1. Introduction

High-energy ultrashort-pulse fiber lasers have been extensively investigated due to their widespread applications in science, micromachining, and medicine [1–3]. However, in the field of micromachining, operating in a single pulse state can result in rapid dissipation of pulse energy, which can easily cause micro-explosions, micro-cracks, and other detrimental effects [4]. It has been shown that an ultrashort pulse burst with a high repetition rate sub-pulse can effectively reduce the aforementioned effects [5]. Due to the short time period of the adjacent subpulse, the residual heat energy from the previous subpulse does not have enough time to dissipate from the active region before the next pulse arrives. Thus, a thermal modification zone is established to temporarily alter the material properties in this specific area in order to achieve improved machining outcomes. However, an ultrahigh repetition-rate sub-pulse will lead to plume-shielding effects [6], which will affect the outcome of micromachining. The intra-burst repetition rate at the GHz level is suitable for micromachining [5,7]. On the other hand, to avoid the damage caused by thermal accumulation, inter-burst repetition rate below the MHz level is desired [2,8].

In recent years, there has been increasing attention on the amplification of high-energy GHz pulse bursts due to their significant application prospects. To date, there have been many reports about high-energy ultrashort pulse fiber lasers operating at the GHz level [9–12]. The majority of them have a design called master oscillator power amplifier (MOPA). Master oscillators are primarily mode-locked fiber oscillators with repetition rates of several tens of MHz. To achieve mode-locked fiber lasers with a repetition rate at the GHz level, the technique of repetition rate multiplication [13] and harmonic mode-locking are widely used [14]. By contrast, fundamental mode-locking is a more reliable method for passively mode-locked fiber lasers because of their high stability and lower phase noise [15,16]. In order to further boost up the ultrashort pulse energy, chirped pulse amplification (CPA) is usually employed to avoid nonlinear pulse distortion issues in fiber amplifiers [17]. The average power can reach tens of watts, but the pulse duration is limited to several hundred femtoseconds due to the finite gain bandwidth. However, an ultrashort pulse with sub-100 fs duration is of great interest and desired in a various of fields [5,8,18]. For example, in the process of preparing silicon surface microstructures, a narrower femtosecond pulse duration corresponds to a higher peak power. This, in turn, enhances the etching effect and results in the formation of large microstructures.

To obtain ultrashort pulse duration, nonlinear pulse amplification (NPA) is adopted [19]. However, the accumulation of nonlinearity in the fiber could degrade the pulse quality, resulting in the presence of large pedestal or satellite pulses. Self-similar amplification (SSA) [20], cubic amplification [21], and gain-managed nonlinear amplification [22] have been explored to achieve short pulse duration and high-quality femtosecond pulses. Therein, the pulse propagating along the fiber can undergo asymptotic evolution into a parabolic profile in SSA. The chirp of the output pulse is linear, and the spectral broadening dominated by self-phase modulation (SPM) could ensure a compressed pulse duration shorter than the duration of the initial seed pulse. Considering that the SSA is typically performed in a sufficiently long gain fiber with a low absorption coefficient, cascaded amplifiers are used to reduce the gain coefficient of the main amplifier to achieve self-similar evolution over a limited fiber length [23]. Additionally, pre-chirped management of the pulses entering the amplifier will facilitate a fast convergence to the parabolic regime [24]. By managing the pre-chirping, the highest average power beyond 100W with sub-50 fs pulse duration has been achieved [23], the repetition rate of the pulse is several tens of MHz and operating in single pulse mode.

In the field of micromachining, the use of femtosecond pulses operating in burst mode can significantly enhance processing efficiency. GHz pulse bursts with ultra-narrow pulse durations not only enable higher machining accuracy and minimize the impact on surrounding materials, but also expand their application in areas such as nonlinear frequency conversion. However, despite the existing reports of high-energy GHz pulse bursts with pulse durations beyond 300 fs [9–12], there have been no reports to date of high-energy and MHz inter-burst repetition rates with sub-50 fs subpulses at GHz intra-burst repetition rates.

In this work, we present a pulse burst amplification system that combines high-energy and high repetition frequency using both CPA and SSA techniques. The system is capable of generating 22 μJ, 1-MHz inter-burst repetition rates with 35-fs sub-pulses at 1.02-GHz intra-burst repetition rates. To increase the flexibility of the system, the results of amplification and compression under different number of subpulses are investigated. The pre-chirp shaping module is added before the main amplifier to accelerate the process of similar evolution. The module allows for tuning the chirp, energy, and central wavelength of the signal. Moreover, the system incorporates polarization-maintaining single-mode fiber (PMSMF) and double-cladding Yb³⁺-doped fiber, eliminating the requirement for large-mode-area Yb³⁺-doped photonic crystal fiber. Only a simple fusion operation is needed, resulting in a more compact and reliable system.

2. Experiment setup

The schematic diagram of the experimental setup is shown in Fig. 1. The oscillator is a dispersion-managed soliton mode-locked Yb³⁺-doped fiber laser. The cavity length of a fundamental mode-locked fiber laser with a GHz repetition rate is very short, which leads to a severely limited length of available gain fiber. To ensure the sufficient accumulation of a nonlinear phase shift necessary for achieving mode-locked self-start, a dispersion-managed soliton fiber laser is constructed based on nonlinear polarization evolution (NPE) mode locking. Although non-polarization-maintaining fiber is used in the oscillator, it can be approximated as polarization-maintaining fiber [25] due to the very short cavity length and minimal disturbance from the external environment after packaging.

 

Fig. 1. Schematic of experimental setup, ISO: isolator, AOM: acoustic-optical modulator, LD: laser diode, COM: combiner, YDF: Yb³⁺-doped fiber, COL: collimator, BF: bandpass filter, HWP: half-wave plate, M: mirror, PBS: polarizing beam splitter.

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Pulse bursts are obtained by selecting a series of pulses from the original pulse train using a fiber-type acoustic-optical modulator (AOM), which is controlled electronically. The repetition rate of pulse bursts and the number of sub-pulses per burst can be easily tuned. To compensate for power attenuation caused by the AOM and ensure adequate pulse energy for the main amplifier, a two-stage pre-amplifier is used, the length of YDF in the first and second stage is 1 m and 1.2 m, respectively.

In the two-stage pre-amplifier, all gain fibers utilize polarization-maintaining, large-mode-area, double-cladding Yb³⁺-doped fiber (PLMA-YDF-10/250-VIII, Nufern). Additionally, a 43-meter-long polarization-maintaining single-mode fiber (PM980, Nufern) is used as a stretcher to prevent significant nonlinear accumulation in the two-stage pre-amplifier. The output pulse from the second pre-amplifier is directly connected to the pre-chirp and shaping module. This module consists of transmission grating pairs of 1000 lines/mm (LightSmyth Technologies), a 10-nm bandpass filter, and two half-wave plates. By adjusting the incident angle on the filter, one can modify the spectral bandwidth and central wavelength of the signal pulse. By adjusting the distance between the grating pairs, the chirp of the signal pulse can be tuned over a wide range.

In the main amplifier, a 2.5-meter-long polarization-maintaining large-mode-area double-cladding Yb³⁺-doped fiber (PLMA-YDF-30/250-VIII, Nufern) is adopted. After the main amplifier, the pulse undergoes compression using a transmission grating pairs of 600 lines/mm (LightSmyth Technologies) in a double-pass configuration, achieving a maximum compression efficiency ∼94%. Each stage of the cascaded amplifier is isolated by an optical isolator to prevent backward propagation.

3. Results and discussion

Figure 2(a) shows the pulse train generated from the oscillator measured by the oscilloscope. The repetition rate of the pulse train is 1.02 GHz. The corresponding autocorrelation trace of the pulse train is shown in Fig. 2(b). The temporal profile is fitted with a hyperbolic secant lineshape, and the pulse duration is ∼228 fs. The spectrum of the output pulse, as shown in Fig. 2(c) exhibits typical soliton features with Kelly sidebands. The center wavelength of the spectrum is 1029 nm with a 3-dB bandwidth of 10 nm.

 

Fig. 2. (a) Pulse train, (b) autocorrelation trace, (c) spectrum of the output pulse from the oscillator.

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The pulse train is further modulated into pulse bursts by using an AOM as shown in Fig. 1. However, directly amplifying these bursts would result in an uneven distribution of pulse energy within each burst. The temporal profile of each burst will show leading pulses with high amplitude and trailing pulses with low amplitude [12], the trend fits with the exponential function, as depicted in Fig. 3(a), which will have an adverse effect on the micromachining results. This is due to the gain saturation effect in the YDF amplifier, the leading pulses consume most of the number of inversion particles, resulting in the depletion of the gain, and the traling pulses can not be effectively amplified. To achieve smoother shapes of the pulse bursts after the main amplifier, the amplitude modulation with reverse-direction exponential function is applied to the AOM. The coefficients and exponent sign of the exponential function are adjusted appropriately based on the profile of the pulse burst output from the main amplifier. At the same time, due to the non-linear amplification process of pulse bursts, certain sub-pulses within the bursts exhibit high and low amplitudes. In order to achieve a smoother profile of pulse bursts, the amplitudes of these specific sub-pulses are individually modulated. The modulated pulse bursts, after two-stage amplification, are depicted in Fig. 3(b). The repetition rate of the pulse bursts is 1 MHz, and each burst contains 200 sub-pulses. The profile of each burst shows leading pulses with low amplitude and trailing pulses with high amplitude.

 

Fig. 3. (a) Temporal profile of pulse burst after the main amplifier without pre-amplitude modulation of AOM, (b) pulse bursts train and (c) spectrum of the output pulse of the pre-chirp and shaping module.

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To achieve high-power SSA of pulse bursts within a limited gain fiber length, the parameters of the subpulses need to meet the input condition of SSA [26]. In addition to the pulse duration, energy, and spectral width entering the main amplifier, the pulse waveform and the amount of chirp will also affect the rate of self-similar evolution. It is worth noting that the finite gain bandwidth can cause gain shaping effects, which can result in the degradation of de-chirped pulse quality [27]. If the central wavelength of the signal pulse matches the gain peak, it is expected to exceed the gain-narrowing limit and produce a high-quality pulse output with linear chirp [28]. Therefore, the central wavelength of the signal pulse is also one of the parameters that need to be adjusted during the search for the optimum compression point. The pre-chirp and shaping module is inserted between the two-stage pre-amplifier and the main amplifier. The spectrum of the output pulse from the pre-chirp and shaping module is shown in Fig. 3(c). The center wavelength of the spectrum is 1034 nm, and the 3-dB spectral bandwidth is ∼8 nm, which is close to the optimal input condition for SSA. The spectrum profile has minimal modulation, resembling a standard pulse profile. This is attributed to the use of the CPA technique in the two-stage pre-amplifier.

As mentioned earlier, pre-amplitude modulation is applied to the AOM. The temporal profile of the burst after the main amplifier is depicted in Fig. 4(a). It is evident that the burst profile has become smoother compared to Fig. 3(a), the top of the pulse burst is close to flat top. With appropriate adjustment of the pre-chirp amount and the distance between compression grating pairs, the shortest pulse duration of about 35 fs can be obtained when the output average power of the pulse is 22 W, the output power is limited by the available pump power and stimulated Raman scattering effect [29]. The measured autocorrelation trace of the compressed pulse is shown in Fig. 4(b), and the temporal profile is close to a Lorentzian lineshape. The reason why we can achieve such a narrow pulse duration with high quality is that, in addition to utilizing hybrid amplification of CPA and SSA, and pre-chirp shaping technique, we also employ SPM to partially compensate for the positive third-order dispersion in the system [30]. Compared to the output pulse duration of the oscillator, the pulse duration is significantly reduced in a conventional CPA system. The corresponding spectrum is shown in Fig. 4(c), the central wavelength is 1065 nm, there is red shift obviously compared to the central wavelength of the oscillator due to the stimulated Raman scattering effect [29]. The 3 dB bandwidth is 65 nm, which is much wider than the spectrum width of the output pulse from the oscillator. This supports the acquisition of short-duration pulses. According to the Fourier transform limit, the minimum pulse duration is less than 20 fs, while the shortest pulse duration is 35 fs. The reason is that the parameters of the input pulse being just close to the SSA condition. Moreover, the SSA condition is obtained by ignoring gain saturation and the gain bandwidth limitation. The actual gain of a fiber amplifier varies with the length of the fiber, and the gain bandwidth limit will introduce additional nonlinear chirp [26,31].

 

Fig. 4. (a) Temporal profile of pulse burst, (b) autocorrelation trace, (c) spectrum of the optimum compression pulse after the main amplifier stage.

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In order to meet the micromachining requirements of different materials, it is necessary to flexibly set suitable parameters, such as the number of sub-pulses in each burst, energy of individual sub-pulses, inter-burst repetition frequency rate [12]. Here, the effect on the pulse duration after the main amplifier and compression under different numbers of sub-pulses are investigated. The blue circles in Fig. 5 illustrate the relationship between the main-output power and the number of sub-pulses in the amplification system, with the same pump power. It can be observed that as the number of sub-pulses increases, the main-output power also increases. However, it should be noted that the output power eventually reaches a saturation point. With a different number of sub-pulses, the energy of a single pulse will vary, corresponding to different input conditions for self-similar amplification. To obtain the optimum compression results, proper adjustment of the amount of pre-chirp and compression is needed for different numbers of sub-pulses. The red squares in Fig. 5 illustrate the pulse durations of optimum compression versus the number of sub-pulses. It can be seen that all the pulse durations at different numbers of sub-pulses are below 40fs. However, there are obvious pedestals in the compressed pulses with 100 and 400 sub-pulses. These pedestals are mainly caused by SPM in nonlinear pulse amplification. The compressed pulse with high quality is obtained when each pulse burst contains 200 sub-pulses. The measured temporal trace fits well with the ideal Lorentz shape. Here, the ratio of the main-pulse energy to the whole pulse energy to evaluate the pulse quality. The energy ratio of the compressed pulse under 100, 200 and 400 sub-pulses is 65%, 87%, 76%, respectively. The main reason is that the input pulse parameters at 200 sub-pulses are closer to the input condition of SSA compared to 100 and 400 sub-pulses.

 

Fig. 5. The pulse duration (left, red squares) and average power (right, blue circles) versus the number of sub-pulses of the optimum compressed pulse.

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To build an optimal laser for the micromachining system, the power stability and beam quality are crucial parameters. Figure 6(a) shows the long-term power stability of the system. The output power varies by only about 0.27% RMS over a period of 1.5 hours. The measured output beam profile is shown in Fig. 6(b), and the calculated beam profile factor M² is approximately 1.22, indicating excellent beam quality. The amplified laser beam profile is asymmetric due to the astigmatism of the amplified laser. The results indicate that our developed fiber amplification system is reliable in a laboratory-level working environment.

 

Fig. 6. Measured (a) power stability in 1.5 hours and (b) beam profile of the output pulse of main amplifier.

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4. Conclusion

In this work, we have demonstrated a high-energy GHz pulse burst amplification system. To achieve a short pulse duration, a hybrid amplification system combining CPA and SSA is utilized. In this system, the technique of pre-chirp management is employed to accelerate the self-similar evolution process and obtain a shorter pulse duration. Thus, the system generates 35 fs, 22 μJ, GHz pulse bursts with high pulse quality. Meanwhile, the pulse duration after amplification and compression under different number of sub-pulses is less than 40 fs with proper adjustment of the amount of pre-chirp and compression. This high-energy GHz pulse burst with short pulse duration is not only conducive to improving the speed and quality of fine processing, but it can also significantly enhance the efficiency of nonlinear frequency conversion, such as generating green ultra-short pulse bursts through frequency doubling. In addition to the field of micromachining, high-energy GHz femtosecond pulse bursts with short pulse duration also have great potential applications in optical communication, quantum information, and biomedicine.