Optimization of Output Characteristics in Figure-9 Mode-Locked Fiber Laser Based on Black Phosphorus Assistance

Abstract

Utilizing the nonlinear effects of black phosphorus (BP), the self-starting threshold and noise performance were optimized in a figure-9 mode-locked fiber laser configuration. Experimental results demonstrate that a mode-locked pulse output with a spectral bandwidth of 8.2 nm, center wavelength of 1033.5 nm, and repetition rate of 42 MHz is obtained. Compared with single-mechanism mode-locked lasers, the self-starting mode-locked threshold is reduced by 100 mW. Regarding noise characteristics, the signal-to-noise ratio (SNR) is enhanced to 68.4 dB and the phase noise is reduced to −115.6 dBc/Hz at 1 MHz to 10 MHz frequency offsets. The root mean square (RMS) of the output power is optimized to 0.9% and phase noise jitter is reduced to 1.9%. This work proves a novel approach to tackle the challenges of high self-starting thresholds and instability in mode-locked lasers.

1. Introduction

In recent years, mode-locked pulsed lasers have assumed increasingly critical roles across multiple disciplines, owing to their exceptional stability and high-energy characteristics, including attosecond photonics [1], optical frequency combing [2], biomedicine, material processing [3], and laser detection [4]. Common configurations for artificial saturated absorbers include nonlinear polarization rotation (NPR) [5,6,7] and a nonlinear amplifying loop mirror (NALM) [8,9,10,11,12,13]. In particular, the NALM mechanism has matured significantly due to its rapid response time, short relaxation period, and structural simplicity. The introduction of nonreciprocal phase shift elements enables transition from negative to positive feedback states for low-intensity light, thereby facilitating self-starting mode-locked fiber lasers [14,15,16]. Inspired by this concept, researchers proposed a phase-bias-based self-starting figure-9 mode-locked fiber laser, which achieves cavity length reduction and repetition rate enhancement [17].

Nevertheless, challenges still persist in figure-9 configurations. The inherent limitation imposed by the cavity length results in weak nonlinearity, which necessitates high pump power to enhance nonlinearity to achieve self-starting mode-locked operation. Recent advancements have focused on saturable absorber (SA) integration into resonant cavities to enhance nonlinear effects and reduce the self-starting threshold [18]. In 2023, Chen, W. et al. developed a graphene-decorated microfiber (GMF) that leverages thermally induced nonlinear effects to dynamically regulate phase shifts, achieving a 90 mW threshold reduction [19]. This demonstrates that saturable absorbers can compensate for intracavity nonlinearity deficits and attain low-threshold self-starting. In 2024, Qian, X. et al. proposed the integration of a semiconductor saturated absorption mirror (SESAM) at the linear arm terminus of a figure-9 cavity, establishing mode-locked operation and noise suppression [20]. The SNR was improved by 33 dB and the RMS of power fluctuation stabilized at 0.23%@12 h. Comprehensive analysis of the aforementioned research reveals that saturable absorbers not only provide accumulate additional nonlinear effects to reduce the self-starting threshold of lasers but also demonstrate advantages in noise optimization. However, carbon nanotubes (CNTs) [21,22] exhibit a spectral response range that highly depends on diameter, thereby significantly increasing the self-starting threshold. While graphene is a zero-bandgap material with weak absorption properties, these characteristics limit its capacity for optical modulation. Although MXene possesses broadband nonlinear optical response characteristics, its susceptibility to oxidation and poor dispersibility often result in inhomogeneous film formation due to particle agglomeration [23,24]. Additionally, SESAMs are hampered by notoriously high fabrication costs and inherent optical bandwidth limitations [25,26].

In contrast to the aforementioned saturable absorbers, BP demonstrates a distinctive band structure characterized by layer-dependent tunable bandgaps (0.3–2.0 eV) and exceptional nonlinear optical properties. It effectively bridges the technological gap between zero-bandgap graphene and wide-bandgap transition metal dichalcogenide (TMDC). It offers a revolutionary approach to ultrafast laser system design. As a direct bandgap semiconductor, it exhibits aligned conduction and valence bands. This unique electronic configuration enables superior photoelectric conversion efficiency and efficient current switching capabilities, a combination that distinguishes BP from conventional two-dimensional (2D) materials. Furthermore, the bandgap of it can be precisely modulated through layer thickness control to achieve broadband optical wavelength absorption spanning from 600 nm to 4100 nm. This exceptional spectral coverage spanning from near-infrared to mid-infrared regions enables unprecedented compatibility with mode-locked operations across diverse laser gain media [27,28,29,30]. Furthermore, BP demonstrates ultrahigh carrier mobility (up to 10⁴ cm²/V·s) in monolayer structures coupled with picosecond-level ultrafast carrier recovery dynamics [31]. Such exceptional electronic properties endow BP with superior nonlinear response speed and modulation depth, critical for generating stable mode-locked pulses. The weak van der Waals (VDM) interactions make it easy to integrate it with fiber-optic systems, and its high damage threshold and long-term stability further solidify its practicality in photonic devices [32,33,34]. These characteristics make it an ideal candidate material for achieving low-noise and low-threshold mode-locked lasers. In 2018, Song, H. analyzed a fiber laser generating cylindrical vector beams using graphene and BP in a figure-9 cavity [35]. The central wavelength of the spectrum was 1054.3 nm with a repetition rate of 41.1 KHz. However, it only achieved a Q-switched pulse output.

To address these challenges, this work innovatively proposes an optimized figure-9 cavity mode-locked fiber laser enhanced by dynamic nonlinear regulation with BP-SA. By integrating BP-SA (exhibiting 23.8% modulation depth) within the NALM configuration, we achieve the concurrent compensation of nonlinear phase shifts and suppression of relaxation oscillation noise. The experiment shows that the optimized laser architecture achieves a 100 mw reduction in the self-starting mode-locked threshold. The SNR is improved to 68.4 dB and the phase noise is as low as −115.6 dBc/Hz within the 1–10 MHz frequency offset. This work advances a new implementation of high-stability ultrafast light sources in optical frequency comb spectroscopy and attosecond pulse generation systems.

2. Characterization and Nonlinear Saturable Absorption Characteristics of BP

The Raman spectrum of the BP-SA is shown in Figure 1a, exhibiting characteristic peaks at 360.53 cm⁻¹, 436.36 cm⁻¹, and 463.37 cm⁻¹, which correspond to the vibrational modes of the BP crystal lattice [36,37]. The spectral analysis indicates that the BP sample had a thickness of several atomic layers [38]. Subsequently, the BP flakes were dispersed in ethanol for 12 h to achieve homogeneous suspension, followed by centrifugation at 1000× rpm for 60 min to remove unexfoliated bulk particles. The BP was then deposited on the fiber end-faces using an optical deposition method, and low-loss fiber connectors were employed to form a transmissive BP-SA structure. The saturable absorption properties of the BP-SA were quantitatively characterized through a dual-power measurement technique, and the experimental setup is schematically illustrated in Figure 1b. The test light source consisted of a laboratory constructed ytterbium-doped mode-locked fiber laser operating at a center wavelength of 1033.4 nm, with a repetition frequency of 19 MHz and a pulse duration of 792 fs. The modulation depth of BP-SA is 20.2% and the unsaturated loss is 33.5% as shown in Figure 1c.

The input optical intensity was regulated by a variable optical attenuator (VOA). The laser output passed through a 3 dB optical coupler (OC). One output arm was directed through the BP-SA as the test signal and the other served as a reference beam. Both signals were monitored by calibrated power meters (S145C 800–1700 nm, THORLABS, Newton, NJ, USA). Through computational analysis and curve fitting, the saturable absorption characteristics of the BP-SA were derived, as shown in Figure 1c. The modulation depth of the BP-SA was measured to be 20.2%, and the unsaturated loss was 33.5%. When the laser output power was 6 mW, the BP-SA saturable absorption curve was observed to approach a saturation stat with a saturation power value (Is = 12 kW/cm²). These results demonstrate that the BP-SA can be used as a saturable absorber.

3. Experimental Structure and Principle

The experimental configuration of the figure-9 mode-locked fiber laser is illustrated in Figure 2a. The gain medium is a 1.2 m nonpolarization-maintaining ytterbium-doped fiber (YDF, core absorption of 250 dB/m @ 976 nm). The cavity is constructed with single-mode fiber (SMF) with a total length of 2.7 m. The second-order dispersions (SODs) of them at 1030 nm are 0.024 ps²/m and 0.023 ps²/m. The transmission BP-SA is connected behind the YDF to the modulation gain spectrum. The linear arm comprises two polarization beam splitters (PBSs), a faraday rotator (FR), wave plates (WPs), and a metal high-reflectivity mirror. The length of the linear arm is about 0.2 m and the total length of the cavity is 4.1 m. A 1200 l/m grating pair with a grating distance of 3 cm is positioned for pulse width compression at the output of PBS2. The YDF is pumped by a 980 nm laser diode through a wavelength division multiplexer (WDM) and gain laser-facilitated free-space beam delivery by collimators (Col). The laser from Col1 passes through a half-wave plate (HWP) for polarization state adjustment and then transmitted through PBS1 into a non-reciprocal phase shifter comprising an FR and wave plate to induce differential phase delay. The beam is subsequently reflected by the end mirror. The retroreflected beam retraces through the non-reciprocal phase shifter and is reinjected into the cavity through Col2, which completes the resonator configuration.

To observe the characteristics of the mode-locked laser, the output pulse from PBS2 is received through a Col3 and divided into two beams by a 50:50 optical coupler (OC). One of the beams, after passing through a variable optical amplifier (VOA), enters a high-resolution spectrometer (MS9740A, Anritsu, Kanagawa Prefecture, Japan) with a spectral resolution of 0.07 nm to detect the spectrum. The other beam passes through a VOA and a 200 MHz photodetector (PDA1020, 900–1700 nm, KTC, Shenzhen, China) to convert the optical signal into an electrical signal and is divided into two beams by a power divider device (RS2W000103-S, 1–300 MHz, Taylor Microwave, Shenzhen, China). The mode-locked pulse sequence is tested by an oscilloscope (54833A, 1 G Sa/s, Agilent, Santa Clara, CA, USA), and the frequency domain signal and phase noise are measured by a radio frequency (RF) signal analyzer (N9020A, 10 Hz–3.6 GHz, KEYSIGHTNA, Santa Rosa, CA, USA). The duration and shape of the pulse output are measured by an autocorrelation meter (Pulse Check, USB 150, A.P.E, Berlin, Germany).

The self-starting mechanism is determined by the phase shift difference within the figure-9 mode-locked fiber laser. It comprises two distinct components: the inherent nonlinear phase shift from the laser itself and the linear phase shift difference introduced by the non-reciprocal phase shifter. In the absence of a nonreciprocal phase shifter, the transmission curve is illustrated by the black curve in Figure 2b. In this negative feedback regime, the laser remains incapable of achieving self-starting mode-locked operation when operating at the saturation point of the curve. The application of a nonreciprocal phase shifter induces a rightward shift in the transmission curve, effectively transitioning the laser into a positive feedback regime. When the phase bias provided is π/2, the transmission curve undergoes a characteristic rightward displacement, indicated by the green trace in Figure 2b. By increasing the pump power to enhance the intracavity nonlinear phase shift, the initial operating point A on the transmission curve shifts toward the critical position C. This fulfills the self-starting condition for the laser. While theoretically continuing to elevate pump power could theoretically drive the saturable absorption point to its target displacement, in practical implementation, the achievable nonlinear phase shift difference is inherently limited by the asymmetric positioning of the gain fiber. This limits the experimentally accessible pump power levels and achievable nonlinear phase shift differences for reliable the self-starting mode-locked threshold. To overcome the high self-starting threshold and compensate for the inherent nonlinear phase shift, the BP-SA is implemented with a nonlinear compensation strategy. This alteration alters the transmission dynamics by displacing the initial operating point from position A to B on the characteristic curve. Such optimization of the transmission characteristics effectively reduces the requisite pump power density and diminishes the self-starting threshold.

4. Results and Analysis

In this study, we experimentally demonstrated the mode-locked pulse generation in BP-SA within a figure-9 cavity fiber laser. The mode-locked mechanism remained functional across the 44° rotational range of the λ/8 waveplate. The optimized laser demonstrated a self-starting mode-locked threshold at 315 mW, representing a 100 mW reduction compared to the identical cavity configuration without BP-SA integration. As depicted in Figure 3a, the output pulse characteristics reveal an optical spectrum centered at 1033.5 nm with a 3 dB bandwidth of 8.2 nm. The temporal pulse train demonstrated consistent periodicity with a 23.7 ns pulse interval, as shown in Figure 3b. The RF spectrum in the pulse frequency domain is shown in Figure 3c. The SNR was 64.7 dB at the fundamental repetition frequency of 42.2 MHz, indicating exceptional amplitude stability and phase coherence. The autocorrelation trace is shown in Figure 3d. The pulse duration was 316 fs, and the pulse shape was close to Gaussian.

To systematically investigate the performance enhancement induced by BP-SA in the figure-9 mode-locked fiber laser, a controlled experiment was conducted with pump power at 415 m. The comparative experimental results of pulse characteristics with and without BP-SA are shown in Figure 4. The 3 dB spectral bandwidth was 12 nm without the introduction of BP-SA from Figure 4a. These results confirm that the modulation effect of the BP-SA on the spectral width and morphology. This phenomenon can be explained by two interrelated mechanisms: First, the additional nonlinear effects introduced by BP-SA in pulse evolution dynamics lower the mode-locked threshold and accelerate pulse formation. The rapid initiation of mode-locked suppresses temporal pulse broadening, thereby constraining the spectral bandwidth. Second, in nonlinear dynamic equilibrium, spectral modulations typically arise from interactions between self-phase modulation (SPM) and dispersion in the absence of BP-SA. However, it disrupts this equilibrium by suppressing modulational instability caused by intracavity interactions. Additionally, the fast recovery time enables the rapid stabilization of intensity fluctuations, which effectively suppresses the sidebands generated by modulational instability, ultimately producing to a smoother and narrower spectrum. Theoretically, spectral narrowing typically conforms to the time–bandwidth inverse relationship governed by the Fourier transform. In practical systems, when pulses are subjected to shaping or filtering processes, the time–bandwidth product is no longer a constant. The pulse duration may not proportionally increase due to nonlinear chirp accumulation or dispersion management even with spectral narrowing. As evidenced by the autocorrelation traces in Figure 4b, the pulse width with BP-SA was 313 fs.

The noise characteristics of the original cavity architecture exhibit inherent limitations primarily due to the sensitivity of non-polarization-maintaining fibers to environmental perturbations such as temperature fluctuations and mechanical stress. These instabilities, compounded by continuous wave (CW) component oscillations, generate intermodulation products that appear as phase jitter pedestals distributed on the fundamental RF signal. This directly caused the SNR of 47.3 dB measured in the unimproved configuration. The integration of BP-SA facilitates a hybrid mode-locked mechanism and attenuates CW component fluctuations and stochastic noise perturbations. This approach simultaneously enhances the stability of mode-locked pulse and ensures the self-starting capability in the laser system. As shown in Figure 5a, the optimized fundamental frequency component at 42 MHz demonstrated a significantly enhanced SNR of 68.4 dB. This validates the efficacy of BP-SA in noise suppression. Furthermore, the phase noise test results in Figure 5b demonstrate a marked reduction from −102.4 dBc/Hz to −115.6 dBc/Hz within the range of the 1 MHz to 10 MHz frequency offset with the assistant of the BP-SA. To comprehensively evaluate the temporal stability of phase noise, time-domain jitter measurements across 100 consecutive sampling points at 10 MHz offset frequency were quantitatively analyzed, as shown in Figure 5c. Phase noise timing jitter was effectively reduced to 1.9% with the implementation of the BP-SA. This confirms the significant phase noise suppression effectiveness of BP-SA in mode-locked laser. The experimental data demonstrate that this method not only stabilizes self-starting mode-locked pulses but also improves noise indicators.

The output pulse power and energy characteristics were measured, as shown in Figure 6a. The cavity demonstrated a 100 mW reduction in the self-starting threshold compared to the reference configuration. Under identical 415 mW pump power conditions (Figure 6b,c), the reference cavity produced 540 pJ pulses with 0.92 kW peak power, while the BP-SA integrated system generated 464 pJ mode-locked pulses with peak power reaching 1.4 kW. To quantify power stability improvements, we compared the RMS values of the laser output power within 30 min intervals under identical environmental conditions. As shown in Figure 6d, the advanced figure-9 cavity exhibited enhanced robustness to environmental perturbations and the RMS value was improved to 0.9%. This confirms the ability of BP-SA in noise suppression.

5. Discussion

This work represents the first investigation about the dual role of BP in optimizing the self-starting performance and noise suppression of figure-9 mode-locked fiber lasers to the best of our knowledge. Previous studies have confirmed the potential of saturable absorbers in controlling the mode-locked threshold [39], but they often have limitations. Previous approaches have either relied on the thermal nonlinear effects [19] or only focused on a single performance indicator such as noise suppression [40,41,42]. Consequently, the beneficial effects of saturable absorbers on the mode-locked threshold and noise suppression have not been synergistically unexplored. To address this issue, we propose a BP-assisted figure-9 mode-locked laser. Through the nonlinear dynamics of the BP-SA, it achieves the simultaneous optimization of both stability and self-starting performance while maintaining the original linear phase shift difference in the figure-9 fiber laser.

In the selection of real saturable absorbers, BP demonstrates a broader spectral absorption range compared to graphene’s constrained absorption bandwidth [43]. In contrast, MXene exhibits inherent limitations including oxidation susceptibility and compromised dispersibility. Under high-power conditions, non-uniform deposition induces localized heat accumulation, which accelerates material damage, compromises laser output stability and introduces experimental discrepancies [23,24]. Similarly, CNTs are constrained by the diameter-dependent spectral response range, which not only confines their applicability to specific wavelength regimes but also impairs their capacity to reduce self-starting thresholds [44]. As a superior alternative, BP demonstrates a uniquely tunable bandgap (0.3–2.0 eV), combining the broadband responsiveness and strong nonlinear effects characteristics of graphene. With high carrier mobility and exceptional modulation depth, devices outperform conventional saturable absorbers in both mode-locked threshold reduction and long-term stability maintenance. Therefore, the proposed BP-SA assisted figure-9 laser system enables dual-functional enhancement through nonlinear dynamics optimization. The self-starting mode-locked threshold was reduced to 315 mW through the nonlinear phase shift dynamic compensation mechanism of BP-SA in this work. Additionally, saturable absorption characteristics effectively suppressed noise fluctuations, enhancing the SNR to 68.4 dB and reducing phase noise to −115.6 dBc/Hz in the range of the 1–10 MHz frequency offset. Furthermore, the optimized system demonstrated excellent power stability with an RMS fluctuation of 0.9%. We believe that this architecture will provide substantial advancement for nonlinear dynamics control and noise suppression in ultrafast laser systems.

There are some assumptions that need to be acknowledged. The core of this study is the optimization of the mode-locked threshold and noise index of the laser. However, the output pulse power is relatively low. The following methods can be employed to enhance power: (1) Increasing the pump power: In current experimental setups, pump sources are constrained mode instabilities induced by thermal effects and fiber damage thresholds, which introduce additional noise interference. Implementing a bidirectional pumping scheme can enhance amplified spontaneous emission (ASE) gain while preventing the introduction of high-power noise. (2) Gain fiber length optimization: Utilizing high-concentration doped fibers reduces optical absorption losses, further achieving better equilibrium between gain and loss. (3) Intracavity loss mitigation: Primary intracavity loss sources include splice points between fibers, free-space optical couplers, and inherent losses from inserted components. Through the monolithic integration of collimators with WDMs and other devices, the number of free-space components and fiber fusion points can be reduced. This integrated approach can simultaneously reduce cavity losses and satisfy high pulse energy output requirements. These synergistic improvements can establish robust, low-threshold, low-noise femtosecond pulse generation. These coordinated optimizations can collectively enable a robust femtosecond laser system characterized by a low oscillation threshold and minimized noise levels throughout pulse generation processes.

6. Conclusions

This work introduces a novel methodology for enhancing the self-starting capability of figure-9 cavity fiber lasers through nonlinear dynamic modulation with BP-SA, while preserving the linear phase bias established by the nonreciprocal phase shifter. Experimental results demonstrate two synergistic effects. Firstly, the self-starting mode-locked threshold is reduced to 315 mW through a nonlinear phase shift compensation mechanism. Secondly, the saturable absorption dynamics of BP-SA effectively suppress noise, promoting the SNR to 68.4 dB and reducing the phase noise to −115.6 dBc/Hz across the 1–10 MHz frequency offset. This study confirms the dual functionality of 2D materials in nonlinear dynamics modulation and noise suppression. It establishes a new paradigm for environmentally robust ultrafast laser development in precision metrology and optical sensing.