Design of a two-dimensional (2D) heterostructure saturable absorber
In our experiments, 2D materials were mechanically exfoliated and sequentially stacked to form MoS-BN-graphene-BN-MoS heterostructures. These heterostructures were then transferred onto the end facet of a single-mode optical fiber and aligned with another fiber (Fig. 1a, b and Figs. S1, S2; see "Materials and methods" section for fabrication details). Owing to the disparity in the refractive indices of MoS and BN (nMoS = 4.1 and n = 2.1 at 1550 nm), the heterostructure forms a nanocavity with a nonuniform optical field distribution (Fig. 1c). Our simulations indicate that the optical field intensity in the graphene layers can be either suppressed or enhanced by varying the thickness of the BN layers (Fig. 1d). The enhancement factor, defined as I/I, varies from 20% (with an BN thickness of 55 nm) to 230% (with an BN thickness of 240 nm). Fiber-integrated SA components with bare graphene and heterostructures were experimentally prepared. The corresponding nonlinear absorption curves are presented in Fig. 1e. As the pump peak intensity increases, their total transmission monotonically rises and can be modeled by the following equation:
where I represents the pump peak intensity, α is the modulation depth, α is the nonsaturable absorption, and I is the saturation intensity.
From the fitting, we find a modulation depth of 4.2% and a saturation intensity of 62.9 MW/cm for the SA component with bare graphene. Because of the enhanced optical field, the SA component with the heterostructure with an BN thickness of 240 nm has a modulation depth of 5.0% and a saturation intensity of only 22.0 MW/cm. In contrast, no evident saturable absorption effect is observed for the SA component with the heterostructure with a suppressed optical field intensity (with an BN thickness of 55 nm, Fig. S3).
We subsequently designed an all-fiber ring cavity and integrated the bare graphene and heterostructure for mode-locking, respectively (Fig. 2a). The output laser spectra from bare graphene and the heterostructure have similar central wavelengths and spectral bandwidths at a pump power of 62 mW (Fig. 2b). The spectra display clear Kelly sidebands, indicating conventional soliton generation. In the bare graphene-SA spectrum, there are obvious nonsoliton components near the central wavelength at 1565.8 nm. This component significantly influences the soliton behavior through long-range soliton interactions, eventually leading to pulse splitting, as evidenced by the blue trace in Fig. 2c. For the heterostructure system, the spectrum broadening (Fig. 2b) facilitates the generation of shorter pulse duration. Simultaneously, the suppression of the nonsoliton components enhances the stability of the single-soliton mode-locked output (Fig. 2c). In addition, the radio frequency (RF) spectrum reveals a signal-to-noise ratio of 45 dB for the heterostructure (at 13.2 MHz), demonstrating a significant improvement over the value of 22 dB for bare graphene (at 14.0 MHz, Fig. 2d). For more precise temporal characterization, Fig. 2e presents autocorrelation traces of mode-locked pulses from the heterostructure and graphene, showing similar full width at half maximum (FWHM) values of 1.20 ps and 1.45 ps, respectively. With excitation power increasing, the output power grows linearly, and no laser-induced damage is observed at a pump power approaching 92.5 mW (Fig. S4).
To further understand the mechanism of mode-locking with the graphene-based SA, we explore the soliton buildup and evolution dynamics via the time-stretch dispersive Fourier transform (TS-DFT) technique. Figures 3a, b depict the typical buildup processes of solitons with graphene and the heterostructure as SAs, capturing more than 27,000 and 14,000 consecutive cavity roundtrips, respectively. Both of these SAs can effectively circumvent the Q-switching process prior to mode-locked self-starting, thereby preventing potential damage from excessive single-pulse energy exposure. Under identical pumping conditions at 58 mW, the bare graphene-SA and heterostructure-SA exhibit significantly different behaviors. The bare graphene-SA undergoes four distinct stages of evolution: relaxation oscillation, beating dynamics, transient single-pulse formation, and the final double-pulse state (Fig. 3a). Before the first 13,300 roundtrips, multiple pulses with similar intensities energetically compete to form a soliton. Subsequently, background pulses gradually dissipate, and soliton P emerges, driven by nonlinear pulse shaping and self-phase modulation (Fig. 3c). The transient single-pulse state is quite unstable, with energy fluctuations of approximately 11%, surviving the following ~5000 roundtrips (Fig. 3d). Concurrently, another pulse gains energy from residual background pulses, triggering rapid energy accumulation and leading to the formation of a new soliton P at ~20,000 roundtrips. The original soliton P is reshaped and sheds excess energy to P, achieving a more stable state. Ultimately, a double-pulse state forms, with solitons P and P exhibiting the same intensity and FWHM, due to the energy quantization effect.
In contrast, the formation of a soliton with the heterostructure-SA proceeds through three stages: relaxation oscillation, beating dynamics, and stable single-soliton mode-locking (Fig. 3b). During the relaxation oscillation stage, background pulses are significantly suppressed, thus avoiding the possibility of multiple soliton generation and promoting stable single-soliton mode-locking. Three selected typical cross-sections, shown in Fig. 3e, emphasize the buildup of pulse formation. A single soliton with clear Kelly sidebands finally forms at nearly 11,000 roundtrips. Its energy remains remarkably steady during propagation, with fluctuations of only approximately 3% (Fig. 3f). No pulse splitting is observed throughout the entire test, indicating a perfect single-soliton mode-locking performance. And the single-shot measurements and averaged spectrum (detected by the spectrometer) profile show remarkable congruence (Fig. S5).
The stable single-soliton buildup dynamics indicate an improvement in the robustness of the heterostructure-SA for mode-locking. To experimentally investigate the polarization tolerance of the bare graphene-SA and heterostructure-SA in mode-locking, we use an automatic polarization controller -- equivalent to a continuous rotation of a half-wave plate, quarter-wave plate, and another half-wave plate sequence -- to manipulate the intracavity polarization state (Fig. 4a). Polarization states that traverse the entire Poincaré sphere can be obtained (Fig. S6). The output pulse train is monitored by an oscilloscope in real time to evaluate the mode-locking state. Without any SA, no mode-locking operation is achieved (Fig. S7), and the output polarization state distribution is plotted in Fig. 4b. With the bare graphene-SA or heterostructure-SA equipped in the fiber ring cavity, mode-locking operation becomes possible. However, under different intracavity polarization states, various output states are observed, including continuous-wave laser, single-pulse mode-locking, harmonic mode-locking, soliton rain, and pulse splitting (Fig. 4c), which is consistent with previous results.
To describe the quality of the output laser states, we integrate the area of the primary pulse at the fundamental repetition rate on the oscilloscope (the area marked around time zero shown in Fig. 4c). Figure 4d shows the Poincaré sphere with spots color-coded by the integral intensity, and the radius value of the spots represents the degree of polarization. The degree of polarization of the output laser is greater, and the integral intensity is generally higher for the heterostructure-SA. Statistics on the integral intensity for the graphene-SA and heterostructure-SA are shown in Fig. 4e, f. Only 20% of the polarization configurations support single-pulse mode-locking for the bare graphene-SA. For the heterostructure-SA, the possibility of pulse splitting is greatly reduced under different polarization states, achieving single-pulse generation in approximately 85% of the configurations.