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Abstract
Mamyshev oscillators can generate high-power femtosecond pulses, but starting a mode-locked state has remained a major challenge due to the suppression of continuous-wave lasing. Here, we study the starting dynamics of a linear Mamyshev oscillator designed to generate high-power femtosecond pulses while avoiding component damage. Reliable starting to stable mode-locking is achieved with a combination of modulation of the pump power and shifting of a filter passband. The starting process is automated, with full electronic control. The laser delivers 21-nJ pulses that are dechirped to 65 fs in duration outside the cavity.
© 2021 Optical Society of America
1. INTRODUCTION
Ultrafast fiber lasers have widespread use in several fields, such as machining, imaging, and screening of protein crystals [1–3]. They have become an attractive alternative to solid-state lasers due to their waveguide nature, excellent thermal-optic properties, and robust operation. Recently, the performance of femtosecond fiber oscillators has become comparable to their solid-state counterparts [4].
In the past few years, a new type of mode-locked fiber laser has been developed. It is based on an effective saturable absorber (SA) that arises from offset spectral filtering. The idea of offset spectral filtering was first proposed by Piché to explain mode-locking in solid-state lasers but did not receive wide attention [5]. Mamyshev later proposed a technique for regeneration of pulses in telecommunication systems based on offset spectral filtering [6]. Pitois et al. considered the asymptotic solutions of concatenated regenerators [7], and in 2015, Regelskis et al. showed that a laser based on this concept could generate nanojoule-energy and ${\sim}150 \; {\rm{fs}}$ pulses [8].
Offset spectral filtering benefits from the sharp contrast of filter transmission/reflection and the tunability of filter wavelengths. In particular, with increased filter separation, a so-called Mamyshev oscillator generates higher-energy short pulses. The peak power of lasers constructed with ordinary single-mode fibers (SMFs) surpassed 1 MW a few years ago [9–11]. Recent work has pushed the key parameters further: pulses with 400-nm bandwidth and 17-fs full-width at half-maximum (FWHM) duration [12] have been generated, and a laser based on large-mode-area fiber generates 1-µJ and 41-fs pulses, for 13-MW peak power [11]. A practical feature is that Mamyshev oscillators can be built with polarization-maintaining (PM) fibers for environmental stability.
However, the Mamyshev SA has a disadvantage: the suppression of continuous-wave (CW) lasing when the filters do not overlap naturally hinders the growth of fluctuations. As a result, starting a mode-locked state from noise becomes a major challenge. Overlapped filter passbands (where CW lasing can occur) allow starting of a linear Mamyshev oscillator; however, this approach yields only relatively low-energy pulses due to the reduced filter separation [13]. Nonlinear polarization evolution (NPE) can be coupled with the offset spectral filtering for self-starting, but this sacrifices environmental stability [12]. In addition to allowing the existence of a CW state to ignite pulsation, several studies have instead used an external seed pulse or an acousto-optic modulator [8,9,11]. Also, self-starting a ring Mamyshev oscillator with overlapped filter passbands has been achieved by modulating the pump [14]. To avoid sacrificing pulse energy for starting with a reduced filter separation, a non-PM $Q$-switching arm was introduced to start a laser that generates 190-nJ pulses at 1 µm [10]; the same technique was applied to obtain 31-nJ pulses at 1550 nm [15]. Although these techniques succeed in starting Mamyshev oscillators, they all compromise performance and/or environmental stability, or require a coherent seed pulse.
A linear Mamyshev oscillator offers simplicity of construction and compactness and requires fewer components than its ring counterpart. However, to date, linear Mamyshev oscillators have not come close to the performance achieved by ring-cavity designs. This then raises questions about (1) the limits of performance of the linear-cavity versions and (2) whether a high-performance linear cavity can be started without introducing additional drawbacks as mentioned above.
In this paper, we first report an investigation of a high-power linear Mamyshev oscillator. Although it offers good performance, we find it susceptible to damage of the gain fiber during the starting process. A design based on the control of polarizations is then proposed to avoid the damage. We can reliably start the linear Mamyshev oscillator by modulating the pump power and separating the filters, processes that can be fully automated. Dispersive Fourier transform (DFT) [16] measurements provide insight to the starting process. The laser delivers 21-nJ and 65-fs pulses, for peak power 15 times higher than prior linear Mamyshev oscillators.
2. LINEAR MAMYSHEV OSCILLATOR
We started with the experimental setup of the linear Mamyshev oscillator in Fig. 1(a). The fibers have 6-µm core diameter and are PM for environmental stability. A half-wave plate and a polarizing beam splitter are introduced after each collimator to eliminate unwanted contributions from the other polarization. Two interference filters with 4-nm FWHM bandwidth are employed for offset spectral filtering, which is illustrated with the spectral evolution in Fig. 1(a). The center wavelength of the blue filter is fixed at 1027 nm, while that of the red filter can be varied with a motorized rotation stage to attain 0–15 nm separation of filter center wavelengths.
Fig. 1. (a) Schematic of linear Mamyshev oscillator. The spectra illustrate the Mamyshev saturable-absorber mechanism. PF, passive fiber; YDF, Yb-doped fiber; ${F_{{\lambda _ -}}}$, blue filter (${\lambda _ -} = 1027 \; {\rm{nm}}$); ${F_{{\lambda _ +}}}$, red filter; $\lambda /2$, half-wave plate; PBS, polarizing beam splitter; OC, output coupler (${\sim}85\%$); P, pump light from a 976-nm diode laser; C, collimator; M, mirror. (b) Spectra of 47-nJ pulses and the filters. (c) RF spectrum; ${f_{{\rm{rep}}}} = 16.8 \;{\rm{MHz}}$: repetition rate of the laser (10-Hz resolution bandwidth). (d) Measured and reconstructed FROG traces of the dechirped pulses. (e) Temporal profiles of the retrieved (R) and transform-limited (TL) pulses.
To start this laser, two steps are applied: (1) the filter passbands are overlapped to initiate lasing and pulse formation and (2) the filter separation is subsequently increased for evolution to a high-energy single-pulse state. With a filter separation of 6 nm, the laser starts in a multi-pulse state. By increasing the filter separation to 12 nm, we achieve a 47-nJ single-pulse state with 130-nm bandwidth [Fig. 1(b)]. The pulse is dechirped by a 1000-line/mm grating pair to 35-fs FWHM duration {frequency-resolved optical gating (FROG) traces in Figs. 1(d) and 1(e) [17]}. The corresponding peak power exceeds 1 MW. The radio-frequency (RF) spectrum exhibits 78-dB contrast [Fig. 1(c)], which represents stable mode-locking.
This linear cavity achieves the goal of offering excellent performance without sacrificing environmental stability or requiring an external coherent seed pulse. However, we sometimes observed catastrophic damage of the Yb-doped fibers while starting the laser. We suspect that stimulated Brillouin scattering (SBS) is the reason for the damage. SBS has been observed in linear oscillators and is responsible for self-$Q$-switching or random pulsing [18–22]. Because we employ overlapped filter passbands for self-starting, SBS can occur. We suspect that the generated pulses can be uncontrollably amplified above the damage threshold in the gain fiber. Attempts to avoid damage by starting the laser with reduced pump power failed.
It is worth mentioning that recently Boulanger et al. demonstrated a self-polarizing linear Mamyshev oscillator that delivers 21-nJ pulses at ${{1550}}\;{\rm{nm}}$ [23]. They started it with a reduced filter separation and SA mirror. However, they did not report any damage while starting the laser. More study on the damage mechanism with overlapped passbands is thus required.
3. DAMAGE-FREE LINEAR MAMYSHEV OSCILLATOR
A. Design and Starting Process
To avoid damage from SBS, we built a linear oscillator whose pulses propagate with orthogonal polarizations in opposite directions (Fig. 2). Two Faraday rotators (FRs) are introduced to allow only $y$-polarized light propagating toward the output but $x$-polarized light in the opposite direction. The Stokes wave is mainly linearly co-polarized with the exciting pulse [24]; as a result, it will be blocked by the polarizing beam splitters after traversing the FRs.
Fig. 2. Schematic of a damage-free linear Mamyshev oscillator with Faraday rotators. The left passive fiber, including the pigtail of the collimator, is 2 m, while the right one is 0.5 m. The YDF is 3 m. FR, Faraday rotator.
Unfortunately, we fail to observe self-starting of the laser with the FRs, regardless of the filter separation. Although SBS is catastrophic for high-energy pulse generation, we conclude that it is essential for starting a PM linear Mamyshev oscillator. It acts as an intrinsic generator for coherently self-seeding an oscillator. We observe successful starting only without the FRs in the cavity.
To start the linear cavity with FRs, we adopt a strategy based on modulation of the pump power [14]. The steps are illustrated in Fig. 3: (1) initially, the laser requires overlapped filter passbands; (2), (3) we turn on and off the pump modulation to obtain a (possibly multi-pulsing) stable mode-locked state; (4) we increase the filter separation and/or pump power to reach a high-energy mode-locked state.
Fig. 3. Starting procedure of a damage-free linear Mamyshev oscillator with pump modulation and a moving filter.
B. Starting a Mode-Locked State
1. Pump Modulation
We first studied the effect of pump modulation frequency on starting. For this work, we chose 50% duty cycle and 100% modulation depth for the pump. While several modulation frequencies have been studied, here we show only representative results for 1 kHz [Fig. 4(a)] and 80 kHz [Fig. 4(b)]. When the modulation frequency is below 70 kHz, we observe sporadic broadband self-$Q$-switching. This is more likely to be observed with larger pump power. When the modulation frequency is above 70 kHz, mode-locking occurs. Pulses are emitted at the cavity repetition rate, with the envelope of the pulse train modulated by the pump. In contrast to the self-$Q$-switched states, the pulses continue propagating in the cavity without dying out as the pump power varies. We do not know why the mode-locking starts with modulation frequencies above 70 kHz. However, this general range is not surprising because it is not far from the relaxation oscillation frequency. Details of the starting process are presented below.
Fig. 4. Analysis of pump modulation with different filter separations. (a) Self-$Q$-switched state under 1-kHz modulation frequency and (b) modulated mode-locked state under 80-kHz modulation.
We also studied the influence of filter separation on laser behavior. Figure 4 shows that we can obtain self-$Q$-switching and modulated mode-locked states only for filter separations near 3 nm. With larger separations, CW breakthrough is hindered, and only amplified stimulated emission remains. For smaller separations, CW lasing occurs because it is the condition of least loss in the cavity. Besides appropriate filter separations, large modulation depth is also found helpful to initiate pulsation.
Based on these results, we can reliably achieve mode-locking with 80-kHz modulation frequency and 3.4-nm filter separation. In contrast to frequent failure to obtain a stable mode-locked state with self-$Q$-switching at low modulation frequency, this modulated mode-locked state is found to evolve reliably into a stable mode-locked state as the modulation is turned off to create a CW pump.
2. Various States During Starting
To understand the pulse formation, we perform both DFT and pulse-train measurements for the starting process. An 18-km spool of SMF-28 maps the pulse spectrum into the time domain through chromatic dispersion. Figure 5(a) illustrates how the state of the laser evolves within the starting procedure where the transitions of states occurring at 0, 100, and 400 ms are labeled; correspondingly, their DFT measurements are shown in Figs. 5(b)–5(d). Instead of directly evolving into a modulated mode-locked state, self-$Q$-switching is observed at the beginning of pump modulation [Fig. 5(b)]. After a duration that can span over 16,000 modulation cycles (200 ms), it spontaneously evolves into a broadband modulated mode-locked state that exhibits a periodically pump-modulated spectrum [Fig. 5(c)]. The gain varies on the 100-µs time scale with 4-W pump power [25], which is much slower than the pump modulation; therefore, the pulse train can be maintained when the pump is at the minimum. Rather than irregular spectral broadening during the transition of self-$Q$-switching into a modulated mode-locked state, we see a smooth transition of the spectrum into the stable CW-pumped one [near 1200 round trips in Fig. 5(d)]. The laser can reach a stable mode-locked state from a modulated mode-locked state with over 99% success rate.
Fig. 5. Starting dynamics with pump modulation. (a) Illustration of the concept; scale is not quantitative. (I) Temporary self-$Q$-switched state appears after turning on the 80-kHz modulated pump, and then (II) it spontaneously evolves into a periodically modulated mode-locked state. (III) A stable mode-locked state is reached after the pump modulation is turned off. (b)–(d) DFT measurements of the transitions of states. Note that the time axis in (b) is in units of the modulation cycle, instead of the round-trip time of the cavity, to better reveal the self-$Q$-switching. We attribute the spikes at the end of the modulation to the pump laser overshooting as the modulation is turned off.
C. Path to High-Energy Pulses
1. Strategies for Choosing the Path
The initial mode-locked state generally has multiple pulses in the cavity. To obtain a high-energy single-pulse state, the laser is adjusted on a path of increasing pump power and filter separation after successful starting [path 1 in Fig. 6(a)]. This path includes two major steps with specific goals: (1) to obtain a single-pulsing state (black line) and (2) to obtain a high-energy state (orange line).
Fig. 6. (a) Path to a high-energy state after successful starting and (b) spectral evolution along path 1. Two paths are shown. Path 1 (black and orange lines) can reach the desired state, whereas path 2 (blue) fails. Red and blue lines in (b) are different trials of moving along the path. Three pulse trains, plotted in one round-trip time, are shown to indicate the number of pulses in the cavity.
To ensure single-pulse operation, the filter separation is increased in the first step. An increased filter separation raises the pulse peak power required to produce enough spectral broadening for the pulse to pass both filters. This discriminates against slightly weaker pulses and amplifies the rest with a fixed amount of gain. The laser is then forced to operate with a reduced number of pulses in the cavity. During this step, we observe stepwise increases in the spectral bandwidth [Fig. 6(b)]. The steps correspond to the transitions into states of fewer pulses. The transition from a stable multi-pulsing mode-locked state to a stable single-pulsing state is successful in 64% of trials, with failure most often happening where reduction of the number of pulses occurs.
After a single-pulsing state is established, a so-called ${A^*}$ path-finding algorithm [26,27] is applied to search for the path to the desired high-energy state. The cost function is one if the laser stops mode-locking and zero if mode-locking is maintained. A Gaussian potential centered at the high-energy state is used as a heuristic to guide the search. The filter separation is increased from 3.4 nm to 8.1 nm and the pump power from 1.2 W to 1.8 W, beyond which mode-locking is not stable. The final single-pulse state reaches 90-nm bandwidth [Fig. 7(a)] and 21-nJ pulse energy. The mode-locked state shows 83-dB contrast in its RF spectrum [Fig. 7(b)]. The pulse can be dechirped to 65-fs FWHM duration with a grating pair, although there is significant secondary structure [Figs. 7(c) and 7(d)].
Fig. 7. (a) Spectra of delivered pulses and corresponding filters. (b) RF spectrum; repetition rate of the laser ${f_{{\rm{rep}}}} = 16.1 \; {\rm{MHz}}$ (10-Hz resolution bandwidth). (c) Measured and reconstructed FROG traces after dechirping. (d) Temporal profiles of the retrieved (R) and transform-limited (TL) pulses.
2. Discussion
There are various paths that can be taken, but not all of them reach states with desired parameters. Besides the previously discussed path (path 1), we also studied varying only the filter separation while maintaining the desired pump power (path 2). This type of path was used for the linear Mamyshev oscillator without FRs (Fig. 1) and can directly reach a high-energy single-pulse state. However, with the FRs, the mode-locked state is lost at ${\sim}6.5 {-}{\rm{nm}}$ filter separation when the laser is still multi-pulsing. The threshold filter separation for single-pulsing is larger than that for mode-locking. Therefore, the pump power needs to be reduced for single-pulsing operation. Path 1 is then followed to successfully obtain a single-pulsing state.
Overall, the starting sequence reaches a stable mode-locked state on 64% of trials, which is dominated by the success rate of getting single-pulsing. It takes less than 10 s to perform the process, so when it fails, it can be repeated. Although the sequence involves controlling and monitoring several parameters of the laser, it can be automated easily, and we have implemented it in our laboratory.
4. NUMERICAL SIMULATIONS
We obtain further insight into the operation of the linear Mamyshev oscillator by performing numerical simulations. The generalized nonlinear Schrödinger equation is solved in each section of fiber in conjunction with the rate equations of the Yb-doped fiber [25,28]. Saturation of the gain by both co- and counter-propagating pulses is considered because Yb ions respond slowly compared to the repetition rate of the laser.
Figure 8 shows the results with 21-nJ output pulse energy. The output spectrum [Fig. 8(b)] is consistent with the experimental results in Fig. 7(a). Figure 8(c) shows that the pulse evolves with symmetric broadening by self-phase modulation (SPM) when propagating away from the output coupler [Fig. 8(a)]; on the other hand, it enters a gain-managed nonlinear regime when propagating toward the output [Fig. 8(b)] [29]. The spectrum is broadened asymmetrically by following the gain spectrum during the evolution. The pulses can accumulate large nonlinear phase and spectral broadening, which allows a short transform-limited pulse duration and maintains good pulse quality. The simulations show that gain saturation by pulses from both directions results in the SPM regime; otherwise, the two pulses would both undergo gain-managed evolution.
Fig. 8. Results of numerical simulations. The spectra observed just before the two filters are (a), (b) plotted separately, while (c) the entire spectral evolution within the cavity is also shown. Note that the spectra in (c) are plotted on a logarithmic scale.
With optimization of the fiber lengths and pump power, the simulation predicts stable pulse energies up to 50 nJ and duration of 30 fs after dechirping. This performance is approached experimentally in our linear Mamyshev oscillator without FRs (Fig. 1). Thus, we are optimistic about ultimately achieving such high performance with FRs. Because the parameter space of the single-pulsing regime becomes narrower as the pulse energy increases, it may require a dense search of the paths of pump power and filter separation to reach the higher-performance states.
5. CONCLUSION
In conclusion, we have shown that a linear Mamyshev oscillator can deliver 40-nJ and 35-fs pulses. However, it is susceptible to damage of the gain fiber; hence, a new design with two FRs is applied to suppress SBS. The oscillator can be started reliably by modulating the pump power to obtain a mode-locked state, which is then optimized by adjusting the filters and pump power. Full electronic control of this starting procedure is achieved. The laser generates 21-nJ and 65-fs pulses. It offers excellent performance and is environmentally stable. Even with the addition of the FRs, this approach may offer lower cost and complexity than a ring cavity, and the laser can be more compact. We believe that it can be an attractive source for various applications.
Funding
National Institutes of Health (EB002019); U.S. Department of Energy (DE-SC0019546).
Disclosures
The authors declare that there are no conflicts of interest related to this paper.
REFERENCES
1. X. Liu, D. Du, and G. Mourou, “Laser ablation and micromachining with ultrashort laser pulses,” IEEE J. Quantum Electron. 33, 1706–1716 (1997). [CrossRef]
2. L. M. Haupert and G. J. Simpson, “Screening of protein crystallization trials by second order nonlinear optical imaging of chiral crystals (SONICC),” Methods 55, 379–386 (2011). [CrossRef]
3. C. Xu and F. W. Wise, “Recent advances in fibre lasers for nonlinear microscopy,” Nat. Photonics 7, 875–882 (2013). [CrossRef]
4. W. Fu, L. G. Wright, P. Sidorenko, S. Backus, and F. W. Wise, “Several new directions for ultrafast fiber lasers [invited],” Opt. Express 26, 9432–9463 (2018). [CrossRef]
5. M. Piché, “Mode locking through nonlinear frequency broadening and spectral filtering,” Proc. SPIE 2041, 358–365 (1994). [CrossRef]
6. P. V. Mamyshev, “All-optical data regeneration based on self-phase modulation effect,” in 24th European Conference on Optical Communication (ECOC) (1998), Vol. 1, pp. 475–476.
7. S. Pitois, C. Finot, L. Provost, and D. J. Richardson, “Generation of localized pulses from incoherent wave in optical fiber lines made of concatenated Mamyshev regenerators,” J. Opt. Soc. Am. B 25, 1537–1547 (2008). [CrossRef]
8. K. Regelskis, J. Želudevičius, K. Viskontas, and G. Račiukaitis, “Ytterbium-doped fiber ultrashort pulse generator based on self-phase modulation and alternating spectral filtering,” Opt. Lett. 40, 5255–5258 (2015). [CrossRef]
9. Z. Liu, Z. M. Ziegler, L. G. Wright, and F. W. Wise, “Megawatt peak power from a Mamyshev oscillator,” Optica 4, 649–654 (2017). [CrossRef]
10. P. Sidorenko, W. Fu, L. G. Wright, M. Olivier, and F. W. Wise, “Self-seeded, multi-megawatt, Mamyshev oscillator,” Opt. Lett. 43, 2672–2675 (2018). [CrossRef]
11. W. Liu, R. Liao, J. Zhao, J. Cui, Y. Song, C. Wang, and M. Hu, “Femtosecond Mamyshev oscillator with 10-MW-level peak power,” Optica 6, 194–197 (2019). [CrossRef]
12. C. Ma, A. Khanolkar, Y. Zang, and A. Chong, “Ultrabroadband, few-cycle pulses directly from a Mamyshev fiber oscillator,” Photon. Res. 8, 65–69 (2020). [CrossRef]
13. J. Želudevičius, M. Mickus, and K. Regelskis, “Investigation of different configurations and operation regimes of fiber pulse generators based on nonlinear spectral re-shaping,” Opt. Express 26, 27247–27264 (2018). [CrossRef]
14. I. Samartsev, A. Bordenyuk, and V. Gapontsev, “Environmentally stable seed source for high power ultrafast laser,” Proc. SPIE 10085, 201–209 (2017). [CrossRef]
15. M. Olivier, V. Boulanger, F. Guilbert-Savary, P. Sidorenko, F. W. Wise, and M. Piché, “Femtosecond fiber Mamyshev oscillator at 1550 nm,” Opt. Lett. 44, 851–854 (2019). [CrossRef]
16. K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7, 102–112 (2013). [CrossRef]
17. R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Springer, 2012).
18. S. V. Chernikov, Y. Zhu, J. Taylor, and V. P. Gapontsev, “Supercontinum self-Q-switched ytterbium fiber laser,” Opt. Lett. 22, 298–300 (1997). [CrossRef]
19. A. Hideur, T. Chartier, C. Özkul, and F. Sanchez, “Dynamics and stabilization of a high power side-pumped Yb-doped double-clad fiber laser,” Opt. Commun. 186, 311–317 (2000). [CrossRef]
20. B. Upadhyaya, A. Kuruvilla, U. Chakravarty, M. Shenoy, K. Thyagarajan, and S. Oak, “Effect of laser linewidth and fiber length on self-pulsing dynamics and output stabilization of single-mode Yb-doped double-clad fiber laser,” Appl. Opt. 49, 2316–2325 (2010). [CrossRef]
21. D. Mallek, A. Kellou, H. Leblond, and F. Sanchez, “Instabilities in high power fiber lasers induced by stimulated Brillouin scattering,” Opt. Commun. 308, 130–135 (2013). [CrossRef]
22. P.-H. Hanzard, M. Talbi, D. Mallek, A. Kellou, H. Leblond, F. Sanchez, T. Godin, and A. Hideur, “Brillouin scattering-induced rogue waves in self-pulsing fiber lasers,” Sci. Rep. 7, 45868 (2017). [CrossRef]
23. V. Boulanger, M. Olivier, F. Guilbert-Savary, F. Trépanier, M. Bernier, and M. Piché, “All-fiber Mamyshev oscillator enabled by chirped fiber Bragg gratings,” Opt. Lett. 45, 3317–3320 (2020). [CrossRef]
24. G. Agrawal, “Chapter 9–stimulated Brillouin scattering,” in Nonlinear Fiber Optics, 5th ed. (Academic, 2013), pp. 353–396.
25. R. Lindberg, P. Zeil, M. Malmström, F. Laurell, and V. Pasiskevicius, “Accurate modeling of high-repetition rate ultrashort pulse amplification in optical fibers,” Sci. Rep. 6, 34742 (2016). [CrossRef]
26. P. E. Hart, N. J. Nilsson, and B. Raphael, “A formal basis for the heuristic determination of minimum cost paths,” IEEE Trans. Syst. Sci. Cybern. 4, 100–107 (1968). [CrossRef]
27. D. Delling, P. Sanders, D. Schultes, and D. Wagner, Engineering Route Planning Algorithms (Springer, 2009), pp. 117–139.
28. H.-W. Chen, J. Lim, S.-W. Huang, D. N. Schimpf, F. X. Kärtner, and G. Chang, “Optimization of femtosecond Yb-doped fiber amplifiers for high-quality pulse compression,” Opt. Express 20, 28672–28682 (2012). [CrossRef]
29. P. Sidorenko, W. Fu, and F. Wise, “Nonlinear ultrafast fiber amplifiers beyond the gain-narrowing limit,” Optica 6, 1328–1333 (2019). [CrossRef]
