; (Inset) RF spectrum within 0.8 GHz.
Figure 5 reveals the evolution of the optical properties as a function of the pump power variation from 202 to 827 mW in detail. Figure 5(a) illustrates the spectral variation under different pump powers, which reveals the RP generation and enhancement with increasing pump power. When the pump power is less than 531 mW, the intensity of the Raman pulse is much lower than that of the main NLP component. After that point, due to the increasing Raman gain and the excess of main NLP energy, a higher efficient transfer of the main NLP to the RP is realized via the SRS process. And thus, the anti-Stokes Raman peak at ∼ 1076 nm increases more than the main NLP peak at 1028.8 nm as the pump power increases. With the increasing of the pump power, the enhancement of the RP intensity reaches to be ∼ 22 dB. At the maximum pump power of 827 mW, the intensity of the Raman component is almost at the same level as that of the main NLP component. It is found that the output spectrum of main NLP or the RP is blue-shifted during the increasing process. As the pump power changes, the double scale AC trace can always be observed, which indicates the operation always in the NLP state. Figure 5(b) illustrates the corresponding evolution of the coherent peak of the AC traces. The modulation depth of the beating is dependent on the intensity ratio of two pulses at the dual wavelength [29]. The closer the value of the intensity ratio is to 1, the deeper the modulation depth. As is depicted, the peak profile demonstrates apparent modulation at the maximum pump power of 827 mW, demonstrating the strong interaction between the NLPs and RPs. As the pump power decreases, the modulation depths of the NLP + RP complex become smaller while maintaining an unchanged pulse duration of ∼ 85 fs and pulse separation of ∼ 77 fs. And finally, the fringe pattern fades away thoroughly at the minimum pump power of 202 mW, since the intensity of the Raman component is much smaller than that of the main NLP. Figure 5(c) illustrates the single pulse profile under different pump powers. With the decrease of pump power, the whole pulse duration becomes narrower from 4.99 ns to 0.98 ns, the number of pulse splitting becomes less and it turns into a stable single pulse in the end.
Fig. 5. Optical properties under different pump powers: (a) optical spectra; (b) the coherent peaks of the AC traces; (c) pulse trains.
The measured output power of the NLP + RP complex and estimated RP component versus the pump power are shown in Fig. 6. It can be seen that although both the main NLPs and the RPs undergo the growth of the pulse energy, the main NLPs demonstrate a significant SRS conversion process when the pump power exceeds the expected Raman threshold. As the pump power increases, the proportion of the RP is gradually growing from ∼ 4% to ∼ 34%. And obviously, a sufficient Raman gain is provided to amplify the RP as the pump power increases. With the maximum pump power of 827 mW, the total average output amounted to 102.5 mW, which corresponds to a pulse energy of 19.1 nJ at 5.36 MHz repetition rate for the pulse complex. Considering 34% of the energy belongs to the RP, the pulse energy of the RP is estimated to be 6.5 nJ.
Fig. 6. The output power of the complex (in black) and NL-RP (in red) as a function of the pump power.
In order to further verify the influence of the SRS effect in the mode-locking process, two band-pass filters (filters A@1030 nm and B@1080 nm with the bandwidth of 8 nm and 5 nm respectively) are employed to split the main NLP and RP for the study of their properties. The measured characteristics of the separated pulses are shown in Fig. 7. It can be seen from Fig. 7(a) and Fig. 7(b) the optical spectrum has been split by filters into two spectral components: the fundamental component at 1030 nm and the Raman component at 1080 nm. The AC traces of both the separated main NLP and RP demonstrate a double-scale structure with a narrow peak riding on a broad pedestal, confirming these two pulses both operate in the noise-like regime. The corresponding coherent peaks of the AC traces of two spectral components have been measured, as demonstrated in Fig. 7(c) and Fig. 7(d), respectively. The pulse durations of the coherent peaks are 299 fs and 348 fs, respectively. It can be seen that the interference pattern has disappeared, indicating the single-wavelength pulse operation. As shown in Fig. 7(e) and Fig. 7(f), the single pulse profile is as the same as that directly from the cavity shown in Fig. 3(d) and indicates these two components inherit the original pulse state. The comparation between the direct and the separated output in the single pulse profile and the AC traces demonstrate the synchronization and coherence between the dual wavelength pulses.
Fig. 7. (a) Optical spectrum, (c) the AC trace, and (e) single pulse profile filtered by filter A; (b) optical spectrum, (d) the AC trace, and (f) single pulse profile filtered by filter B.
4. Summary
We have proposed and demonstrated the generation of multicolor NLP complex in a Yb-doped mode-locked fiber laser based on GIMF-SA. By proper adjusting the PC, stable dual-wavelength mode-locking pulses which consist of the main NLP and the cascaded RP are obtained in the noise-like operation regime. These dual pulses demonstrate the mutual synchronization and coherence with the emerging fringe pattern in the coherent peak of the AC trace. As the pump power changes, the intensity of the coherence changes as well. The results indicate that the Raman component participates in the mode-locking operation as a ‘signal’ instead of ‘noise’ and offer new possibilities for intra-cavity Raman soliton generation based on all-fiber SAs.
Funding
National Natural Science Foundation of China (61805225, 11804323).
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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