High-repetition-rate ultrafast fiber lasers enabled by BtzBiI₄: a novel bismuth-based perovskite nonlinear optical material

2.1 Preparation of BtzBiI₄

This research investigates lead-free, bismuth-based perovskite crystals containing ionic liquids, which were successfully synthesized through an in situ method. The preparation process, illustrated in Figure 1, involved adding 0.2 mL of benzothiazole to a mixed solution of 3.0 mL acetonitrile and 2.0 mL methanol. The mixture was stirred for 10 min, followed by the addition of 1.0 mL hydriodic acid and 0.589 g BiI₃. After stirring for 30 min, the resulting red transparent solution was subjected to ultrasonic treatment for 4 h. The solution was then transferred to a 15 mL stainless steel autoclave and heated at 140 °C for 72 h. Gradual cooling to room temperature allowed for the slow formation of high-quality crystals (C₈H₈NSBiI₄, CCDC: 2388135). Upon completion, the product, isolated as a single crystalline phase with an 81 % yield (based on the bismuth content), exhibited distinct red massive crystals and was designated as BtzBiI₄.

Figure 1:

Schematic illustration for the preparation of BtzBiI₄ crystals.

2.2 Characterization of BtzBiI₄

The morphology, crystal structure, optical absorption, and scattering properties of the synthesized BtzBiI₄ crystals were characterized prior to use. After coating the sample with gold for 1 min using an ion sputtering apparatus (GVC-2000, Oxford Quorum), the morphology and particle size distribution of the BtzBiI₄ dispersion were examined using a scanning electron microscope (SEM, Zeiss Sigma 300). Figure 2a(I)–(III) show images at scales of 2 μm, 1 μm, and 500 nm, respectively. The dispersed material exhibited an irregular block-like morphology (Figure 2(a)) with clear layered structures visible in Figure 2a(I) and (II). Transmission electron microscopy (TEM, FEI Tecnai F20) was used to analyze the crystal distribution at micro- and nanoscale levels. Figure 2b(I)–(III) show images at scales of 1 μm, 200 nm, and 10 nm, respectively. The BtzBiI₄ samples displayed uniform lattice arrangements with consistent distribution. A selected lattice fringe in Figure 2b(III) reveals a calculated lattice spacing of 0.217 nm, indicating high crystallinity and structural stability of BtzBiI₄. Elemental distribution was analyzed using energy-dispersive spectroscopy (EDX, Oxford Xplore 30), and the EDX mapping results are shown in Figure 2(j). The analysis indicated a mass ratio of Bi to I of approximately 2:5, consistent with the molecular formula. Figure 2(c) presents the elemental mapping, where yellow, purple, red, blue, and green represent I, Bi, C, S, and N, respectively, confirming the uniform distribution without agglomeration. Single-crystal X-ray diffraction (SCXRD) analysis reveals that the BtzBiI₄ molecular structure consists of two primary components: a discrete M⁺ cation (with M corresponding to Btz in BtzBiI₄) and a one-dimensional, continuous anionic chain of (BiI₄)⁻ (Figure 2(d) and (e)). Within the unit cell of BtzBiI₄ (Figure 2(f)), eight (Btz)⁺ cations are symmetrically arranged along the four sides of the unit cell, whereas the (Bi₂I₁₀)⁴⁻ anionic fragments are located at the base-centered positions.

Figure 2:

Characterization of BtzBiI₄. (a) SEM images of BtzBiI₄, (b) TEM images of BtzBiI₄, (c) mapping images of BtzBiI₄, (d) view of the centroid-to-centroid π⋯π interaction between two adjacent Btz⁺ countercations, (e) the edge shared BiI₆ octahedral in BtzBiI₄, (f) side view of single unit cell of BtzBiI₄ along the a direction, (g) AFM image of BtzBiI₄ nanosheets, (h) height profile extracted from the AFM image, illustrating the thickness characteristics, (i) XRD pattern of BtzBiI₄ powder, (j) EDX spectrum of BtzBiI₄ powder, (k) Raman spectrum of BtzBiI₄ powder, and (l) UV-VIS-NIR spectrum of BtzBiI₄ powder.

To precisely determine the thickness of the BtzBiI₄ nanosheets employed in the sandwich-structured SA, atomic force microscopy (AFM) analysis was carried out using a Bruker Dimension ICON system. As presented in Figure 2(g), the AFM image reveals that the nanosheets exhibit a uniform and smooth surface morphology, indicative of high-quality material preparation. The corresponding height profile shown in Figure 2(h) confirms that the nanosheets possess a thickness ranging from approximately 3–5 nm. This ultrathin configuration significantly enhances the light–matter interaction at the nanoscale, thereby contributing to efficient nonlinear optical modulation, which is crucial for the realization of high-performance ultrafast photonic devices. The crystal structure of BtzBiI₄ was examined via X-ray diffraction (XRD) using a Bruker D8 Advance system. As depicted in Figure 2(i), the blue and red lines represent the simulated and experimental values, respectively. The experimental diffraction spectrum exhibits pronounced peaks at 2θ = 8.18°, 9.34°, 13.67°, 27.46°, and 41.66°, which align precisely with the simulated diffraction peaks. To further investigate the molecular structure of BtzBiI₄, Raman spectroscopy (Horiba Scientific Labram HR Evolution) was employed, and the Raman scattering spectra are shown in Figure 2(k). Three characteristic Raman vibrational modes were identified at 101.54 cm⁻¹, 134.55 cm⁻¹, and 269.14 cm⁻¹, corresponding to the Bi–I bonding structure within the (BiI₄)^- unit. These results are consistent with those reported for (BAH)BiI₄ crystals in previous studies [48]. To elucidate the absorption properties of BtzBiI₄ nanosheets, Ultraviolet-Visible-Near Infrared (UV-VIS-NIR) optical spectra were measured using a UV-3600-Plus spectrophotometer (Shimadzu). The absorption spectra, as shown in Figure 2(l), exhibit broadband absorption in the 1,500–1,600 nm range. Overall, these characterization results demonstrate that BtzBiI₄ possesses remarkable crystallinity, uniform particle size distribution, and absorption capability at 1.5 µm, thereby ensuring its reliability and stability for optoelectronic device applications.

3.1 Fabrication of BtzBiI₄-SA

A sandwich-structured BtzBiI₄-SA was successfully fabricated using a direct coupling technique, and its nonlinear saturable absorption properties were systematically characterized. To prepare the device, 10 mg of the synthesized BtzBiI₄ crystals were placed in a glass petri dish for selection. Using an optical microscope (DVE3630, Otter Optics), a crystal with a relatively regular morphology and a diameter of approximately 125 μm was identified. The selected crystal was then carefully transferred onto the end face of an optical fiber using a fiber probe. Under microscopic observation, it was confirmed that the crystal completely covered the fiber core, ensuring effective coupling. Finally, two optical fiber jumpers and a flange were assembled to create the sandwich structure, thereby completing the fabrication of the BtzBiI₄-SA (Figure 3(a)).

Figure 3:

Characterization of BtzBiI₄. (a) Preparation of BtzBiI4-SA. (b) Schematic of the balanced twin-detector technique. (c) Saturable absorption characteristics of BtzBiI4-SA. (d) Schematic diagram of open-aperture Z-scan system. (e) Z-scan curves of BtzBiI4 nanomaterials. (f) The 2D transient absorption color-coded map of BtzBiI4 material. (g) Dynamic curves at 1,550 nm of BtzBiI4 nanomaterials.

3.2 Saturable absorption of BtzBiI₄-SA

Examining the nonlinear optical response, underlying mechanisms, and the interaction of light with nanostructures provides a broader context for understanding the unique characteristics of BtzBiI₄-SA. Recent studies on the nonlinear behavior of quantum dot materials and the interaction of light with nanostructures offer valuable comparisons to our work. For instance, Yu et al. [49] investigated the nonlinear optical response of lead telluride quantum dots in all-solid-state pulse lasers, while Zhu et al. [50] developed MXene V₂CT_x nanosheet/bismuth quantum dot heterostructures, enhancing nonlinear optical properties. Additionally, Finke et al. [51] explored temperature-resistant quantum dot saturable absorbers for integration into semiconductor lasers. Other studies, including those on Ag₂S quantum dots [52] and phosphorene quantum dots [53], focus on their applications in biosensing and optoelectronic detection [54], [55]. Building on these insights, the nonlinear optical response of BtzBiI₄-SA was systematically investigated using a balanced twin-detector configuration, as shown in Figure 3(b). This approach provides a detailed understanding of the material’s nonlinear characteristics, essential for its potential in ultrafast photonic applications. The experimental apparatus comprises a high-power seed laser, a tunable variable optical attenuator (pVOA-1550-1-B-30-SM-B, Max-ray Photonics), and an optical coupler (OC). The seed laser, a custom-built erbium-doped fiber laser employing nonlinear polarization rotation (NPR) for mode-locking, generates pulses at a central wavelength of 1,562.32 nm, with a pulse width of 788 fs and a repetition frequency of 25.12 MHz. The NPR fiber laser system integrates a 976 nm laser diode (Model: PUMPL-976-1550-FA-B-YP), two polarization controllers (PCs), and a polarization-dependent isolator (PD-ISO) to sustain stable NPR mode-locking. Additional components include erbium-doped fiber (EDF), single-mode fiber (SMF-28), a wavelength division multiplexer (WDM), and an optical coupler. In this configuration, 20 % of the laser output is guided through the tunable attenuator and subsequently divided into two channels by a 50:50 optical coupler. One path is directly injected into a power meter, while the other path passes through the BtzBiI₄-SA before being directed into the same power meter. By adjusting the parameters of the optical attenuator, the output power of the NPR fiber laser can be modulated. A nonlinear transmission curve was derived from the measured data and subsequently fitted using a standard saturable absorption model (Eq. (1)).

In the nonlinear absorption model, T(I) represents the transmittance, ΔT is the modulation depth, I is the incident light intensity, I _sat is the saturation intensity, and T _ns denotes the nonsaturable losses. The measurement results are shown in Figure 3(c), indicating that as the incident light power increases, the absorption of BtzBiI₄-SA gradually decreases and eventually reaches saturation. The ΔT is 8.51 %, the I _sat is 47.19 MW/cm², and the T _ns is 60.09 %. These results demonstrate that BtzBiI₄-SA exhibits excellent nonlinear saturable absorption properties, making it a promising SA for passive mode-locking fiber lasers. Compared with conventional SAs (Table S1, see Supplementary Material), BtzBiI₄ exhibits a MD of 8.51 %, which is competitive with materials such as NbTe₂ and BP. Notably, BtzBiI₄ demonstrates an exceptionally high I _sat of 47.19 MW/cm², surpassing many reported materials (e.g., MXene-film and MXene-DS), and thus shows great potential for high-power ultrafast laser applications. A high I _sat typically indicates strong tolerance to intense laser irradiation, although it may also imply an elevated damage threshold. For ultra-high-power lasers, appropriate protective measures are recommended to ensure material stability and prevent damage under prolonged high-intensity exposure. Overall, BtzBiI₄ presents significant advantages as a saturable absorber, especially for high-power and HRR lasers. Nevertheless, for certain extreme operating conditions, it is crucial to balance the high saturation intensity with the material’s damage threshold to ensure long-term operational reliability.

The saturable absorption properties of 2D materials are fundamental to their role as absorbers in pulsed laser systems. At low light intensities, these materials exhibit linear absorption. However, as the incident optical power increases, their absorption behavior becomes nonlinear. As the intensity rises, the absorption decreases, and the transmission increases, which is characteristic of the saturable absorption effect in 2D materials [56]. To probe the nonlinear absorption characteristics of BtzBiI₄, the open-aperture Z-scan technique, based on spatial beam distortion, was employed for the measurements. As illustrated in Figure 3(d), a custom-built NPR mode-locking fiber laser, amplified by an erbium-doped fiber amplifier (EDFA-PA35-B), was used as the light source for the Z-scan system. The optical beam was collimated using a fiber collimator (GCX-L30APC-1550) and subsequently split by a 10:90 beam splitter (GCC-403234). Ninety percent of the beam was directed through a focusing lens with a focal length of 50.8 mm (GCL-M010109N) and a quartz plate (φ25 mm × 2  mm, infrared, JGS3) coated with BtzBiI₄ material, and then detected by a thermopile detector (GCI-080202). The power was recorded using an optical power meter (GCI-08). The remaining 10 % of the beam was directly detected by a second thermopile detector as a reference. During the experiment, the power values were varied by continuously adjusting the position of the quartz plate along a sliding track. The Z-axis zero point was positioned at the focal point of the lens, with the propagation direction of the beam aligned along the positive Z-axis. As the sample moved along the positive Z-axis, the intensity of the incident light varied due to the self-focusing or self-defocusing effects occurring within the sample. By comparing the data recorded by detector 1 and detector 2, the nonlinear absorption properties of the sample were obtained. The normalized transmittance T(z) was calculated using the following formula (Eq. (2)):

where T is the normalized transmittance, z represents the relative position of the sample along the Z-axis with respect to the lens focal point, L _eff denotes the effective length of the material, z ₀ is the Rayleigh length, and β ₀ and I ₀ correspond to the nonlinear absorption coefficient and the peak axial intensity at the focal point (z = 0), respectively. As shown in Figure 3(e), the β ₀ was determined to be 1.03 × 10⁻¹¹ m/W through curve fitting. Nonlinear absorption typically results from a combination of SA, reverse saturable absorption, and two-photon absorption. While reverse saturable absorption and two-photon absorption contribute to enhanced optical absorption, saturable absorption leads to an increased irradiance threshold for effective absorption in the material. This interplay of mechanisms defines the material’s nonlinear optical behavior and its potential applications in ultrafast photonic devices.

3.3 Transient absorption characteristics of the as-prepared BtzBiI₄ nanomaterials

To explore the ultrafast carrier dynamics of BtzBiI₄ in greater detail, femtosecond time-resolved transient absorption (TA) spectroscopy was applied to investigate the carrier relaxation pathways (Figure S1; see Supplementary Material). An 1,150 nm pump laser was utilized to promote electrons from the ground state to the excited state, while a broadband white light source spanning 1,300–1,700 nm functioned as the probe beam. The delay time, representing the temporal difference between the pump and probe pulses, was employed to monitor the evolution of the carrier dynamics. The TA modulation signals (ΔA = A ₁ − A ₀) were derived by measuring the absorption levels in the presence (A ₁) and absence (A ₀) of pump excitation, providing insights into the absorption behavior under high and low excitation conditions. As illustrated in Figure 3(f), BtzBiI₄ exhibits broadband absorption near 1,550 nm, with pronounced absorption in the long-wavelength region (>1,300 nm) facilitated by electronic transitions. Figure 3(g) presents the dynamic curve at a probe wavelength of 1,550 nm, showing the evolution of ΔA with delay time. These results demonstrate a dynamic transition from photoinduced excited-state absorption to a bleaching signal. The TA curves were fitted using a three-exponential decay function (Eq. (3)):

In this context, A ₁, A ₂, and A ₃ denote the amplitude components, while t represents the delay time. The parameters τ ₁, τ ₂, and τ ₃ correspond to the response times associated with distinct carrier dynamic processes. Upon pump excitation, ground-state electrons – including those localized at oxygen vacancy defects – are elevated to excited states. When subjected to probing at different wavelengths, these excited electrons absorb photon energy, facilitating their transition to higher excited states. This phenomenon manifests as photoinduced absorption peaks, which are indicated by the dashed regions in Figure 3(g). The formation of photoinduced absorption peaks is closely associated with carrier thermalization and relaxation processes [57]. The high intensity of the photoinduced absorption peaks indicates the strong photo absorption capability and high carrier density of BtzBiI₄, underscoring its excellent saturable absorption properties and significant potential for nonlinear optical applications. Moreover, the rapid picosecond-scale decay process is attributed to bulk electron–hole recombination, while the longer bleaching duration is linked to defect-state electron trapping and recombination with holes [58], [59], [60]. The transient absorption characteristics of BtzBiI₄ are particularly vital for mode-locking lasers. A shorter τ ₁ facilitates rapid responses, enabling the generation of ultrashort pulses in mode-locking lasers. Meanwhile, intermediate τ ₂ and longer τ ₃ contribute to stabilized mode-locking and HRR pulse outputs, making BtzBiI₄ highly suitable for applications requiring pulse-width tuning or pulse shaping.

5.1 Fundamental mode locking

When the coupled pump power was increased to 97 mW, mode-locking was initiated, leading to the generation of multiple pulses within the cavity. By adjusting the polarization state, a pulse train with a repetition rate of 9.294 MHz was achieved. Under the fundamental mode-locking state, the laser’s performance was evaluated at an output power of 365 mW, as recorded in Figure 5. To begin with, the mode-locking spectrum reveals a central wavelength of 1,560.388 nm, accompanied by a 3 dB spectral bandwidth of 3.24 nm (Figure 5(a)). Notably, the presence of distinct Kelly sidebands in the spectrum confirms that the laser operates within the conventional soliton regime, signifying soliton-like behavior. Furthermore, the pulse train shown in Figure 5(b) exhibits uniformly spaced pulses, which clearly indicate stable mode-locking operation. The pulse interval, measured as 107.6 ns, corresponds precisely to the cavity length of 22.11 m, thereby validating the experimental setup’s precision. In addition, a detailed view of a 5 μs pulse sequence highlights consistent spacing and stable intensity, further emphasizing the reliability and temporal stability of the mode-locking mechanism. Moving on to the pulse duration, the autocorrelation trace fitted with a sech² function reveals a duration of 844 fs (Figure 5(c)). The calculated time-bandwidth product (TBP) is 0.3529, close to the Fourier transform limitation (0.315) for sech²-shaped pulses, suggesting the presence of slightly chirped pulses. To further assess the laser’s operational stability, the radio frequency (RF) spectrum was analyzed (Figure 5(d)). The measured signal-to-noise ratio (SNR) of 66.15 dB underscores the high stability of the BtzBiI₄-SA-based laser system. Additionally, the pulse spectrum recorded over a 1 GHz span confirms uniformly distributed pulses, providing further evidence of excellent stability and pulse quality (Figure 5(e)). As the pump power increased from 164 mW to 472 mW, both the average output power and single-pulse energy exhibited a linear growth trend. The average output power rose from 2.97 mW to 10.92 mW, while the corresponding single-pulse energy increased from 0.319 nJ to 1.175 nJ (Figure 5(f)). This linear relationship suggests efficient energy conversion in the laser cavity, reflecting the stability and scalability of the mode-locking performance under varying pump powers. The optical spectra at various power levels, the 12-h pulse train at fixed pump power, and the 12-h output power stability test indicate that the fabricated SA maintains long-term stable operation under high irradiance without degradation, ensuring consistent and high-quality laser output (Figure S2a–c; see Supplementary Material).

Figure 5:

Characteristics of fundamental mode locking. (a) Optical spectrum. (b) Oscilloscope trace. (c) RF spectrum. (d) RF spectrum within the 1 GHz range. (e) Autocorrelation trace. (f) Spectral variations at different pump powers.

5.2 Harmonic mode locking

By carefully tuning the PC and progressively increasing the pump power, HML pulses with varying repetition rates were successfully generated. During the transition to higher harmonic orders, transient instabilities in the pulse train were observed, which subsequently stabilized into new harmonic states as a result of intracavity nonlinear effects and gain competition. At a pump power of 391 mW, the pulse characteristics under the 28th, 41st, 55th, 65th, 70th, 76th, 92nd, and 106th HML conditions are presented in Figure 6. As shown in Figure 6(a), the pulse trains of different harmonic orders exhibit uniform and stable distributions. The measured peak time intervals were 3.843 ns, 2.62 ns, 1.96 ns, 1.655 ns, 1.537 ns, 1.416 ns, 1.169 ns, and 1.015 ns, respectively. These intervals directly correspond to the repetition frequencies of the harmonic pulses, demonstrating a significant decrease in pulse spacing as the harmonic order increases. The RF spectra in Figure 6(b) validate the precise repetition frequencies, measured as 260.21 MHz, 381.68 MHz, 510.2 MHz, 604.11 MHz, 650.58 MHz, 704.23 MHz, 855.43 MHz, and 985.22 MHz for the respective harmonic orders. Furthermore, the SNRs of these pulses exceed 70 dB, indicating stable signals with minimal noise, while the side-mode suppression ratios (SMSRs), all above 30 dB, confirm excellent spectral purity and reduced mode competition (Figure 6(d)). The optical spectra of the HML pulses, depicted in Figure 6(c), exhibit typical soliton features with prominent Kelly sidebands. The central wavelength remains stable around 1,558 nm, as illustrated in Figure 6(e). However, the 3 dB spectral bandwidth narrows from 3.08 nm to 2.58 nm as the harmonic order increases, likely due to spectral filtering effects in high-order harmonics. The relationship between harmonic order, pulse duration, and average output power is detailed in Figure 6(f). Notably, while the pulse duration broadens from 1 ps to 1.25 ps with increasing harmonic order—likely due to nonlinear effects, dispersion, and phase-matching constraints—the average output power remains nearly constant, indicating conserved energy per pulse (Figure S3a–h; see Supplementary Material).

Figure 6:

Harmonic soliton output characteristics based on BtzBiI₄-SA: (a) oscilloscope trace. (b) RF spectrum. (c) Optical spectrum. (d) SNR and SMSR of harmonic mode-locking pulses. (e) Central wavelength and 3 dB bandwidth variation with repetition frequency. (f) Pulse width and average output power variation with harmonic order.

By gradually increasing the pump power, the repetition rate exceeded 1 GHz when the pump power was adjusted to 413 mW. Further tuning of the polarization state enabled the capture of HML at the 108th, 112nd, 114th, 122nd, 126th, and 131th orders. Detailed pulse characteristics are presented in Figure 7. Figure 7(a) shows the pulse train captured by the oscilloscope, where the pulse intervals correspond to 1/108, 1/112, 1/114, 1/122, 1/126, and 1/131 of the fundamental mode-locking pulse interval. The exact repetition frequencies were measured by a radio frequency spectrum analyzer (DSA875, RIGOL) with a resolution of 3 kHz (Figure 7(b)), yielding values of 1.005 GHz, 1.041 GHz, 1.06 GHz, 1.134 GHz, 1.17 GHz, and 1.22 GHz. In all cases, the SMSRs exceeded 30 dB, demonstrating the stability of harmonic mode-locking. The spectral profiles remained consistent across different harmonic orders. As the pump power continued to increase, enhanced nonlinear effects within the cavity led to significant suppression of the Kelly sidebands. The central wavelength stabilized around 1,556 nm, with a 3 dB bandwidth of approximately 1.6 nm (Figure 7(c)). Furthermore, autocorrelation measurements indicated pulse durations ranging from 1.49 ps to 1.75 ps, confirming high-quality pulse characteristics in the HML regime (Figure S4a–f; see Supplementary Material).

Figure 7:

Harmonic soliton output characteristics based on BtzBiI₄-SA: (a) oscilloscope trace. (b) RF spectrum. (c) Optical spectrum.

At a pump power of 472 mW, a maximum repetition rate of 1.3202 GHz was achieved, corresponding to the 142nd-order HML. Figure 8(a)–(d) present the detailed characteristics of this high-order harmonic state. As shown in Figure 8(a), the measured pulse interval is 0.7575 ns, precisely 1/142 of the fundamental mode-locking interval. The inset of Figure 8(a) displays a long-duration pulse train, highlighting the excellent stability of the HML operation. The RF spectrum in Figure 8(b) further confirms this stability, with the measured repetition rate of 1.3202 GHz exactly matching 142 times the fundamental frequency, thereby validating the harmonic generation. Notably, the RF spectrum exhibits a high SNR of 52.55 dB, indicative of low noise and high spectral purity. Moreover, the inset of Figure 8(b), depicting a 3 GHz span of the RF spectrum, shows no spurious peaks, providing additional evidence of stable HML operation. The autocorrelation trace in Figure 8(c), fitted with a sech² profile, yields a pulse duration of 1.78 ps. The corresponding TBP is calculated to be 0.346, suggesting slight chirping in the pulses. Spectral analysis in Figure 8(d) reveals a central wavelength of 1,556.46 nm and a 3 dB bandwidth of 1.57 nm. This spectral narrowing aligns with typical characteristics of high-order HML and further supports the soliton-like behavior of the pulses.

Figure 8:

Characteristics of 142nd-order harmonic mode locking and bound-state solitons. (a) Pulse sequence of the 142nd-order soliton, (b) frequency spectrum of the 142nd-order soliton, (c) autocorrelation trace of the 142nd-order soliton, (d) spectrum of the 142nd-order soliton, (e) optical spectrum of bound-state solitons, (f) autocorrelation trace of bound-state solitons, (g) pulse sequence of bound-state solitons, (h) RF spectrum of bound-state solitons, and (i) RF spectrum of bound-state solitons with a 500 MHz sweep width.

5.3 Bound-state solitons

A fiber laser operates as a dynamically balanced system, highly responsive to variations in cavity parameters such as dispersion, nonlinearity, gain, and loss properties. In a laser cavity with a net negative dispersion, the interplay between self-phase modulation and group velocity dispersion creates an environment conducive to the formation of optical solitons. As the pump power continues to rise, intensified nonlinear interactions combined with peak power limitations trigger the breakup of a single soliton into multiple subpulses, each exhibiting lower peak energy. These emerging pulses engage in complex interactions characterized by both repulsive and attractive forces. When these opposing forces achieve a dynamic balance, the system stabilizes, resulting in the formation of bound solitons with robust coherence [61], [62]. These are characterized by two or more pulses being bound together and moving as a group within the cavity, maintaining a constant time interval and fixed phase difference. In our study, a pair of stable bound solitons was observed when the pump power increased to 384 mW. Figure 8(e) shows the spectrum, which, in addition to the symmetric Kelly sidebands, exhibits modulation with a period of 1.965 nm. Furthermore, a significant dip at the central wavelength of 1,560.04 nm indicates that the phase difference between the bound solitons is π. The relationship between the spectral modulation period (Δλ) and the time-domain pulse interval (Δτ) can be expressed using the theoretical formula (Eq. (4)):

In this context, λ _c denotes the central wavelength of the bound solitons, while c represents the speed of light in a vacuum. According to this formula, the pulse interval Δτ is calculated to be 4.128 ps. The autocorrelation trace shown in Figure 8(f) exhibits three distinct peaks, indicating the presence of a dual-pulse bound soliton mode-locking state. The peak spacing is measured to be 4.073 ps, which corresponds well with the theoretical soliton temporal interval Δτ. Gaussian fitting reveals that the widths of the three peaks are approximately 1.282 ps, with an intensity ratio of 1:2:1, confirming that the dual solitons exhibit identical pulse durations and intensities. The time interval between adjacent solitons is 107.6 ns, corresponding to a repetition frequency of 9.294 MHz shown in Figure 8(g). The SNR of the bound-state soliton radio frequency spectrum recorded in Figure 8(h) is 64.45 dB, demonstrating high operational stability. Additionally, the spectrum within a 500 MHz range shown in Figure 8(i) further validates the soliton’s stability.

Table S2 summarizes the key performance parameters of previously reported systems alongside our work. Compared with prior studies, our laser demonstrates a significantly higher harmonic order of 142 and an ultra-high repetition rate of 1.3202 GHz, while maintaining a short pulse duration of 1.78 ps. These results confirm that our laser system not only achieves outstanding repetition performance but also preserves excellent pulse quality. Collectively, this highlights the effectiveness of the fabricated saturable absorber in enabling high-order harmonic mode-locking and its promising potential for high-speed optical communication and precision measurement applications. Building on this, Table 1 presents recent advancements in perovskite-based saturable absorbers for ultrafast lasers. Various perovskite materials have exhibited favorable nonlinear optical properties, supporting their application in mode-locked laser systems. For example, CsPbBr₃ and CH₃NH₃PbI₃ have demonstrated notable modulation depths and operational performance at near-infrared wavelengths, while Ba₂LaTaO₆ and PEA₂PbI₄ NCs have successfully extended operating wavelengths beyond 1,570 nm, enhancing their versatility in telecommunications and industrial laser applications. In this context, our work introduces BtzBiI₄ as a distinctive lead-free alternative, offering both environmental sustainability and excellent nonlinear optical response. Its demonstrated ability to support high-order harmonic mode-locking at ultrahigh repetition rates distinguishes it from previously studied materials, underscoring its potential for demanding applications such as optical frequency comb generation and high-speed optical communication systems.