1. Introduction

High-repetition-rate ultrafast fiber lasers are indispensable tools for various of applications including e.g., precise material processing, frequency metrology, high-speed optical sampling, and spectroscopy [1–9]. In the field of ablation-cooled micromachining, high-repetition-rate femtosecond lasers reduce the demand of single pulse energy by more than one order of magnitude in comparison with traditional low-repetition-rate counterparts [1,10]. In the ablation-cooled regime, repetition rate of the intra-burst pulses needs to be sufficiently high to keep the local temperature of the area being ablated continuously rising between successive pulses [1,11]. Ablation-cooled processing is promising to increase the efficiency of micromachining, but the repetition rate requires to reach gigahertz (GHz) range. Therefore, ultrafast lasers with GHz repetition rate are essential to this application.

There are several techniques being proposed to generate GHz pulses, such as fundamental mode-locking, harmonic mode-locking, repetition rate multiplication with optical delay lines [10,12–17]. Therein, fundamental mode-locking is comparatively a more reliable solution for passively mode-locked fiber lasers due to their high stability and lower phase noise. Linear cavity is one of the most commonly used configurations to achieve GHz repetition rate in the fundamental mode-locking regime [18,19]. Generally, an ultrashort segment of gain fiber with heavy dopant concentration (phosphate fiber in most cases) is integrated in the cavity and constitutes a Fabry-Perot structure with high-reflectivity coatings on both ends of the fiber [13,20]. Utilizing the linear cavity, multi-GHz pulses were generated in the 1 µm, 1.5 µm, and 2 µm wavebands [16,20–22]. However, the output pulse width is typically limited to picosecond range. To obtain sub-300 fs pulses at the 1 µm region, dispersion compensation is crucial. A multilayer structure that acts as dispersion compensator was introduced in a linear fiber oscillator, which generates 206 fs pulses at the fundamental repetition rate of 3 GHz, however, the intricate coating technology may make it difficult to realize mass production [23]. Grating pairs that provides flexible tunability and huge amount of negative chirp was brought in a ring fiber cavity with nonlinear-polarization evolution (NPE) mode-locking, which generates 64 fs pulses at the repetition rate of 1 GHz [24]. However, the use of non-polarization-maitaining (non-PM) fiber degrades the laser’s environmental immunity to some extent; in addition, the large-size Faraday rotator to maintain single-direction operation limits the repetition rate boosting of ring cavities.

On the other hand, in the process of ultrashort pulses amplification, nonlinear phase accumulation degrades temporal pulse quality greatly, consequently having a bad influence on the processing quality. Self-phase modulation (SPM) is the main cause of nonlinear phase distortion, which is equivalent to the impact of a dispersive component with corresponding dispersion orders determined by the maximum SPM-induced phase shift and the nth-order derivatives of the pulse shape [25]. Therefore, high-energy amplified pulses with higher temporal quality can be obtained with the input of appropriate waveforms. Spatial light modulator [26,27] and acousto-optic modulator [28,29] are ubiquitous to choose the desired waveforms. However, these techniques are expensive or relying on active control to some degree. Therefore, a simpler and cost-effective way to provide tunable waveforms is desirable.

In this letter, we demonstrate a novel GHz-repetition-rate, ring cavity Yb-doped femtosecond fiber laser with SESAM fundamentally mode-locking. The exploitation of an isolator-free structure enables a high repetition rate and bidirectional operation. Two polarization-multiplexed output pulse trains with different chirp characteristics generated from the bidirectional mode-locked laser are demonstrated synchronous in time. Consequently, tunable waveforms and spectra are obtained by the combination of two synchronous pulses outside the oscillator. As a result, 177-fs pulses at a repetition rate of 1.048 GHz are obtained with reduced pedestal and shorter pulse width in comparison to the two individuals. Another similar-structure GHz mode-locked fiber laser with a grating-based filter that generates picosecond pulses is also demonstrated. We believe the proposed lasers could serve as the front-end for GHz ultrashort-pulse amplification systems and furthermore ablation-cooled micromachining.

2. Experimental setup

The schematic of the isolator-free ring cavity fiber laser is illustrated in Fig. 1. The so-call semi-WDM is an integrated component that plays the role of a wavelength-division multiplexer and a collimator at the same time. In conjunction with the semi-WDM a pigtail of 110 mm long polarization-maintaining (PM) Yb-doped fiber (Coherent: PM-Yb401) is used and no passive fiber is implemented in the cavity. The gain fiber can be pumped by two 976 nm laser diodes each with a maximum average power of 1 W from opposite directions. When only one laser diode is connected to a semi-WDM via passive fiber, the other passive fiber serves as a pump dumper. To provide negative group-delay dispersion (GDD), a pair of gratings (LightSmyth: 1000 lines/mm) set at the Littrow incident angle is incorporated whose perpendicular distance can be tuned from 2 mm to 8 mm with 1 mm increment. To control the output splitting ratio, a polarization-beam splitter (PBS) together with a half-wave plate are implemented in the cavity. The mode-locking mechanism is enabled by a SESAM (BATOP: SAM-1030-30-1ps), which is mounted on the copper plate to dissipate the accumulated heat. The beam with a diameter of 0.5 mm from the semi-WDM is focused on the mode-locker via a plano-convex lens characterizing a focal length of 9.8 mm. The quarter-wave plate is inserted to turn the polarization of the P-polarized beam into S-polarized when it is passed through twice, and vice versa, thus enabling the light to travel back to the ring structure. The laser can be operated bidirectionally thanks to the isolator-free structure. The two polarization-multiplexed output pulse trains from the laser are measured after the PBS outside the ring cavity, and another half-wave plate is inserted between the two PBSs to tune the proportions of the two orthogonal-polarized output pulses projected to the P-polarized direction.

 

Fig. 1. Schematic of the isolator-free GHz ring cavity mode-locked fiber laser. The components in the left dotted box can be substituted by those in the right blue dotted box to construct a GHz picosecond fiber laser. PM Yb: fiber, polarization-maintaining Yb-doped fiber; PBS, polarization-beam splitter; λ/2, half-wave plate; λ/4, quarter-wave plate; OSA, optical spectrum analyzer; FROG, frequency-resolved optical gating; AC, autocorrelator; OSC, oscilloscope; BD, balanced detector.

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The output characteristics after combination are measured by an optical spectrum analyzer (Anritsu MS9740B), a frequency-resolved optical gating (MesaPhotonics MP-001.X), an autocorrelator (APE PulseCheck-USB150), a broadband oscilloscope (KEYSIGHT DSOV134A, 13 GHz bandwidth) and a balanced detector (Thorlabs PDB450C). A similar structure that generates GHz picosecond pulses is also illustrated in Fig. 1, where the only difference is shown in the dotted box. In the picosecond mode-locked ring cavity fiber laser, a grating-based filter is implemented instead of the grating dispersion compensator in the aforementioned femtosecond fiber laser, therefore the laser is operated in the normal-dispersion regime. The central wavelength can be tuned by adjusting the translation stages.

3. Experimental results and discussion

The GHz femtosecond mode-locked fiber laser is self-started with the clockwise pumped power of 432 mW when the output ratio is set at a certain value. The gratings separation is 4 mm corresponding to a net GDD of -7970 fs². The angle tolerance of the half-wave plate to keep stable mode-locking is approximately 5 degrees, which confirms a broad range of mode-locking conditions. In comparison with most of the low-repetition-rate mode-locked fiber lasers, there is no need to set the pump power to a high value that may lead to multi-pulsing before reduce it to single-pulse mode-locking. As a result, 100% success rate is achieved in the 100-times self-starting tests. The laser keeps stable mode-locking until the pump power is increased to 610 mW at which multi-pulsing occurs. The polarization-multiplexed output power as a function of pump power is illustrated in Fig. 2. The axial direction of the PM fiber inside the semi-WDM does not matter on whether the laser can be mode-locked, consequently, the half-wave plate which should have been inserted between the left-most semi-WDM and PBS is removed. In order to rule out the possibility of nonlinear polarization evolution mode-locking, a mirror was used in substitution of the lens and SESAM to test if the laser can be mode-locked, but no indication of mode-locking was observed.

 

Fig. 2. Output power of the two orthogonal-polarized individuals (P-polarized output in red circles and S-polarized output in blue diamonds) from the femtosecond laser as a function of clockwise pumped power.

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The two orthogonal-polarized pulse trains are synchronized, which is confirmed by the almost same fundamental repetition rates with <1 kHz deviations in 5 minutes measured by two radio frequency (RF) spectrum analyzers (Fig. 3(a), where the inset shows a representative RF spectrum that indicates a fundamental repetition rate of 1.048 GHz), and the non-oscillation characteristics of the pulse trains combining the two orthogonal-polarized components in the millisecond range (Fig. 3(b)). Furthermore, the autocorrelation of the combined pulse showing no sub-pulse in the 50 ps range (Fig. 3(c)), as well as the balanced detection showing no interferogram also indicates the synchronicity of the P and S-polarized pulses (Fig. 3(d)).

 

Fig. 3. Time-domain synchronicity demonstration of the two orthogonal-polarized pulses from the femtosecond laser: (a) measured repetition rate difference within 5 minutes (inset shows a representative RF spectrum); (b) combined pulse train; (c) autocorrelation trace of the combined pulse; (d) balanced detection result of the combined pulse.

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The measured output spectra, autocorrelation traces, waveforms, and phases of the two orthogonal-polarized individuals at the pump power of 550 mW are illustrated in Fig. 4, which is measured with the removal of the half-wave plate outside the cavity. Owing to the opposite sequences the two pulse trains pass through inside the cavity, the two individuals have different phases; the P-polarized pulses characterize a descending phase in the leading edge and a rising phase in the trailing edge (Fig. 4(c)), while the S-polarized pulses have a reverse trend (Fig. 4(f)), therefore possibly giving rise to the cancellation of the front and trailing edges of the combined waveforms. The P-polarized output pulses have a nonnegligible pedestal in the leading edge shown in the FROG trace and as a result, the corresponding autocorrelation shape is well-fitted by a Lorentzian function (Fig. 4(b)). The S-polarized FROG trace is comparatively cleaner and thus the AC trace can be well-fitted by a Secant hyperbolic function (Fig. 4(e)).

 

Fig. 4. Spectral and temporal characteristics of the output P-polarized pulse (a-c) and S-polarized pulse (d-f) from the femtosecond laser: (a), (d) spectrum; (b), (e) autocorrelation trace; (c), (f) FROG trace.

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Furthermore, three representatives of the combined pulses with different spectra and waveforms are illustrated in Fig. 5, which are obtained by rotating the half-wave plate between the two PBSs to different angles. Figure 5(c) demonstrates a waveform with less pedestal and shorter pulse width can be obtained by the combination of the two individuals, therein the AC trace (Fig. 5(b)) is fitted by a hyperbolic Secant function because it is cleaner. Moreover, the spectrum illustrated in Fig. 5(a) indicates a larger contribution of the P-polarized pulse, since the shape of the peak is similar to the right peak in Fig. 4(a). In addition, a tilted waveform whose AC trace can be fitted by a Gaussian function is shown in Fig. 5(e). The waveform and its corresponding spectrum are similar in shape, and the pulse width is 1.12 times of its transform-limitation which corresponds to the minimum output time-bandwidth product in the experiment. The worst case that the waveform has a dip in the center is illustrated in Fig. 5(i), which seems like splitting into two pulses. However, the transform-limited pulse shape (purple dotted line in Fig. 5(i)) calculated from the FROG trace indicates only one peak with a tiny pedestal, which testifies the synchronicity of the two orthogonal pulses again. Last but not least, the shortest output pulse widths from the femtosecond laser with Lorentzian, hyperbolic Secant, and Gaussian pulse assumed are 144 fs, 179 fs and 363 fs respectively, calculated from Fig. 5(b), Fig. 5(e) and Fig. 5(h).

 

Fig. 5. Spectral and temporal characteristics of three specific representatives (a-c, d-f and g-i, respectively) of the combined pulses from the femtosecond laser: spectra in the first column, autocorrelation traces in the second column and FROG traces in the third column.

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The similar configuration to generate GHz picosecond pulses is described in the experimental setup. Despite having bidirectional outputs, the beam transmitted clockwise in Fig. 1 is diffused due to the single grating. Therefore, only the anti-clockwise output, i.e., P-polarized output pulse is discussed here. The picosecond laser starts mode-locking at the pump power of 480 mW and has a stable mode-locking range from 480 mW to 640 mW, shown in Fig. 6. The corresponding output power can be increased linearly from 43 mW to 59 mW before the output pulses collapse at the pump power of 644 mW. The laser is operated at the fundamental repetition rate of 1.12 GHz, where the RF spectrum and the output pulse train are illustrated in Figs. 7(a) and 7(b). The output central wavelength can be continuously tuned from 1026.6 nm to 1034.3 nm by adjusting the translation stages when keeping the pump power of 520 mW. The black curve in Fig. 7(c) represents the spectrum with the largest output spectral width of 1.14 nm, corresponding to the shortest transform-limit output pulse width of 1.37 ps with Gaussian pulse assumed, illustrated in Fig. 7(d).

 

Fig. 6. Output power as a function of pump power from the picosecond laser.

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Fig. 7. Output characteristics of the P-polarized pulse from the picosecond laser: (a) RF spectrum; (b) pulse train; (c) tunable spectra; (d) autocorrelation trace corresponding to the black curve in (c).

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4. Conclusion

In conclusion, we propose and demonstrate a novel GHz femtosecond Yb-doped ring cavity PM fiber laser fundamentally mode-locked by SESAM, and a similar structure that generates GHz picosecond pulses. The GHz femtosecond mode-locked fiber laser is bidirectionally operated and polarization-multiplexed. With combination of the two orthogonal-polarized and synchronized pulse trains outside the cavity, different waveforms whose autocorrelations are well-fitted by Lorentzian, hyperbolic Secant and Gaussian functions, as well as different spectra can be obtained. Moreover, thanks to the opposite chirp in the leading and trailing edges of the two polarization-multiplexed individuals, an obvious cancellation of the pulse pedestal is observed. The shortest output pulse width from the femtosecond laser with Lorentzian, hyperbolic Secant, and Gaussian pulse assumed is 144 fs, 200 fs, and 363 fs, respectively, and the repetition rate is 1.048 GHz. We believe the proposed GHz fiber lasers are promising for applications in need of high repetition rate and tunable waveforms.