1. Introduction

Fiber lasers continue to be an attractive field of research as they can provide practical and robust sources for various applications. Especially fiber lasers around 2 µm offer unique possibilities in certain fields such as mid-IR supercontinuum generation, tissue ablation and spectroscopy [1–4]. Different optical effects lead to rich intracavity dynamics for fiber lasers resulting in a diverse set of lasing regimes. By manipulating these effects, a wide variety of pulse forms including solitons, dissipative solitons, and dissipative soliton resonances have been demonstrated around 2 µm [5–8].

Noise-like pulses (NLPs) are long wavepackets that contain many sub-pulses with randomly varying amplitude and duration and they can be formed within laser cavities with higher intracavity nonlinearities compared to solitons and dissipative solitons [9]. Therefore, it is possible to obtain NLPs in the same cavity as other pulse forms by adjusting the birefringence or increasing the pump power regardless of the net cavity dispersion [10–12]. Under these conditions, mode-locked single pulses transform into a wavepacket that is composed of sub-pulses with different amplitudes, pulse durations and phases as a result of various formation mechanisms such as soliton collapse, peak power clamping or nonlinear instabilities [13–16]. Real-time analysis has shown that intra-cavity NLP formation does not require as delicate of a balance between cavity parameters and strict pulsing mechanism as stable mode-locking [17–19]. Numerical simulations suggest the instabilities leading to NLP formation can be generated in a cavity in just a few round-trips [20]. Recently, it has been shown that similar mechanisms inducing pulse collapse can be mimicked to generate NLPs in a single-pass nonlinear amplifier, demonstrating that positive feedback within a laser cavity is not the only mechanism for NLP formation [21]. Regardless of the generation method, the temporally stable NLP structure is characterized by a double-scale intensity autocorrelation (IAC) trace where a coherence spike of sub-picosecond duration is superimposed on top of a wide pedestal with a typical duration of tens of picoseconds to few nanoseconds [14]. The wide pedestal corresponds to the overall wavepacket duration, whereas the spike represents the average duration of the sub-pulses [21]. NLPs can also be identified by their broad and smooth optical spectrum. The averaging effect originating from the contribution of each sub-pulse’s optical spectrum leads to a spectral feature that is challenging to generate otherwise [22]. These distinctive temporal and spectral profiles make NLPs a promising candidate for numerous applications, namely for low-coherence interferometry, micromachining, and supercontinuum generation [23–25].

So far, studies focusing on wavelengths around 2 µm have demonstrated only in-cavity NLP generation and have shown that different cavity configurations can form NLPs with various pulse energies, pedestals, and spike durations [26–29]. NLP lasers that employ 2D-material based saturable absorbers are limited to pulse energies of several nano-Joules with a coherence spike duration of ∼400 fs and differing pedestal durations between 25 ps to 300 ps [27,30]. Although cavities using nonlinear-polarization evolution (NPE) can generate higher energy levels by reaching >10 nJ with comparable spike durations, the pulses are accompanied with pedestal durations from several hundred picoseconds up to one nanosecond [28,29,31]. However, pedestal durations in the nanosecond range can be undesirable in certain cases such as material processing and pedestal compression methods have been studied at 1 µm [32]. Nonlinear-optical loop mirror-based oscillators can deliver NLPs with pulse energies of ∼250 nJ, however, they also suffer from extremely long pedestal durations of several hundred picoseconds [25]. Direct amplification of NLPs has been demonstrated as an effort to harvest higher pulse energies while keeping the pedestal durations as short as possible. Although an amplified NLP energy of ∼10 µJ has been achieved using multiple preamplifiers and a large-mode area power amplifier, the pedestal duration was reported as ∼4.2 ns [33]. To the best of our knowledge, there is only a single study that reports sub-100 ps pedestal duration and an energy level of ∼50 nJ by amplifying NLPs from an NPE mode-locked cavity [30]. The coexistence of NLPs with solitons and dissipative solitons in the same cavity has been shown at 2 µm, albeit not simultaneously [34,35].

In this study, we show that it is possible to generate NLPs externally to the oscillator, in a nonlinear fiber, when soliton pulses with a pulse energy of 1 nJ and a pulse duration of 1.5 ps are used as seed pulses for the first time in literature. Using nonlinear fiber lengths of 100 m and 140 m enables the generation of NLPs with different densities and varying pedestal/spike durations. In both cases, the NLPs follow similar power scaling trends and result in a pulse energy of ∼200 nJ, a spike duration of ∼200 fs, and a pedestal duration of sub-40 ps, which are the shortest durations reported for comparable energy levels in literature. Since the characteristics of the generated NLPs are functions of the nonlinear fiber length, the proposed method allows a certain control over the output without changing any other parameters adding enhanced reproducibility and robustness to the generation process. Additionally, the external generation of NLPs provides a system where solitons and noise-like pulses can co-exist simultaneously.

2. Experimental setup

The NLP laser system consists of three stages: (i) an all-fiber oscillator with an amplification stage followed by (ii) a nonlinear fiber to generate noise-like pulses, and (iii) two fiber amplifiers to boost the NLP power to multi-Watt levels (Fig. 1(a)). The all-fiber cavity facilitates a carbon-nanotube saturable absorber for mode-locking and generates soliton pulses at 1886 nm with a 3-dB bandwidth of 3.2 nm and a repetition rate of 21.3 MHz (Fig. 1(b)). The average power of 0.63 mW from the 10% output coupling port corresponds to an output pulse energy of 29.5 pJ. The output pulses from the oscillator are directly amplified to an average power of 21 mW in a 138-cm long thulium-holmium (Tm/Ho) co-doped, core-pumped preamplifier. The preamplifier gain is kept at 15.2 dB to minimize nonlinear effects and to preserve the optical spectral shape (Fig. 1(b)). The preamplified pulses have a hyperbolic secant profile and a duration of 1.52 ps, which is longer than the transform-limited pulse duration due to accumulated dispersion. The preamplified solitons (seed pulses) are then launched into a nonlinear fiber for the NLP generation. For the nonlinear fiber, a silica fiber with a core diameter of 2.4 µm and a nonlinear coefficient of γ ≈ 10 W^-1·km^-1 is used with different lengths of 100 m and 140 m. A second core-pumped Tm/Ho co-doped preamplifier with 7.1 dB gain (161 cm fiber length) compensates for losses experienced in the nonlinear fiber. The last stage consists of a backward pumped double-clad amplifier with a 104-cm long Tm-doped fiber that boosts the average power up to 5.19 W, corresponding to a pulse energy of 244 nJ. To protect the earlier stages from the unabsorbed pump and the signal propagating in the cladding, a cladding pump stripper (CPS) is used before the main amplifier.

 

Fig. 1. (a) Schematic of the NLP laser system: the amplified soliton seed pulses (stage i) generate NLP in a nonlinear fiber (stage ii) and the NLPs are amplified up to 5.19 W power (stage iii). TDF, thulium-doped fiber; WDM, wavelength division multiplexer; OC, output coupler; CNT-SA, carbon-nanotube saturable absorber; PC, polarization controller; ISO, isolator; MPC, multi-pump combiner; DC, double-clad, (b) Comparison of the oscillator (blue) and preamplifier spectra (red) shows almost no change during preamplification, (c) Intensity autocorrelation profile of the soliton seed pulses. Sech² fitting (black) to experimental data (blue) results in a pulse duration of 1.52 ps.

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3. Results and discussion

3.1 Noise-like pulse generation

In our experiments, soliton pulses evolve into NLPs during propagation in the nonlinear fiber. To understand the NLP generation mechanism better, we investigate the effect of the fiber length on the output pulse characteristics. Keeping the seed pulse energy constant at 1 nJ, two different lengths of the nonlinear fiber, 100 m and 140 m, are tested. While NLPs can also be generated in longer nonlinear fibers, the pulse energies are significantly lower due to the propagation losses at 1.9 µm. Optical characteristics of NLPs generated in 100-m and 140-m long nonlinear fibers, which are referred to as NLP-I and NLP-II, are summarized in Fig. 2. When the nonlinear fiber length is 100 m, NLPs (NLP-I) have a 3-dB bandwidth of 17.7 nm (Fig. 2 (a)). Usually, NLPs have a broad and smooth spectrum, since they represent the average of many highly structured spectra, each of which corresponds to an individual pulse in the wavepacket [36]. Thus, the pulse number in the wavepacket plays a direct role in determining the overall spectral shape of NLP. Since longer fiber lengths induce a higher nonlinear phase accumulation that leads to a stronger pulse breaking, NLPs generated with 140-m long nonlinear fiber (NLP-II) have a higher number of sub-pulses within the wavepacket. This results in a smoother spectrum compared to the shorter fiber case and a wider bandwidth of 26.6 nm (Fig. 2(a)).

 

Fig. 2. (a) The optical spectra of NLPs generated within 100-m long (NLP-I, blue, top) and 140-m long (NLP-II, red, bottom) nonlinear fibers feature a 3-dB bandwidth of 17.7 nm and 26.6 nm, respectively. (b) Double-scale intensity autocorrelation trace of NLPs with a pedestal-to-peak ratio of 0.85 and a pedestal duration of 51.1 ps at the output of the 100-m long nonlinear fiber. The IAC trace of the spike as inset shows a spike duration of 363 fs. (c) The IAC trace of the NLPs with a pedestal-to-peak ratio of 0.7 and a pedestal duration of 56.9 ps at the output of the 140-m long nonlinear fiber. The IAC trace of the spike as inset shows a spike duration of 345 fs.

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NLP-I and NLP-II have slightly different energies of 0.5 nJ and 0.35 nJ, respectively. For a pulse duration measurement, we amplify the signals to 1.45 nJ and 0.97 nJ. Figure 2(b) and Fig. 2(c) show the IAC traces for NLP-I and NLP-II. In both cases, the pedestal profile is Gaussian and has a full width at half maximum duration of 51.1 ps and 56.9 ps, respectively. Although the tails of the pedestals are clipped on both sides due to the limited scan range of the autocorrelator, we ensure that the pedestal durations are accurate by confirming the pulse duration of a single pulse with comparable and known duration. For both nonlinear fiber lengths, the autocorrelation traces feature a double-scale structure, which is characteristic for NLPs [14]. The pedestal-to-peak intensity ratio is 0.85 for NLP-I, see Fig. 2(b), and 0.7 for NLP-II, see Fig. 2(c). This ratio indicates the density of the wavepackets and sparse NLPs have ratios close to 1. As the density of the wavepacket increases and the intensity of the sub-pulses fluctuate fully stochastically, that ratio converges to 0.5 [37]. Thus, the ratio of 0.85 for NLP-I suggests a certain level of coherence among the sub-pulses and that they are sparsely located within the wavepacket. This smaller ratio of 0.7 for NLP-II indicates a denser wavepacket with a stochastic intensity variation of the sub-pulses. Spike durations, shown in the insets of Fig. 2(b) and Fig. 2(c), are measured as 363 fs and 345 fs. The shorter spike duration of NLP-II also points out a lower coherence among the sub-pulses compared to a shorter length [36].

Both spectral and temporal measurements indicate that NLP can be generated inside the 100-m and 140-m long nonlinear fibers with slightly different characteristics. Considering the symmetrical spectral broadening, self-phase modulation (SPM) is the dominant nonlinear effect and with stronger SPM, pulse breaking sets in as well as soliton collapse. The higher nonlinearity associated with longer fiber lengths leads a more pronounced NLP generation. As a result, the pulses have distinct optical spectra and autocorrelation traces unique to NLPs that set them apart from any multi-pulsing regimes [38]. Compared to incoherent supercontinuum generation associated with Raman scattering in all-normal dispersion photonic crystal fibers [39–41], the optical spectrum in Fig. 2 is symmetrically broadened, indicating a minimal contribution of Raman scattering in this case. The weak birefringence of the nonlinear fiber allows different polarization states to emerge during the pulse splitting and improves the NLP properties similar to the in-cavity NLP formation where highly nonlinear fibers are utilized for broader bandwidths [42]. It should be noted that no feedback is needed for the NLP generation in our system, since it is based on soliton collapse similar to the evolution of dissipative solitons into NLPs in a nonlinear amplifier [21].

3.2 Amplification of noise-like pulses

To demonstrate power scaling, we amplify both NLP-I and NLP-II in a double-clad Tm doped fiber amplifier. It should be noted that in both cases, the NLPs are directly sent into the fiber amplifier without any prior stretching, since the stochastic nature of the pulses minimizes the dispersive effects [43,44]. When we amplify the NLP-I, an average power of 5.19 W is obtained for an incident pump power of 18 W, which corresponds to an amplifier slope efficiency of 28.9% and a gain of 22.3 dB. The pulse energy is calculated as 244 nJ. Optical characteristics of the amplified NLP-I are shown in Fig. 3.

As the output power increases from 0.77 W to 5.19 W, the 10-dB bandwidth broadens from 41 nm to 105 nm (Fig. 3(a)). The asymmetric broadening favoring longer wavelengths indicates that Raman induced nonlinear effects such as self- and cross-frequency shifts become effective in addition to SPM due to higher peak powers [33]. For all output power levels, the double-scale intensity autocorrelation trace preserves its shape and the pedestal-to-signal ratio improves to 0.7 when the output power is 5.19 W (Fig. 3(b)), indicating a loss of coherence among the amplified sub-pulses. The same effect also reveals itself as a compression in the spike duration from 312  fs to 150 fs (Fig. 3(c)) [37]. This can be potentially explained by more pulse breaking within the generated NLPs with stronger nonlinear effects as the pulses are amplified. Continuous narrowing of the spike duration as the pump power increases indicates shorter spike durations are possible. The pedestal duration increases from 36.4 ps to 38.1 ps, however, it does not increase monotonously, similar to the results on NLP amplification at 1.5 µm [37]. This indicates that the newly generated sub-pulses are still within the existing wavepacket.

 

Fig. 3. Amplification of the NLPs obtained with a 100-m long nonlinear fiber (NLP-I). (a) The spectral evolution of the NLPs with respect to output power shows asymmetric broadening, (b) The IAC trace of the NLP when the output power is 5.19 W has a spike and pedestal duration of 150 fs and 38.11 ps, respectively. (c) Variation of the spike and pedestal durations as a function of output power. The spike durations show a clear compression trend for higher powers.

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During amplification, an asymmetric spectral broadening sets in already at lower output powers for NLP-IIs, and spectra become broader for the same output power levels. This is a result of the higher nonlinearity accumulation associated with the longer nonlinear fiber length before the amplification stage. An average power of 4.14 W is obtained for a pump power of 18 W, corresponding to an amplifier slope efficiency of 23% and a gain of 22.9 dB. The lower slope efficiency is due to the lower input power into the amplifier compared to the previous case. The pulse energy is calculated as 194 nJ at the amplifier output. Figure 4 summarizes the amplified NLP-II characteristics.

Both spectral and the temporal profiles follow the same trends as the amplified NLP-I. The 10-dB bandwidth broadens from 35 nm to a maximum of 181 nm at 18 W (Fig. 4(a)) as the output power increases. The double-scale intensity autocorrelation trace indicates that the NLP nature is preserved (Fig. 4(b)). Since the coherence among the wavepacket is already low, the spike compression is limited and the duration decreases from 286 fs to 177 fs. Similar to the amplified NLP-I, the compression trend shows that shorter spike durations are possible for higher output powers. One important difference between the two cases is the visible broadening in the pedestal duration from 34.3 ps to 42.3 ps for NLP-II. Since the spectrum is wider in this case, the temporal walk-off between the pulses is more pronounced, which causes a broadening in the wavepacket.

 

Fig. 4. Amplification of the NLPs obtained with a 140-m long nonlinear fiber (NLP-II). (a) The spectral evolution of the NLPs with respect to output power indicates a broadening of the 10-dB bandwidth from 35 nm to 181 nm. (b) The IAC trace of the NLP with an output power of 1.08 W has a spike and pedestal duration of 286 fs and 34.3 ps. (c) Variation of the spike and pedestal durations as a function of output power. The spike durations show a clear compression trend, whereas the pedestal duration monotonously broadens with higher output powers.

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4. Conclusion

In summary, we demonstrated that soliton pulses at 1.9 µm can evolve into noise-like pulses outside of the cavity when coupled into a nonlinear fiber. The amount of the accumulated nonlinearity for different nonlinear fiber lengths determines the generated NLP profile, its spectral broadening and pulse properties. Amplification of the pulses results in NLPs with a pulse energy of ∼200 nJ, a spike duration of ∼200 fs, and a pedestal duration of sub-40 ps. The reported NLP durations are the shortest reported to the best of our knowledge for comparable energy levels at 1.9 µm. Further scaling of the NLPs while preserving their characteristic properties should be achievable as well. We therefore presented a novel pathway to generate NLPs from soliton pulses externally to the cavity, offering versatility and flexibility in a robust fiber system that can fuel a wide range of applications from micromachining to low coherence interferometry.