Synchronized pulse sources with disparate colors are highly desirable for applications in coherent pulse synthesis^[1], nonlinear frequency conversion^[2], time-resolved imaging and spectroscopy^[3], and the discovery of novel wavepackets^[4]. Due to their enormous superiorities in stability, efficiency, and compactness, mode-locked Q-switched fiber lasers have been regarded as the best advanced pulse sources^[5,6], including the synchronized multi-color pulse fiber laser. However, the synchronization is challenged by the inherent first-order dispersion of fiber, which renders multi-color pulses propagating with different group velocities and colliding periodically inside the cavity^[7,8]. To date, the solutions can be categorized into three classes: (i) nonlinearly coupled multi-cavity configuration^[9-11]; (ii) near-zero group velocity dispersion (GVD) cavity^[12-14]; (iii) group delay compensation using programmable pulse shapers^[15-17]. The above methods have been widely applied in synchronized mode-locked fiber lasers.

Compared with synchronizing multi-color ultrashort pulses, synchronizing multi-color pulses with larger durations seems less dependent upon the cavity dispersion, such as synchronized multi-color Q-switched lasers, which show great potential in coherent Doppler and differential absorption LiDAR^[18]. For example, in 2012, Wang et al. achieved the synchronized dual-color µs pulse in a Q-switched fiber laser despite the large net cavity GVD of −1.45ps2^[19]. Hence, scientists mainly focused on how to generate multi-color Q-switched pulses in a single cavity regardless of the dispersion, which is the other key issue of great concern. Due to the mode competition induced by the homogeneous broadening of gain, the single-cavity laser usually operates at a single-color state^[20].

Currently, spectral filters have been widely adopted to generate the synchronized multi-color Q-switched pulse in a single cavity^[19-25]. Among those, fiber Bragg gratings (FBGs) attracted more attention because of their unique potential for all-fiber integration. Luo et al.^[21] and Zhang et al.^[22] reported the synchronized dual-color Q-switched fiber laser with wavelength spacing below 0.4 nm by the FBG with two reflection peaks, originating from the polarization-dependent reflection. By cascading two FBGs along the cavity, Liu et al. demonstrated a synchronized dual-color Q-switched fiber laser with wavelength spacing of 0.8 nm^[24]. In this scheme, the wavelength spacing is determined by the two cascaded FBGs. However, cascading two or more FBGs along the longitudinal space of cavity, in fact, is a multi-cavity configuration, where accurate control of the cavity-length mismatch is required to ensure the synchronization^[25]. Consequently, the multi-color filters for a single cavity with customizable operation wavelength, wavelength spacing, and wavelength number deserve further exploration. Moreover, the intracavity synchronization mechanism of multi-color Q-switched pulses, including the role of cavity dispersion, has not been unveiled.

In this Letter, we demonstrate the synchronized multi-color Q-switched pulse in a single cavity by using a parallel-integrated fiber Bragg grating (PI-FBG), which acts as a customizable multi-color reflector without introducing additional group delay. The multi-color Q-switched pulses are always self-synchronized when the group delay difference (GDD) varies from −3.4 to 3.4 ps. The dynamic analyses reveal that the intracavity self-synchronization is dominated by the active Q-switching and cross saturable absorption modulation (XSAM) effect between the multi-color Q-switched pulses.

Figure 1 shows the experimental setup of the synchronized multi-color Q-switched erbium-doped fiber (EDF) laser, which consists of a 980/1550 nm wavelength division multiplexer, 3.5 m EDF (D,−18.5psnm–1km–1, Nufern EDFL-980-HP), a three-port circulator, a PI-FBG, a polarization controller (PC), and a carbon nanotube saturable absorber (CNT-SA). The other fibers, including pigtails of all fiber components, are standard single-mode fibers (SMFs) (D,17psnm–1km–1, Corning SMF-28e+) with the total length of 4.5 m. The total cavity length and net cavity GVD are estimated as 8 m and −0.015ps2, respectively. The laser is pumped by a 976 nm laser diode, Q-switched by the CNT-SA, optimized by the PC, and output from the transmission port of the PI-FBG. The measured modulation depth, non-saturable absorption, and saturation intensity of the CNT-SA, with the tube diameter ranging from 1.0 to 1.5 nm, are 6.1%, 38.6%, and 160.2MW/cm2, respectively. The PI-FBG, composed of multiple parallel-inscribed FBGs with different wavelengths in the core of a standard SMF, is fabricated by a femtosecond laser with a point-by-point parallel inscription method^[26,27]. Compared with previously reported cascaded FBGs along the cavity^[24,25], the PI-FBG multiplexes FBGs in the transverse space of SMF and not only provides the robust multi-color filtering but also ensures the propagation of multi-color pulses along the same path in the cavity without additional group delay, which is beneficial to achieve the intracavity synchronization operation.

A PI-FBG with two parallel-inscribed FBGs is first fabricated and applied in the laser cavity. As shown in Fig. 1, the PI-FBG is composed of two parallel-inscribed FBGs in the core of the SMF, with the grating pitch of 1.608 and 1.612 µm, which exhibits two reflection peaks at 1551.9 and 1555.6 nm with the reflectance of 31.0% and 26.4%, respectively. Stable self-synchronized dual-color Q-switched pulses can be achieved in the laser when the pump power is higher than 20 mW. Figure 2 presents the typical state of the synchronized dual-color pulse centered at 1552.0 nm (λ2) and 1555.9 nm (λ1). Notably, only one pulse can be observed on the oscilloscope trace [Fig. 2(b)]. The color-resolved pulse measurements, implemented by a tunable bandpass filter, validate that the lasers at two colors operate at the Q-switched state with the same pulse interval of 47.3 µs [Fig. 2(b)], indicating that two pulses are synchronized and overlapped in the temporal domain. The total (λ1+λ2) and individual pulses (λ1, λ2) share the same repetition rate of 21.1 kHz [Fig. 2(c)], further confirming the synchronization of the dual-color pulses. The full width at half-maximum of the total pulse and individual pulse is 3.5 and 3.4 µs, respectively [Fig. 2(d)]. In addition, the central wavelengths of the dual-color pulse exhibit 0.1–0.3 nm redshift in contrast to the reflection spectrum of the PI-FBG (Fig. 1), due to the thermal accumulation induced increment of the grating pitch under high-energy pulse irradiation. Due to the polarization-dependence of the PI-FBG, the laser performances, including startup threshold, stability, and relative intensity of dual-color pulses, can be flexibly optimized by the adjustment of the PC.

The evolutions of the synchronized dual-color pulse are studied by altering the pump power while keeping the other settings fixed. As the pump power enlarges from 20 to 320 mW, the durations of the total and individual pulses decrease while their repetition rates increase, as depicted in Figs. 3(a) and 3(b), which is the typical feature of Q-switched lasers^[21-23,28]. During the evolution process, their repetition rates are always the same, indicating the robust synchronization of the dual-color pulses. Such a synchronization operation state can be maintained at least 2 hours. The pulse-to-pulse intensity stability for the dual-color pulses is approximately ±5%. The average output power and single pulse energy of the dual-color pulse increase with the pump strength and reach the maximum values of 19.0 mW and 0.3 µJ, respectively [Figs. 3(c) and 3(d)].

In fact, it is not surprising that the aforementioned dual-color pulses can synchronously circulate in the cavity because their GDD is near zero (∼0.043ps). As the first-order dispersion of the cavity plays a vital role in the synchronization of multi-color pulses, the tolerance of the synchronization toward the first-order dispersion, i.e., the GDD between the pulses at two neighboring colors, is necessary to be analyzed. To flexibly regulate the GDD, a programmable pulse shaper (PPS) is inserted into the cavity between the circulator and PC, similar to our previous works^[15,17]. By imparting a linear group delay over the operation bandwidth, the GDD for the dual-color pulses can be continuously tuned. It is found that, when the net GDD varies from 0 to 3.4 ps or −3.4ps, the spectral intensity of the pulse at λ2 gradually decreases and finally disappears while that at λ1 changes slightly [Fig. 4(a)]. This phenomenon shows that the generation of the pulse at λ2 is directly related to the temporal overlapping degree of the pulses at λ2 and λ1, indicating a kind of nonlinear interaction between them. Therefore, the pulse at λ2 is triggered by the Q-switching based on nonlinear absorption loss modulation^[18-24], not by the gain-switching based on linear gain modulation^[29-32], which cannot be affected by varying the GDD. Meanwhile, the average power of the total pulse almost remains unchanged, while that at λ1 gradually increases and at λ2 evolves contrarily [Fig. 4(b)]. This suggests that the first-order cavity dispersion dominates the synchronization of the dual-color Q-switched pulses in the laser.

The RF measurement in Fig. 4(c) confirms that when the net GDD varies from −3.4 to 3.4 ps, the dual-color pulses are always self-synchronized with the same repetition rate. Beyond the critical point of ±3.4ps, the pulse at λ2 suddenly disappears, and only the pulse at λ1 survives. As illustrated in the inset of Fig. 4(c), after propagation over one Q-switched period in the cavity, the relative temporal walk-off (τd) between the dual-color pulses can be calculated as τd=GDD·T/Tr, where T and Tr are the pulse interval and roundtrip time of the cavity, respectively. Here, the effective total cavity length including the optical path in PPS is 8.24 m, corresponding to the Tr of 41.2 ns. In Fig. 4, the maximal GDD and T are 3.4 ps and 47.3 µs, respectively. Therefore, the maximal τd is estimated as 3.9 ns, which is determined by the temporal overlapping degree of the dual-color pulses. It means, if the one-period relative time delay exceeds the critical value, the synchronized dual-color pulse circulation cannot be self-consistent inside the cavity. It is also observed that, when reducing the pulse duration, the tolerance to the GDD weakens, further validating that the temporal overlapping degree affects the synchronization.

To elucidate the intracavity self-synchronization mechanism, we further study the starting dynamics of the synchronized dual-color Q-switched laser. As visualized in Figs. 5(a)–5(c), a continuous wave (CW) lasing first emerges at λ1 because of the relatively lower threshold compared with that at λ2. Then, the CW starts to pulsate, and a Q-switched pulse at λ1 is formed due to the saturable absorption of CNT-SA, which is a passive Q-switching process. After that, a CW lasing at λ2 arises and rapidly transforms into a Q-switched pulse state with the same repetition rate and duration as the pulse at λ1, as shown in Figs. 5(d) and 5(e). Finally, the dual-color pulses evolve into a steady state with similar intensity. In our experiments, the pulse at λ1 always first self-starts and then the pulse at λ2 follows.

The dynamics can be interpreted as follows. The startup of the pulse at λ2 is synchronously triggered by the pulse at λ1 through the active Q-switching mechanism, where the first self-starting passively Q-switched pulse at λ1 periodically bleaches the CNT-SA and hence periodically modulates the Q-factor of the cavity for the CW lasing at λ2, leading to the startup of the pulse at λ2 with a repetition rate the same as that at λ1. During the steady-state operation, the dual-color pulses mutually modulate through the XSAM effect in the CNT-SA, resulting in the robust temporal synchronization and overlap. Such an effect in nanomaterial-based SA has been demonstrated for the all-optical modulation and passive synchronization of multi-color ultrashort pulses^[12-15,33]. When the GDD increases from 0 to ±3.4ps, the XSAM effect gradually weakens due to the reduced overlapping degree of the dual-color pulses, while the synchronization state is still maintained; when the GDD exceeds ±3.4ps, the XSAM effect is insufficient to compensate the large temporal walk-off, leading to the synchronization breaking and the active Q-switched pulse at λ2 vanishing, which coincides well with the results in Fig. 4.

The synchronized triple-color Q-switched pulse can be obtained using a PI-FBG with three parallel-inscribed FBGs [Figs. 6(a) and 6(b)]. During the experiments, only one stable single-pulse train is observed, and the color-resolved pulse trains exhibit the same pulse interval as well as the repetition rate, indicating the synchronization of the triple-color pulses. As the central wavelength, wavelength spacing, and wavelength number of the synchronized pulse are determined by the PI-FBG, it is believed that synchronized multi-color (≥4) Q-switched fiber lasers can be actualized by controlling the spatial distribution, grating number, and grating pitch of the PI-FBG.

In summary, we demonstrate the synchronized multi-color Q-switched EDF lasers using PI-FBGs. The multi-color Q-switched pulses are self-synchronized when the GDD between neighboring spectra spans from −3.4 to 3.4 ps. The dynamic analyses reveal that the intracavity self-synchronization is attributed to the saturable absorption effect of the CNT-SA: (i) the pulse at one color first self-starts through passive Q-switching and then forces the CW lasing at another color to start synchronously through active Q-switching; (ii) the XSAM effect between the multi-color pulses in the CNT-SA can spontaneously compensate to some extent the temporal walk-off of the multi-color pulses due to the first-order cavity dispersion. It is believed that, based on such a self-synchronization mechanism, the synchronized Q-switched pulse with customizable colors can be achieved by integrating the PI-FBG into fiber lasers. The synchronized multi-color Q-switched fiber laser can be used as the laser source in multi-wavelength coherent Doppler and differential absorption LiDAR for remote sensing, pollution monitoring, and medical diagnosis.