1. Introduction

The development of high-power femtosecond pulse laser offers a variety of applications such as ultrafine material processing, multi-photon microscopy, and generation of coherent extreme ultraviolet (XUV) radiation [1]. Although Ti: Sapphire based systems have widely demonstrated to be essential tools, the average power scaling is restricted to a few watts due to the detrimental thermo-optical effects. Ytterbium-doped fiber lasers appear as promising alternatives regarding the prominent advantages on power scalability. Owing to large ratio of surface-to-volume of the fiber geometry and high optical pumping efficiency, sub-picosecond pulses with average power beyond 1 kW have been achieved in the Yb-fiber amplifiers [2, 3]. In fiber amplifiers, the main challenge to achieve high-power ultrashort laser pulses comes from the difficult control of large amount of accumulated nonlinear phase shifts, which often distort the pulse or even lead to wave-breaking during amplification. The chirped pulse amplification (CPA) is the straightforward technique to solve this problem. The seed pulse is sufficiently stretched to a long pulse duration (normally hundreds of ps or a few ns) in time domain to avoid optical nonlinearities in fiber amplifiers, then the power-scaled pulse is recompressed to a pulse duration in the sub-ps time scale. As limited by the finite gain bandwidth, the pulse is hardly shorter than 100 fs from a fiber CPA system [4–7]. Nonlinear compression of the pulse by the optical parametric chirped pulse amplification or nonlinear spectrum broadening in a solid-core fiber or gas-filled hollow fiber, the pulse duration could be further reduced at the expense of output efficiency and system complexity.

An alternative approach is recently developed known as self-similar amplification [8–13]. In contrast to fiber CPA scheme, the optical nonlinearities in the amplifiers are harnessed to broaden the output spectrum. The self-similar amplification exploits self-phase modulation (SPM) and normal group velocity dispersion in the gain medium to produce a linearly chirped parabolic pulse. As the parabolic pulse propagating in fiber, the chirp remains linear and the spectrum is broadened in the nonlinear regime. The amplified pulse acquires an extended spectrum beyond the gain bandwidth and accordingly, the SPM-dominated spectral broadening could ensure a compressed pulse duration shorter than the initial seed pulse. In order to complete an asymptotical evolution into the parabolic profile, a sufficiently long gain fiber with low absorption coefficient is widespread used. The interplay of spectral gain-narrowing and SPM-broadening determines the acquired spectral bandwidth in long-fiber amplifier. A pulse duration as short as 48 fs has been achieved [10]. Nevertheless, the output average power was so far limited to 18 W. This was mainly caused by the fact that high-energy pulses typically experienced observable deviation from parabolic amplification, which resulted in considerable satellite structures of the compressed pulse at high powers [11]. High average power could be achieved with a gain fiber of large mode diameter [12], and short-length fiber amplification may lessen the gain-narrowing effects. Recent experiment demonstrated that pre-chirping of the seed pulse could promote a fast convergence to the parabolic regime even in a short gain fiber [13]. Therefore, high quality compressed pulses could be achieved at high powers.

In this letter, we scale up the parabolic pulse to an unprecedented average power of 80 W with sub-40 fs pulse duration through the pre-chirping management. The obtained shortest compressed pulse is determined by the interplay between SPM and finite gain bandwidth. Additionally, the power scalability is ultimately limited by stimulated Raman scattering (SRS).

2. Experimental setup

The experimental setup is schematically shown in Fig. 1. The system consisted of a home-built Yb-fiber oscillator, a fiber stretcher, three stages of fiber amplifiers, a pre-chirper, and a pulse compressor. The front end Yb-fiber oscillator mode-locked by nonlinear polarization evolution was used as the seed source. The Yb-fiber oscillator was operated in the stretched-pulse mode-locking regime. It produced a pulse train with a repetition rate of 60 MHz and ~10 mW average power. The spectral width was 45 nm around the centerwavelength of 1030 nm. The pulse train from the oscillator was stretched to 20 ps by 20-m single-mode fiber (SMF28), and then amplified to an average of 2 W by an all-fiber pre-amplifier and a free-space pre-amplifier. The output of the pre-amplified pulse was pre-chirping managed by a 1250 lines/mm transmission grating pair. The pre-chirped pulse could tune to a shortest pulse duration of 190 fs at zero dispersion with an efficiency of 75%. The self-similar amplification was achieved in the main amplifier, which was constructed from a 2-m polarization-maintaining large-mode-area photonic crystal fiber (PM LMA-PCF) with a pump absorption of 10 dB/m at 976 nm. The core and inner cladding had the diameter of 40 and 200 μm, respectively. The relatively short-length gain fiber with large core diameter was employed for the purpose to increase the SRS threshold. Each stage of the cascaded amplifier was isolated by optical isolators (OIs) to keep away from the backward propagating. The spectrally broadened pulse was compressed by another 620 lines/mm transmission grating pair in a double-pass configuration.

 

Fig. 1 Schematic of the experimental setup. WDM: wavelength-division multiplexing; OI: optical isolator; Yb-SMF: Yb-doped single-mode fiber; LMA Yb-PCF: large-mode-area Yb-doped photonic crystal fiber; DM: dichroic mirror.

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The average power of the output signal together with the compressed pulse is depicted in Fig. 2. The maximum output power was 120 W with a slope efficiency of 57%. A further increase of launched pump power was not favorable due to the onset of SRS, which led to the distortion of the compressed pulse. Thanks to the throughput efficiency of 67%, the highest average power of the compressed signal is achieved up to 80 W, corresponding to a pulse energy of 1.3 μJ.

 

Fig. 2 Output power of the main amplifier versus launched pump power before (black square) and after (red dotted) compression.

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Compared to the previously reported results [10–13], the power scalability has increased several times in our self-similar amplifier. The quality of the recompressed pulse at high gain was improved mainly through pre-chirping management [14]. In a gain fiber with enough length, initial pulse was doomed to evolve into parabolic profile regardless of pulse duration and pre-chirp. Short active fiber is generally not considered for the self-similar evolution. Nevertheless, the optimization of the pre-chirp could significantly accelerate the rate toward an asymptotic parabolic pulse regime.

To verify the importance of pre-chirp management on the power-amplified parabolic pulse, four autocorrelation traces of recompressed pulse were measured at different group-delay dispersion (GDD) for comparison. Figure 3(a) shows the results at a fixed compressed average power of 80 W. As mentioned above, the amount of GDD was adjusted by fine tuning the grating pair separation.

 

Fig. 3 (a) The measured autocorrelation trace of 80-W compressed pulse at different pre-chirping GDD of 1.0 × 10⁴ fs² (black), 0 (red), −2.2 × 10⁴ fs² (blue), and −3.0 × 10⁴ fs² (yellow), respectively. Inset picture shows the pulse profile with Gaussian fitting at −2.2 × 104 fs² pre-chirping GDD. (b) The optimal pre-chirping versus compressed average power.

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The recompressed pulse exhibited considerable secondary structures at a positive GDD of 1.0 × 10⁴ fs², where 44% of the total energy was contained in the main peak with 45 fs pulse duration. Tuning the GDD to a value around 0, the pulse quality was slightly improved with 58% energy concentrated in the 41 fs main peak. When the pre-chirp was set to −2.2 × 10⁴ fs², a nearly transform-limited pulse with minimal pedestals was generated. The best compressed pulse exhibited a shortest pulse duration of 38 fs with 96% pulse energy contained in the main peak as shown in the inset picture of Fig. 3(a), corresponding to a peak power of 33 MW. Further increasing the grating separation to get a GDD of −3.0 × 10⁴ fs², the pulse energy was shifted into the side lobes with down to 68% energy remained in the 55-fs main peak. Since the pulse evolution was dependent on the gain parameter in the parabolic amplifier, the optimal pre-chirping was varied at different output power. The optimal pre-chirping as a function of the compressed average power is shown in Fig. 3(b). The optimized pre-chirp exhibited a monotonous change from slightly positive to considerable negative value. According to the criterion for self-similar amplifier designed in [9], the optimal input pulse duration is inversely proportional to the fiber gain. Therefore, a short pulse gives the best convergence to the parabolic solution. Tuning the pre-chirp to negative at high output powers, the pulse experienced an initial pulse compression due to the interplay of negative chirp and SPM. Then the convergence rate was accelerated to complete the full evolution. Because of the required linear chirp reducing with the increased power, current grating pair could possibly be replaced by the broadband chirped mirrors to enhance the throughout efficiency in the pulse compression stage.

After optimization of the pre-chirp, the spectra across the parabolic amplification regime are summarized in Fig. 4(a). The spectral broadening in the amplifier evolved with a flat-top and smooth edge, showing a typical feature of parabolic pulse. Although the spectrum was symmetric for an ideal parabolic pulse, the fiber gain profile caused a spectral asymmetry. The increase of gain extended the spectrum towards the longer wavelength induced by SPM. Simultaneously, the short wavelength side was slightly extended with a cut off wavelength at 980 nm due to the finite gain bandwidth. In consideration of the fact that the SPM-broadened spectrum exhibits a series of peaks in the linear scale coordinate [15], the full-width at half maximum (or 3-dB bandwidth) is not suitable to characterize the spectral bandwidth. In order to quantitatively analyze the evolution of the spectral bandwidth, the 10-dB bandwidth was introduced. Figure 4(b) shows the dependence of spectral bandwidth and recompressed pulse duration on the compressed output average power. At an average power of 7 W, the parabolic pulse was compressed with 75 fs duration and 44-nm bandwidth. The spectral bandwidth nearly linearly increased and the pulse duration linearly decreased with the output power until 40 W. In this regime, SPM broadened the spectral bandwidth to 85 nm, and the pulse duration progressively decreased to 46 fs. As output power further increased, the spectral broadening slowed down in the presence of finite bandwidths. Beyond a power of 60 W, the interplay between the SPM-broadening and gain-narrowing was prone to balance. The spectral broadening became nearly saturated at~104 nm bandwidth and the pulse was no longer shortened at a pulse duration of 38 fs.

 

Fig. 4 (a) The evolution of spectrum with output power across the parabolic amplification regime. (b) The spectral bandwidth and recompressed pulse duration versus the average power of the compressed pulse.

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It is addressed that the main bottleneck was SRS for the further output power scaling. Figure 5 shows the measured spectrum and recompressed pulse above SRS threshold. When the output power exceeded 90 W, the self-similar evolution was perturbed. The spectrum exhibited Stokes peaks respectively at 1180 and 1210 nm, along with the sharp peak near 1030 nm due to the gain narrowing. Increasing output power to 120 W, the spectral structure was completely distorted with oscillatory structures. Although the main peak of the compressed pulse remained below 40 fs, the pedestal and wings lead to unstable pulses.

 

Fig. 5 The spectrum (a) and autocorrelation trace (b) of the recompressed pulse above the SRS threshold with 90 W (red curve) and 120 W (blue curve) average power output.

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3. Conclusions

In summary, we have demonstrated an Yb-doped fiber laser with sub-40 fs pulse duration and 80-W average power at a repetition rate of 60 MHz based on pre-chirp management of parabolic pulse amplification. The interaction between SPM and finite gain bandwidth results in a broad spectral bandwidth of 104 nm (10-dB bandwidth) in the self-similar amplification regime. The onset of SRS limits the obtained pulse power. This fiber laser would be an essential driving source for the XUV frequency comb.