1. Introduction

Ultrafast laser sources delivering picosecond or femtosecond pulses have attracted much attention over the past decades because of their increasing roles in versatile scientific and industrial applications, i.e., biomedical imaging [1–3] and laser micromachining [4,5]. The fiber-based pulse source offers the advantages of simplicity, low cost, and robustness. In particular, with the rapid development of laser and fiber fabrication technologies, the performance of ultrafast fiber lasers has been demonstrated to be comparable to the traditional solid-state lasers [6,7]. However, further pulse energy scaling of ultrafast fiber lasers is still limited owing to the wave breaking induced by overdriven nonlinear effect [8]. In fact, the major challenge to promote pulse peak power in fiber lasers is cavity nonlinearity management. Generally, the overdriven nonlinear effect can be alleviated by employing the large mode area (LMA) gain fiber or engineering the fiber dispersion in laser cavity [9–13]. For example, to date the pulse energy up to several tens of nJ can be obtained directly from the fiber laser with an all-normal dispersion design [11,12]. However, with LMA fiber or intracavity dispersion management, the nonlinear phase shift could still be excessive and lead to pulse breaking, which places a restriction on further enhancement of the fiber laser performance. Therefore, the above-mentioned limitations motivate laser scientists to look for new approaches to generate high-quality ultrashort pulse from fiber-based oscillators.

Recently, a high-performance fiber oscillator that delivers high-peak-power pulse, namely, the fiber Mamyshev oscillator (MO) has been intensively investigated [14–16]. The operation principle relies on the self-phase modulation (SPM)-enabled spectral broadening and offset spectral filtering, leading to regeneration and reshaping of a seed pulse with a step-like saturable absorber [17–19]. Under such scheme, large tolerance of the nonlinear phase shift for a mode-locked pulse could be achieved, which allows for the generation of much higher energy pulse with environmentally stable design compared to the traditional mode-locked fiber lasers. The first fiber MO operating at 1.06 µm was proposed and demonstrated by Regelskis et al., which delivers ultrashort pulse with 2.8 nJ energy directly from the oscillator [15]. Then the 40-fs pulse with about 1 MW peak power was demonstrated by Wise group with the proper management of filter separation and the design of intracavity parabolic pulse evolution [16]. The potential of MO has stimulated intensive investigations, i.e., pursuit of higher pulse energy [20–22], broadband spectrum [23,24], and multi-pulse operation [25–29]. In particular, by introducing a large-mode-area photonic crystal gain fiber, the output pulse energy was further boosted to the order of µJ directly from the MO [30].

Nevertheless, one main drawback of the MO is that the oscillator generally cannot be self-starting, because that the continuous wave (CW) signal is greatly suppressed by the step-like saturable absorption effect [14,17]. To date, various approaches have been proposed to ignite the MO, such as external seeding [16,30], self-seeding [20,31] and pump modulation [32,33]. The most straightforward way to ignite the MO is to employ an external pulse source to serve as a seed signal [30]. Generally, the seed signal is a train of pulses from a mode-locked fiber laser, resulting in the successive injection of pulse into the oscillator. And it is found that multi-pulse starting operation of fiber MO could be frequently observed with external seeding approach, which is different from the traditional ultrafast fiber lasers and unfavorable for pulse energy scaling. Therefore, one would naturally like to identify the starting dynamics from the seed signal to oscillator pulse in MOs with step-like saturable absorption, and in particular, for the case of multi-pulse generation. Moreover, from the viewpoint of performance improvement, it would be interesting to find the conditions suitable for the single-pulse starting operation of MO.

In this work, we investigated the evolution dynamics from seed signal to oscillator pulse in a fiber MO. It was demonstrated that, owing to the gain competition among the successive injection of seed pulses, higher pump power that supports buildup of multiple oscillator pulses was required to ignite the MO. In this way, the MO was starting with a multi-pulse operation. The multiple oscillator pulses were demonstrated to be evolved from the external seed pulses. Moreover, we proposed the highly intensity-modulated pulse bunch with large temporal bunch separation as the seed signal to reduce the gain competition effect, and thus, to facilitate the single-pulse starting operation of the MO. Finally, we also implemented numerical simulations to reproduce the experimental results.

2. Experimental setup

The schematic of the proposed fiber MO is shown in Fig. 1, whose ring cavity consists of two cascaded Mamyshev regenerators. The MO is seeded by a homemade dissipative soliton fiber laser through a 50% optical coupler (OC 1). To achieve the stable pulse propagation in the MO, two offset bandpass filters are introduced in the cavity, namely filter 1 and filter 2. Filter 1 is a super-Gaussian fiber filter with a central wavelength of 1549 nm and a 3-dB bandwidth of 5 nm, and filter 2 is a tunable one which is constructed by a collimator and a reflection diffraction grating (center wavelength: 1561 nm; spectral bandwidth: 3 nm) [16]. The transmission curves of two bandpass filters are shown in the inset of Fig. 1. Two segments of 10-m erbium-doped fibers (EDFs) are used as gain media for two arms. The other fibers in the oscillator are all standard single-mode fibers (SMFs), and the total oscillator length is ∼30.9 m (corresponding to 147 ns cavity roundtrip time). The isolator ensures unidirectional operation, and 5% port of OC 2 is used to measure the output pulse characteristics. To capture the real-time spectral profile, a 15-km long SMFs with a group velocity dispersion of -21ps²/km is utilized to realize the dispersive Fourier transform (DFT) technique [34–37], which results in a total dispersion of -315 ps². Then a high-speed real-time oscilloscope is used to record DFT spectra.

 

Fig. 1. Schematic of the fiber MO. LD, 976 nm laser diode; WDM, wavelength division multiplexer; EDF, erbium-doped fiber; OC, optical coupler; ISO, optical isolator.

Download Full Size | PDF

3. Experimental results

In order to ignite the MO, a homemade dissipative soliton fiber laser was used as the seed signal. The performance of the seed soliton fiber laser is summarized in Fig. 2. Here, the mode-locked spectrum shows a rectangular profile with a 3-dB bandwidth of 32 nm, which is typical feature of dissipative soliton fiber laser operating in net-normal dispersion, as shown in Fig. 2(a). It can be seen that the spectral range covers that of filter 1, which is suitable for igniting the MO. The fiber laser delivers the pulse train with a fundamental repetition rate of 15.53 MHz, corresponding to 64 ns cavity roundtrip time, as presented in Fig. 2(b). The autocorrelation trace of the seed dissipative soliton is plotted in Fig. 2(c), exhibiting that the pulse duration is 5.38 ps. When the pump powers imposed on arm 1 and arm 2 are 140 mW and 150 mW, respectively, the MO could be ignited with the injected seed pulses. In this case, the multi-pulse operation could be always seen from the MO. However, by carefully decreasing the pump powers on two arms, single pulse operation could be still achieved. The single-pulse performance of the MO is presented in Figs. 2(d)-(f). Here, the spectral profile of the MO is clearly different from that of seed pulse, owing to the SPM induced spectral broadening. The pulse repetition is about 6.79 MHz, which is decided by the fiber length of the MO. The pulse duration emitted from the MO is about 1.07 ps, as depicted in Fig. 2(f). In addition, the corresponding output power of the single-pulse operation is ∼3.5 mW. Nevertheless, it can be further improved by optimizing the MO parameters such as wavelength separation of the offset filters.

 

Fig. 2. The performance of seed laser and MO. (a-c): Optical spectrum, pulse train and autocorrelation trace of seed laser. (d-f): Optical spectrum, pulse train and autocorrelation trace of MO.

Download Full Size | PDF

As mentioned above, the MO has always been starting with multi-pulse operation in our experiments. The most frequently observed multi-pulse pattern at the pump power of 140 mW and 150 mW on two arms is a four-pulse scenario with randomly temporal distribution. In order to reveal the transition process from seed pulses to oscillator pulses more clearly, the DFT technique was used to record the real-time spectral evolution of the optical pulses, as presented in Fig. 3(a). According to our schematic, the seed signal is injected at OC 1, thus the injected seed signal and the oscillator pulse can be measured simultaneously at OC 2. In contrast, measurements taken after EDF 2 cannot provide a comprehensive observation of the injected signal due to the offset bandpass filter 2. Therefore, all the measurement results in this work are obtained at OC 2. Meanwhile, we also plotted the corresponding pulse train against the cavity roundtrips in Fig. 3(b). From the spectral and temporal evolutions of the oscillator starting process, it can be clearly observed that the multiple oscillator pulses are evolved directly from the seed pulse. Here, although ∼10 seed pulses are trying to evolve into oscillator pulses, the number of the successfully built pulses is finally limited to 4. It has been demonstrated that the pulse number in fiber oscillators depends on the pump power level, because the sufficient optical gain is critical to support the formation of stable pulse circulating in the laser cavity [26,27]. In fact, the successful buildup of seed pulses is in relation to the individual pulse intensity and the acquired optical gain. Note that the seed pulses propagating in the fiber MO also suffer intensity fluctuations owing to the gain competition. In this case, the selection of the seed pulses that evolve into the stabilized oscillator pulses is also somewhat random.

 

Fig. 3. Transition process from seed pulses to oscillator pulses. (a) Real-time spectral evolution recorded by DFT technique and (b) corresponding pulse train. (c) Expanded view of the pulse 1. The green curve presents the energy evolution. The yellow curve is the average spectrum of the last 10 roundtrips. (d) Single-shot spectrum before (red curve) and after (blue curve) ignition of the MO. Green curve: spectrum after stop injecting the seed pulse.

Download Full Size | PDF

For better clarity, the real-time spectral dynamics of pulse 1 from starting to stabilization was presented in Fig. 3(c). Here, we defined the immediate starting of pulse 1 as 1st roundtrip. Therefore, within the roundtrips before the 1st roundtrip, there is only the seed signal being injected in the MO. We can see that the duration from starting to stabilization takes about 400 roundtrips. During the buildup process of the pulse 1, the spectral bandwidth firstly broadens with oscillating behavior and gradually decreases. The green curve in Fig. 3(c) exhibits the energy evolution of pulse 1, which is obtained by integrating the real-time spectral profiles. A sudden increase of energy can be observed at the initial stage of the oscillator pulse generation. Then the energy gradually decreases with fluctuation for the first 400 roundtrips when the MO is operating towards the stable operation. It should be noted that energy integrated by the real-time spectra is a superposition of seed signal and oscillator pulse due to the successive injection of seed pulse. Therefore, there are many spikes on the energy evolution curve, which is actually the energy of the seed pulses. Figure 3(d) depicts the spectral profiles before (-22nd roundtrip, red curve) and after (718th roundtrip, blue curve) ignition of the MO. Here, the spectral profile of the seed pulse deviates from the original one shown in Fig. 2(a), owing to the bandpass filtering and spectral broadening induced by SPM in the MO. After ignition of the MO, the seed pulse and oscillator pulse are co-propagating in the cavity, where they share the optical gain of the EDF. Meanwhile, the gain sharing among the co-propagating seed and oscillator pulses lead to the lower intensity of the seed pulse at 718th roundtrip than that at -22nd roundtrip. Thus, it is expected that the spectral profile of the oscillator pulse will change if we stop injecting the seed pulse. The green curve in Fig. 3(d) provides the spectrum of the MO running in a stable multi-pulse pattern after stopping the injection of seed pulses. By comparing the blue and green curves in Fig. 3(d), the differences of spectral profiles could be attributed to variation of the optical gain acquired by the oscillator pulse.

To gain deeper insight into the starting dynamics of the MO, we provided the zoom-in plot of Fig. 3(c) (marked by white dashed box) from -25th to 40th roundtrip in Fig. 4(a), which further shows the buildup dynamics of the oscillator pulse. It is evident that the seed and oscillator pulses were not synchronized owing to different repetition rates. The corresponding details of the real-time spectral and temporal evolutions can be found in Visualization 1. Meanwhile, Fig. 4(b) shows several single-shot spectra during the buildup process of the oscillator pulse. Consequently, we are able to identify the initial spectrum of the seed pulse that evolves into the oscillator pulse. Due to the fixed output port of the MO, the circulating seed pulses possess almost the same profiles after propagating same roundtrips in MO. Nevertheless, a slight difference among the spectra of the circulating seed pulses still can be observed after propagating one roundtrip time, for example, the pulse spectra at -3rd and 1st roundtrips. For better clarity, Fig. 4(c) provides the details of the pulse spectra at -3rd and 1st roundtrips. It can be identified that the energy of the seed pulse at 1st roundtrip is higher than that of -3rd roundtrip. Then the seed pulse with higher energy will be selected and boosted into an oscillator pulse. Note that the cavity roundtrip time of the MO is about 147 ns and the interval of the circulating seed pulse is 64 ns along the oscillator cavity. Therefore, such a mismatch of repetition rates would lead to absence of pulses within the temporal range of 20 ns, i.e., at -1st roundtrip in Fig. 4(b). In Fig. 4(a), we can see that only one selected seed pulse would start to oscillate in MO, and the other seed pulses vanish eventually. When the new oscillator pulse is generated, the spectrum of the seed pulse varies due to the gain redistribution among the whole circulating pulses in the cavity of the MO, as indicated in Fig. 3(d). Therefore, from Fig. 3 and Fig. 4, we can conclude that the multiple pulses in MO are indeed evolved from the multiple seed pulses.

 

Fig. 4. (a) Zoom-in plot of the marked by white dashed box in Fig. 3(c). (b) Single-shot spectra during the buildup process. (c) Single-shot spectra at -3rd and 1st roundtrips.

Download Full Size | PDF

In our experiment, the starting number of the oscillator pulse can be reduced to 2 by decreasing the pump power without changing the seed laser source and other oscillator parameters. Although the MO can be ignited with single pulse operation under proper adjustment of oscillator parameters, such as wavelength separation of two bandpass filters, in our current setup the single-pulse starting cannot be obtained despite the fine tuning of the pump power on two arms. On the other hand, the successive injection of seed pulses is from a mode-locked laser, where the seed pulses have almost the same peak power as well as the nonlinear effect experienced in the MO. We note that there may exist strong gain competition among the injected seed pulses as well as simultaneous amplification of multiple seed pulses. In this case, the pump power for ignition of the MO would be higher than the threshold that supports the single-pulse operation. Therefore, the multi-pulse starting operation could be always observed in our MO.

In fact, the single-pulse starting operation would be preferred from the viewpoint of practical applications. As mentioned above, the major challenge to achieve the single-pulse starting operation is to alleviate the gain competition among the successively injected seed pulses. Suppose that a seed laser source operates in a pulse bunch regime with large intensity modulation and long bunch interval, the gain competition could be also significantly reduced, and thus it will facilitate the ignition of MO with a single-pulse operation. As a proof-of-concept experiment, we enable the seed fiber laser to operate in a critical state between the mode-locking and CW regimes by adjusting the pump power to around mode-locking threshold. The temporal profile of a typical pulse bunch is plotted in Fig. 5(a), from which we can see that the intensity of the pulse train is highly modulated with an interval of the pulse bunch of ∼25 µs. And the single bunch contains ∼30 pulses. Then we injected the pulse bunch into the MO, while the pump powers of two arms were kept for the single-pulse operation corresponding to the case of Fig. 2. As expected, the single-pulse starting operation could be observed with such a seed laser source. It should be noted that, when the pump power is sufficiently high, it is still possible to achieve multi-pulse starting by using the intensity-modulated pulse bunch as the seed signal. Again, the single-pulse starting process from seed signal to oscillator pulse was captured by the real-time spectral evolution with the DFT technique, as presented in Fig. 5(b). The overall spectral dynamics as well as the energy evolution of single-pulse starting are similar to those of multi-pulse starting one. However, the seed pulse with higher intensity acquires larger gain and quickly dominates the buildup process of the MO. As one seed pulse with higher intensity was evolving into the oscillator pulse, the optical gain distributed to other seed pulses is insufficient to build up. Therefore, the single-pulse starting operation could be effectively achieved from the MO despite the successive injection of the seed pulses. In addition, the evolution interval from the seed signal to oscillator pulse only lasts for about 10 roundtrips, which can be observed evidently from the energy evolution plotted as green curve of Fig. 5(b). Note that the oscillator stabilizing duration for single-pulse starting operation is much shorter than that of the multi-pulse starting scenario, which can be attributed to the reduced gain competition in the MO. Again, the pulse spectra recorded by optical spectrum analyzer (OSA) and DFT are plotted in Fig. 5(c), which are in well agreement with each other. It should be also noted that, for the same pump powers of MO, the spectra of the stabilized single-pulse would preserve the same profiles despite the different input seed signals, i.e., in Fig. 2(d) and Fig. 5(c), which is a typical feature of the dissipative optical systems [38].

 

Fig. 5. Single-pulse starting process of the MO. (a) Seed pulse. Inset: seed pulse train over 40 µs span. (b) Transition process from seed pulse to oscillator pulse. Green curve: energy evolution. (c) Red curve: averaged spectrum of last 10 roundtrips in (b). Blue curve: pulse spectrum measured by OSA.

Download Full Size | PDF

4. Numerical simulations

Numerical simulations allow us to further understand the pulse evolution dynamics within the MO. According to the experimental parameters, a numerical model was adopted to simulate the pulse dynamics. The pulse propagation in the optical fiber is described using the modified nonlinear Schrödinger equation [37,39]:

In our simulations, a weak hyperbolic secant pulse is used as a seed to initiate the MO. It has been confirmed that for a given set of cavity parameters, the shape of the weak seed signal does not affect the final profile of the stabilized pulse in dissipative optical systems [20]. The parameters in the simulations are set according to the experimental conditions. The following parameters are used in our simulations: ${\beta _2} = 15\; f{s^2}/mm$, ${\beta _3} = 86\; f{s^3}/mm$, $\gamma = 4.4\; {W^{ - 1}}k{m^{ - 1}}$ for EDF, ${\beta _2} ={-} 21\; f{s^2}/mm$, ${\beta _3} = 86\; f{s^3}/mm$, $\gamma = 1.1\; {W^{ - 1}}k{m^{ - 1}}$ for SMF. The length of EDFs and SMFs are 20 m and 10.3 m, and the spatial optical path of ∼0.6 m that constitutes filter 2 is neglected in the simulation. When ${E_s}$ is set to 650 pJ, the seed pulse is able to convert to an oscillator pulse and eventually evolves into a steady state. The simulation results are summarized in Fig. 6.

 

Fig. 6. Numerical simulation results for single pulse operation. (a) Optical spectrum. (b) Output pulse with cavity roundtrips. (c) Spectral and (d) temporal evolution of the pulse within the cavity.

Download Full Size | PDF

The pulse spectrum of the stable state is plotted in Fig. 6(a). The overall profile of the pulse spectrum is similar to the experimental one shown in Fig. 2(d), where the strong spectral peaks can be attributed to the super-Gaussian filter and SPM effect. The corresponding pulse evolution with the cavity roundtrips is presented in Fig. 6(b). The pulse duration is ∼2.3 ps. The simulated pulse duration is slightly larger than that of the experimental result, which could be caused by the pulse compression effect in the pigtailed fiber linking to the autocorrelator. Here, the seed pulse quickly evolves into the stable oscillator pulse after 3 roundtrips. Note that the duration from seed pulse to oscillator one is also dependent on the pump power and the intensity of seed signal. To show the pulse evolution dynamics more clearly, Fig. 6(c) and Fig. 6(d) provide the intracavity evolution of the oscillator pulse both in the spectral and temporal domains, respectively. The spectrum and pulse exhibit strong breathing behavior during the propagation along the fiber MO. After passing through the bandpass filter 1, the spectral bandwidth and pulse duration are both decreased. Then the oscillator pulse is amplified in the gain fiber with dramatically spectral broadening. Meanwhile, the pulse duration is gradually broadened owing to the normal dispersion of gain fiber. The gain fiber is followed by a segment of SMF with anomalous dispersion. Thus, the pulse width is compressed here while the spectral width is slightly broadened. The oscillator pulse then passes through the bandpass filter 2 and undergoes similar evolution dynamics to that after the filter 1. Finally, the oscillator pulse could be stabilized.

As demonstrated above, the single-pulse starting operation of the MO could be easily obtained if we only inject single seed pulse. However, for the practical situation, the seed signal is generally a train of ultrashort pulses from a mode-locked laser. To simulate the experimental results more closely, the seed signal was changed to be 5 equally spaced pulses with the same intensity, as shown in Fig. 7(a). During the simulations, the oscillator parameters are kept unchanged except for ${E_s}$. As depicted from Figs. 7(b)-(d), the number of starting pulses in MO is increased with the increasing ${E_s}$. Note that the optical gain for individual seed pulse would be reduced under the condition of multiple seed pulses for a fixed ${E_s}$, owing to the gain sharing among these seed pulses. Therefore, being different from the case of injection of single seed pulse, the ${E_s}$ for ignition of the MO should be significantly increased to 1287 pJ. It is also worth noting that only a small range of ${E_s}$ (∼7 pJ) can support the single-pulse starting operation of the MO, where 7 pJ is corresponding to less than 1 mW of pump power in practice. In this case, it is difficult to achieve the single-pulse starting operation for injecting multiple pulses with equal intensity, which is the same as that in the experimental observation.

 

Fig. 7. Numerical simulation for multi-pulse starting operation. (a) Seed pulses same intensity. (b) Threshold for ignition the MO. (c) Threshold for 2-pulses starting. (d) ${E_s}$ is large enough for 5-pulses starting. (e) Seed pulses with unequal intensity. (f-h) are similar to (b-d). Note that each figure is individually normalized.

Download Full Size | PDF

Then we injected 5 pulses with unequal intensity into the MO as seed signal, as shown in Fig. 7(e). It is expected that the seed pulse with higher intensity will dominate the starting process because of more gain acquired during the gain competition. That is, the seed pulse with higher intensity can survive and evolve into the oscillator pulse, while the other seed pulses quickly collapse due to inadequate gain. The single-pulse starting operation of the MO can be achieved at a lower pump power level because of the reduced gain competition effect among the seed pulses. In this scenario, although the multi-pulse starting operation is still observed at a higher pump power, the single-pulse starting operation can be obtained with a wide range of pump power, namely from 833 pJ to 2044 pJ, as indicated from Fig. 7(f) and Fig. 7(g). This is also the reason why the single-pulse starting operation can be easily observed if a pulse bunch with large intensity modulation is used as the seed signal in the experiment. Nevertheless, all the intensity-modulated pulses in the bunch can be converted into oscillator pulses as long as ${E_s}$ is large enough, as shown in Fig. 7(h). The simulation results verify the hypothesis well that the gain competition among seed pulses block the achievement of single-pulse starting operation in a MO.

5. Conclusion

In summary, we have experimentally and numerically investigated the starting dynamics of a fiber MO from seed signal to oscillator pulse. It is identified that the multi-pulse starting operation is actually evolved from the multiple seed pulses instead of the pulse splitting effect in the MO with larger offset spectral filtering. The real-time spectral dynamics during the starting process are revealed by the DFT technique. We also demonstrated that the gain competition among the successively injected seed pulses is a major obstacle to achieving the single-pulse starting operation. The highly intensity-modulated pulse bunch was proposed to be a promising seed signal to avoid the multi-pulse starting operation, which can effectively reduce the gain competition of the multiple seed pulses in the MO. These results could deepen our understanding of the pulse dynamics in MOs, which would be also attractive to the communities dealing with ultrafast lasers and nonlinear optics.