Nowadays, on-demand applications require more sophisticated spectral-temporal control of lasers. In addition to the routine manipulation of spectral components, a wide tuning range of pulse widths is also required, typically from picoseconds to nanoseconds. Therefore, ultra-narrow bandwidth passively mode-locked lasers, which combine high spectral purity and long pulse duration, have received more attention in the past decade.1^–13 On the one hand, such a new type of laser behaves controversially with long pulse duration compared with conventional femtosecond lasers. On the other hand, the characteristics of a narrow bandwidth mode-locked laser dictate the pulse spectral-temporal features that may be utilized across various unusual applications. Using volatile Q-switched operation in fiber-based lasers or narrow linewidth continuous-wave (CW) lasers with external modulators, flexible spectral-temporal features have been achieved. However, such schemes are usually accompanied by significant experimental complexity and, more importantly, typically produce outputs with high noise figures (timing jitter and so on) or no pulse-to-pulse coherence.5 A strong pulse-to-pulse coherence and high signal-to-noise manifesting ideal source for advanced applications, i.e., single-photon LIDAR14 and coherent anti-Stokes Raman scattering (CARS) imaging.15^–18 In particular, lasers that can generate a broader range of pulse widths are beneficial for the ablation of single-crystal diamonds.19^,20 For example, both ps and ns pulses offer distinct advantages: picosecond lasers have demonstrated superior suitability for high-precision machining demands associated with high-quality diamond microstructures; nanosecond lasers are generally more effective for cutting and machining high aspect ratio microstructures within diamond substrates. Moreover, laser stealth cutting for three-dimensional chip integration demands a spectral pure laser with a pulse width ranging from ps to ns. This type of laser can hence induce a large modified area for wafer separation while minimizing the roughness of the cross-section simultaneously.21^–24 It is accordingly expedient to suitably design the fiber laser cavity with adjustable pulse duration, whereas unfortunately narrow-bandwidth passively mode-locked lasers with wide tunable pulse widths have been unexplored.

Mode-locked pulses are generally established as a balance among gain, loss, dispersion, and nonlinearity within the laser cavity. As a prerequisite for pulse width tuning, various types of saturable absorbers (SAs) have been widely applied to the generation of long pulses, mainly including artificial and physical optical absorbers. In the past two decades, single-walled carbon nanotubes (SWCNTs) have manifested their virtues as promising contenders in SAs. Compared with other SAs [e.g., semiconductor saturable absorber mirrors (SESAMs)], SWCNTs have shown significant advances in terms of fast recovery time (down to a few hundred femtoseconds), low unsaturated loss, and cost-effective fabrication, showing excellent performance in supporting stable pulse generation from fs to ps range.25^,26 For spectral control, the incorporation of a narrow-bandwidth filter (such as micro-resonators,5 fiber Bragg gratings,4^,6^,12 or rare-earth-doped fibers11) restricts the number of longitudinal modes within the cavity, therefore enabling the realization of a narrow-bandwidth long-pulse output. The bandwidth of these filters limits the ultimate pulse duration that the laser could leap forward, from which pulse duration exceeding picoseconds is insensitive to dispersion. Moreover, the nonlinear phase shift undergone by narrow linewidth mode-locked pulse is quite small, i.e., ∼0.1π, which restricts its ability to manipulate nonlinearity within the cavity for achieving tunable pulse widths. Nevertheless, most narrow bandwidth filters (e.g., nonlinear microcavities,5 commercial bandpass filters8) used usually have a fixed bandwidth, and the pulse suffers from an inflexible pulse duration.

By far, only a few narrow-bandwidth passively mode-locked fiber lasers have been demonstrated, showing a very limited range of tunable pulse widths. For example, by extruding the fiber Bragg grating to modify the reflectance spectral bandwidth, Liu et al.3 demonstrated a flexible output from 7 to 150 ps. Alternatively, by optimizing pump power, adjustable pulse widths between 60 and 160 ps can be realized in a long fiber cavity.8 Although a short-cavity laser structure had been developed to enlarge the pump power range, the pulse width adjustment range has been limited to ∼40ps.12 Hence, tailoring the pulse duration tuning range toward ns is still challenging. In addition to the small tuning range of the pulse width, the spectral width of these lasers has been constrained to GHz.

In this paper, we demonstrated a SWCNT mode-locked narrow-bandwidth laser with a pulse duration tunable from 481 ps to 1.38 ns. An ultra-narrow bandwidth filter is constituted using the extremely narrow overlapping region of reflection spectra between the two fiber gratings. By applying mechanical stress to either grating, the overlapping interval of the reflection spectra between two filters can be reconfigured, and the laser output characteristics in the tunable process are implemented. The tuning range close to 1 ns which is the largest in narrow-bandwidth passively mode-locked fiber lasers. When the pulse is 1.38 ns, the spectral width of 4 pm is obtained, corresponding to 502 MHz. In addition, the long cavity structure of the laser not only provides enough nonlinear integral path against the strong filtering effect so that the stable mode-locked state can be achieved at a low pump power compared with a short cavity but also makes the repetition frequency of the laser less than 1 MHz, which meets the needs for a broad range of applications. Furthermore, we use numerical simulation to model the obtained ns pulse output, and the results are in good agreement with the experimental results. By simulating the pulse time-frequency characteristics at different positions in the cavity, the evolution process under this composite filter structure is theoretically revealed. We provide a simple, flexible, and tunable method for narrow bandwidth passively mode-locked fiber lasers and also offer a special and more ideal light source for important fields such as laser stealth cutting.

The experimental arrangement in a unidirectional ring cavity configuration based on the SWCNT and dual filter is shown in Fig. 1(a). A 980-nm pump laser is introduced into the cavity by a 980/1550nm wavelength division multiplexer (WDM). A segment of 0.7-m-long erbium-doped fiber (EDF; LIEKKI Er80-8/125) serves as a gain medium to realize the inversion of particle number. A polarization controller (PC) is used to optimize the laser mode-locking operation by adjusting the state of polarization. The SWCNT-based SA is sandwiched between two fiber ferrules. The nonlinear transmission of the SWCNT is measured by the typical two-in-power method as shown in Fig. 1(b). In Fig. 1(b), we can clearly see that the modulation depth α0 reaches 7.08%, indicating an effective SA function. Besides, the non-saturable loss and saturable energy of the SWCNT saturable absorber are 53.82% and 1.02μJ/cm2, respectively. Two filters are incorporated in the cavity to compress the spectral bandwidth and broaden the pulse duration. A commercial optical sensing interrogator (Micron Optics, sm125) is utilized to characterize the filters over the scanning range from 1510 to 1590 nm (with 1-pm resolution). The measured reflection spectra of the two filters are shown in Fig. 1(c). The center wavelengths of the two filters are 1545.25 and 1545.42 nm, respectively, and the reflectivities of both are 99%. Because the center wavelengths of the two filters are close to each other and the reflectance bandwidths of the two filters are both only 0.19 nm, there is an extremely narrow overlap in their reflection spectra, resulting in an ultra-narrow spectral output from the laser, as shown in the inset in Fig. 1(c). Because the number of modes in the cavity affects the stability of the pulse train, to ensure that there are more longitudinal modes in a given filter bandwidth, we add a 200-m single-mode fiber (SMF) in the cavity to reduce the longitudinal mode interval. We selected different lengths of SMF and discovered that a shorter length SMF results in a higher pump power for the laser to reach a stable mode-locked state under the same filtering bandwidth. The 200-m SMF ensures that we can achieve a tunable output at a low pump power, which is the optimal SMF length for our device. The total cavity length is ∼228.3m, with a net dispersion of ∼−5.22ps2. The laser output is characterized by extracting light from the cavity through 80% of the ports in an 80/20 fiber coupler. By extracting a significant portion of the energy within the cavity, the optical Kerr effect in the fiber can be appropriately mitigated, thereby suppressing pulse breakup induced by the Kerr effect in a long-cavity configuration. Due to the extremely narrow spectrum of the output, a high-resolution 0.8 pm optical spectrum analyzer (OSA, APex AP2081A) is used to measure the spectrum. A high-speed oscilloscope (OSC, Keysight DSAZ592A, 59 GHz) connected with an ultra-fast photodiode detector (PD, Finisar XPDV2120R, 50 GHz) is employed to record the output pulse train and pulse duration. A 3.2-GHz spectrum analyzer (Siglent SSA3032X) monitors the radio frequency (RF) response.

We first test the laser output when the two gratings under a natural state. Under the pump power of 168 mW, the CW laser output is obtained. When the pump power is 210 mW, the CW light is converted to a mode-locked pulse train by properly rotating the PCs. Figure 2 depicts the output laser performance of the stable mode-locking regime. The spectrum is centered on 1545.33 nm and has a bandwidth at full width at half-maximum (FWHM) of 15 pm, as illustrated in Fig. 2(a). Figure 2(b) depicts the stable mode-locked pulse train with a pulse interval of 1.1μs. The waveform of the pulsed laser in the time domain is illustrated in Fig. 2(c), with a measured pulse duration of 481 ps. The electric spectrum of the mode-locked pulse trains is presented in Fig. 2(d). The signal-to-noise ratio (SNR) at the fundamental repetition rate center is 56 dB. The measured repetition rate of the pulse train is 908 kHz, which aligns well with the cavity length. The longer cavity length not only reduces the repetition rate but also enables the laser to achieve a stable mode-locked state at a relatively low pump power compared with a short cavity. In our experiment, when the laser cavity length is less than 50 m, the nonlinear spectrum broadening is not enough to balance the strong filtering effect, and a stable mode-locking state is hard to achieve. The inset of Fig. 2(d) displays the global spectrum over a 50 MHz range with a 1-kHz resolution, providing evidence for stable single-pulse mode-locking operation. The average output power from the laser is 1 mW, corresponding to a pulse energy of 1.1 nJ.

Next, filter 2 is securely mounted on the displacement platform using an optical fiber gripper. By meticulously adjusting the knob on the displacement platform, horizontal stress is applied to filter 2, resulting in a shift of its center wavelength. As the center wavelength distance between the two filters increases, the overlap of the reflection spectra of the two filters is gradually reduced, and a tunable filter with ultra-narrow bandwidth from 16 to 32 pm is constructed. In the process of constantly adjusting the filter bandwidth, the laser output is shown in Fig. 3. The typical output spectra are shown in Fig. 3(a), and the change in the center wavelength of filter 2 causes the wavelength of the overlapping part to gradually shift from 1545.330 to 1545.352 nm. The FWHM spectral bandwidths are about 15, 10, 6, and 4 pm at filter bandwidths of 32, 26, 18, and 16 pm, respectively. The spectral width has always been much smaller than that of conventional passively mode-locked fiber lasers and has never exceeded the filter bandwidth. This is also consistent with previous reports that, in narrow-bandwidth passively mode-locked lasers, the filter bandwidth is the boundary condition for laser single pulse operation.3^,4 Meanwhile, due to mode competition in the cavity, not all frequencies within the filter bandwidth are phase-locked, so the output spectral width is narrower than the filter width. As shown in Fig. 3(b), the spectral cut by the narrow filter causes a lengthening of the pulse duration, the pulse width variation on a large scale from 481 ps to 1.38 ns by flexible bandwidth of the filter and slightly adjusting the PC. This tunable range is primarily influenced by the characteristics of the two filters. To mitigate the impact of sidebands and achieve a minimal filtering bandwidth, it is essential for the filter to exhibit a steep reflection spectral edge and be apodized.

The purple curve in Fig. 3(c) shows the change of the mode-locking threshold with filtering bandwidth. The decreased filter bandwidth corresponds to the higher pump power required for single-pulse laser operation. This is mainly due to the reduction of reflection spectrum overlap between the two filters, which increases the loss in the cavity. If a constant pump power is maintained, the balance between gain and loss will be disturbed, making it hard to achieve a stable mode-locked state. At the same time, the output power also gradually increases from 1 to 3.2 mW as shown in Fig. 3(c), orange curve. Because the cavity length does not change, the repetition rate remains 908 kHz, and the calculated single-pulse energy in the cavity increases from 0.27 to 0.88 nJ. Although the single-pulse energy increases, the pulse width also increases gradually, so the peak power of the intracavity pulse under different filtering bandwidths is about 0.6 W. In a fiber system, the nonlinear phase φNL can be calculated by φNL=γP0Leff (γ, P0, and Leff are the nonlinear coefficient of the utilized fiber, the pulse peak power, and the effective fiber length, respectively). The constant cavity length makes both γ and Leff in the formula constant. The cumulative nonlinear phase shift within the cavity is directly proportional to the peak power. This nearly constant peak power suggests that the nonlinear phase shift demonstrates minimal sensitivity to variations in filter bandwidth. The value φNL is roughly calculated to be 0.07π, providing evidence that the laser operates in the weak nonlinear effect region under strong filtering.

Furthermore, during adjustments to achieve tunable pulse widths, the SNR shown in Fig. 3(d) is above 50 dB (100 Hz resolution over a 1-MHz span). In particular, we observe that the SNR and peak power within the cavity exhibit nearly identical variations with filter bandwidth during tunable processes. This phenomenon primarily arises from the long cavity structure of the laser, which leads to an increased nonlinear cumulative path. Therefore, compared with a narrow bandwidth passively mode-locked fiber laser with a shorter cavity length, the enhancement of the integral path enables the laser to reach the mode-locked state with a limited range of pump power. In our experiment, the adjustable range of pump power is only about 10 mW, which defines the peak power of the mode-locked pulse in a nearly fixed value. Minor fluctuations in peak power can significantly disrupt stability in the mode-locked state and affect the SNR. Consequently, there is a nearly identical trend observed in both the change curves of SNR and peak power.

It is of great significance for us to note that when the center wavelength of the overlapping region between the two gratings is 1545.352 nm, the spectral bandwidth of the laser measures a mere 4 pm, corresponding to a pulse width of 1.38 ns. This achievement marks a groundbreaking advancement beyond the nanosecond scale in narrow bandwidth passively mode-locked lasers based on SWCNT. At the same time, it is important to note that as the reflectivity decreases, the overlap bandwidth of the filters also diminishes. If filter 2 continues to exert stress in an attempt to further reduce the overlap bandwidth between the two filters, the resulting reflectivity at their overlap may become excessively low. This reduction could hinder the achievement of a stable mode-locked state. The laser output is illustrated in Fig. 4. As shown in Fig. 4(a), the measured spectral bandwidth of 4 pm corresponds to a frequency bandwidth of 502 MHz, and calculations indicate that there are ∼553 phase-locked longitudinal modes present, which is far less than the conventional passively mode-locked fiber laser. The inset of Fig. 4(a) shows the normalized spectral contour (gray line) and Gaussian fitting (pink-dashed line). Due to only a few longitudinal modes within this cavity configuration, the spectral profile closely aligns with a Gaussian distribution.27Figure 4(b) presents an oscilloscope trace exhibiting a pulse interval of 1.1μs, which correlates with a fundamental repetition rate of 908 kHz. Photodetectors were employed to convert optical signals into electrical signals before being analyzed via an oscilloscope; this process yielded a measured pulse width of 1.38 ns and resulted in a calculated time-bandwidth product (TBP) value close to 0.6, nearly the Fourier transform limits. As shown in Fig. 4(d), at a resolution setting of 100 Hz, the measured SNR is 57 dB. In addition, from the inset in Fig. 4(d), one can discern that over a broad frequency span exceeding 50 MHz, with resolution set at precisely 1 kHz, the RF spectrum indicates stable single-pulse operation.

To further explore the evolution process of pulse in the cavity under strong filtering, the characteristics of narrow-band fiber laser pulse are numerically simulated using the nonlinear Schrödinger equation (NLSE) i∂A∂z=12β2∂2A∂T2−γ|A|2A−ig2A,(1)where A is the slowly varying electric field envelope; g, γ, and β2 are the gain coefficient, nonlinear coefficient, and group velocity dispersion parameter of the fiber, respectively. The propagation distance and pulse time delay are expressed by Z and T in Eq. (1). The laser in numerical simulations performs the same configuration as the experimental setup, which mainly includes EDF, OC, SMF, SA, and filter. Set up the gain fiber as a standard propagation with saturable gain according to the following model: g(z)=g0/(1+E/E0), where g0 and E0 are the small-signal gain and the gain saturation energy determined by the pump power. E is the pulse energy which can be calculated by E(z)=∫dt|A|2. For the mode-locking mechanism of SA, we use a simple transfer function module: T=1−q0/[1+P(t)/P0], where q0 and P0 are the unsaturated loss and the saturation power, respectively. The instantaneous pulse power P(t) can be expressed by P(z,t)=|A(z,t)|2. The measured normalized filter reflectance spectra provide a reference for the filter setup in the simulation. The other parameters, such as SMF and OC, used in the numerical simulation are similar to their nominal or estimated experimental values. It may be assumed that the laser runs clockwise, successively passing through EDF, OC, SA, SMF, and filter. A small amplitude Gauss pulse is given in front of the EDF to simulate the spontaneous emission noise pulse in the gain fiber.

In our simulation, parameters of EDF are set as gain bandwidth of 40 nm, gain saturation energy Esat of 0.7 nJ, and nonlinear coefficient of 0.0014W−1m−1; parameters of SMF are set as β2 of −0.028ps2/m and nonlinear coefficient of 0.0011W−1m−1. We utilized a data array to set the time window to 6 ns and determined the number of points as 211. As the number of round trips increases, the pulse error between adjacent round trips gradually diminishes and exhibits a tendency toward convergence. When the error falls below 10−5, it can be considered that the pulse converges and the laser reaches the mode-locked state. In the simulation, the pulse converges after 588 round trips. The simulated results are shown in Figs. 5(a) and 5(b). The spectral width obtained by simulation is 3.1 pm and the pulse width is 1.38 ns. The spectrum obtained through simulation exhibits asymmetric characteristics, primarily due to the differing edge steepness of the two filters employed. This discrepancy results in varying filtering degrees on the left and right sides of the spectrum. When the laser converges in a stable mode-locked state, the evolution diagrams of the intracavity spectrum and time domain are shown in Figs. 5(c) and 5(d), respectively.

In addition, to deeply understand the dynamic process of pulse transmission in the cavity, Fig. 6 shows the distribution of the simulated pulse electric field envelope in the time domain and frequency domain at different positions in the last round trip. It can be seen that the laser maintains a very low breathing in both the time and frequency domains. Because the laser operates in the region of weak dispersion and weak nonlinear effects, the spectral width and pulse duration remain almost unchanged as it passes through different parts of the laser. As shown in the inset figure, the spectrum and pulse width change only once at the position of 222 m, which corresponds to the pulse passing through filter 1. This phenomenon primarily arises from the fact that the output of a narrow-bandwidth passively mode-locked fiber laser is predominantly influenced by the filter bandwidth. When the pulse initially propagates through filter 1, the composite filter structure formed by filters 1 and 2 ceases to exist, resulting in a transition of the filter bandwidth from an extremely narrow overlap width of 16 pm to the reflection spectrum width of filter 1. Consequently, this leads to a certain degree of spectral broadening. According to Fourier transform principles, this broadened spectrum corresponds to a reduced pulse width, as illustrated in the internal diagram of Fig. 6(b). Nevertheless, it is important to note that overall changes in both time and frequency domains of the pulse at various positions within the laser remain relatively minor. It is worth noting that for simulations with pulse widths on the order of picoseconds, the evolution of time-frequency characteristics at different positions in the cavity is similar to the evolution of ns pulses.

In conclusion, tunable pulse duration with ultra-narrow bandwidth can be generated via the combination of a composite filter structure and SWCNTs. Tunable pulse width of ∼1ns is the widest tuning range in narrow-bandwidth passively mode-locked lasers. Considering the difficulty of realizing a wide-range tunability of narrow-bandwidth filter pulse output, we provide a simple, flexible, and efficient pulse width tunable method. SWCNTs exhibit a large modulation depth and minimal additional filtering effects on the spectrum, which facilitates the establishment of stable pulses. The overlap between the two filter reflectance spectra constitutes an ultra-narrow bandwidth filter, which limits the number of longitudinal modes of the laser. By changing the stress, filter 2 drifts to the longer wavelength to further reduce the bandwidth of the overlapping part and finally achieve a wide tunable range of 481ps−1.38ns. More importantly, we believe that this method has the potential to further achieve a wider pulse-width tunable range. In the experiment, we only changed the center wavelength of filter 2. If filter 1 is mechanically stretched, so that its center wavelength shifts toward a longer wavelength, the reflection overlap between the two filters will be wider, corresponding to a shorter pulse width, and the overall tuning range will be extensively increased. Especially when the center wavelengths of the two filters are tuned to completely coincide, it corresponds to the maximum filter bandwidth, which is likely to result in a pulse duration much less than 481 ps.

During the tuning process, it has to be noted that the gradual decrease of filter bandwidth results in a continuous increase of intracavity loss, and single pulse generation depends on an increased pump power for gain compensation. We recognized that under the strong filtering effect, the pulse width generated is up to hundreds of picoseconds, so the corresponding dispersion length (>106m) and nonlinear length (>103m) are so long that neither dispersive nor nonlinear effects play a significant role during pulse propagation. On the other hand, compared with the short-cavity laser, the long-cavity provides a longer nonlinear integral path, and the pump power adjustable range after reaching the mode-locked state is limited, which makes the pulse peak power change small upon different filtering bandwidths. A small change in the peak power will hence cause the pulse to destabilize, resulting in a decrease in the SNR. The variation of SNR in the tunable process shows the same trend as that of peak power. We would like to mention that our laser is different from the commonly used Mamyshev oscillator although using two offset filters. This is simply because significant spectral broadening is absent in our laser.

Based on the nonlinear Schrödinger equation, theoretical simulation of ns pulse behaviors in the ultra-narrow bandwidth mode-locked laser has been unveiled for the first time. When the pulse is 588 round trips in the simulation, the convergence solution is obtained, and the pulse width obtained by simulation is 1.2 ns and the spectral width is 3.1 pm, which is close to the experimental results. The simulation results show that both the time domain and frequency domain maintain very low breathing when the pulse propagates in the cavity. This is in contrast to the conventional mode-locked laser bearing high nonlinearity.

Overall, our less than MHz repetition rate light source not only takes into account the high spectral purity and large pulse duration but also has a flexible output, which is preferred for important fields such as the ablation of single crystal diamonds and laser stealth cutting. Moreover, our demonstrated laser may help us gain an in-depth understanding of laser physics, ultra-weak nonlinear optics, etc.

Weixi Li is a PhD student at the Shanghai University. She is mainly engaged in research on narrow bandwidth passively mode-locked fiber lasers.

Biographies of the other authors are not available.