Impact of spectral filtering in coexistence of noise-like pulse and dissipative soliton Open Access

Fiber lasers are an attractive research area that can provide practical and powerful light sources for various applications.^1–3 Passively mode-locked fiber lasers serve as an excellent light source for generating ultrashort pulses. Fiber lasers have rich intracavity dynamics due to multiple nonlinear effects existing in the cavity, resulting in different pulse states such as dissipative soliton resonance,⁴ noise-like pulse (NLP),⁵ soliton explosions,⁶ soliton rains,⁷ and so on. NLP is a common operation mechanism in passively mode-locked fiber lasers. Experimental and numerical studies have shown that the NLP is a wave packet containing many ultrashort pulses with a complex and variable structure. Since the NLP has very stable overall behavior and higher energy,⁸ it has a wide range of applications in the fields of supercontinuum spectrum generation,⁹ laser-induced breakdown spectroscopy,¹⁰ and sensing.¹¹ 

Passively mode-locked fiber lasers can achieve soliton output with different repetition frequencies through bidirectional-multiplexing,¹² polarization-multiplexing,^13,14 and wavelength-multiplexing technologies.¹⁵ Using wavelength-multiplexing technology, passively mode-locked fiber lasers can output the dual-wavelength same-type soliton, like dual-wavelength dissipative soliton (DS) and dual-wavelength conventional soliton.^16–18 The coexistence of different soliton types can also be realized, such as harmonic soliton molecules and rectangular NLP,¹⁹ NLP and high repetition rate harmonic soliton,²⁰ NLP and conventional soliton,²¹ and NLP and dark pulse.²² These studies are mostly based on anomalous dispersion or near-zero dispersion cavities. There are fewer studies of the coexistence of NLP and DS observed in ytterbium-doped fiber lasers (YDFLs). A study observed the pulse dynamics of switching between NLP coexisting with DS, and dual-DS using the time-stretched dispersive Fourier transform technique for the first time in YDFL by introducing the Sagnac filter.¹⁵ In addition, the generation of NLP is not limited to the mode-locking mode and dispersion region of the laser,^23–25 so its formation mechanism has been widely studied by researchers.^26–29 A number of studies have shown that the generation of NLP in passively mode-locked fiber lasers based on nonlinear polarization rotation (NPR) is mainly due to the peak power clamping effect of NPR.^26,29 The mechanism of NLP generation in passively mode-locked fiber lasers based on saturable absorbers (SAs) is affected by spectral filtering effects^30,31 and reverse saturable absorption (RSA).³² Except for the semiconductor saturable absorber mirror (SESAM), many new types of SAs are currently being used for mode-locked lasers in different wavelength bands to achieve multiple pulse type outputs have been widely reported.^33–35 Mechanisms of pulse formation in mode-locked fiber lasers based on SA have been reported.^30–32 However, there are few reports on the mechanism of the coexistence of NLP and DS.

In this work, we introduce a Lyot–Sagnac filter in the laser based on SESAM, which can achieve NLP and DS coexistence with switchable wavelength interval outputs. Numerical simulation reveals that the filtering effect plays an important role in the balance of gain and loss in the cavity. The coexistence and switching of different pulse types are achieved when the filtering bandwidth is varied. The study enriches the investigation of the coexistence mechanism of NLP and DS, and provides a new way to study the coexistence of NLP and DS. Meanwhile, it has potential applications in the field of dual combs.

The schematic of the wavelength interval and pulse switchable fiber laser based on SESAM is shown in Fig. 1. It has a ring cavity that is coupled to a Lyot–Sagnac filter through a 50/50 optical coupler (OC1). The 980 nm laser diode (LD) pumps the 0.35 m ytterbium-doped fiber (YDF) [Liekki Yb1200, group velocity dispersion (GVD) = 24.22 ps²/km] through a 980/1060 nm wavelength division multiplexing (WDM). The polarization-independent isolator (PI-ISO) guarantees the unidirectional propagation of pulses in the cavity. The mode locker is implemented by SESAM mounted on a standard ferrule connector/physical contact (FC/PC) fiber connector. The SESAM has a modulation depth of 20% as well as a relaxation time constant of 1 ps. A three-port polarization-independent circulator is used to incorporate the SESAM into the cavity. The 10/90 OC2 splits 10% of light pulse energy for measurement, while 90% of the light continues to transmit in the cavity.

According to Eq. (1), the transmission spectrum at different wavelength intervals obtained by simulation and measured in the experiment are shown as blue and red curves in Figs. 1(b) and 1(c), respectively. The blue curves in Figs. 1(b) and 1(c) are the simulated transmission spectrum for θ₁ − θ₂ = π/2 and θ₁ = θ₂, respectively. It can be seen that the wavelength intervals measured in the experiments correspond to the simulations.

Single-wavelength DS can be achieved at a pump power of 115 mW. The mode-locked spectrum of DS exhibits a central wavelength of 1031.21 nm and a 3 dB bandwidth of 2.88 nm, as shown in Fig. 2(a). Figure 2(b) displays the RF spectrum with a fundamental frequency of 14.25 MHz, which corresponds to the cavity length of 14.4 m. The signal-to-noise ratio (SNR) is 63 dB, indicating that the laser is in a stable mode-locked state. The pulse train on the oscilloscope is shown in Fig. 2(c). The time interval between adjacent pulses is 70.2 ns, and the real pulse train recorded by the oscilloscope in the range of 2 ms also shows that the laser is in a stable mode-locked state. The pulse autocorrelation trace in Fig. 2(d) demonstrates a pulse width of 11.33 ps under Gaussian fitting and a time-bandwidth product of 9.20.

We achieved the transition from DS to NLP by increasing the pump power to 140 mW. The NLP spectrum has a central wavelength of 1031.71 nm and a 3 dB bandwidth of 2.60 nm, illustrated in Fig. 2(e). The RF spectrum is presented in Fig. 2(f), with a fundamental repetition frequency of 14.25 MHz. The SNR is 51 dB, which is significantly lower than that of the stable mode-locked state. There is an obvious noise pedestal on both sides of the fundamental repetition frequency, which is one of the typical features of NLP and is mainly caused by amplitude noise. In Fig. 2(g), the time interval between adjacent pulses is 70.2 ns, and the amplitude is unstable, which can be clearly seen from the pulse train in the range of 2 ms. Figure 2(h) displays the dual-scale autocorrelation trace of the NLP, where the full pedestal width could not be measured due to the limitation of the measurement range of the autocorrelator used (up to 50 ps), but clear spikes can be seen, with a spike width of 1.27 ps under Gaussian fitting. Meanwhile, we observe the interesting phenomenon that the NLP can be switched to DS by adjusting PC1 and PC2 without changing the pump power, which is considered to be due to the change of filtering that prompts this transition, and the detailed analyses are described in the simulation.

The wavelength-tunable DS can be achieved by adjusting PCs while keeping the pump power at 115 mW. The spectrum of the wavelength-tunable DS is illustrated in Fig. 3(a), and the pulse widths under Gaussian fitting are depicted in Fig. 3(b). It can be seen that the 3 dB bandwidth changes from 3.12 to 1.78 nm as the central wavelength of the DS is tuned from 1027.96 to 1048.21 nm. The single-wavelength DS tuning range is up to 20.25 nm. When the central wavelength is tuned to 1044.89 and 1048.21 nm, the pulse position is slightly shifted to measure the pulse width more accurately due to the limitation of the measurement range of the autocorrelator, which does not affect the measurement results.

When the pump power is increased to 160 mW, dual-DS output can be achieved. By adjusting the PCs, the filter interval of the Lyot–Sagnac filter can be changed to achieve dual-DS with different wavelength intervals, as shown in Figs. 4(a), 4(b), 4(e), 4(f), 4(i), and 4(j). The central wavelengths of the dual-DS are 1030.99 and 1045.04 nm, respectively, as indicated in Fig. 4(a), and the central wavelength spacing is 14.05 nm (corresponding to the filtering interval when the effective fiber length is 0.2 m). The RF spectrum displayed in Fig. 4(b) illustrates a repetition frequency difference of 1800 Hz, and several small peaks symmetrically distributed on both sides correspond to the beat frequency of the two pulses. The difference in repetition frequency is caused by fiber dispersion, proving the existence of asynchronous pulses, which can be seen in the interferometric pattern of the dual-wavelength pulse train. As shown in Fig. 4(e), the interval between beat signals is 556 μs, which is consistent with the repetition frequency difference of 1800 Hz. Figure 4(f) represents a random pulse train triggered by the oscilloscope. The time interval between the two pulse trains is 70.2 ns. The time difference between the asynchronous pulses is 54.4 ns. By adjusting the PCs, dual-DS output is achieved at the central wavelengths of 1034.92 and 1043.43 nm with a wavelength interval of 8.51 nm, as depicted in Fig. 4(i) (corresponding to the filtering interval when the effective fiber length is 0.34 m). The RF spectrum presented in Fig. 4(j) illustrates a repetition frequency difference of 1189 Hz.

When the pump power is increased to 180 mW, the coexistence of NLP and DS at different wavelength intervals can be achieved, as depicted in Figs. 4(c), 4(d), 4(g), 4(h), 4(k), and 4(l). Without changing the polarization states in Fig. 4(a), the output from dual-DS to the coexistence of NLP and DS can be achieved by increasing the pump current to 180 mW only. The central wavelengths of NLP and DS are 1030.98 and 1045.15 nm, respectively, and the wavelength interval is 14.17 nm. The RF spectrum presented in Fig. 4(d) illustrates a repetition frequency difference of 1812 Hz. As shown in Fig. 4(g), the interval between beat signals is 552 μs. Under constant pump power, the coexistence output of NLP and DS can be achieved at 1034.52 and 1043.45 nm with a wavelength interval of 8.93 nm by adjusting PCs, as shown in Figs. 4(k) and 4(l). The RF spectrum presented in Fig. 4(l) illustrates a repetition frequency difference of 1200 Hz. The NLP is always formed at short wavelengths because of the higher gain intensity at short wavelengths than at long wavelengths in the gain fiber. When the pump power is 180 mW, NLP coexists with DS and dual-DS can be switched by adjusting the PCs, which cannot be achieved at low pump power. This relates to filtering losses and cavity gain.

The transmission curves of SESAM for different RSA coefficients and the saturable absorption states and RSA states are shown in Fig. 5. The blue curves in Fig. 5 are the SESAM transmission curves obtained from Eq. (6) for RSA coefficients of 0.5 and 1.5 km⁻¹, respectively. The red curve represents the instantaneous power P of the pulse and the transmission power after passing through SESAM, that is, the product of the SESAM transmission and instantaneous power. The saturation absorption and RSA curves inside the cavity are shown in red in Figs. 5(a) and 5(b). The power corresponding to the critical point of saturable absorption and RSA is the critical saturation power (CSP).³⁹ Considering that the transmittance T is related to the saturable absorption inside the cavity, the CSP from saturable absorption to RSA is at the maximum product of instantaneous power P and the corresponding transmission.⁴⁰ Points A and B represent the positions of CSP in Fig. 5. When the peak power of the pulse exceeds CSP, it will cause a peak power clamping effect. We select β = 0.5 km⁻¹ for the simulation.

To better understand the formation of NLP and the coexistence of NLP and DS, it is necessary to investigate how the pulse varies with the pump intensity and the filter bandwidth. Keeping the fiber laser operating in a single pulse state, varying the filter bandwidth and pump intensity yields the simulation results shown in Fig. 6. Figures 6(a)–6(i) show the simulation results after 850 round-trips for g₀ = 37.20 m⁻¹ and Δλ₁ at 5, 6, and 7 nm, respectively. When Δλ₁ = 5 nm, the initial noise field gradually evolves into a stable single-DS pulse. Figure 6(a) displays the spectral evolution, and the inset shows the peak power variation of the pulse with round-trips. Figure 6(b) indicates the pulse evolution. Combining Figs. 6(a) and 6(b) shows that after the initial noise field incidence, the pulse evolves into a stable single-DS with round-trips, and the energy variation tends to be stable. Figure 6(c) shows the autocorrelation trace of the final round-trip output pulse.

When Δλ₁ = 6 nm, a stable single-DS pulse is also formed; however, the spectral bandwidth decreases compared to that in Fig. 6(a), the peak power of the pulse decreases [see the insets of Figs. 6(a) and 6(d)], and the pulse duration increases [see Figs. 6(c) and 6(f)]. This is due to the fact that the filter bandwidth increases, the filter loss decreases, and the pulse energy increases. At the same time, the pulse narrowing ability is weakened, so the pulse duration increases, which leads to lower peak power of the pulse. The spectral width also decreases as the lower peak power leads to less self-phase modulation.^28,30 When Δλ₁ = 7 nm, a stable DS is unable to be formed, and the initial noise field gradually evolves into a single NLP, as shown in Figs. 6(g)–6(i). The spike structure of the dual-scale autocorrelation trace of the NLP is shown in the inset of Fig. 6(i). A noteworthy point is that throughout the pulse evolution in Fig. 6, the peak power of the pulse does not exceed the CSP corresponding to point A in Fig. 5(a), meaning that the SESAM keeps operating in a saturable absorption state; thus, the NLP generation is not due to the RSA.

It has been shown that the filter bandwidth plays an important role in the formation of pulses, and when the filter bandwidth is too narrow, it leads to pulse break-up or a multi-pulse state. When the filter bandwidth is increased, NLP is generated.^31,41,42 This is due to the fact that when the filter bandwidth is larger, the loss of the filter is reduced and the pulse has higher energy. At this point, the losses in the cavity are not enough to balance with the gain, nonlinearity, and dispersion, and the gain is too high to result in the pulses not forming a stable DS, but operating as pulse clusters in the cavity. It can be observed that the number of round-trips to form a stable DS increases significantly for Δλ₁ = 6 nm compared to Δλ₁ = 5 nm. Running as NLP in the cavity for some time before the formation of a single DS can verify this explanation. Whereas, when Δλ₁ = 7 nm, the loss in the cavity is not enough to support the DS generation so that NLP is formed. For further verification, Δλ₁ = 6 nm is fixed, and we only increase g₀ to 37.30 m⁻¹ finding that a stable DS cannot be formed but the NLP is formed. The simulation results are shown in Figs. 6(j)–6(l). Therefore, when the pump intensity is large and the filtering effect is small, the intracavity effect cannot be sufficiently balanced to form a DS, prompting the pulse to round-trip as an NLP in the cavity.

Afterward, we increase g₀ to ensure that the cavity can operate in a dual-wavelength state. Varying the filter bandwidth and pump intensity yields the simulation results shown in Fig. 7. Figures 7(a)–7(i) show the simulation results for 850 round-trips with g₀ = 37.65 m⁻¹, Δλ₂ = 6 nm, and Δλ₁ at 5, 6, and 7 nm, respectively. When Δλ₁ = 5 nm, the initial noise field gradually evolves into stable dual-wavelength DS, and when Δλ₁ = 6 nm, Δλ₁ = Δλ₂, also forming stable dual-wavelength DS. However, does having different filter bandwidths at the two wavelengths have any effect on the pulse? The 200th round-trip of the pulse after the OC at Δλ₁ = 5 nm and Δλ₁ = 6 nm is output as shown in Fig. 8. When the filter bandwidths are different in the cavity, a smaller filter bandwidth results in a narrower pulse width, decreased pulse duration, and higher pulse peak power, as illustrated in Fig. 8(a). And when Δλ₁ = 6 nm, the peak power difference of dual-wavelength DS pulses is very small, as shown in Fig. 8(b). In addition, the different spectral reconstruction times of the two soliton collisions can be clearly seen in Figs. 7(a) and 7(d). The reason is that soliton collisions induce soliton explosions but each soliton explosion is different from the other, which is called a “periodic” soliton explosion.⁴³ 

When Δλ₁ = 7 nm, the initial noise field gradually forms two pulse clusters, while the pulse at 1043 nm can form a single DS pulse due to the smaller filter bandwidth. Due to the larger filter bandwidth at 1031 nm, the filter loss is small with the pulse having higher energy. At this time, the losses in the cavity are not enough to balance with the gain, nonlinearity, and dispersion. The gain is too high for the pulse to form a stable DS, so it operates in the cavity as a pulse packet. It has been shown that NLP and other solitons not only coexist independently, but also interact with each other.⁴⁴ Since the NLP is a wave packet containing sub-pulses with different peak powers and pulse widths that vary with round-trips, this affects the evolution of the DS pulse, but it does not affect our results. (The OSA used in the experiment collects an average spectrum and therefore does not vary all the time.)

When Δλ₁ is fixed at 6 nm and g₀ is increased to 37.82 m⁻¹, the coexistence of NLP and DS outputs is also achieved, which is due to excess intracavity gain, as illustrated in Figs. 7(j)–7(l). However, the filter bandwidths at the two wavelengths are the same—why is the NLP formed at 1031 nm instead of 1043 nm? This is related to nonlinear effects and dispersion in the cavity, as proved by the fact that in the single-wavelength simulation, the DS and the NLP are formed first at 1031 nm instead of 1043 nm under the condition of low pump intensity.

It can be found that increasing the pumping intensity and varying the filter bandwidth affect the intracavity pulse formation, which leads to the switch between DS and NLP, as well as the coexistence of NLP and DS, mainly due to the alteration of the intracavity gain and loss. Pulse formation is the result of the combined effect of gain loss, nonlinear effects, and dispersion.⁴⁵ When the gain and loss are changed, the pulse formed also varies.

In conclusion, we build a laser which achieves coexistence of NLP and DS with switchable wavelength intervals due to the use of a Lyot–Sagnac filter. The laser also outputs a single-wavelength switchable pulse type, tunable single-DS, and switchable wavelength interval dual-DS. The laser provides new possibilities for pulse-switchable light sources and has potential applications in the field of dual combs. Furthermore, we build a YDFL simulation model and find that the filtering effect plays an important role in the generation of NLP and the coexistence of NLP and DS in mode-locked fiber lasers based on SESAM through numerical simulations. When the gain and filter bandwidth in the cavity are changed, the pulse type is switched. Increasing the filter bandwidth or the pumping intensity prompts the generation of NLP. This study enriches the research on the NLP generation mechanism and provides a new way to study the coexistence of NLP and DS.

This work was supported by the National Natural Science Foundation of China (Grant No. 62375220) and the Shaanxi Key Science and Technology Innovation Team Project (Grant No. 2023-CX-TD-06).

The authors have no conflicts to disclose.

Jiajing Lang: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Resources (equal); Software (equal); Writing – original draft (equal). Chenyue Lv: Conceptualization (equal); Formal analysis (equal); Methodology (equal); Resources (equal); Software (equal); Writing – review & editing (equal). Baole Lu: Conceptualization (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal). Jintao Bai: Conceptualization (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.