Dynamic Observation of Ultrashort Pulses with Chaotic Features in a Tm-Doped Fiber Laser with a Single Mode Fiber–Grade Index Multimode Fiber–Single Mode Fiber Structure

Abstract

In this study, we have demonstrated an ultrafast Tm-doped fiber laser utilizing the nonlinear multimode interference (NL-MMI) effect, with a single mode fiber–grade index multimode fiber–single mode fiber (SMF-GIMF-SMF) structure serving as the saturable absorber (SA). In addition to stable pulses, mode-locked pulses with chaotic features can be obtained in this fiber laser, characterized by a high average output power and pulse energy, resembling noise-like pulses. By employing the time-stretch dispersive Fourier transform (TS-DFT) technology, it can be seen that the sub-pulses constituting these pulses exhibit noisy characteristics with random intensities and energies. Furthermore, the numerical simulations elucidate the corresponding generation mechanism and dynamic evolution. These findings significantly enhance the comprehension of pulse dynamics and offer novel insights into the technological development and application prospects of ultrafast fiber lasers.

1. Introduction

Ultrafast fiber lasers, renowned for their compact design, high peak power, and narrow pulse width, have found increasingly widespread applications in industrial processing, medical, and communication fields [1,2,3,4]. Additionally, due to their excellent nonlinear effects, they also serve as good platforms for probing soliton dynamics [5,6,7]. In ultrafast fiber lasers, saturable absorbers (SAs) are crucial for achieving stable ultrashort pulses [8,9]. Currently, various SAs have been successfully applied to ultrafast fiber lasers, such as nonlinear optical loop mirror (NOLM) [10,11,12], nonlinear polarization rotation (NPR) [13,14,15], nonlinear amplified loop mirror (NALM) [16,17,18], and novel nanomaterials [19,20,21,22]. Notably, the mode-locked fiber lasers utilizing the nonlinear multimode interference (NL-MMI) effect have emerged as a research hotspot in fiber lasers [23,24]. In these fiber lasers, the single mode fiber–grade index multimode fiber–single mode fiber (SMF-GIMF-SMF) configuration serves as an excellent SA, providing the foundation for the generation of ultrashort pulses. The SMF-GIMF-SMF structure has gained attention for its high damage threshold. Furthermore, the SMF-GIMF-SMF SA shows an all-fiber structure, which enables the ultrafast fiber lasers to be more compact and more robust. Thus, the performance of the SMF-GIMF-SMF structure remains stable and impervious to temporal variations, thereby avoiding the degradation issues that are typically encountered with nanomaterials. The development of ultrafast fiber lasers with an NL-MMI-based SA not only enhances the performance of the laser but also opens up new possibilities for the advancement of ultrafast fiber laser technology.

Ultrafast fiber lasers utilizing the NL-MMI effect have been extensively investigated in recent times. In 2019, Zhu et al. integrated a segment of no-core fiber into the SMF-GIMF-SMF, utilized as an SA in an Er-doped fiber laser to obtain conventional solitons [25]. In 2020, Chen et al. incorporated an SMF-GIMF-SMF SA into a linear cavity of Er-doped fiber laser, successfully generating pulses with a peak power of 7.79 kW [26]. In 2022, Cheng et al. demonstrated a 1 μm fiber laser with an SMF-GIMF-SMF structure [23] and observed noise-like pulses and dissipative solitons. In 2023, Ahmad H et al. constructed an ultrafast fiber laser based on the GIMF–step index multimode fiber (SIMF)–GIMF using Er/Yb-co-doped fiber, achieving a maximum average output power of 322 mW [27]. Li H et al. demonstrated different soliton mode-locking operations in a thulium-doped fiber laser using an SMF-NCF (no core-graded index multimode fiber)-GIMF-SMF device as a saturable absorber (SA) [28]. Wang X. et al. proposed an all-fiber SA based on NL-MMI in a short few-mode fiber (FMF) and achieved stable mode-locking operations in a thulium-doped passively mode-locked fiber laser [29]. The experiments proved that the NL-MMI could be used for researching 2 µm ultrafast fiber lasers, and these studies demonstrated the ability of fiber lasers to utilize the NL-MMI effect to generate ultrafast pulses, providing innovative directions and possibilities for the advancement of mode-locked fiber laser technology.

In this study, a thulium-doped fiber laser with an SMF-GIMF-SMF configuration as an SA has been successfully demonstrated. At a lower pump power level, a stable mode-locking pulse state can be easily observed. Upon elevating the pump power and tuning the polarization state, the operation can switch to another pulse regime with a high average output and pulse energy. Moreover, the time-stretch dispersive Fourier transform (TS-DFT) method has been implemented, stretching the temporal information to the frequency domain, revealing more detailed characteristics. The shot-to-shot spectra reveal that the special pulse state actually consists of many sub-pulses that vary randomly in width and amplitude, and is thus described as the pulse bunch, similar to the noise-like pulses. Additionally, as the pump power rises, the number of sub-pulses within the pulse train is also on the rise. At the maximum pump power, the average pulse energy output can reach 116 mW, corresponding to a pulse energy of 18.68 nJ. These findings enhance the comprehension of the ultrashort pulse dynamics in mode-locked fiber lasers utilizing the NL-MMI effect, and pave the way for the development of advanced laser systems with tailored pulse characteristics to meet various application requirements.

2. Experimental Setup

Figure 1a depicts the structure of the mode-locking fiber laser employing the NL-MMI mode-locking technique. A homemade 1570 nm fiber laser is employed as the pump source and the pump light is coupled into the laser cavity via a wavelength division multiplexer (WDM). The gain medium is a 2 m-long thulium-doped fiber (TDF) exhibiting a dispersion parameter of −69 ps²/km at 1.9 μm. A total of 20% of the output within the cavity is extracted through an output coupler (OC) for pulse characteristic monitoring, while the remaining 80% of the light circulates within the cavity for amplification. The laser cavity employs the NL-MMI effect of the SMF-GIMF-SMF to induce mode-locking, with the core diameter of the GIMF being 50 μm. Furthermore, a polarization-independent optical isolator (PI-ISO) is utilized to guarantee unidirectional light transmission within the ring cavity, and a triple-ring polarization controller (PC) is situated between the PI-ISO and the SMF-GIMF-SMF, which is used to optimize polarization states. The pigtails of all optical devices are single-mode fibers with a dispersion parameter of −65 ps²/km at 1.9 μm. The fiber laser operates in the anomalous dispersion regime and the total length is approximately 32.2 m. The length of GIMF is 43 cm. Therefore, the laser cavity shows a total calculated net dispersion value of ~−2.101 ps². The laser output can be characterized using an optical spectrum analyzer (Thorlabs, OSA203C, Newton, MA, USA), an oscilloscope (Rohde & Schwarz, RTP044, Munich, Germany), a commercial autocorrelator (APE-150 PulseCheck, Berlin, Germany), and a radio-frequency (RF) spectrum analyzer (Siglent, SSA5023A, Shenzhen, China) to comprehensively analyze the pulse properties.

Figure 1b depicts the nonlinear optical absorption of the SMF-GIMF-SMF SA. When the light from the SMF enters the GIMF, mode coupling effects excite higher order mode components within the GIMF. As these modes propagate through the GIMF, they experience different phase shifts due to nonlinear effects, leading to interference and the formation of a pulse train. The high-intensity light then couples back into the SMF, where it is amplified in a laser cavity and re-emerges to repeat the process, ultimately resulting in pulse output. Thus, this structure can be used as a reliable SA, facilitating effective mode-locking. The measured modulation depth is approximately 47.1%, and the fitted curve exhibits a modulation depth of ~75.8% with a non-saturable loss of ~20%. These results demonstrate that the SMF-GIMF-SMF-based SA exhibits superior saturable absorption characteristics, rendering it ideal for mode-locking devices in fiber lasers.

3. Results and Discussion

Upon increasing the pump power to 140 mW, unstable pulse trains are observed. Under this condition, by finely adjusting the PC, a stable mode-locking state can be observed. Figure 2 illustrates the output characteristics of this state. Figure 2a shows the optical spectrum with a central wavelength of 1910 nm and 3 dB bandwidth of 3.17 nm. Notably, the Kelly sidebands appear on both sides of the optical spectrum, which suggests that this fiber laser operates in the anomalous dispersion region [30]. Figure 2b depicts the pulse trains where the interval between successive pulses is 161 ns, which corresponds to the time required for the optical signal to propagate around the laser cavity once. Additionally, the uniform distribution of pulse intensity suggests that it is in a relatively stable state. Figure 2c displays a broadband RF spectrum with a good flatness over a range of 500 MHz, indicating that the laser pulses have a stable condition. Figure 2d is the RF spectrum with a small scanning range, showing that the frequency repetition rate is about 6.21 MHz and the signal-to-noise ratio (SNR) is approximately 75 dB. The scanning resolution of the RF spectrum is 100 Hz. At this time, the measured average output power is 1.16 mW and the average pulse energy is calculated to be approximately 0.19 nJ. Due to the low power output in this state, it does not meet the power requirement of the autocorrelator. Therefore, the pulse width corresponding to this state cannot be measured.

Furthermore, when the pump power increases to 520 mW and the PC is finely changed, a new set of mode-locked pulses can be obtained, as depicted in Figure 3a. The optical spectrum has a central wavelength of 1911 nm and a 3 dB bandwidth of 0.81 nm. There is no obvious Kelly sideband observed on the spectrum. The pulse train is displayed in Figure 3b with a pulse interval of 161 ns, and the pulse intensities have some slight changes. Figure 3c displays the RF spectrum, which features an SNR of 64 dB at 6.21 MHz. The scanning resolution of the RF spectrum is 100 Hz. The pulse duration, as displayed in Figure 3d, is measured using an autocorrelator. If a sech2 fitting method is employed, the pulse width is estimated to ~1.43 ps. At this time, the measured average output power is 42.72 mW and the average pulse energy is calculated to be approximately 6.88 nJ, which far exceeds the pulse energy (~0.1 nJ) of conventional solitons [31]. Within 100 min, the output power is measured at intervals of 10 min, resulting in the power variation curve shown in Figure 4. It can be seen that the output power of the state remains essentially constant, indicating that the laser can maintain mode-locking operations for a relatively long period of time without external interference, demonstrating a relative high degree of stability in this mode-locked state.

In order to further explore the characteristics of this regime, the three-dimensional (3D) temporal evolutions based on a high-speed oscilloscope are evaluated, as illustrated in Figure 5a,c. With increasing pump power, more random sub-pulses appear within the pulse bunch, which also exhibit greater intensity. To delve deeper into the evolution of the pulse bunch, the TS-DFT technology is employed to investigate the characteristics of pulses over 1000 roundtrips within the cavity. The dispersive medium used here is a linearly chirped fiber Bragg grating (TeraXion, Quebec City, QC, Canada) with a total dispersion parameter of 300 ps/nm. The spectral resolution based on the DFT is calculated to be ~0.28 nm [32,33]. The shot-to-shot spectral evolution at 520 mW and 920 mW are depicted in Figure 5b,d. These figures reveal the energy intensity distribution of the pulse spectra, with the higher intensity pulses clustered near the central wavelength across both pump powers. The intensity comparison, aided by the color map on the right, shows that Figure 5d exceeds Figure 5b in intensity, suggesting that pulses possess higher energy at elevated pump powers, consistent with the experiments obtained using the OSA. Furthermore, the yellow curve illustrates the temporal energy variations in the pulse bunch, exhibiting non-periodic and irregular changes. Notably, the fluctuations in the energy curve in Figure 5d are more pronounced than those in Figure 5b, indicating a more complex variation in pulse intensity at higher power levels. Additionally, Figure 6 illustrates the variation in output power and pulse energy as the pump power increases from 520 mW to 1020 mW, where there is a noticeable upward trend in the average pulse output power and pulse energy with the increase in pump power. At the maximum pump power, the average pulse output power is approximately 116 mW, which corresponds to an average pulse energy of ~18.68 nJ. When the pump power exceeds 1020 mW, the output state of the laser becomes unstable.

To explore and gain a deeper understanding of pulse characteristics, the nonlinear Schrödinger equation (NLSE) is used to explore the pulse generation in fiber lasers [34].

$${\displaystyle \frac{\partial A}{\partial z}}=-i{\displaystyle \frac{{\beta }_2}{2}}{\displaystyle \frac{{\partial }^{2}A}{\partial t^2}}+i\gamma {\left|A\right|}^{2}A+{\displaystyle \frac{g-\alpha }{2}}A+{\displaystyle \frac{g}{2{\Omega }_g^2}}{\displaystyle \frac{{\partial }^{2}A}{\partial t^2}}$$

(1)

where A represents the pulse amplitude, z is the distance, t is the time, β₂ is the second-order group velocity dispersion, γ signifies the self-phase modulation coefficient, g represents the gain saturation coefficient, α represents the cavity loss, and Ω_g represents the gain bandwidth. The key parameters used in the simulations are generally consistent with the experimental conditions, as shown in

Table 1. The main parameters of the numerical model.

TDF	SMF	SMF-GIMF-SMF SA
β2 = −69 ps2/km	β2 = −65 ps2/km	ΔT = 75.8%
γ = 3 W−1 km−1	γ = 3 W−1 km−1	Tns = 20%
L = 2 m	L = 30.2 m	Psat = 50 W

.

When the parameter is appropriately adjusted, the stable pulse operation can be easily achieved. Figure 7a illustrates the optical spectral evolution. As the cavity roundtrips increase, the spectral envelope remains unchanged, indicating that this state is stable. Figure 7b presents the spectrum with a central wavelength at 1910 nm. Distinct Kelly sidebands are observed on either side of the central wavelength, aligning with the characteristics of the experimental results. Figure 7c shows the pulse train, suggesting that the envelope contains one pulse. By adjusting the gain saturation coefficient g, corresponding to changing the pump power in the experiment, the output pulse regime can switch into a special pulse state. Figure 7d presents the spectral evolution of these pulses. It can be clearly seen that the spectral energy is concentrated at the center, and there are obvious substantial fluctuations with the evolution of cavity roundtrips. As shown in Figure 7e, the red line fits the spectral envelope without Kelly sidebands, indicating that this pulse operation is no longer the conventional soliton state. Figure 7f depicts the pulse train, in which numerous sub-pulses are observed with random pulse amplitudes and widths, exhibiting chaotic pulses characteristics, consistent with the experimental observations.

In the experiment, all devices used are polarization-independent to eliminate the interference of nonlinear polarization rotation (NPR) mode-locking mechanisms on the experimental results. There is a PC in the laser cavity, and by rotating the wave plates of the PC, the intracavity birefringence is altered, which may lead to pulse splitting and the formation of a pulse bunch. Moreover, the formation of pulses with noise characteristics has been extensively studied [35,36]. Due to the critical saturation effect of pulses, strong pumping power can cause pulse collapse, with newly generated pulses concentrating around the original pulse and having uncertain pulse widths and intervals, forming a noise-like pulse bunch [35]. However, the noise-like pulse bunch observed in the experiment differs from those previously reported, which have broad and smooth spectra [37,38]. The mode-locked pulses with chaotic features observed in our experiment have narrower spectra and exhibit irregular peaks due to modulation effects. This can be considered a characteristic of chaotic pulses under the NL-MMI effect.

Table 2. Summary of relevant research achievements of some ultrafast thulium-doped fiber lasers.

Wavelength/nm	Material	Width/ps	Repetition/MHz	Output/mW	Energy/nJ	Ref.
1953	Graphene	2.1	16.93	0.08	1.41	[39]
1951	Cu2Te	1.58	8.1	~3.2	0.39	[40]
1935.7	FePS3	1.47	10.95	1.28	0.117	[41]
1961.2	PbS	1.09	43.86	9.06	0.207	[42]
1911	SMF-FMF-SMF	1.96	15.69	2.8	0.178	[29]
1910	SMF-GIMF-SMF	1.43	6.21	42.72	~6.88	Our

summarizes some of the relevant research achievements of thulium-doped fiber lasers. The results demonstrate that the fiber laser incorporating a GIMF-based structure achieves comparable output pulse performances, highlighting GIMF’s considerable potential for applications in ultrashort pulse lasers.

4. Conclusions

In summary, we demonstrated an ultrafast Tm-doped fiber laser with an SMF-GIMF-SMF configuration. By properly adjusting the pump power and the polarization state, stable mode-locking pulse output could be achieved. Upon further increasing the pump power, the laser transitioned to a chaotic pulse state, with significant spectral changes and the disappearance of the Kelly sidebands. The TS-DFT technology was employed for an in-depth analysis of the pulse bunch, revealing that it contained multiple sub-pulses with random amplitudes and pulse widths, and that the number of sub-pulses increased with pump power. At maximum pump power, the output average power and pulse energy reached ~116 mW and ~18.68 nJ, respectively. Additionally, these pulse characteristics were simulated in theory. These findings will deepen the understanding of the effects of the SMF-GIMF-SMF SA and provide a scientific basis for its application in ultrafast fiber lasers.