1. Introduction

The pursuit towards higher repetition rate pulse sources has accelerated recently due to the strong need, in numerous scientific and technological applications, of pulse trains with gigahertz repetition rates. Semiconductor quantum dot lasers represent one option, offering compactness and integrability with direct electrical control, and led to sub-picosecond pulse generation at repetition rates as high as 346 GHz [1,2]. Compact passively mode-locked lasers based on Er-Yb glass have culminated in an impressive 77 GHz repetition rate at the fundamental cavity frequency [3]. On the other hand, fiber lasers capable to generate short pulses with high repetition rates would also be advantageous due to their robustness, flexibility, higher integrated gain, and superior beam delivery. Passively mode-locked fiber lasers have been under strong investigation during the past decade, especially in the context of producing pulses of shorter durations and higher energies. In order to push the operation into the gigahertz regime, the conventional approach consists in scaling down the cavity length, which runs quickly into the limitations due to the accessible levels of rare-earth doping of the gain fiber and to the practical lengths of fibered components that can be handled for splicing. Another attractive way is to exploit the multiple-pulsing operation of passively mode-locked fiber lasers under intense pumping power. The power scaling-up in fiber lasers and the progress in double-clad fiber technology have enabled the generation of greater numbers of identical soliton pulses per cavity roundtrip. Under specific cavity setting conditions, the interactions between these solitons can induce regular temporal patterns such as harmonic mode locking (HML), where the laser operates at a multiple of its fundamental frequency.

Passive HML in fiber lasers can be obtained through the use of nonlinear polarization evolution (NPE). Since their early realization [4], passive harmonically mode-locked fiber lasers have reached GHz frequencies. More precisely, Yb-doped fiber lasers have generated about 2-GHz pulse rates [5,6] with a supermode suppression level (SSL) of about 45 dB and a timing jitter between 5 and 10 ps [6]. In Er/Yb fiber lasers, best reports to date highlighted the operation at the 75th cavity harmonics (~7 GHz) with a timing jitter of 2.7 ps [7], and at the 634th cavity harmonics (~10 GHz) but with a modest SSL of 16 dB [8]. Meanwhile, the progress in saturable absorber technology resulting from the development of new wideband materials has led to a new wave of HML reports with fiber lasers. The use of saturable absorbers based on carbon nanotubes interacting via evanescent waves enabled demonstration of repetition rates as high as 5 GHz [9], and low-noise operation with a SSL higher than 50 dB [10]. Graphene, a particularly promising saturable absorber material for its unique ultra-broad tuning range, led to a 2.2 GHz HML repetition rate with a supermode suppression of 40 dB [11]. Still, many factors affecting the regular distribution of multiple pulses all along the cavity remain unclear. In particular, the role of a continuous wave (CW) background to act as an efficient interaction mediator between pulses has been advanced [12–14].

In this paper, we use an erbium-doped fiber laser to investigate the wide range of harmonic mode locking dynamical configurations that can be selected at a given pumping power level, by using the polarization degrees of freedom accessible in NPE-based mode locking. The laser is found to operate stably at various harmonics, from the 6th to the 928th, with supermode suppression levels between 19 dB and 41 dB. Repetition rate in excess to 20 GHz is obtained, which is to our knowledge the highest harmonic and repetition rate ever reported in a passively mode-locked fiber laser. Finally, by injecting a highly coherent continuous wave in the cavity, we test the influence of a CW background on the stability of high-harmonic mode locking.

2. Experimental setup

Our fiber ring laser setup is shown in Fig. 1. The laser uses a 3-m long erbium-doped fiber (EDF) as the gain medium, pumped at the wavelength of 1.48 μm by a Raman fiber laser source delivering up to 5 W coupled through a 1480/1550 multiplexer (WDM). Two additional multiplexers are spliced after the EDF in order to reject the remaining pumping light from the rest of the cavity, with a suppression ratio better than 30 dB. Unidirectional laser emission is ensured by the presence of two polarization-insensitive optical isolators (ISO) surrounding the amplifier section. Output couplers are placed before (95/5) and after (97/3) the EDF, which has an anomalous group-velocity dispersion (D = + 15 ps.nm⁻¹.km⁻¹). Fiber components are pigtailed with short lengths of SMF-28 (D = + 17 ps.nm⁻¹.km⁻¹). The cavity also includes a 1.5 m-long dispersion-shifted fiber (DSF, D = −2 ps.nm⁻¹.km⁻¹). The total chromatic dispersion is anomalous (β₂ = −0.013 ps²), which is conducive to mode locking operation with multiple pulses at large pumping power. The cavity comprises an open-air section of one meter, where a polarizer is sandwiched between two sets of polarization controllers (PCs) consisting of a quarter-wave and a half-wave plate. The polarization of the intra-cavity light field can be controlled by these sets of wave plates and mode locking is then achieved through the NPE technique. The fundamental repetition rate is 23.9 MHz. The laser signal is monitored using one port of a 1:4 splitter spliced at the 3% output of the 97/3 coupler and sent to a 45-GHz photodiode whose electrical signal is recorded by a 45-GHz, 120-GSa/s real-time oscilloscope (LeCroy SDA845Zi-A). Another output port of the 1:4 splitter is sent to an optical spectrum analyzer, which has a resolution of 65 pm.

 

Fig. 1 NPE- mode locked fiber laser setup. OC, Output coupler; WDM, Wavelength multiplexer; ISO, optical isolator; PC, polarization controller; PBS, polarization beam-splitter.

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3. Influence of cavity parameters on harmonic mode locking

Mode-locking using NPE offers many degrees of freedom to shape the transfer function of the effective saturable absorber by adjusting the orientation of the polarization controllers. Such shaping drastically affects the balance between dissipative nonlinear effects and impacts the level of quasi-continuous waves that can coexist with soliton pulses in the cavity. This enables the observation of various collective pulse dynamics. We also investigated the influence of the following other cavity parameters on the performances of harmonic mode locking: the total cavity dispersion and additional intracavity spectral filtering. As was expected, best results in terms of high-harmonics and their stability were obtained when the cavity operated at anomalous cavity dispersion without any spectral filtering additional to the gain bandwidth.

For pumping powers ranging from 0.7 to 3 W, we studied the range of the stable repetition rates selectable with the PCs [see Fig. 2(a)], and measured the corresponding SSL [see Fig. 2(b)]. The harmonically mode-locked operation was obtained after a threshold of 0.7 W pumping power and already reached surprisingly the gigahertz level. It depended crucially on the adjustment of the PCs. The highest observed pulse repetition rate, obtained at a pumping power of 2W, exceeded the 20 GHz-level, which is to our knowledge twice the current state of the art. The adjustment of the full degrees of freedom of the polarization controllers allowed selection of the pulse rate between 4 GHz and 22.2 GHz. Noteworthy, supermode suppression levels higher than 30 dB were recorded for repetition rates higher that 10 GHz. The SSL decreased for pulse frequencies above 16 GHz, however was maintained to a level higher than 20 dB. The maximal observed stable repetition rates tended to reduce for pump powers above 3W. According to Fig. 2(a), we conclude that the precise settings of the ML parameters have a larger impact on the HML repetition rate than the change of the pumping power.

 

Fig. 2 Distributions of HML pulse repetition rates for various pumping powers (a). Measured supermode suppression levels according to the pulse repetition rate (b).

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In section 4, we present results obtained at pump powers between 2 and 3 Watts. This pumping power range led to the widest variety of self-organized pulse patterns, controlled by the careful adjustment of the intra-cavity polarization controllers. In particular, we detail the cases of the highest repetition rate and of the best supermode suppression level.

4. Experimental results: 272th and 928th harmonics of the fundamental repetition rate

The best supermode suppression level was obtained at 6.52 GHz, which corresponds to the 272th harmonic of the fundamental repetition frequency. Once harmonic mode-locking is obtained, the laser remains stable for the whole day. The equidistant pulse distribution is confirmed by measuring both the RF spectrum and a long-range optical cross-correlation, using an optical delay line spanning 400 ps, the temporal interval between two successive pulses being equal to 156 ps, as illustrated in Fig. 3(a). The optical spectrum is shown on Fig. 3(b): its central wavelength is 1550 nm and its width (FWHM) is 16.5 nm. Figure 3(c) displays the RF spectrum recorded with a resolution bandwidth of 50 kHz. SSL is higher than 41 dB on a span of 10 GHz. Note that the SSL reaches 62 dB at a span of few hundreds of MHz around the center frequency. The intensity optical autocorrelation function is shown in Fig. 3(a): the central part (inset) has a 1.7 ps FWHM duration. The cross-correlation between two successive pulses has a FWHM of 3.6 ps. This allows measurement of the timing jitter. Assuming a deconvolution factor of 1.54, pulse duration is 1.1 ps and the corresponding timing jitter is 2.3 ps, similar to the best cases of passive harmonically mode-locked lasers reported [6,7]. We note the spectral sidebands located asymmetrically in Fig. 3(b), which are associated to dispersive wave soliton radiation of relatively low coherence.

 

Fig. 3 Harmonic mode locking at 6.52 GHz: (a) autocorrelation (AC) that includes cross correlation between adjacent pulses. Inset is a zoom of the AC trace ; (b) optical spectra on linear and log- (inset) scales and (c) rf spectra at 10 GHz and 200 MHz (inset) spans.

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Let us now present the highest pulse repetition rate achieved with the fiber laser cavity: the frequency is 22.2 GHz, corresponding to the 928th harmonic and was obtained for a 2W-pump power. It is confirmed by the cross-correlation between pulses with a cross-correlation width around 10 ps, reflecting a larger timing jitter than in the 6.52 GHz case. At such record high-harmonic and repetition rate, this still represents an appreciable stability of the pulse train, in absence of any active modulation, and seems to indicate the action of efficient self-stabilization mechanisms that need to be investigated further [12–16]. The RF analysis shows a SSL higher that 26 dB in the whole 20 GHz [see Fig. 4(b)] span and above 30 dB in the 1 GHz span. Compared to the 6.52 GHz HML case, the optical spectrum of the 22 GHz HML, shown on Fig. 4(a), is narrower (7 nm FWHM), and no longer features wide spectral sidebands. Instead, tiny spectral spikes appear close to the maximum. Since the possible role of a CW component in the stabilization of the harmonic mode-locking regime has been conjectured [12–14], we have tested the influence of an injected CW laser beam on the stability of high harmonics.

 

Fig. 4 Harmonic mode-locking at 22.2 GHz repetition rate: (a) optical spectra on linear and log- (inset) scales, RF spectrum at 20 GHz span (b).

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5. Influence of an injected continuous light on high-harmonics

It is very difficult to study the role of a self-generated CW component. However, we can test the robustness of the HML regime against an injected CW component. The injected light is provided by a highly coherent (100 kHz linewidth) 3 mW laser, whose wavelength can be tuned between 1533 and 1571 nm. We used the injection port of the cavity and tuned successively the wavelength by steps of 2 nm. Optical and RF spectra were observed and recorded during the analysis. We adjusted the polarization controllers in order to obtain the 6.52 GHz HML regime presented in Fig. 3. Figure 5(a) presents various RF spectra recorded at 500 MHz spans while changing the wavelength of the injected light. The corresponding optical spectra are given in Fig. 5(b). We note that the main features of the RF spectrum (main frequency, SSL) do not change, with a SSL higher than 40 dB. We can conclude that the highly stable HML regime is not visibly disturbed by the CW component. This possibly rules out the role of a single CW component as an efficient mediator for stabilizing adjacent pulses in HML.

 

Fig. 5 (a) From top to bottom, evolution of the RF spectrum along with the wavelength tuning of the injected cw laser. The resolution bandwidth is 50 kHz (b) Superimposed corresponding optical spectra in log-scale, showing no visible influence of the cw component.

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Importantly, the HML regimes featuring a SSL < 30 dB become more sensitive to the injection of a CW component. In few cases, the CW slightly disturbs the passive harmonic regime: the pulses reorganize themselves and the repetition rate is also slightly changed. In other cases, the HML regime is disrupted and the polarization controllers need to be readjusted to retrieve the HML pulse regime.

7. Conclusion

We have reported a high-repetition-rate harmonically-mode-locked fiber laser at around 1.5 μm. For a pumping power between 0.7 and 3 W, the selection of the repetition rate is dominated by the adjustment of the NPE-based nonlinear transfer function, accessible through polarization control. The laser operates stably at harmonics ranging from the 6th to the 928th (22.2 GHz). The most stable HML is generated at 6.52 GHz (272th harmonic), and features a SSL > 60 dB over 1 GHz bandwidth, and a timing jitter of 2.3 ps. This regime remains unaffected by the injection of a tunable cw laser, whatever its wavelength, which tends to invalidate the positive influence of a single narrow CW component on the pulse-to-pulse stability. However, HML regimes with SSL<30 dB tend to be destabilized by the injection of the cw laser around specific wavelengths. We have reported SSL > 25 dB for repetition rates above the 20-GHz level, so we believe these results could renew the interest for the passive harmonic mode locking alternative to high repetition rate mode locking.

Indeed, it has been demonstrated that extremely stable “macromolecules” of dissipative solitons can form spontaneously in ML lasers [15]. We believe these results will stimulate progress in the understanding of dissipative soliton interactions. The observation of several hundreds of regularly-spaced bound solitons, or “soliton crystals”, have been reported [16], but so far only a ~10% fraction of the total cavity has been filled. We anticipate that at repetition rates of ~50 GHz, the interface between HML and the regime of soliton macromolecules could yield high repetition rate fiber laser sources of unprecedented stability.