We demonstrate the tunable Raman femtosecond solitons generation with a record-breaking power of 1.2 W at 2.3 µm and an ever-reported highest Raman soliton energy conversion efficiency of 99% via precise seed-pulse management in the thulium-doped single-mode fiber amplifier. We find that the central wavelength and the chirp of the incident pulses could dramatically affect the red-shifted soliton energy, locations, conversion efficiency, and the threshold power in fundamental Raman soliton generation. For the first time, we experimentally illustrated how the seed pulse with Kelly sidebands could affect the Raman solitons generation in this amplifier, and obtained the detailed regularity between the parameters of incident pulses and the properties of the generated solitons. This work provides useful guidance for Raman soliton-based high-power mid-infrared femtosecond laser fabrication.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
High-power, wavelength-tunable mid-infrared femtosecond pulsed lasers attract great attention in applications such as gas detection, surgery, multi-photon spectroscopy and attosecond- science [1–4]. At present, there are lots of excellent works on the wavelength tunable 2-µm mode-locked laser. However, limited by the gain spectral width of thulium ion , mode-locking is no longer the effective way for wavelength tuning in 2-µm band. More effective ways were extensively explored in the past decades. In 1986, Mitschke et al. firstly verified the soliton self-frequency shift (SSFS) effect in fibers , many related theories and applications on this effect were then widely explored . Especially in the mid-infrared region, many researchers have made great contributions, such as using silica fibers [8–11], germanium doped core with silica cladding fibers [12–16], fluoride fibers [17–19] and tellurite fibers [20,21] for long-wave Raman solitons generation. Compared with non-silica-based fiber, Raman solitons generation in silica-based fiber is a reliable way to achieve a more compact all-fiber system. Silica fiber has a lower cost, high damage threshold, and lower nonlinearity, supporting pulses with higher energy and average power . Tm-doped fiber amplifiers (TDFA) were demonstrated available for both power amplification and Raman frequency shift in 2-µm band, which has great potential for long-wave watt-level femtosecond solitons generation. Luo et al. demonstrated an SSFS-based tunable laser ranging from 1.98 to 2.31 µm and energy conversion efficiency up to 97% in a TDFA system by optimizing the chirp of input pulses . Liu et al. used the sideband-suppressed mode-locked solitons to seed a Tm-doped fiber amplifier, confirmed that by suppressing of seed laser sidebands, the Raman solitons wavelength tuning range and energy conversion efficiency could be both well improved . Wang et al. achieved a tunable laser covering 1.9-2.36 µm in a dispersion-managed and mode-locked pulse seeded TDFA, the obtained maximum conversion efficiency was as high as 97%, and soliton average power at 2.29 µm was up to 1.16 W .
These pioneering works with persuasive results on TDFA based Raman solitons generation system for reference. However, their works one-sidedly focused on how some factors affect the generated solitons characteristics, and lack of regularity and systematicity. Besides, there is no report exploring how the seed laser wavelength could affect the SSFS in amplifiers.
In this work, by developing a wavelength tunable nonlinear polarization rotation (NPR) mode-locked oscillator, we explored how the key factors, including the seed-laser central wavelength and chirp can affect the SSFS effect in the TDFA system. We find that the changes of abovementioned factors could greatly influence the soliton energy conversion efficiency, the Raman soliton generation threshold (RSGT), and the most red-shifted soliton wavelength locations. Meanwhile, the physical nature of why the seed-laser central wavelengths can affect the Raman soliton characteristics is the gain spectrum induced Kelly sideband suppression effect in amplifier was revealed. Moreover, the pronouncement of the right amount of negative chirp in seed pulse is helpful for Raman solitons long-wavelength extension, and conversion efficiency improvement in amplifier was also confirmed in experiment. In the light of these conclusions, we achieved the highest soliton conversion efficiency of 99% in soliton shifting from 1.9 µm to 2.35 µm, and the highest soliton power of 1.2 W at 2.3 µm.
2. Experimental setup
Figure 1 shows the schematic of the experimental setup, which is consisted of an NPR mode-locked oscillator, a one-stage TDFA, and a UNHA4 fiber-based pulse nonlinear compressor. The oscillator is constituted by a 0.18 m-long highly Tm-doped fiber (TDF, Nufern SM-TSF-5/125), an NPR structure with a half waveplate, a PBS (polarization beam splitter), two quarter waveplates, and a polarization-dependent optical isolator (PD-ISO) to keep the light unidirectional transmission. The laser system is pumped by an erbium-doped CW fiber laser (EDFL) operating at 1560 nm with the maximum output power of 3 W. A 1560/1970 nm wavelength division multiplexer is used for cavity power coupling. To simplify the cavity, the PBS reflection beam also acts as the energy output port. The total cavity length is estimated to be 3.85 m, including the device pigtails and free space distances. In addition, a 10/90 beam splitting mirror was adopted ahead of the amplification stage, the 10% port is for pulse monitoring, and the 90% port is for seeding the amplifier.
For the incident pulse chirp adjustment, a piece of SMF28e was arranged between the oscillator and TDFA, followed by an optical isolator to prevent the back reflection light from disturbance of mode-locking stability. The amplifier with a forward pumping regime, is comprised by a high-power optical combiner and a section 4.5 m-long double-clad Tm-doped fiber (Nufern, SM-TDF-10P/130). The pump is a 793-nm LD with maximum output power of 50 W. For residual pump light striping, a 20 cm-long SMF28e was followed by the TDFA. The resulting Raman soliton pulses nonlinear compression was performed in the UHNA4 and SMF28e fibers. The fiber output port was processed with an 8-degree angle using a special optical fiber cleaver (Vytran, LDC401A) to prevent the Fresnel reflection. The fusion splicing points in TDFA were fixed on the aluminum heat sink by using refractive index-matching UV adhesive.
In pulse performance characterization, the output pulse train was detected by a 2-µm InGaAs PIN photodetector (EOT, ET-5000F) with 10 GHz bandwidth, connected with a 2.5 GHz digital oscilloscope (OSC, Yokogawa DLM2054). The output spectrum was measured by a spectrum analyzer (OSA, Yokogawa AQ6375) with a resolution of 0.05 nm, its response spectral bandwidth covering 1.2-2.4 µm. Radio frequency (RF) spectrum of seed pulse was read and displayed by an RF spectrum analyzer (FSA, Keysight N9000B) with a frequency detector ranging from 9 kHz to 7.5 GHz. Further, an intensity autocorrelator (Femtochrome research, FR-103XL) was employed to check the pulse duration. The average output power of the oscillator and the amplifier was gauged by an integrated sphere sensor power meter (Thorlabs, S140C) and thermal power sensor power meter (Thorlabs, S442C), respectively.
3. Experimental results and discussion
3.1 Wavelength tunable seed pulse in oscillator
Combined with the adjusting of wave plates, a stable self-starting mode-locking is realized when the pump power is increased to 1.1 W. The corresponding output power is measured about 22.2 mW, and the pulse spectrum is shown in Fig. 2(a). We can see that the full width at half maximum (FWHM) and central wavelength of the spectrum location are 6.2 nm and 1932 nm, respectively. Once the mode-locking is started, the pump power can be reduced to 0.91 W without losing mode locking. Limited by the peak power  and the effect of soliton energy quantization , multiple pulse will be formed when the pump power exceeds 1.31 W. Figure 2(b) shows the pulse autocorrelation traces, the pulse with a width of around 660 fs, a time-bandwidth product (TBP) of 0.328, close to the Fourier transform limit. Figure 2(c) shows the pulse train with a pulse interval of 19.14 ns, corresponding to the fundamental frequency of 52.25 MHz. Figure 2 (d) shows that the pulse signal-to-noise ratio (SNR) is as high as 77 dB, indicating excellent mode-locking stability. The RF spectrum in a 1-GHz span shows a pure mono-pulse operation state.
When the pump power is increased to 1.1 W, the pulse central wavelength tuning can be realized by slightly rotating the waveplates in the NPR structure. The continuous wavelength tuning ranges are available from 1896 nm to 1965 nm, covering nearly 70 nm is shown in Fig. 3(a). All spectra show strong Kelly sidebands, which means the oscillator operates in the soliton-based mode-locked regime. The formation of solitons is due to the balance of intracavity nonlinearity and dispersion [28,29]. We measured its SNR and spectral drift within half an hour at each wavelength. We found no obvious changes (fluctuation within 0.1 nm, the optical spectrum analyzer with a resolution of 0.05 nm), the tunable seed-pulse running with high stability. Figure 3(b) shows the spectral width and pulse duration at different wavelengths over the entire tunable range. The FWHM of the spectrum varies slightly from 6.15 nm to 6.94 nm, and the corresponding pulse duration fluctuates between 590 fs and 689 fs, indicating that the spectral width and pulse duration have slight deviation at different wavelengths.
3.2 SSFS process of seed pulse at different central wavelengths in TDFA
To explore the effect of seed laser with different central wavelengths on the Raman soliton generation in TDFA, and to simplify the analysis, four representative wavelengths of 1.96 µm, 1.94 µm, 1.92 µm, and 1.9 µm were selected. The pulses’ corresponding SNRs are 73.6 dB, 74.5 dB, 76.5 dB and 75 dB, and output power were optimized to 21.2 mW, 20.5 mW, 22.1 mW and 19.3 mW, respectively. This ensured that the pulses with high mode-locking stability at these wavelengths and their average power with small differences. The seed-pulse central wavelength in the context is denoted as λs. The length of SMF28e before TDFA is set as 1 m for a readily pulse chirp optimization in the following experiments. The Raman soliton energy conversion efficiency is defined as the ratio of the red-shifted soliton power to the total signal power. In our research, it was measured by filtering the red-shifted solitons out and was then confirmed using spectral integral method. To clearly show and comparatively analyze the soliton evolution and the variation of pulse spectral components in TDFA at different seeding wavelengths, the pulse spectral intensities in Fig. 4 are normalized in each pump condition, and the intensity in each figure of Fig. 5 are uniformly normalized by the maximum intensity value. We can see from Fig. 4(a) that when λs is at 1.96 µm, with the increases of pump power, at the beginning, the soliton sidebands were rapidly amplified while the main pulse energy getting relatively smaller, even the pump power is as low as 1.1 W. Continue to increase the pump power to 3.9 W, as shown in Fig. 5(a), the pulse sidebands on the left side and the main pulse gradually disappeared in the spectrum, the amplitude of the right sidebands are rising apparently. This trend keeps until the pump power is increased to 6.3 W. In this pump condition, the first order soliton appears, which means the initiation of the SSFS effect. With the enhancement of the pump power, solitons nonstop move to longer wavelengths. However, in this process, the right sidebands of the original seed pulse are still there. Figure 5(a) shows the pulse right sidebands intensities experienced a process of a linearly increase initially when pump power increased from 1.1 W to 6.3 W, then remained unchanged when pump power is varied between 6.3 W to 8.4 W, and a gradual increase with the continuous promotion of pump power. With the adjusting of the seeding laser to shorter wavelengths, in comparison, we can see from Fig. 4(b), (c) and (d) that the solitons generation threshold, frequency shift efficiency, soliton energy, and the longest soliton wavelength were also greatly changed. The overall trend is with the moving of seeding wavelengths to 1.94 µm, the fundamental soliton generation threshold increased to 7.0 W, and the red-shifted soliton energy and efficiency experienced an increase first and then decreased. The most striking difference is the sidebands variation, as seen from Fig. 4(b) and Fig. 5(b). The rollercoaster-type sidebands intensity variation indicates an intense energy transformation and competition among pulse spectral components. With the variation of pulse sidebands intensity and the increase of the pump power, the shifted soliton energy also changes accordingly. While the seeding wavelength is adjusted to 1.92 µm, the soliton power proportion and the pulse spectral variation can be seen in Fig. 4(c) and Fig. 5(c). Compared with the results in Fig. 4(b) and Fig. 5(b), we can find that the changes in most red-shifted soliton location, the soliton energy, and the sidebands intensity fluctuation could be viewed clearly. It is worth mentioning that with the seeding wavelengths getting shorter, the most remarkable difference in Raman solitons generation is the soliton energy ratio improvement greatly, especially in moderate pump power conditions. This trend is more apparent while the seeding wavelength was shifted to 1.9 µm. As is shown in Fig. 4(d) and Fig. 5(d), the sidebands of the seeding pulse are well inhibited with the scaling of pump power. Meanwhile, the proportion of soliton energy in pulses was significantly improved when the pump increased from 10 W to 13 W, and the corresponding energy conversion efficiency can reach as high as 97%. The maximum soliton energy is up to 22.9 nJ. In addition, aided by the mechanism mentioned above, the most red-shifted soliton wavelength is well extended to 2.324 µm. However, the continued increase of pump power to 16.2 W resulted in the rise of the second-order solitons and residual pump energy. Besides, the fundamental soliton conversion efficiency is not further improved anymore. In addition, the tendency of soliton pulse energy attenuation is mainly due to the intensified fiber loss in the long-wavelength region and the distance from the gain band of Tm3+ ion.
The comparative analysis shows that the pulse Kelly sidebands can seriously affect the Raman frequency shift efficiency and the most red-shifted soliton positions. This conclusion was also confirmed by using a Lyot filter to suppress the Kelly sideband for high-efficient Raman solitons generation . However, in our experiment, the Kelly sideband suppression mechanism is very different from the hard spectral cutting.
Figure 6 shows the measured amplified spontaneous emission (ASE) spectra of Tm3+-doped double-clad single-mode silica fiber in different pump powers at 793 nm. The ASE spectral range and intensity vary with the changes in pump power. For comparison, the pulse spectra with different central wavelengths and the generated ASE spectra under different pump powers were presented in the same picture. The seed-pulse spectra locate at different positions in the ASE spectrum. We can find that with the blue-shift of the seed laser central wavelengths, the seed laser spectrum gradually creeps away from the high ASE region. Therefore, in the laser amplification, with the vary of locations of sidebands and the distribution of fiber gain, the amplification of spectrum components is selective. The components that are located at the high gain region will be amplified in priority and more rapidly. This results in the selective inhibition or amplification of seed-pulse sidebands in the TDFA, and forms the naturally spectral shaping effect. This comprehensive mechanism led to the differences in pump-wavelength induced SSFS effect in TDFA. To confirm that the seed-pulse wavelength is the exclusive factor that can greatly affect the SSFS effect in TDFA, some other causes that can potentially affect this nonlinear process, including the input pulse power, pulse duration, pulse SNR, and pulse spectral bandwidth were intentionally managed in the experiment. The fluctuations of these parameters were controlled within a very small range. Moreover, the dispersion differences at each wavelength (showing in Fig. 6) were also considered, its GVD values are -0.0689 ps2/m, -0.0712 ps2/m, -0.0732 ps2/m, and -0.0756 ps2/m, respectively. The variation of Kelly sidebands’ intensity in amplifier is mainly due to the competition between the main pulse spectral components and sidebands for pump energy. This process can be divided into three stages. In the first stage, when the pump power at 793 nm was gradually increased to the appearance of the first-order Raman soliton, all the signal pulse spectral components were synchronously amplified, including the sidebands. However, since the Kelly sidebands are located at the high gain coefficient region, its intensity increasing speed is higher than that of the main pulse components. In the second stage, as the pump power increases, most of the original pulse energy of the signal light is converted to the first-order Raman soliton with a longer wavelength. The well overlapping of the red-shifted soliton pulse spectrum with the peak of the gain curve leads to the rapid boosting of soliton energy, resulting in the relative weakening of the Kelly sidebands’ intensity. In the third stage, with the continuous wavelength red-shifting of the first-order Raman solitons, its spectrum location gradually far from the high gain region of the thulium ion. However, the sidebands are still there, and their intensity rapidly increases with the nonstop pump energy injection.
The detailed effects of seed-pulse central wavelength on the conversion efficiency and output power of Raman solitons are shown in Fig. 7(a). Figure 7(a) shows the soliton average power and conversion efficiency variation with the soliton wavelengths in TDFA at different pump wavelengths. We can see that with the incident pulse wavelength shifts from 1.96 µm to 1.9 µm, the overall tendency of the Raman solitons output power shows an uptrend, and the conversion efficiency presents a tendency to increase in short and then decline in the long-wavelength region. This trend is more apparent in long-wavelength seeded conditions. Since the soliton power is closely related to efficiency, the Raman soliton power shows a similar trend. The main difference is the power in short seeding wavelength is linear increase with Raman soliton wavelength extension while it is a parabolic distribution at seeding wavelength of 1.96 µm. The falling tendency in the power and efficiency curves at the long-wavelength edge is mainly due to the non-soliton radiation , the emerging of second-order solitons and the increase of fiber loss. Moreover, the position of inflection points is very different, and the shorter the seeding wavelength, the longer the turning wavelength. This is very similar to the reported results [24,25]. It is worth mentioning that when seeding at 1.9 µm, the obtained maximum Raman soliton power is as high as 1.2 W at 2.3 µm, the corresponding pulse energy up to 22.9 nJ, and the energy conversion efficiency exceeds 90% in the range of 1.9-2.3 µm.
The fundamental soliton RSGT is also a critical factor in Raman soliton generation. On most occasions, we expect a single fundamental soliton with high power and enough energy for applications. However, with the increase of pump power, the emergence of higher-order solitons will degenerate the properties of fundamental solitons. In Fig. 7(b), the experimental results show that the RSGT is closely dependent on the seeding wavelengths. The overall trend is RSGT decrease with the increase of seeding wavelength. Therefore, in our experiment, the highest threshold power is 9.3 W when seeding at 1.9 µm.
3.3 Influence of seed pulse chirp on SSFS
Along with the seed laser wavelengths, the pulse chirp also has a great effect on the Raman solitons generation. For a systematical exploration, the SMF28e between the oscillator and amplifier is designed for seed-pulse chirp adjustment in our experimental scheme. The central wavelength of the incident pulse is 1.9 µm, and the pulse chirp has a linear relationship with the length of SMF28e, which is calculated based on the SMF28e dispersion of -0.067 ps2/m. When the initial pulse is unchirped and the pulse profile is sech2 type, the calculation of chirp coefficient can be referenced from . Limited by the length of the device pigtail, chirp variations can be adjusted from -0.0179 to -0.185. In Fig. 8(a), when the chirp value C increases from -0.0179 to -0.185 (the chirp value changes step is around 0.006), we recorded the fundamental soliton RSGTs and the maximum red-shifted soliton wavelength. As seen from Fig. 8(a) and Fig. 8(b), with the increase of pulse chirp value C, the RSGT increases from 8.1 W to 12.9 W, and the fundamental Raman soliton most red-shifted wavelength decreases from 2.35 µm to 2.265 µm. The results show that when pulse chirp variation within a certain range, the smaller the chirp value, the lower the RSGT and the wider the fundamental soliton frequency shift range. However, while the C value decreased to a certain value of -0.036, and varies from -0.0179 to -0.036, the maximum Raman soliton frequency shift position decreases with the lowering the chirp value. Figure 8(b) shows the change of Raman soliton conversion efficiency at different soliton wavelengths when chirp value C is increased from -0.0179 to -0.185, finding that the impact of chirp on the soliton conversion efficiency of short-wave Raman solitons is smaller than that of long-wave Raman solitons. When the Raman soliton wavelengths are below 2.28 µm, the efficiency in most chirp values can reach above 90%, and it smoothly decreases with the increase of C. However, the trend changes remarkably when the central wavelength of Raman soliton is located at 2.3 µm. This indicates that the Raman soliton wavelength and soliton conversion efficiency can be improved by optimizing the seed-pulse chirp. An optimal chirp value is beneficial for the high-quality Raman soliton generation. In addition, this experiment also confirmed the view point that a moderate negative pre-chirp improves their Raman displacement efficiency, which had been verified in Ref. [31,32].
When C is optimized to -0.036, we obtained the most red-shifted Raman soliton wavelength of 2.35 µm. The relationship between the Raman solitons wavelength shifting and the 793 nm pump power is shown in Fig. 9(a). Compared with the results in Fig. 9(a) with Fig. 4(d), we can learn that by optimizing the incident pulse chirp, one can significantly improve the soliton conversion efficiency to 99% at 2.14 µm, the efficiency is above 92.3% in 1.9-2.3 µm region, and can simultaneously assist the most red-shifted soliton extension to 2.35 µm. In this case, the RSGT lowered to 8.2 W, and the maximum soliton power reduced to 1.06 W accordingly. Combined with the Raman soliton conversion efficiency and power variation curves in Fig. 9(b), in the region of wavelength beyond 2.3 µm, a tendency of dramatical decline of power and efficiency is presented. This is mainly due to the appearance of higher-order solitons and the increase of fiber loss. Therefore, it is concluded that the optimal chirp value of incident pulse is helpful for realizing the high-power and broadband Raman soliton with a wide tuning range. The further exploration of the Raman soliton pulse duration and spectral width at different central wavelengths is shown in Fig. 9(c). The pulse width varies between 241 and 432 fs, and the FWHM of the corresponding spectral width varies between 19.22 and 27.67 nm. The results clearly show that the pulse width increases and the spectral width decrease with the soliton moves to longer wavelengths. When the pulse shape is assumed to be Gaussian, the estimated results show that the output Raman soliton pulses are in the vicinity to the Fourier transform limit.
To achieve a narrower pulse width at 2.3 µm, we tried to conduct a nonlinear compress of the 2.3-µm Raman soliton by using a 35-cm-long UHNA4 fiber. This fiber has a small (0.053 ps2/m) normal dispersion at 2.3 µm. In Fig. 10(a), we can see a typical self-phase modulation (SPM) effect dominated fourfold (from 20.6 nm to 81 nm) spectrum broadening happened in this process. The broadened spectrum makes it possible for a narrower pulse duration compression. Meanwhile, a section of SMF28e is adopted as the compressor. As a result, the pulse is compressed from 389 fs to 230 fs when the pulse shape is assumed to be Gaussian, as shown in Fig. 10(b). Although the pulse duration is still longer than the Fourier transform limit, further compression is possible by using a prism-based or grating-based compressor.
In the past few years, many researchers have done excellent work on SSFS in TDFA, which provides useful references for us, as listed in Table 1. In comparison, our work provides a more systematic analysis of Raman solitons generation in TDFA. It has distinct advantages in soliton conversion efficiency, soliton power, and most red-shifted pulse wavelength.
In conclusion, we developed a compact Tm-doped NPR mode-locked and wavelength-tunable femtosecond pulse laser as a seed to systematically explore the Raman solitons generation in different seeding pulses. We found that the seed laser wavelength and pulse chirp could significantly impact the generated Raman solitons, including conversion efficiency, pulse energy, fundamental soliton generation threshold. Meanwhile, some conclusive results were also obtained. To further explain the dramatic effects of seed wavelength positions on Raman solitons, we experimentally demonstrated that the gain spectrum of Tm3+ ion could potentially inhibit the sidebands of the seed pulse and then naturally modulate the red-shifted Raman solitons. These experimental conclusions and the achieved regularities show us a clear figure on how the seed laser can affect the generated solitons. Moreover, it helped us in the realization of broadband (1.9-2.35 µm) and high efficiency (99%) tunable pulses generation in TDFA. Eventually, the 2.3-µm Raman soliton duration was nonlinearly compressed from 389 fs to 230 fs, and a fourfold broadened pulse spectrum was obtained simultaneously by using a UHNA4 fiber and an SMF28e combined structure. This confirms the availability for high-power and broadband tunable laser fabrication using SSFS technology in the TDFA system.
National Natural Science Foundation of China (61627815, 61905126, 62090064); Natural Science Foundation of Zhejiang Province (LQ21F050005); K. C. Wong Magna Fund in Ningbo University.
The author declares no conflicts of interest related to this article.
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.
1. J. E. Bertie and Z. Lan, “Infrared intensities of liquids XX: The intensity of the OH stretching band of liquid water revisited, and the best current values of the optical constants of H2O(l) at 25°C between 15,000 and 1 cm−1,” Appl. Spectrosc. 50(8), 1047–1057 (1996). [CrossRef]
2. G. M. H. Berlien, Applied Laser Medicine, (Springer-Verlag, 2003).
3. A. B. Seddon, “Mid-infrared (IR)-A hot topic: The potential for using mid-IR light for non-invasive early detection of skin cancerin vivo,” Phys. Status Solidi 250(5), 1020–1027 (2013). [CrossRef]
4. P . Agostini and L. F . DiMauro, “The physics of attosecond light pulses,” Rep. Prog. Phys. 67(6), 813–855 (2004). [CrossRef]
5. S. D. Jackson and T. A. King, “Theoretical modeling of Tm-doped silica fiber lasers,” J. Lightwave Technol. 17(5), 948–956 (1999). [CrossRef]
6. F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11(10), 659–661 (1986). [CrossRef]
7. G. P. Agrawal, Nonlinear Fiber Optics, (Academic, 2001).
8. D. Klimentov, N. Tolstik, V . V . Dvoyrin, R. Richter, and I. T. Sorokina, “Flat-top supercontinuum and tunable femtosecond fiber laser sources at 1.9-2.5 µm,” J. Lightwave Technol. 34(21), 4847–4855 (2016). [CrossRef]
9. J. Z. Wang, S. H. Lin, X. Y . Liang, M. M. Wang, P. G. Yan, G. H. Hu, T. Albrow-Owen, S. C. Ruan, Z. P. Sun, and T. Hasan, “High-energy and efficient Raman soliton generation tunable from 1.98 to 2.29 µm in an all-silica-fiber thulium laser system,” Opt. Lett. 42(18), 3518–3521 (2017). [CrossRef]
10. P. Wang, H. X. Shi, F. Z. Tan, and P. Wang, “Tunable femtosecond pulse source from 1.6 to 2.3 µm with 100 kW peak power in an all-fiber system,” Chin. Opt. Lett. 14(9), 091405 (2016). [CrossRef]
11. B. Li, M. Wang, K. Charan, M. Li, and C. Xu, “Investigation of the long wavelength limit of soliton self-frequency shift in a silica fiber,” Opt. Express 26(15), 19637–19647 (2018). [CrossRef]
12. H. Delahaye, G. Granger, J.-T. Gomes, L. Lavoute, D. Gaponov, N. Ducros, and S. Fevrier, “Generation of 35 kW peak power 80 fs pulses at 2.9 µm from a fully fusion-spliced fiber laser,” Opt. Lett. 44(9), 2318–2321 (2019). [CrossRef]
13. Y . H. Li, T. J. Du, B. Xu, H. Y . Xu, Z. P . Cai, V . M. Mashinsky, and Z. Q. Luo, “Compact all-fiber 2.1-2.7 µm tunable Raman soliton source based on germania-core fiber,” Opt. Express 27(20), 28544–28550 (2019). [CrossRef]
14. E. A. Anashkina, A. V. Andrianov, M. Y. Koptev, V. M. Mashinsky, S. V. Muravyev, and A. V. Kim, “Generating tunable optical pulses over the ultrabroad range of 1.6-2.5 µm in GeO2-doped silica fibers with an Er:fiber laser source,” Opt. Express 20(24), 27102–27107 (2012). [CrossRef]
15. E. A. Anashkina, A. V . Andrianov, M. Y . Koptev, S. V . Muravyev, and A. V . Kim, “Generating femtosecond optical pulses tunable from 2 to 3 µm with a silica-based all-fiber laser system,” Opt. Lett. 39(10), 2963–2966 (2014). [CrossRef]
16. T. J. Du, Y . H. Li, K. J. Wang, Z. P. Cai, H. Y . Xu, B. X. V . M. Mashinsky, and Z. Q. Luo, “2.01-2.42 µm all-fiber femtosecond Raman soliton generation in a heavily germanium doped fiber,” IEEE J. Sel. Top. Quant. Electron. 25(4), 1–7 (2019).
17. S. Duval, J. C. Gauthier, L. R. Robichaud, P. Paradis, M. Olivier, V . Fortin, M. Bernier, M. Piché, and R. Vallée, “Watt-level fiber-based femtosecond laser source tunable from 2.8 to 3.6 µm,” Opt. Lett. 41(22), 5294–5297 (2016). [CrossRef]
18. Y . Tang, L. G. Wright, K. Charan, T. Y . Wang, C. Xu, and F. W. Wise, “Generation of intense 100 fs solitons tunable from 2 to 4.3 µm in fluoride fiber,” Optica 3(9), 948–951 (2016). [CrossRef]
19. Z. R. Li, N. Li, C. F. Yao, F. Wang, Z. X. Jia, F. Wang, G. S. Qin, Y . Ohishi, and W. P. Qin, “Tunable mid-infrared Raman soliton generation from 1.96 to 2.82 µm in an all-solid fluorotellurite fiber,” AIP Adv. 8(11), 115001 (2018). [CrossRef]
20. M. Y . Koptev, E. A. Anashkina, A. V . Andrianov, V . V . Dorofeev, A. F. Kosolapov, S. V . Muravyev, and A. V . Kim, “Widely tunable mid-infrared fiber laser source based on soliton self-frequency shift in microstructured tellurite fiber,” Opt. Lett. 40(17), 4094–4097 (2015). [CrossRef]
21. L. Zhang, T. L. Cheng, D. H. Deng, D. Sega, L. Liu, X. J. Xue, T. Suzuki, and Y . Ohishi, “Tunable soliton generation in a birefringent tellurite microstructured optical fiber,” IEEE Photonics Technol. Lett. 27(14), 1547–1549 (2015). [CrossRef]
22. S. D. Jackson, “Towards high-power mid-infrared emission from a fiber laser,” Nat. Photonics 6(7), 423–431 (2012). [CrossRef]
23. J. Q. Luo, B. Sun, J. H. Ji, E. L. Tan, Y. Zhang, and X. Yu, “High-efficiency femtosecond Raman soliton generation with a tunable wavelength beyond 2 µm,” Opt. Lett. 42(8), 1568–1571 (2017). [CrossRef]
24. F. Liu, J. Li, H. Luo, Q. Wu, X. Wu, F. Ouellette, and Y. Liu, “Study on soliton self-frequency shift in a Tm-doped fiber amplifier seeded by a Kelly-sideband-suppressed conventional soliton,” Opt. Express 29(5), 6553–6562 (2021). [CrossRef]
25. P. Wang, H. Shi, F. Zhou, and P. Wang, “Enhanced tunable Raman soliton source between 1.9 and 2.36 µm in a Tm-doped fiber amplifier,” Opt. Express 25(14), 16643–16651 (2017). [CrossRef]
26. E. R. Thoen, E. M. Koontz, M. Joschko, P. Langlois, T. R. Schibli, F. X. Kartner, E. P. Ippen, and L. A. Kolodziejski, “Two-photon absorption in semiconductor saturable absorber mirrors,” Appl. Phys. Lett. 74(26), 3927–3929 (1999). [CrossRef]
27. D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, “Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers,” Phys. Rev. A 72(4), 043816 (2005). [CrossRef]
28. X. Li, J. Feng, W. Mao, F. Yin, and J. Jiang, “Emerging uniform Cu2O nanocubes for 251st harmonic ultrashort pulse generation,” J. Mater. Chem. C 8(41), 14386–14392 (2020). [CrossRef]
29. Y. Zhao, W. Wang, X. Li, H. Lu, Z. Shi, Y. Wang, C. Zhang, J. Hu, and G. Shan, “Functional Porous MOF-Derived CuO Octahedra for Harmonic Soliton Molecule Pulses Generation,” ACS Photonics 7(9), 2440–2447 (2020). [CrossRef]
30. N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51(3), 2602–2607 (1995). [CrossRef]
31. Y . Rosenberg, J. Drori, D. Bermudez, and U. Leonhardt, “Boosting few-cycle soliton self-frequency shift using negative prechirp,” Opt. Express 28(3), 3107–3115 (2020). [CrossRef]
32. J. Santhanam and G. P. Agrawal, “Raman-induced spectral shifts in optical fibers: general theory based on the moment method,” Opt. Commun. 222(1-6), 413–420 (2003). [CrossRef]