Fiber lasers that generate ultrashort light pulses can offer practical advantages over solid-state lasers for some applications. However, the achievement of high peak power with environmentally stable designs remains a major challenge for fiber oscillators. We demonstrate that an environmentally stable source based on cascaded Mamyshev regeneration can reach peak power at least an order of magnitude higher than that of previous lasers with similar fiber mode area. By designing the oscillator to support parabolic pulse formation and exploiting the step-like saturable absorber characteristic of Mamyshev regeneration, unprecedented nonlinear phase shifts can be managed. Numerical simulations reveal key aspects of the pulse evolution and realistically suggest that (after external linear compression) peak powers approaching 10 MW are possible from an ordinary single-mode fiber. Experiments with a ring-cavity oscillator based on ytterbium-doped fibers are limited by available pump power, but they still yield 50-nJ and 40-fs pulses for peak power. The combination of environmental stability, established previously, with the performance described here should make the Mamyshev oscillator extremely attractive for applications.
© 2017 Optical Society of America
A consensus goal of research on ultrafast fiber lasers has been to develop an alternative to the solid-state mode-locked oscillator, with these purported benefits of the fiber platform: relatively low cost, simplicity, and robustness. Ultrafast lasers provide precise and intense fields that have enabled many important advances, such as biomedical imaging and laser micromachining [1,2]. Fiber ultrafast instruments could be transformative in enabling both widespread scientific and industrial applications of ultrafast pulses. However, for this they must simultaneously reach sufficient performance and be amenable to both cost-effective manufacturing and use by non-experts. For a long time, the primary challenge to achieving high peak power was the management of nonlinearity in the waveguide medium. In the past decade, this challenge has been met with several developments. New pulse evolutions based in a normal dispersion fiber now provide a means of tolerating high nonlinearity [3–7]. In laboratory prototypes that utilize nonlinear polarization evolution (NPE) as an effective saturable absorber, these sources rival solid-state oscillators. Their typical performance of and sub-100 fs pulses from standard single-mode fiber (SMF) represent order of magnitude higher peak power than early soliton  and stretched-pulse fiber oscillators . However, for widespread use and commercialization, NPE is undesirable, because it is highly sensitive to the random birefringence of the fiber, and consequently, mode-locking is easily disrupted by environmental perturbations. This has become the impediment to the proliferation of fiber lasers in applications that employ femtosecond oscillators. It has stymied commercial instruments that reach beyond the scientific market.
Substantial effort has been devoted to solving this problem. Fiber lasers constructed with all polarization-maintaining (PM) fibers are robust against such environmental perturbations. To date, no work has been able to combine the high performance of NPE in standard SMFs with an all-PM design. Semiconductor saturable absorber mirrors (SESAMs) [10,11] and nonlinear loop mirrors using PM fibers [12–14] have been employed as alternative saturable absorbers. Material-based saturable absorbers, however, suffer from long-term reliability and poor power-handling capabilities. Nonlinear loop mirror (NOLM) and nonlinear amplifying loop mirror (NALM) based designs require precise control of the splitting ratio between loop directions, and their transmission cannot be easily and continuously tuned. Furthermore, although significant steps have been made, lasers based on SESAMs, NOLMs, and NALMs have still not generated more than 5-nJ and sub-100 fs pulses.
Devices based on reamplification and reshaping have been considered as an alternative for the generation of short pulses [15–19]. This approach relies on self-phase-modulation (SPM) induced spectral broadening and offset spectral filtering, which leads to an effective self-amplitude modulation. Mamyshev proposed the use of the process for signal regeneration , and several studies focused mainly on pulse generation with telecommunication parameters . The pulse energies and durations (usually picojoules and picoseconds) were limited by nonlinear phase accumulation in long fibers and narrow filter separation [17–19,21]. Regelskis et al. first demonstrated a Mamyshev oscillator aimed at high-energy femtosecond pulses . This environmentally stable oscillator produced modest-energy () pulses with 2-ps in duration. The measured spectral bandwidth could support transform-limited pulses, but the compressed pulse duration was not measured. These researchers also reported that the oscillator could be started by reflecting light rejected by the filter back into the cavity . Very recently, starting a Mamyshev oscillator by modulating the pump laser at 20 kHz to induce -switching was reported . This oscillator featured an all-fiber construction and generated impressive 15-nJ pulses, which were dechirped to 150-fs duration.
The recent works by Regelskis et al. and Samartsev et al. nicely illustrate the potential practical advantages of Mamyshev oscillators over conventional mode-locked lasers. However, they do not address the nature of the intracavity pulse propagation beyond the self-amplitude modulation that arises from the offset filtering. As a result, important questions remain about fundamental aspects of their operation. Additionally, the peak power obtained with such devices still lags behind that of mode-locked lasers that employ NPE. If Mamyshev oscillators cannot reach high performance levels, the benefits they provide over alternative environmentally stable designs will be limited. Alternatively, if the performance limits of the Mamyshev oscillator meet or even exceed those of previous designs, the combination of performance and practical advantages may enable widespread applications. Clearly, there is ample motivation to understand pulse propagation and performance limits. Finally, the mechanisms of self-starting are still unclear.
Here, we report the results of a theoretical and experimental study of pulse propagation in a Mamyshev oscillator. Insight gained about the pulse propagation allows us to achieve record performance for a femtosecond fiber oscillator and forecasts ultimate performance limits, yielding nearly an order of magnitude higher peak power. Numerical simulations show that an oscillator comprised of ordinary SMF, when seeded by a low-energy short pulse (), can support mode-locked pulses with 190-nJ energy and dechirped duration (Fourier transform-limited). These parameters correspond to peak power. The simulations reveal that this performance follows from the remarkable capacity of the oscillator to manage the nonlinear phase. In a suitably designed cavity, the pulse evolves to a parabolic shape before it enters the gain fiber, which enables control of the nonlinear phase accumulated in the gain segment. Theoretically, the pulse can accumulate a round-trip nonlinear phase shift of and still be stable. In experiments, and pulses (after compression) at 17 MHz are generated, with the energy limited by the available pump power and/or damage to the PM fiber. Even so, the peak power is about 10 times higher than that produced by a mode-locked fiber laser constructed with ordinary SMF . The accumulated nonlinear phase shift is , which is times larger than the largest reported for stable pulses with well-controlled phase from a mode-locked laser. We attribute this to the parabolic pulse propagation along with the step-like saturable absorber behavior of the Mamyshev process, which will be elaborated on below. These results represent a significant step toward a high-energy, short-pulse fiber source that can be environmentally stable. The outlook for self-starting Mamyshev oscillators, along with extensions to other wavelengths, will be discussed below. Finally, we consider fundamental aspects of the Mamyshev oscillator in the context of other driven nonlinear systems.
2. NUMERICAL AND EXPERIMENTAL RESULTS
The experimental configuration of the oscillator is schematically illustrated in Fig. 1. The laser operates in the all-normal dispersion regime (as do all prior Mamyshev oscillators). A ring oscillator allows more design freedom to control the propagation, compared to a linear oscillator. The ytterbium-doped fiber provides the gain, and all fibers are PM. The use of Gaussian spectral filters is important for maximizing the pulse quality and peak performance (see Supplement 1, section 3). To accomplish this, we use the overlap of the beam diffracted from a grating with the spatial mode of the fiber . These filters inherit the Gaussian shape from the fundamental mode shape of the SMF, and they were tuned to longer () and shorter () wavelengths than the peak of the gain spectrum. An isolator ensures unidirectional operation. Polarizing beam splitters are used as the output couplers. The steady-state operation cycle consists of amplification (gain fiber 1), spectral broadening (gain fiber 1 and the following passive SMF), pulse energy adjustment (PBS 1), filtering (filter 2), amplification (gain fiber 2), spectral broadening (gain fiber 2 and the following passive SMF), output (PBS 2), and spectral filtering (filter 1). Half-wave plates are used to adjust the polarization state of light going into the PM fiber and to optimize the output coupling ratio. To ignite pulsation in the cavity, a seed pulse is directed into the fiber via a grating.
We performed numerical simulations of the oscillator shown in Fig. 1 using the standard split-step method with accurate fiber parameters (the parameters are given in Supplement 1, Table S1). The simulation includes the Kerr nonlinearity, stimulated Raman scattering, and second and third-order dispersion. The oscillator is seeded with different initial pulses (picosecond or femtosecond duration), but for given cavity parameters, the simulations always converge to the same solution. The simplified gain dynamics and small temporal window of our simulations prevent our current numerical model from providing realistic insight into starting of pulse formation from noise. Numerical simulations predict that the cavity may generate up to 190-nJ pulses, which can be dechirped to below 20 fs. The pulse energy is limited by deviations of the pulse from a parabolic shape, which causes wave breaking, and by stimulated Raman scattering (see Supplement 1, Fig. S1). Another example, for which 50-nJ pulses are produced, is shown in Fig. 2 for comparison to the experimental results. The pulse duration and bandwidth grow monotonically in the passive (80 cm), gain (2.5 m) and second passive fiber (80 cm) segments in both arms. The spectral filters (F1 and F2) shape the pulse to a narrow-band and short-duration pulse that seeds the propagation in the subsequent arm [Fig. 2(a)]. Over the course of its evolution, spectral breathing by a factor of 16 is observed. The pulse evolves quickly to a parabolic shape in the passive fiber [Fig. 2(b)]. This parabolic pulse is subsequently amplified in the gain fiber. The parabolic shape is maintained through this gain fiber and into the following passive fiber. This is in contrast to regenerative similariton lasers, where the self-similar evolution is localized to the gain fiber [26,27]. The output in the time domain is a nearly linearly chirped parabola [Fig. 2(c)] with 110-nm bandwidth [Fig. 2(d)], which corresponds to a transform-limited pulse.
Experiments were performed with guidance from the simulations. A Yb-doped, PM double-clad fiber with 6-μm core is employed in the gain segments. The 2.5-m-long gain segments support the parabolic evolution and absorb most of the pump light. All the passive fibers are standard PM-980. The repetition rate of the oscillator is . The separation of the two filters was adjusted to eliminate continuous-wave (CW) operation, while allowing for the highest output pulse energy. With the seed pulses launched into the cavity, the optimal mode-locking conditions were found by adjusting the output coupling in each arm with the waveplates. The seed pulses can be quite weak, and their duration is not important. For example, reliable starting was obtained with 80-pJ and 10-ps pulses or with and 3-ps chirped pulses with 20-nm bandwidth. The bandwidth of the seed pulse is a significant factor, because it determines whether a seed can circulate and be amplified in the first round-trip; if the bandwidth is not wide enough, larger seed energy or higher gain is needed to provide enough spectral broadening. Once pulsation is initiated, as indicated by a broad output spectrum, the seed pulse can be blocked and pulses will continue to circulate in the cavity. While the oscillator is running, physical perturbations such as twisting or shaking the fiber do not alter the operating state of the laser. Once the optimal conditions are found, oscillation can be extinguished by blocking the cavity or turning off the pump and then restarted to the same state by launching seed pulses without any additional adjustment. Moreover, an isolated seed pulse is not necessary, as the pulsed operation is stable in the presence of continuous seeding (we tried different continuously running pulsed lasers as seed sources, operating at 1 MHz and 40 MHz).
The oscillator generates 6-ps chirped pulses. The output spectra and autocorrelation traces of the dechirped pulses for a range of pulse energies are shown in Fig. 3. Here the output is taken from the output coupler directly before the isolator, and the energy is modified by changing the pump power. As the energy increases, the spectrum broadens due to stronger SPM [Fig. 3(a)], and the dechirped duration decreases. We find that, using only a grating compressor (), the dechirped pulses appear relatively clean, without pedestals or structure [Fig. 3(b)]. For the energy range shown, the dechirped pulse duration is within 1.5 times the transform limit. This deviation can be accounted for by the third-order dispersion in the grating compressor. We estimate that the 50-nJ pulses accumulate a nonlinear phase of . This shows that the huge nonlinear phase accumulation in the Mamyshev oscillator is well-controlled: it is converted into a nearly linear chirp. Eventually, the higher-order phase, which cannot be compensated by the grating pair, becomes significant, and the minimum dechirped duration grows, despite increasing bandwidth (50-nJ trace). The pulses are limited by the maximum available pump power; we do not observe multi-pulsing, which commonly limits the pulse energy in mode-locked lasers.
The pulse peak power is verified by launching the dechirped pulse into 2-m of SMF with a 6 μm core diameter (HI1060) and measuring the SPM-induced spectral broadening. The measurements are compared with the results of numerical simulations in Fig. 4(a). In simulation, we launch a Gaussian pulse with the same energy and transform-limited duration and, with the residual third-order dispersion from the grating compressor, into a fiber with the parameters of 2-m of HI1060. The calculation accounts for fiber dispersion up to the third order, SPM, and intrapulse Raman scattering. The simulation reproduces the root-mean-square bandwidth observed for the experimental pulses accurately, which indicates the high quality of the output pulses.
The stability of the output pulse train was investigated using an RF spectrum analyzer. The resolution and dynamic range of the spectra are instrument-limited but still confirm the stable mode-locking and absence of sidebands and harmonic frequencies to at least 80 dB below the fundamental frequency [Fig. 4(b)]. This is similar to the performance of mode-locked fiber oscillators.
For the conditions described above, the oscillator does not start from noise. Self-pulsation originating from amplified spontaneous emission (ASE) has been predicted  and demonstrated in long cavities () with highly nonlinear fibers (HNLF) [18,19]. Starting is favorable in these cavities owing to the narrow filter separation, along with the possibility for sufficient nonlinear phase accumulation by even low-power fluctuations in the long HNLF. We speculate that the recently described dissipative Faraday instability (DFI) can account for self-starting in this case, since the small separation between the filters overlaps with the DFI gain spectrum [28,29]. For broadband, high-energy pulses, the optimal filter separation is much broader than the DFI gain spectrum. In this regime, self-starting was proposed  and reported  by the use of controlled feedback of ASE in the linear cavity, through a so-far unexplained mechanism. We have recently confirmed self-starting operation of a linear cavity in our laboratory, at power levels lower than those reached by the ring cavity (see Supplement 1, section 2). As will be discussed below, although the nature of the Mamyshev oscillator suggests that it is incompatible with self-starting, these initial results provide optimism about the near-future realization of a fully self-starting, environmentally stable fiber oscillator with the high performance demonstrated here.
The performance of mode-locked lasers is fundamentally limited by nonlinear effects. Solitons and dispersion-managed solitons are stable for, at most, a round-trip peak nonlinear phase shift of . Experiments showed that passive similariton, dissipative soliton, and amplifier similariton can support and pulses, which corresponds to an nonlinear phase shift [7,31]. Simulations of these evolutions, assuming ideal saturable absorbers, indicate that higher performance can be achieved with higher pump power. These high-energy pulses, that is, larger nonlinear phase shift, require a very high modulation-depth saturable absorber to suppress the CW background . While NPE can be close to an ideal absorber, there is still a significant gap between simulations and experiments, and currently represents an approximate limit for experiments. This value is consistent with the numerical prediction for dissipative soliton oscillators . Table 1 summarizes the performance of representative Yb-doped mode-locked fiber lasers. [Actual pulse energies are scaled to the values that would be obtained with the same core size (6 μm)].
The Mamyshev oscillator overcomes these limitations. If the nonlinearity is correctly managed, high-energy, wave-breaking-free pulses with good phase profile can be generated—apparently even well beyond the gain bandwidth limit. This performance follows from the step-like saturable absorber realized by the combination of two filters and the fiber. As pointed out by Pitois et al., the cascaded frequency-broadening and offset filtering creates an effective transmission function that is step-like, with zero transmittance at low power and an abrupt transition to a constant value at high power . This step-like saturable absorber means that the mode-locking pumping rate is below the CW lasing threshold; so, the Mamyshev oscillator only supports mode-locked operation. This eliminates the nonlinearity limit from the saturable absorber  and allows for much higher energy. Already, the compressed pulse we obtain has a peak power roughly an order of magnitude above previous results. The performance is comparable that of the best commercial Ti:sapphire lasers, the current workhorses of ultrafast laser applications (Table 1).
Of course, the step-like saturable absorber property creates a challenge for starting a Mamyshev oscillator from noise. Despite this, two methods of starting similar cavities have recently been demonstrated: pump modulation  and controlled feedback of ASE . Our own initial investigations confirm that the latter is, remarkably, a reliable and robust means of circumventing the starting problem (see Supplement 1, section 2). While the pump modulation scheme demonstrated by Samartsev et al.  is important, using a coupled cavity to start the Mamyshev oscillator has the practical benefit of being completely passive. It is surprising that any starting technique can be successful, because of the inevitable trade-off between starting and performance and the bias here toward performance due to the step-like saturable absorber property. That researchers have demonstrated such methods in similar cavities suggests that related techniques may be used for the ring cavity presented here. Future work will be focused on developing such techniques.
Prospects for further optimization and scaling of the Mamyshev oscillator are exciting. While simulations of ultrafast fiber sources have systematically suggested much higher performance than has been observed, we are more optimistic about our extrapolations for the Mamyshev oscillator. The discrepancy between experimental performance and anticipated results in conventional fiber lasers likely follows from uncertain starting conditions and overly optimistic saturable absorber parameters. Starting the oscillator from a pulse systematically produces higher performance than starting from noise . In contrast, our observations in the self-starting linear Mamyshev oscillator show that pulse-seeded and self-starting performance are similar. Meanwhile, standard numerical techniques for modeling ultrashort-pulse fiber lasers neglect gain relaxation dynamics and use a restricted temporal window. These fail to account for nanosecond laser spiking or other effects that may play an important role in starting and, ultimately, the steady-state performance. In the Mamyshev oscillator, CW lasing is completely suppressed: the CW lasing threshold is much higher than the pulse threshold. Consequently, if achieved, starting should be more deterministic, and the maximal nonlinear phase shift can be much higher than in a cavity where CW lasing needs to be constantly suppressed.
The approach described here can be extended in several directions. Scaling from the experimental results presented here, with large mode area (25 μm diameter) PM fiber, we expect that Mamyshev oscillators will reach the microjoule level. Simulations also indicate that by changing the fiber length, the oscillator repetition rate can be tuned from hundreds of MHz to without sacrificing the performance (at lower repetition rates, additional dispersion compensation inside of the cavity is required). This will allow it to be a useful tool for both scientific and industrial applications. In addition, linearly chirped parabolic output pulses are attractive for applications such as highly coherent continuum sources and optical signal processing, etc. . High performance Mamyshev oscillators at other wavelengths can be expected. If normal-dispersion gain fiber is available (e.g., as is the case at 1550 nm), the design could be very similar to that presented here.
Given that it has taken more than a decade for the Mamyshev pulse generator to gain serious consideration as an alternative to conventional mode-locked fiber lasers, it is worthwhile to reconsider the broader impacts of this system. Numerous works [17,21] have explored optimization of the Mamyshev oscillator for signal regeneration. The results presented here explore the system in connection and contrast to mode-locked fiber lasers. Much work remains to optimize oscillator designs for this purpose. However, a crucial difference between the Mamyshev oscillator and a conventional mode-locked laser is that, in the Mamyshev oscillator, the pulsed state is bistable with ASE. This kind of bistability is also a key characteristic of systems supporting cavity solitons (where usually the pulsed state is bistable with the CW field). Hence, the Mamyshev oscillator should be compared and contrasted not only with mode-locked lasers but also with systems that support cavity solitons, such as coherently driven cavities, which have lately been explored extensively for producing mode-locked frequency combs [35–38]. Two features of the pulse evolution we demonstrate here are worth noting. First, the Mamyshev oscillator can produce a stable pulse train, even with extremely high round-trip nonlinear phase shift and spectro-temporal breathing. This suggests that in a suitably designed device, an octave-spanning frequency comb could be generated directly, possibly exceeding the bandwidth, and certainly the power, of microresonator combs. Second, as in fiber lasers, the round-trip gain and loss are much higher than in coherently driven cavities. This may allow more straightforward control over circulating pulses, at the point of minimum pulse energy by, for example, an intracavity electro-optic modulator or coupling to an external source of optical bits. Furthermore, following from the possibility for extreme nonlinear phase and pulse evolution, much more elaborate information processing schemes could be devised. Ultimately, these suggestions are only speculative examples of the more important message. Many questions remain about the Mamyshev oscillator, and its unique features suggest a wide variety of uses and phenomena that, to date, have been under-explored, compared to conventional mode-locked laser cavities and coherently driven high-Q optical resonators.
In conclusion, these results show that the Mamyshev oscillator allows a surprising and significant leap in the ongoing central challenge of high-power ultrafast fiber lasers: the management of nonlinearity. This is due to the formation and amplification of parabolic pulses and the step-like artificial saturable absorber formed by the Mamyshev regeneration mechanism. By making the CW lasing threshold above the threshold for mode-locking, the Mamyshev oscillator supports stable mode-locking with huge nonlinear phase shifts. To harness this nonlinearity for the generation of clean, high-energy ultrashort pulses, we designed the oscillator to support parabolic pulse formation. Combined, these factors translate to unprecedented performance—our initial design already yields an order of magnitude higher peak power than any previous fiber oscillator with the same core size. As prior work has shown, the Mamyshev oscillator supports an environmentally stable, fiber-format design that can be self-starting, thus solving a major practical impediment to the widespread use of ultrashort-pulse fiber sources in applications. Taken together, these features should make Mamyshev oscillators extremely attractive for applications in ultrafast science and technology.
Office of Naval Research (ONR) (N00014-13-1-0649); National Institutes of Health (NIH) (EB002019).
The authors gratefully acknowledge helpful discussions with J. Zeludevicius. Z. Ziegler acknowledges support from an ELI undergraduate research award at Cornell University.
See Supplement 1 for supporting content.
1. W. R. Zipfel, R. M. Williams, and W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol. 21, 1369–1377 (2003). [CrossRef]
2. R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2, 219–225 (2008). [CrossRef]
3. F. O. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004). [CrossRef]
4. A. Chong, J. Buckley, W. Renninger, and F. W. Wise, “All-normal-dispersion femtosecond fiber laser,” Opt. Express 14, 10095–10100 (2006). [CrossRef]
5. A. Chong, W. H. Renninger, and F. W. Wise, “All-normal-dispersion femtosecond fiber laser with pulse energy above 20 nJ,” Opt. Lett. 32, 2408–2410 (2007). [CrossRef]
6. B. Nie, D. Pestov, F. W. Wise, and M. Dantus, “Generation of 42-fs and 10-nJ pulses from a fiber laser with self-similar evolution in the gain segment,” Opt. Express 19, 12074–12080 (2011). [CrossRef]
7. A. Chong, L. G. Wright, and F. W. Wise, “Ultrafast fiber lasers based on self-similar pulse evolution: a review of current progress,” Rep. Prog. Phys. 78, 113901 (2015). [CrossRef]
8. L. F. Mollenauer and R. H. Stolen, “The soliton laser,” Opt. Lett. 9, 13–15 (1984). [CrossRef]
9. K. Tamura, E. P. Ippen, H. A. Haus, and L. E. Nelson, “77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser,” Opt. Lett. 18, 1080–1082 (1993). [CrossRef]
10. U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996). [CrossRef]
11. A. Chong, W. H. Renninger, and F. W. Wise, “Environmentally stable all-normal-dispersion femtosecond fiber laser,” Opt. Lett. 33, 1071–1073 (2008). [CrossRef]
12. C. Aguergaray, N. G. R. Broderick, M. Erkintalo, J. S. Y. Chen, and V. Kruglov, “Mode-locked femtosecond all-normal all-PM Yb-doped fiber laser using a nonlinear amplifying loop mirror,” Opt. Express 20, 10545–10551 (2012). [CrossRef]
13. C. Aguergaray, R. Hawker, A. F. J. Runge, M. Erkintalo, and N. G. R. Broderick, “120 fs, 4.2 nJ pulses from an all-normal-dispersion, polarization-maintaining, fiber laser,” Appl. Phys. Lett. 103, 121111 (2013). [CrossRef]
14. J. Szczepanek, T. M. Kardaś, M. Michalska, C. Radzewicz, and Y. Stepanenko, “Simple all-PM-fiber laser mode-locked with a nonlinear loop mirror,” Opt. Lett. 40, 3500–3503 (2015). [CrossRef]
15. U. Keller, T. H. Chiu, and J. F. Ferguson, “Self-starting femtosecond mode-locked Nd:glass laser that uses intracavity saturable absorbers,” Opt. Lett. 18, 1077–1079 (1993).
16. M. Piche, “Mode locking through nonlinear frequency broadening and spectral filtering,” Proc. SPIE , 2041, 358–365 (1994).
17. 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]
18. K. Sun, M. Rochette, and L. R. Chen, “Output characterization of a self-pulsating and aperiodic optical fiber source based on cascaded regeneration,” Opt. Express 17, 10419–10432 (2009). [CrossRef]
19. T. North and M. Rochette, “Regenerative self-pulsating sources of large bandwidths,” Opt. Lett. 39, 174–177 (2014). [CrossRef]
20. P. V. Mamyshev, “All-optical data regeneration based on self-phase modulation effect,” in 24th European Conference on Optical Communication, Madrid, Spain (IEEE, 1998), pp. 475–476.
21. L. Provost, C. Finot, P. Petropoulos, K. Mukasa, and D. J. Richardson, “Design scaling rules for 2R-optical self-phase modulation-based regenerators,” Opt. Express 15, 5100–5113 (2007). [CrossRef]
22. K. Regelskis, J. Zeludevicius, K. Viskontas, and G. Raciukaitis, “Ytterbium-doped fiber ultrashort pulse generator based on self-phase modulation and alternating spectral filtering,” Opt. Lett. 40, 5255–5258 (2015). [CrossRef]
23. K. Regelskis and G. Raciukaitis, “Method and generator for generating ultra-short light pulses,” European patent WO2016020188 A1, February 11, 2016.
24. I. Samartsev, A. Bordenyuk, and V. Gapontsev, “Environmentally stable seed source for high power ultrafast laser,” Proc. SPIE 10085, 100850S (2017). [CrossRef]
25. W. H. Renniger, A. Chong, and F. W. Wise, “Self-similar pulse evolution in an all-normal-dispersion laser,” Phys. Rev. A 82, 021805 (2010). [CrossRef]
26. C. Finot, S. Pitois, and G. Millot, “Regenerative 40 Gbit/s wavelength converter based on similariton generation,” Opt. Lett. 30, 1776–1778 (2005). [CrossRef]
27. T. Northa and C. S. Bres, “Regenerative similariton laser,” APL Photon. 1, 021302 (2016). [CrossRef]
28. A. M. Perogo, N. Tarasov, D. V. Churkin, S. K. Turisyn, and K. Staliunas, “Pattern generation by dissipative parametric instability,” Phys. Rev. Lett. 116, 028701 (2016). [CrossRef]
29. N. Tarasov, A. M. Perego, D. V. Churkin, K. Staliunas, and S. K. Turitsyn, “Mode-locking via dissipative Faraday instability,” Nat. Commun. 7, 12441 (2016). [CrossRef]
30. J. Zeludevicius, Center for Physical Sciences & Technology (CPST) Savanoriu Ave. 231, LT-02300 Vilnius, Lithuania (personal communication, 2015).
31. W. H. Renninger and F. W. Wise, “Fundamental limits to mode-locked lasers: toward terawatt peak powers,” IEEE J. Sel. Top. Quantum Electron. 21, 1100208 (2015). [CrossRef]
32. A. Fernandez, T. Fuji, A. Poppe, A. Fürbach, F. Krausz, and A. Apolonski, “Chirped-pulse oscillators: a route to highpower femtosecond pulses without external amplification,” Opt. Lett. 29, 1366–1368 (2004). [CrossRef]
33. V. G. Bucklew, W. H. Renninger, P. S. Edwards, and Z. Liu, “Iteratively seeded mode-locking,” Opt. Express 25, 13481–13493 (2017).
34. C. Finot, J. Dudley, B. Kibler, D. Richardson, and G. Millot, “Optical parabolic pulse generation and applications,” IEEE J. Quantum Electron. 45, 1482–1489 (2009). [CrossRef]
35. F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010). [CrossRef]
36. T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014). [CrossRef]
37. Y. K. Chembo and C. R. Menyuk, “Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators,” Phys. Rev. A 87, 053852 (2013). [CrossRef]
38. S. Coen and M. Erkintalo, “Universal scaling laws of Kerr frequency combs,” Opt. Lett. 38, 1790–1792 (2013). [CrossRef]