Passively mode-locked fiber lasers are being extensively investigated due to their stable, alignment-free operation and compact design, making them attractive platforms for studying new pulse dynamics ^[1]. A common technique to generate ultrafast pulses in fiber lasers is soliton mode-locking, where an intracavity pulse is shaped by a balance of cavity dispersion and pulse-triggered nonlinear effects ^[1,2]. In this regime, a single pulse is normally circulating in the laser cavity, with a repetition rate (typically ∼10MHz) proportional to the inverse of the cavity length ^[1,2]. Higher repetition rates, desirable for applications such as two-photon microscopy ^[3], frequency comb ^[4], or fiber-optic communications ^[5], are possible by shortening the cavity length ^[2]. However, using this approach becomes challenging to compensate for dispersive effects ^[6]. A different technique relies on harmonic mode-locking (HML), where multiple pulses can circulate in the laser cavity with a pulse-to-pulse equal temporal spacing ^[7]. HML is typically achieved by increasing the intracavity power, which can contribute unbalanced nonlinear effects, finally causing the circulating pulse to break up into multiple pulses ^[8]. Depending on the physical effects governing the interaction between the as-formed pulses, these can self-organize into two or more closely (temporally) spaced pulses ^[9,10]. For example, cross-phase modulation between pulses can lead to the formation of a soliton pair, termed bound states (BS) or soliton molecules, with a temporal spacing (Δτ) limited to several times of their pulse duration ^[11]. BS can then undergo many resonator round trips with constant Δτ and phase, i.e., they remain mutually coherent ^[12], with the resulting optical spectrum being modulated with a period Δν=1/Δτ ^[13]. BS in passively mode-locked fiber lasers have been extensively studied in connection with their potential applications in optical communications and high-resolution spectroscopy ^[3,5]. Techniques as varied as nonlinear polarization rotation (NPR) ^[14,15], nonlinear optical loop mirrors (NOLMs) ^[16], semiconductor saturable absorber mirrors (SESAMs) ^[17], carbon nanomaterials ^[18,19], or other nanomaterials ^[20–22] have been used to study BS.

Among the techniques typically implemented to mode-lock fiber lasers ^[1], carbon nanotubes (CNTs) and graphene ^[23] have emerged as promising saturable absorbers (SAs), with a number of favorable properties for laser development ^[24–29]. In CNTs, broadband operation can be achieved by using a distribution of tube diameters ^[30], while this is an intrinsic property of graphene ^[31]. This, along with ultrafast recovery time ^[32], low saturation fluence ^[33], and ease of fabrication and integration into all-fiber configurations ^[23,34], makes graphene an excellent broadband SA. Consequently, mode-locked lasers using graphene SAs (GSAs) have been demonstrated for a broad spectral range ^[35–38]. A variety of techniques have been implemented in order to integrate graphene into lasers ^[23]. For example, graphene can be integrated into various optical components, with the possibility of controlling the modulation depth ^[39]. Because of their simplicity, low cost, and highly reliable performance, fabrication techniques based on graphene solutions ^[40] are widely used ^[41–45]. Although BS generation has been reported based on a multilayer GSA prepared by chemical vapor deposition (CVD) ^[19,46], HML was not detected, which is required in order to generate high repetition rate pulses, important, e.g., for high-resolution spectroscopy ^[3,47]. Moreover, flakes grown by CVD require high substrate temperatures, followed by transfer to the target substrate ^[40]. Graphene-based solutions have the advantage of scalability, room temperature processing, and high yield, and do not require any substrate, which can be easily integrated into various systems ^[40].

Here, we use a graphene solution deposited on a fiber-based connector as SA. Based on this, we demonstrate BS HML of an all-fiber laser, achieving stable pulses with 720 fs and 409.6 MHz repetition rate. Such a simple and environmentally robust light source could be used for a variety of applications, including nonlinear imaging and spectroscopy.

The GSA is prepared by using a reduced graphene oxide solution based on a modified Hummers method ^[48]. Graphite oxide is prepared from natural graphite powder stirred into a mixture of sulfuric acid (98 wt.%) and hydrogen peroxide (30 wt.%) (20:1 by volume), followed by rinsing with deionized water, and heating (after evaporation) at 1000°C for 30 s. Graphite oxide is then exfoliated via ultrasonic treatment in a solution of deionized water, and subsequently reduced by hydrazine hydrate at 95°C for 12 h. Finally, a graphene ethanol solution is obtained by ultrasonication for 3 h. Absorption measurements, presented in Fig. 1(a), show a featureless spectrum from 250 to 1600 nm (the alcohol contribution was subtracted), with the UV peak a signature of the van Hove singularity in the graphene density of states ^[49].

To integrate the graphene solution in our fiber laser, we use a simple method based on optical deposition ^[50,51]. A fiber connector for physical contact (FC/PC), to be used in the laser, is immersed in the graphene solution. Tens of mW of optical power is then launched into the FC/PC from a 1550 nm continuous wave (CW) laser for ∼10min. After alcohol evaporation, a graphene film is obtained at the center of the fiber core on the FC/PC tip, as shown in Fig. 1(b). To check the film quality after deposition, we characterize it by Raman spectroscopy at 514 nm. Figure 1(c) plots the Raman spectrum of the graphene film on the FC/PC tip. A small D peak (∼1354cm−1) indicates negligible graphene defects ^[52]. Next, we measure the GSA nonlinear optical transmittance with a pulsed fiber laser (Calmar), which delivers 220 fs pulses with 24.97 MHz repetition rate at 1550 nm. The optical transmittance is determined by monitoring the input and output power, and is shown in Fig. 1(d). An ∼3.2% change in transmittance is noticed for an input average power of 16.5 mW. Further increasing the transmittance is feasible, but limited in our setup by the maximum available peak power. The GSA modulation depth is estimated at ∼6.6% ^[53], which is preferred for mode locking of fiber lasers ^[54], which typically operate with higher gain and cavity losses ^[1] than their solid-state counterparts ^[55]. The GSA has ∼2.7dB insertion loss.

The experimental configuration of our all-fiber laser is shown in Fig. 2. We use a 48-cm-long erbium-doped fiber (EDF, Er110-4/125, with 110 dB/m absorption at 1530 nm, and 12ps2/km second-order dispersion) as a gain medium pumped by a 980 nm CW laser diode (LD) through a fused wavelength-division multiplexer (WDM). The rest of the cavity is formed by ∼12.7m of standard single-mode fiber (SMF-28 with ∼−23ps2/km second-order dispersion). This gives −0.29ps2 net intracavity second-order dispersion, typical of soliton lasers ^[1]. Unidirectional operation is ensured by a polarization-insensitive isolator (PI-ISO), while a polarization controller (PC) is used for mode-locking optimization and stabilization. The 10% port of a fused coupler provides the laser output. The laser operation is monitored by an optical spectrum analyzer, a 2 GHz oscilloscope via a 1 GHz photodetector, a second-harmonic-generation (SHG) autocorrelator, and a radio frequency (RF) signal analyzer.

Mode-locking self-starts at ∼50mW pump power (Pp). A set of typical results is shown in Fig. 3. The output optical spectrum, shown in Fig. 3(a), has a 3.1 nm full width at half-maximum (FWHM) centered at λ=1558nm. The spectrum features Kelly sidebands, a signature of soliton-like operation ^[56]. The fundamental repetition rate, shown in Fig. 3(b), is 15.75 MHz, as determined by the 13.2 m cavity length. Figure 3(c) shows the intensity autocorrelation trace with 950 fs pulse duration, calculated by fitting a sech2 profile to the pulse, as expected for soliton-like mode-locking ^[6]. The time-bandwidth product (TBP) is 0.354, close to the theoretical value (0.315) for transform-limited sech2-shaped pulses. The output pulse energy is 11.2 pJ. The laser stability is characterized by RF measurements ^[57]. Figure 3(d) plots the RF spectrum around the fundamental repetition rate recorded with 10 Hz resolution. A ∼70dB signal-to-noise ratio (SNR) indicates low-amplitude fluctuations ^[57]. There is no spectral modulation over 1 GHz [see inset of Fig. 3(d)], which, when combined with long-range autocorrelation measurements, rules out multiple pulsing ^[57].

We investigate BS operation. By slightly increasing Pp and tuning the PC, we observe spectral periodic modulations, a typical signature of BS interference ^[9,11]. We find the spectral modulations, shown in Figs. 4(a)–4(c), dependent on the intracavity polarization state, as expected for BS operation ^[18]. Further tuning the PC, the CW peaks (an indication of laser stability ^[58]) shown in Figs. 4(a) and 4(b), are eliminated. A resulting spectrum is shown in Fig. 4(c), when the laser delivers two pulse molecules, i.e., BS ^[11]. A set of typical BS results is shown in Figs. 4(c)–4(f). The spectrum in Fig. 4(c) reveals a modulation period Δν=Δλνλ=38.19GHz, for Δλ=0.31nm at λ=1560nm. The corresponding intensity autocorrelation trace is shown in Fig. 4(d), with Δτ=26.2ps time delay between pulses (center to side peaks), in agreement with the spectral modulation period (i.e., Δν=1/Δτ). The pulse duration, shown in the inset of Fig. 4(d), is 720 fs. The pulses circulate in the cavity at 15.75 MHz repetition rate (63.5 ns delay), according to its length ∼13.2m, as shown in Fig. 4(e). An SNR of ∼68dB, shown in Fig. 4(f), recorded with 10 Hz resolution, confirms BS operation stability ^[57].

We investigate HML operation by further increasing Pp and tuning the PC. HML harmonics can be generated with orders from the first to the 26th. Figure 5(a) shows the HML spectrum centered at 1558 nm with 3.4 nm FWHM for Pp∼310mW (inset, the intensity autocorrelation trace for the 26th harmonic pulses). The pulse duration is 840 fs, corresponding to a TBP of 0.343, in agreement with that of fundamental mode-locking. The repetition rate is 409.6 MHz, corresponding to ∼2.44ns delay between pulses [Fig. 5(b)], i.e., the 26th harmonic. Figure 5(c) shows an ∼42dB supermode suppression, for the 26th harmonic [recorded over 800 MHz span with 20 kHz resolution bandwidth (inset, 1.5 GHz span)] and an ∼65dB background noise, indicating stable HML operation of our laser ^[59]. We also investigate the harmonic order and the output power as functions of Pp, as shown in Fig. 5(d). Depending on the PC orientation, the laser can operate either in normal or BS mode-locking when Pp is ∼50 to 63 mW. Further increasing Pp results in HML operation, with the second harmonic achieved for Pp∼63mW. As indicated in Fig. 5(d), the harmonic order and output power increase gradually with Pp up to the 26th harmonic, when Pp is ∼310mW, giving ∼18.7mW output power. Higher Pp, limited in our case to ∼320mW, could further increase the harmonic order. We monitor the laser operation for a 4-h period and observe power variations below ∼0.2% for different mode-locking states. We did not observe any damage to the GSA.

Compared to NPR, NOLMs, or SESAMs, our all-fiber design, exploiting a GSA, is simpler to assemble, needing no critical alignment. BS graphene-based all-fiber setups have been reported ^[19,46]; however, the use of multilayer CVD graphene structures complicates the fabrication process. Compared to CNT-based SAs, which limit the operation wavelength, our GSA can operate at any wavelength.

We report the generation of BS of solitons and HML from a graphene mode-locked all-fiber laser. BS of solitons are observed by adjusting the laser intracavity polarization. HML, with orders from the first to the 26th, is also detected by further increasing the pump power, making the laser attractive for applications such as nonlinear imaging or spectroscopy.