In recent years ultrashort pulse laser systems have been steadily developed towards higher output powers and shorter pulse durations. Therefore, fiber technology plays an important role in generation and amplification of ultrashort laser pulses in compact, efficient, and stable setups with an excellent beam quality at high-power levels and high repetition rates in near infrared (NIR). A wide field of applications can benefit from new high-power ultrashort pulse laser systems such as material processing and high-field physics. Of particular importance to the latter, is high-harmonic generation (HHG) [1], a process allowing the up-conversion of a coherent NIR beam into a coherent extreme ultraviolet (XUV) beam. The generated radiation has found widespread applications in photoelectron spectroscopy [2], attosecond science [3], and free-electron laser seeding [4]. HHG at high repetition rates is achieved by using appropriate high average power ultrashort pulse laser systems [5] or the cavity-enhancement technology [6–8]. The latter relies on the coherent superposition of ultrashort pulses inside a high-finesse resonator resulting in an enhancement of peak and average power up to few orders of magnitude. In this way, at high-repetition rates peak intensities can be achieved, which allow the up-conversion to high photon energies via HHG in an intracavity gas target. However, to mitigate limitations related to cavity operation with a gas target [9] and to increase the conversion efficiency to high-energy photons, the availability of pulses as short as possible is desirable. Consequently, pulse-shortening techniques play a pivotal role for efficient high-power HHG. One possible pulse-shortening technique is nonlinear compression. It incorporates spectral broadening via self-phase-modulation (SPM), which also imposes a chirp on the pulses. After removing this chirp, e.g., with chirped mirrors, the pulses are shortened in time. Most commonly, gas filled hollow-core or solid-core fibers can be used for SPM. Laser pulses with peak powers beyond the selffocusing threshold of bulk materials can be shortened with the hollow-core compression technique using a gaseous medium [10,11]. However, in these stages the propagation losses can be comparatively high. Conversely, with a short piece of solid-core fiber acting as nonlinear fiber [12,13], losses are limited to input coupling/mode matching and Fresnel reflections (the latter being suppressible by anti-reflection coated endcaps), whereas propagation losses are significantly lower as long as the peak power stays below the self-focusing threshold (around 4 MW for linear polarization in fused silica [14]).

Here, we report on a femtosecond fiber chirped-pulse amplification (CPA) system operating at a 250 MHz repetition rate (footprint $2.2\mathrm{m}\times 1.4\mathrm{m}$) with a solidcore nonlinear pulse-shortening technique achieving an unprecedented combination of repetition rate, average, and peak power, which makes this system suitable for both direct HHG and cavity enhancement.

The principle setup is illustrated in Fig. 1. A 250 MHz modelocked fiber oscillator (MenloSystems orange) with a pre-amplification unit and an isolator is integrated for seeding the highpower laser system. 18 ps pulses are emitted from the seed source with a broadband spectrum ranging from 1005 to 1055 nm and with an average output power of 2.5 W. Due to the dimensions of the optical components inside the grating stretcher (polarization depending low loss grating, $1740\text{lines}/\mathrm{mm}$) the bandwidth of the spectrum is 18 nm centered at 1040 nm. Consequently, the average power is reduced to 900 mW (pulse duration around 870 ps). After the stretcher the pulses are amplified to more than 50 W of average power in a preamplifier consisting of a 1.5 m long bendable photonic crystal fiber (PCF) with a cladding/core diameter of $170/40\mathrm{\mu m}$. An isolator between the pre- and main-amplifier protects the preamplifier against back reflections. In the main amplifier a PCF with a cladding/core diameter of $500/35\mathrm{\mu m}$ is employed. The output power from this 12 m long fiber is limited to 480 W (B-Integral below 3 rad) due to the occurrence of mode instabilities at higher power levels [15]. Therefore, the gain factor of around 10 will not give rise to gain narrowing or spectral shifts. After the main-amplifier a polarization-dependent grating compressor, with the same gratings as inside the stretcher, is used to compress the pulses. The $M^2$ after the compressor is measured to be smaller than 1.2 with a near-field pinhole reducing the residual cladding light (5%, which shows that only a small fraction of the output power is inside the cladding). Consequently, the corrected compressed output power has an excellent beam quality, which is 360 W. Even without the near-field pinhole hardly any cladding light can be seen in the near-field beam profile, which is shown in Fig. 2(a). By considering 5% cladding light the output power versus the pump power of the laser system is illustrated in Fig. 2(b). Figure 3(a) shows the spectrum after the compressor. The Fourier-limited pulse duration is 230 fs (autocorrelation width of 320 fs, deconvolution factor 0.72). The measured autocorrelation width of 370 fs of the compressed pulses [Fig. 3(b)] is longer, which is due to residual material dispersion in the amplifiers and aberrations/mismatches in the stretcher-compressor unit. Assuming that the de-convolution factor is 0.72 from the Fourier-limited pulse, then the measured pulse duration is 265 fs.

 

Fig. 1. Schematic setup of the fiber CPA with solid-core nonlinear compression stage.

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Fig. 2. (a) Near-field beam profile without pinhole and (b) compressed output power of the laser system considering the near-field pinhole.

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Fig. 3. (a) Spectrum measured after the compressor (b) measured autocorrelation trace.

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As mentioned above, fibers are very suitable for observation of nonlinear effects. In our case we use a small piece of photonic crystal fiber based on the largepitch concept well known for its fundamental mode operations at large modefield diameters [16]. The mode-field diameter of the large-pitch fiber (LPF) used for the fundamental mode is 59 μm. The peak power, fiber length, and mode-field diameter determines the SPM broadened spectrum. Calculations based on the laser-system parameters show that the specified bandwidth of the chirped mirrors fit together with an obtained SPM spectrum using a 9 cm long flat, cleaved piece of the LPF. As noted above, self-focusing sets a limit for the peak power of the input pulses. The estimated peak power from the laser system is around 4 MW considering the pulse shape (see autocorrelation trace and simulations below). In order to operate below the critical power for self-focusing and to avoid damage to the nonlinear fiber we increased the selffocusing threshold to about 6 MW by converting the linear polarization into circular polarization using a quarter-wave plate (QWP) [14]. After propagation the polarization is converted back to linear by another QWP. Additionally, a half-wave plate (HWP) adapts the linearly polarized beam to the $s$-polarization of the chirped mirror compressor. Behind this HWP we reach a degree of linear polarization of over 95%. In order to measure the power inside the core of the nonlinear fiber we employed a near-field pinhole. The core-power content is measured to be 79%. With the use of the near-field

pinhole the $M^2$ (after the LPF) is measured to be 1.3 (four-sigma), which is an excellent value for fibers with such large mode-field diameters. The SPM-broadened spectrum [Fig. 4(a)] allows for Fourier-limited pulse durations of 18.5 fs. In the logarithmic scale the measured spectrum contains a negligible amount of spectral components in the range of 1150 nm, which could be generated by other nonlinear effects such as Raman scattering or four-wave mixing. In order to compress the pulses we compensate the second-order dispersion with 24 bounces in a chirped-mirror compressor. Each mirror is specified with $-100{\mathrm{fs}}^2$ per bounce resulting in $-2400{\mathrm{fs}}^2$ for the complete compression stage. We measure an autocorrelation width of 31 fs for the compressed pulses pulses with a small pedestal due to not perfectly compensated dispersion [Fig. 4(b)]. The average power behind the mirror compressor is measured to be more than 250 W, after a concave lens, in order to cut the residual cladding light at the aperture of the power meter (Fig. 5).

 

Fig. 4. Pulse-shortening by nonlinear compression. (a) Measurement and calculation of SPM-broadened spectrum after 9 cm of nonlinear fiber. A broader-band spectral scan revealed no extra structure outside the wavelength range shown here. (b) Measured autocorrelation trace of the compressed pulses in comparison with the simulation.

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Fig. 5. Output power versus pump power of the nonlinear compression stage.

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In order to estimate the main pulse energy and the pulse peak power we compare our measurement results with simulations. For that purpose we numerically solve the nonlinear Schrödinger equation including nonlinear effects such as SPM, self-steepening, and the Raman effect [17]. First, a post pulse with 12% of pulse energy is added to the main pulse (Fourier transform limit of the fiber CPA spectrum from Fig. 3(a)). This simple assumption has been made to explain the occurrence of the pre/post pulses in the autocorrelation traces [Figs. 3(b) and 4(b)]. In the second step we calculate the propagation of these laser pulses along the 9 cm long LPF by considering the power content inside the core and the surface reflection at the end facet of the fiber. The calculated spectrum is compared to the measured one in Fig. 4(a) showing a good agreement. In a last step we compensate the second order dispersion with $-2340{\mathrm{fs}}^2$ by compressing the pulse to 23 fs. The calculated autocorrelation trace duration (31 fs) fits to our measurement [Fig. 4(b)]. After the chirped-mirror compressor we estimate from simulation the peak power to 34 MW and the main pulse energy to 0.9 μJ.

In conclusion, we demonstrated a high-power fiber CPA system operating at 250 MHz repetition rate (360 W of average power) and providing 265 fs pulses with an $M^2$ of 1.2. Subsequent nonlinear compression in a short piece of solid core photonic-crystal fiber (LPF) reduces the pulse duration by more than one order of magnitude to 23 fs. At the same time we achieve an average power of 250 W and an excellent beam quality ($M^2=1.3$). The peak power of the compressed pulses is estimated to be 34 MW (0.9 μJ main pulse energy). This laser system is important for driving enhancement cavities with MW of average power [18].