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Abstract
In this paper, we report for the first time on an all-multimode fiber spatiotemporal mode-locked figure-eight laser operating at 1.0 µm. This laser utilizes a multimode gain fiber and a nonlinear amplifying loop mirror mechanism. It can generate mode-locked noise-like pulses at different central wavelengths. Additionally, we observed the presence of a multi-soliton state within the cavity by reducing intracavity gain. This study contributes to a broader investigation of various pulse phenomena in spatiotemporal mode-locked lasers and provides valuable insights into further exploring the evolution of spatiotemporal dynamics in such systems.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
As a mature technology, mode-locked (ML) lasers have found extensive applications in various fields such as biomedicine, fiber communication, laser processing, terahertz technology and many others [1–4] . Single-mode fibers (SMFs) offer advantages like low loss, cost-effectiveness, and modal-free dispersion [5]. Therefore, mode-locked lasers based on SMFs have been fully designed and applied in the past decades. Due to the limited mode field area of SMFs, they struggle to fulfill the increasing demands for higher information capacity and power. Compared to SMFs, multimode fibers (MMFs) have larger mode field area and additional spatial degrees of freedom [6] . They are considered to be an important medium for solving these problems. In 2017, Wright et al. generated significant attention by realizing the first spatiotemporal mode-locked (STML) pulsed lasers by simultaneously locking the transverse and longitudinal modes using graded-index (GRIN) MMFs in an oscillator [7] . Following this breakthrough, extensive research on STML lasers has been conducted, leading to the successful design of various STML lasers with spatial and all-fiber structures.
All-fiber STML lasers offer the advantages of compactness and low loss when compared to spatial structures. As a result, various ML techniques have been implemented for all-fiber STML lasers. These methods include the utilization of carbon nanotubes (CNT) [8], and semiconductor saturable absorption mirror (SESAM) [9,10] as real saturable absorbers (SA), nonlinear polarization rotation (NPR) effect [11,12], and nonlinear amplifying loop mirror (NALM) [5,13,14] as artificial SA. Comparatively, artificial SA mainly rely on the nonlinear effects within the fiber to achieve saturable absorption, offering a high damage threshold. Consequently, they are more conducive to generating high-energy pulses. While STML lasers based on the NPR effect have been widely reported, there is a relative scarcity of STML lasers based on NALM. Currently, STML lasers based on NALM technology are primarily focused on few-mode fibers (FMF) [5,13]. To the best of our knowledge, there is only one literature report on a MMF STML laser, but it is based on a few-mode gain fiber [15]. Compared with few-mode fibers, multimode fibers can support more transverse modes, which makes the nonlinear dynamics between modes in multimode fibers more complex, and as a result the establishment of STML in multimode fiber lasers more difficult [5,13,16]. Therefore, designing STML lasers with an all-multimode fiber structure based on multimode gain fibers and utilizing NALM technology can help further explore the potential of NALM technology.
On the other hand, various pulse phenomena in STML lasers have been extensively reported. These include soliton molecules [17], dissipative solitons [18], multiple solitons [19], dispersion-managed solitons [20,21], multimode solitons [22,23], dissipative soliton resonances [14,15], and amplified self-similar pulses [24], showcasing the potential of STML. Despite these advancements, there is a limited number of studies on noise-like pulses (NLP) in STML lasers [25].
In this work, we present the design of an all-multimode fiber STML laser, utilizing multimode gain fiber and nonlinear amplifying loop mirror (NALM) technology. We have successfully generated NLP mode-locking operations, and the central wavelength can be modulated by adjusting the pump power and intra-cavity polarization. Additionally, we observed the presence of a multi-soliton state within the cavity by reducing intracavity gain. The obtained results help to enrich the study of pulse phenomena in STML lasers and further elucidate the nonlinear dynamical processes in STML lasers.
2. Experimental setup
The schematic of this experimental design is depicted in Fig. 1, where the laser employs the NALM to achieve STML operation. The entire system is pumped by a semiconductor laser with an output wavelength of 976 nm. Connecting the NALM to the unidirectional ring (UR) is a 2 × 2 multimode optical coupler (OC, fused pull-cone type) with a coupling ratio of 50:50. A 90-cm segment of step-index ytterbium-doped fiber (STIN YDF, Nufern LMA-YDF-20/125-9 M) serves as the gain medium, capable of accommodating approximately six modes with a numerical aperture (NA) of ≈0.08. The pump light is coupled into the cavity through a multimode combiner.
Fig. 1. Experimental setup. Combiner, pump beam combiner; YDF, step-index ytterbium-doped multimode fiber; PC1 and PC2, polarization controllers; Filter, spectral filter; 50/50 OC, 2*2 optical coupler; PD-ISO, polarization-dependent isolator; 20/80 OC, 1*2 optical coupler.
The NALM consists of a YDF, a combiner, a polarization controller (PC), and a multimode interference-based filter; PC is used to manipulate the polarization state of laser, and the filter is used to balance the modal dispersion in the cavity. In the UR, in addition to the PC, there is a polarization-dependent isolator (PD-ISO) with a function to maintain the unidirectional transmission of laser. 20:80 OC is used to extract 20% of the laser light to test the laser performance. In the whole optical path, the combiner and the PD-ISO pigtails are passive step-index fiber (Nufern LMA-GDF-20/125-M) matched with YDF, and the specific structure of the filter [18,26] is shown in Fig. 1. Its bandwidth is about 10 nm. The rest of the part of the fibers are graded-index multimode fibers (OM4, 50/125). The cavity length of the whole laser is about 15.6 m, and part of the fiber is properly bent and coiled into a circle to save space. The introduction of the filter further increases the asymmetry in NALM, accumulating a sufficient nonlinear phase shift difference in both loops. And high gain and reverse saturation absorption help to realization NLP mode-locking [25]. Mismatched fusion splices between fibers with different core diameters play a role in spatial filtering to a certain extent [15]. Cooperating with the filter and the filtering function that NALM itself has, the balance of nonlinearity, dispersion, gain and loss is successfully achieved [5]. It is very important for the realization of STML state.
The experimental data were obtained by observing the pulse trains with a fast InGaAs photodetector (Thorlabs, DET08C/M) with 5 GHz bandwidth and a digital oscilloscope (LeCroy WavePro 7300A) with 3 GHz bandwidth. Spectrum were measured by a spectrum analyzer (ANDO, AQ6317B). The output pulse train was analyzed in the frequency domain by an Agilent N9020A RF analyzer (10 HZ ∼ 3.6 GHz). The autocorrelation (AC) trace of the pulse was measured by an intensity autocorrelator (Femtochrome, FR-103XL).
3. Results and discussions
3.1 All-multimode fiber spatiotemporal mode-locked figure-eight laser
The thresholds for continuous-wave (CW) output are quite high owing to losses stemming from mismatched fusion points and spatial filters in the optical path. The laser starts to generate CW when the pump power is increased to 1.4 w. With a further increase in pump power, pulse envelopes similar to Q-Swtiched mode-locking (QSML) occurs. By progressively increasing the pump power to 4.6w, while making a simple polarization controller (PC) adjustment, the laser achieves a stable NLP mode-locking state at a fundamental frequency repetition rate of 13.22 MHz. To ensure the safety of the device, the pump is adjusted within a range of 5 watts during the experiment. Figure 2(a) displays the pulse sequence measured at 5µs/div, with a selected portion presented in Fig. 2(b). At this pumping power, the laser achieves an average output power of 53.4 mW, and the corresponding single-pulse energy of the wave packet is 4.06 nJ. Figure 2(c) shows the variation of average output power and single pulse energy with pump power in NLP mode-locking regimes, showcasing a linear increase with pump power.
Fig. 2. Typical pulse train at (a) 5 µs/div and (b) 103 ns/div, monitored by an oscilloscope, with a pump power of 5.0W. (c) Average output power (black line) and single-pulse energy (red line) versus pump power in NLP mode-locking state.
Figure 3(a) shows the radio frequency (RF) spectrum around the fundamental repetition frequency of 13.22 MHz, observed at a 10 Hz resolution bandwidth (RBW). With a signal-to-noise ratio (SNR) of 43 dB, it is evident that there is a pair of distinct symmetric spectral sidebands around the fundamental repetition frequency, indicating the presence of random peak modulation in the mode-locked pulse [27,28]. This noise pedestal is typical of NLP mode-locking. The inset of Fig. 3(a) provides the RF spectrum in the 1 GHz range, measured at 100 Hz RBW, revealing the uniform intensity pattern of the pulses. Figure 3(b) exhibits the autocorrelation (AC) trace measured using an autocorrelator, which presents as a spike riding on a broad base. This feature is typical of noise-like pulses, confirming the presence of NLP mode-locking [29]. Figure 3(c) illustrates the linear spectrum before and after the establishment of the NLP mode-locking state. Additionally, the logarithmic scale spectrum of the NLP mode-locking state is also measured, displayed in Fig. 3(d). In this state, the central wavelength of the output laser is 1046 nm.
Fig. 3. Various parameters of the laser: (a) RF spectrum with 80kHz span at 10 Hz resolution bandwidth; the inset is the RF spectrum in the 1 GHz range measured at 100 Hz resolution. (b) Autocorrelation traces in NLP mode-locking state. (c) linear spectrum before and during NLP mode-locking. (d) Measured spectrum in log scale before and during NLP mode-locking.
The characterization of the beam profile is a crucial aspect in STML lasers [12]. We employ a CCD camera (Beam on U3) for beam profile measurements. Specifically, Fig. 4(a) and Fig. 4(b) show the beam profile before and during the NLP mode-locking state, respectively. Notably, The laser's output beam profile exhibits complexity due to the additional transverse mode degrees of freedom in the MMFs [13]. The beam profile undergoes significant changes upon the establishment of the NLP mode-locking state, primarily due to the transfer of energy between modes that occurs during NLP mode-locking [30,31].
Fig. 4. Sampling results of beam profile: Beam profile (a) before and (b) during NLP mode-locking. (c) Spectrum corresponding to the sampling points (S1, S2, S3) shown in (a). (d) Spectrum, (e) RF spectrum and (f) pulse train corresponding to the sampling points (S1, S2, S3) shown in (b).
In order to characterize the temporal features, spectrum, and RF spectrum at specific locations within the beam profile, the beam profile is sampled at marked points (as shown in Fig. 4(a) and (b)). Figure 4(c) and Fig. 4(d) show the spectra sampled at different positions within the beam profile before and during the NLP mode-locking state. Differences in the spectra at these sampling points indicate variations in the frequency components of the beam profiles, providing evidence for the existence of different transverse modes [32]. Moreover, Fig. 4(e) and Fig. 4(f) display the RF spectrum and pulse trains corresponding to various positions within the beam profile during the NLP mode-locking state. These observations offer compelling evidence that different transverse modes are simultaneously in a mode-locked state [6,12,32].
In this system, the fusion splicing of fibers with different core diameters introduces a multimode interference effect [13,26]. This effect, combined with the wavelength-dependent filtering function inherent in NALM, makes it possible to achieve switchable laser center wavelengths. By adjusting the pump power and carefully tuning the PCs, the nonlinearity, loss, gain, and dispersion of the total system are balanced [5,15]. As a result, during the experiment, the NLP with center wavelengths of 1034 nm, 1039 nm, and 1046 nm are realized, respectively. The corresponding spectra, along with their respective beam profiles, are illustrated in Fig. 5.
Fig. 5. NLP mode-locking state at different wavelengths: (a) spectrum at 1040 nm; (b) spectrum at 1044 nm; (c) spectrum at 1074 nm; and (d)–(f) the corresponding beam profiles.
Zhou et al. describes, through numerical simulations and experiments, the evolution of pulse states from solitons to noise-like pulses in a normal dispersive cavity with increasing cavity gain [33]. In turn, we subsequently reduced the intracavity gain by decreasing the pump power and increasing the output coupling ratio to 30%. Consequently, a stabilized soliton state is observed at a pump power of 3.4W. The various parameters of the soliton state are shown in Fig. 6.
Fig. 6. Various output parameters of multi-soliton state: (a) the beam profile; (b) the pulse train; (c) the autocorrelation trace; and (d) the measured spectrum.
Figure 6(a) illustrates the beam profile in the soliton state, which exhibits obvious multimode characteristics. The pulse trains and autocorrelation traces are shown in Figs. 6(b) and (c), respectively. From the autocorrelation trace, it can be seen that this is a this is a multi-soliton state [34]. It should be noted that the autocorrelation trace is incomplete due to the limitation of the autocorrelator range. Therefore, we cannot determine the exact number of solitons present. The corresponding linear spectrum, shown in Fig. 6(d), exhibits distinct modulation fringes resulting from the interference between the transverse modes [13]. It should be noted that the center wavelength corresponding to this state is distinctly different from the previous results. This phenomenon can be attributed to changes in intracavity gain and polarization state, allowing the new wavelength to gain a competitive advantage in the gain competition [9,35].
4. Conclusion
In conclusion, we have successfully designed and constructed an all-multimode fiber spatiotemporal mode-locked figure-eight laser using a multimode gain fiber. It operates at 1µm with NALM technology. Additionally, we obtained NLPs with three different central wavelengths by adjusting the pump power and the intracavity polarization state. Additionally, we observed the presence of a multi-soliton state within the cavity by reducing intracavity gain. This work will contribute to the advancement of research on various pulse phenomena in STML lasers and offer a new platform for gaining deeper insights into the nonlinear dynamical processes within STML lasers.
Funding
Beijing Municipal Natural Science Foundation (4212052); Fundamental Research Funds for the Central Universities (2022YJS128, 2019JBM069); National Natural Science Foundation of China (61735005, 61935010).
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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