1. Introduction

Passively mode-locked fiber lasers with high repetition rate (over 1 GHz) have been playing pivotal role in increasing applications, including high-precision frequency metrology, high speed optical sampling, optical arbitrary waveform generation, material micromachining, and the calibration of astrophysical spectrographs [1–5]. Generally, there are several ways to realize lasers with repetition rate on the order of multi-gigahertz, such as harmonic mode-locking [6,7], pulse repetition rate multiplication [8], and fundamental mode-locking [9]. Comparatively speaking, higher repetition frequency can be obtained by using pulse repetition rate multiplication and harmonic mode-locking techniques, which, however, lead to relatively large intensity and phase noise. Their counterpart, fundamental mode-locking, can effectively fix those problems.

Experimentally, the passively mode-locked fiber lasers with multi-gigahertz fundamental repetition rates have been realized with different mode lockers, e.g., carbon nanotubes (CNTs), graphene saturable absorbers (GSAs), and SESAMs, among which SESAM technology is most widely used due to their high thermal damage threshold and stable structure. Therefore, SESAM mode-locked fiber lasers with fundamental repetition rate exceeding 1 GHz have been extensively studied. In 1.5 μm waveband, Martinez et al. presented a CNT mode-locked Er/Yb co-doped phosphate glass fiber (PGF) laser with a fundamental repetition rate of up to 19.45 GHz, which is the highest fundamental repetition rate to date [9]. Thapa et al. reported a 12 GHz mode-locked laser oscillator using 0.8 cm highly Er/Yb doped PGF [10]. Zhou et al. demonstrated a compact SESAM mode-locked Er/Yb co-doped PGF laser with a fundamental repetition rate of 3.2 GHz [11]. Chen et al. demonstrated a 3 GHz femtosecond mode-locked laser with a heavily Er/Yb co-doped PGF [12]. However, highly Er/Yb co-doped PGFs were used, without exception, in all the aforementioned works, which are actually not commercially available yet. Thus far, the reported highest fundamental repetition rate with commercially available Er-doped silica fibers is 2.68 GHz at 1.5 μm wavelength region [13], which is much lower than that (19.45 GHz) with Er/Yb co-doped PGF [9]. In addition, long term operation was not demonstrated. Except for experiments, SESAMs-based high repetition rate passively mode-locked fiber have also been numerically studied and analyzed [14–17]. A model was developed to explain the pulse instability of a high repetition rate fiber laser considering the changes of small-signal gain coefficient of the gain fiber [16]. Importantly, appropriate choice of the SESAM parameters is critical to prevent Q-switch instabilities for stable operation of high-repetition-rate passively mode-locked fiber lasers [18]. The highly stable mode-locking at GHz repetition rate, whether at anomalous dispersion or normal dispersion regions, can only be achieved with SESAMs with small modulation depth [14]. Lately, different repetition rates have been numerically studied by changing the total cavity length [17], according to which different pulse repetition rates ranging from 1.0 GHz to 10.0 GHz could be achieved. However, only 1.0 GHz and 2.2 GHz cavity were realized experimentally by using a SESAM with a modulation depth of 37% and saturation fluence of 30 μJ/cm².

Usually, it is widely accepted that fiber lasers exhibit very high gain compared with their solid-state laser counterpart. So, SESAMs with high modulation depth and low reflectivity were typically employed for passively mode-locked fiber laser with repetition rate on the order of ∼100 MHz. However, for passively mode-locked fiber laser with multi-gigahertz repetition rate, the gain fiber length has to be very short, i.e. few centimeters or shorter than 1 cm, which is similar to the length of crystal used in mode-locked bulk lasers. In this case, fiber gain becomes much lower than that in typical ∼100 MHz case, so the so called “fiber laser” in its short limit gradually develops into “solid state lasers”. Therefore, lessons on selection of SESAMs and management of cavity loss and dispersion could and should be drawn from SESAM mode-locked bulk lasers, when multi-gigahertz SESAM mode-locked fiber laser is designed and configured.

In this contribution, basic design guidelines for high repetition rate passively mode-locked fiber lasers are discussed, based on which, a 5 GHz fundamental repetition rate passively SESAM mode-locked fiber laser is demonstrated with commercially available Er-doped silica fiber. The central wavelength is at 1561.0 nm with an SNR of 62.1 dB and a bandwidth of ∼0.69 nm. After amplification, the pulse width and the 3-dB bandwidth were measured to be 3.86 ps and 1.16 nm, leading to a time-bandwidth product (TBP) of 0.55, which is a little higher than the transform-limited TBP of 0.44 for Gaussian-shaped pulse.

2. Experimental setup

Figure 1(a) illustrates the schematic diagram of the experimental setup for GHz passively mode-locked all-fiber laser at 1.5 μm. The laser system consists of a EDF oscillator and an external EDF amplifier. A 2.09-cm-long commercially available EDF (Liekki Er110-4/125) with a gain coefficient of 1 dB/cm at 1550 nm acted as a gain medium. The gain fiber was pumped by a single-mode pigtailed 976 nm laser diode (LD) through a wavelength division multiplexer (WDM). The EDF was inserted and glued in a ceramic ferrule with an inner diameter of 127.5 μm and an outer diameter of 2.5 mm. Both end facets of the gain fiber were perpendicularly polished. One end of the EDF was butt-coupled to dielectric films (DFs) coated on a passive fiber ferrule end facet, which was fusion spliced to the common port of WDM. The DFs, which were prepared by the ion beam assisted deposition technique, exhibit a high transmittance of ∼99% at the pump wavelength of 976 nm, as well as a high reflectivity of over 98% at 1550 nm, as shown in Fig. 1(b). The opposite end of the EDF was perpendicularly connected to a SESAM with a chip area of 4.0 mm × 4.0 mm and a thickness of 450 μm. Two different SESAMs were used in this work for comparison. The characteristics of the SESAMs are listed in Tab. 1. To dissipate the possible heat, the SESAM was glued on a copper heat sink and thereafter mounted on a linear piezo-motor driven stage (Newport AG-LS25) via a bracket assembly to accurately control the relative position between the facet of the EDF and SESAM for enabling stable mode locking.

 

Fig. 1. (a) The schematic diagram of the experimental setup for 5 GHz mode-locked Er-doped silica fiber oscillator and amplifier. The inset of (a) shows the photograph of the laser cavity, (b) The reflectance of the dielectric film. The inset of (b) illustrates the reflectance on a span of 50 nm. LD, laser diode; PC, polarization controller; WDM, wavelength division multiplexer; DF, dielectric films; EDF, Er-doped fiber; SESAM, semiconductor saturable absorber mirror; ISO, isolator.

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Table 1. Characteristics of semiconductor saturable absorber mirror

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A photograph of the FP fiber laser cavity is shown in the inset of Fig. 1(a). The dispersion of the SESAM is ∼1000 fs² at 1.56 μm and the second-order dispersion of the used EDF is 15 fs²/mm at 1.55 μm. Then, the net cavity dispersion is estimated to be ∼1313.5 fs². The output pulses from the oscillator were amplified by one-stage EDFA. An isolator (ISO) was used to prevent unwanted intracavity reflections between the oscillator and amplifier. The optical spectrum was measured using an optical spectrum analyzer (Yokogawa AQ6370D). The pulse train was detected by using a 12 GHz bandwidth photodetector (New Focus 1554-B), and monitored with a 16 GHz mixed signal oscilloscope (Tektronix MSO 71604C). The pulse duration was measured by an autocorrelator (APE PulseCheck). A signal analyzer (Keysight N9020B) was employed to characterize the radio-frequency (RF) spectrum and phase noise.

3. Comparison with solid-state lasers

A number of passively mode-locked fiber lasers [19–30] and solid-state lasers [31–43] operating at 1.5 μm have been extensively investigated to achieve reliable mode-locking performance. An overview on selected best results of fundamentally mode-locked lasers is made to illustrate the difference between fiber lasers and their solid-state laser counterpart, summarized in Fig. 2. The trends of modulation depth of SESAMs used in fiber lasers and solid-state lasers are indicated by red line and blue line. Like that shown in Fig. 2, as the repetition rate increases, the two lines keep approaching. When high repetition rate (≥1 GHz) is achieved, the gap between two lines becomes extremely small. It is worth mentioning that there is an exception reported in Ref. [10] where a SESAM with strong modulation depth of 54% was used as the mode locker. Although the strong modulation depth will lead to large cavity loss, the gain coefficient of as high as 6 dB/cm in PGF is enough to meet stability condition, as discussed later. From the analysis of the Q-switched mode-locked operation in Ref. [18], one can see that a proper choice of the SESAM characteristics, such as: modulation depth, saturation fluence, and absorbance, plays a key role in obtaining stable self-starting CW mode-locked operation with a high repetition rate. An important parameter for SESAM mode-locked laser is the critical intracavity pulse energy E_c, which is defined as the minimum intracavity pulse energy required for obtaining stable CW mode-locking. The criterion parameter E_c is given by [18]:

 

Fig. 2. A summary diagram of selected studies on 1.5 μm SESAM mode-locked fiber lasers and solid-state lasers to show the general trends. Note: not all related papers are included here.

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4. Experimental results and discussion

In order to verify our conjecture, the experiments were carried out with two SESAMs (both produced by Batop GmbH): SESAM-1, with a weak modulation depth ΔR=3% and a small saturation fluence Φ=15 μJ/cm², and SESAM-2, with a relatively strong modulation depth ΔR=15% and a large saturation fluence Φ=30 μJ/cm². It is worth noting that when SESAM-2 is used as the mode locker, the highest repetition rate of CW mode-locking is only 2.43 GHz, corresponding to 4.26 cm cavity length. Attempt with 5 GHz cavity (∼2 cm cavity length) was failed to deliver CW mode-locking, only Q-switched mode-locking was achieved with SESAM-2. The minimum intracavity pulse energy required by SESAM-1 and SESAM-2 in CW mode locking was denoted as E_c-1 and E_c-2. The ratio E_c-1/E_c-2 = 0.32 highlights the fact that SESAM-1 (with lower value for both modulation depth and saturation fluence) requires smaller intracavity pulse energy to maintain CW mode locking operation. Thus, commercially available EDF with relatively low gain coefficient can provide sufficient gain to initiate the pulsed behavior.

To get a stable CW mode-locked laser, careful adjustments of relative position between the fiber end and SESAM-1 were carried out. The relationship between the output power of the oscillator and launched pump power is depicted in Fig. 3. Once pump power threshold of 44 mW is reached, the laser operates in Q-switched mode locking state and the output power increases linearly with increasing pump power. Above launched pump power of 241 mW, self-started mode locking is realized and the output power keeps linearly dependence on injected pump power but with a slightly higher slope. The insets of Fig. 3 show the shape of pulse trains in different mode locking regimes over a 10 μs time scale. No pulse breaking or Q-switched mode-locking operation can be found in the range of 241-302 mW, indicating a CW mode-locking condition.

 

Fig. 3. Laser output power with respect to the launched pump power.

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To clearly show how the mode-locking conditions was satisfied, the output power P_out = 1.2 mW, and the output coupler transmission T = 1.5% are used to calculate the intracavity pulse energy. ${E_p} = {P_{out}}{T_R}/T$ is the energy of a mode-locked pulse in the cavity where T_R is the cavity round-trip time. Thus, the calculated intracavity pulse energy is 16.2 pJ. The mode areas on the SESAM, A_eff,a is estimated to be 32.5 μm², which is determined by effective mode area of the gain fiber. The intracavity pulse fluence of SESAM, ${F_s} = {E_p}/{A_{eff,a}}$ can be calculated to be 49.9 μJ/cm², which is 3.3 times of the saturation fluence of SESAM-1. Therefore, CW mode-locking can be realized. In the CW mode locking regime, the maximum output power obtained from the oscillator is 1.37 mW with the pump power of 302 mW. When the pump power was higher than 302 mW, the pulsation was observed due to the periodic modulation of the pulse train triggered by excessive pump power [16].

 Figure 4(a) illustrates the mode-locked spectrum at the pump power of 274 mW, centered at 1561.0 nm with a 3-dB bandwidth of 0.69 nm, which is limited by the weak modulation depth of the SESAM [15]. It is believed that shorter pulse duration and broader bandwidth can be expected by employing a dispersion-controlled fiber mirror in the laser cavity. From enlarged central portion of the spectrum, the longitudinal mode structure of the laser can be clearly observed. As depicted in the insert of Fig. 4(a), a spectral fringe with a period of 0.041 nm was obtained, corresponding to the intrinsic 4.95 GHz longitudinal mode spacing of the FP laser cavity. The RF spectrum was recorded by using a signal analyzer with a resolution bandwidth of 1 kHz, as shown in Fig. 4(b). The fundamental repetition rate of the fiber laser was measured to be 4.947 GHz and a SNR of greater than 60 dB without Q-switching sidebands confirms that steady state CW mode-locking is achieved. The inset to Fig. 4(b) shows the broad-span RF spectrum of the fundamental repetition frequency and its harmonics in a span of 13.5 GHz (limited by the bandwidth of the signal analyzer). As shown in Fig. 4(c), the laser delivered uniform pulse trains with a temporal period of 203 ps exiting the cavity.

 

Fig. 4. (a) Optical spectrum of the fundamental mode-locking operation at a pump power of 274 mW. Inset: magnification of the top peak of the optical spectrum. (b) Measured RF spectrum of the oscillator with a resolution bandwidth of 1 kHz. Inset: the broad-span RF output spectrum. (c) Typical pulse train of fundamental mode-locked fiber laser with 4.95 GHz repetition rate.

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Given the highest average output power of CW mode-locked oscillator is 1.37 mW, the maximum single pulse energy can be calculated to be 0.24 pJ. In order to measure the intensity autocorrelation trace, the output power of the oscillator was amplified to 27 mW. A series of measurements pertaining to amplified laser pulse are displayed in Fig. 5. The spectrum is shown in Fig. 5(a) with a 3-dB bandwidth of 1.16 nm, whose moderate spectral broadening is mainly due to the nonlinear self-phase modulation effect. As plotted in Fig. 5(b), the measured autocorrelation trace shows a Gaussian profile, with a full width at half-maximum (FWHM) of 5.46 ps, corresponding to a pulse width of 3.86 ps with a deconvolution factor of 1.41. The pulse width is slightly longer than the transform limited pulse width of 3.54 ps, which could be attributed to chromatic dispersion and optical nonlinearities during propagation. Figure 5(c) shows the stability of the output power at 27 mW for 3 hours, with a root mean square (RMS) noise of 0.72%. The inset of Fig. 5(c) shows 3-hour recording of the spectrum, indicating the stability of the high repartition rate fiber laser. A logarithmic plot of the phase noise is displayed in Fig. 5(d). The phase noise is -31 dBc/Hz at 10 Hz offset and decreases to -150 dBc/Hz at 10 MHz offset. The resulting timing jitter integrated from 10 MHz down to 10 Hz is calculated to be 3.77 ps.

 

Fig. 5. (a) The optical spectra measured after amplification. (b) The autocorrelation trace measured at an output power of 27 mW. (c) the stability record of the output power for 3 hours. The inset of (c) shows false color map of optical spectra of high repetition-rate mode-locked laser recorded per minute for 3 hours. (d) the phase noise and the corresponding integrated timing jitter of the amplified pulses.

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5. Conclusion

In conclusion, the fundamental repetition rate of 5 GHz all-fiber passively mode-locked EDF laser was demonstrated. A 2.09 cm commercial EDF was employed as the gain medium in the compact and robust oscillator. By using high reflectivity SESAM and the dielectric films, the CW mode-locking pump threshold power is optimized to 241 mW. The mode-locked fiber laser operated at 1561.0 nm, and the pulse width after amplification was measured to be 3.86 ps. Meanwhile, the stability of mode locking within 3 hours was verified by monitoring of spectrum and power fluctuation. The timing jitter integrated from 10 MHz to 10 Hz was 3.77 ps. Further theoretical investigations disclose that the modulation depth of the SESAM plays an important role in achieving high repetition rate CW mode locking. We except higher repetition rate could be obtained by employing SESAMs with lower modulation depth.