1. Introduction

Fiber lasers have earned the reputation to be an average power scalable concept due to their outstanding thermo-optical properties. It has been shown that several kW can be extracted in cw operation [1]. When using fibers for amplification of ultrashort pulses the operation becomes more challenging due to the onset of nonlinear effects. However, by applying chirped pulse amplification and the use of ultra large mode area fibers it became possible to extract 1 mJ, sub-picosecond pulses at repetition rates of 50 kHz [2].

In addition, recently there is been particular interest in high average power ultrashort pulse laser sources that can be used for high harmonic generation (HHG). When focusing to intensities on the order of 10¹⁴ W/cm² odd multiples of the laser frequency can be generated, which are typically in the extreme ultraviolet (EUV) spectral range. This radiation preserves the coherence of the driving laser making this a very attractive source for a variety of applications [3–6]. Especially, the table-top size setups are an interesting alternative to large scale facilities. However, one of the major drawbacks is the conversion efficiency, which typically is lower than 10⁻⁶ in phase matched HHG [7]. When phase matching cannot be achieved quasi-phase matching schemes have to be used [8–10]. Additionally, schemes relying on enhancement of the electrical field, such as cavity [11,12] or other enhancement schemes [13,14], have been successfully demonstrated for low energy high repetition rate laser systems. The use of high repetition rate driving laser systems without the need for enhancement has been increasingly important over the last years [15–18]. A main requirement for efficient harmonic generation is to have ultrashort pulses (~10 optical cycles [19]) to prevent the built up of ionization. This ionization eventually reduces the harmonic yield, since phase matching cannot be achieved above a critical value. In [18] we have shown that, as expected, fiber chirped pulse amplification (FCPA) systems have limited conversion efficiency due to their pulse duration of several hundred femtoseconds. To overcome this and fully exploit the advantages of fiber lasers for HHG, we have used pulse compression techniques by nonlinear compression in noble gas filled hollow core fibers [20] and few-cycle optical parametric chirped pulse amplification systems [21,22] to reduce the pulse duration, increase the peak power and increase the conversion efficiency [18]. Especially, the nonlinear compression has proven to be a robust and simple architecture for this purpose.

This compression scheme has been widely used for Ti:Sapphire based laser systems to obtain the shortest possible pulses [23]. In recent years there has been work on increasing the pulse energy and average power of these systems. To date the highest compressed pulse energy is 5 mJ at 1 kHz corresponding to 5 W of average power [24].

In this work, we show a double stage nonlinear compression of a fiber chirped pulse amplification system, where automated pulse shaping is used to extract 1 mJ, 50 kHz, 480 fs pulses with almost fourier transform limited pulse duration. These pulses are sent into a 53 cm long, 200 µm inner diameter hollow core fiber filled with xenon. Subsequent compression yields 24.5 W, 50 kHz, 490 µJ, 68 fs pulses. The second stage is a 20 cm long, 200 µm inner diameter hollow core fiber filled with argon for further spectral broadening. Compression to 35 fs, 380 µJ, 5.7 GW is achieved by a chirped mirror compressor making this a very attractive source for high harmonic generation. This a significant improvement in pulse energy (quadrupled), average power (tripelt), peak power (factor of 6) and pulse duration (factor of 2 shorter) in comparison to our previous work [20].

2. Fiber chirped pulse amplification system

The fiber chirped pulse amplification (FCPA) system is a modified version of the system presented in [2]. In contrast to [2] we have added a pulse shaping device (BioPhotonics Solutions Inc.) that uses the multi photon intrapulse interference phase scan for phase measurement and optimization of the pulse compression. This device is integrated before the amplifiers, thus pre-compensating the nonlinear phase that is basically accumulated in the main amplifier fiber, a rod-type photonic crystal fiber. This fiber allows for extraction of 1.3 mJ of pulse energy. Using a compressor with >70% efficiency we obtain 1 mJ of compressed pulse energy at a repetition rate of 50 kHz equalling an average power of 50 W.

Due to the pulse shaping device the pulses can be shortened to less than 500 fs pulse duration. We have been performing temporal pulse measurements with an autocorrelator and a FROG, which agree well with one another (Fig. 1 (a) ). Additionally, the spectrum retrieved by the FROG measurement is in good agreement with the one measured by an optical spectrum analyzer (Fig. 1 (b)). From this measurement the pulse duration and peak power can be estimated to be 480 fs (Fourier limit: 400 fs) and 1.8 GW (Fig. 1 (c)).

 

Fig. 1 Performance of the fiber chirped pulse amplification system. (a) Measured autocorrelation (blue) together with the autocorrelation retrieved by the FROG measurement (gray). (b) Measured spectrum (blue) together with the corresponding spectrum (gray) and phase (green) retrieved by the FROG measurement. (c) Temporal pulse profile (blue) and phase (green) of the compressed pulses retrieved by the FROG measurement indicating a peak power of 1.8 GW.

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This pulse shaping helps to overcome the limitations we have encountered in [20], where spectral broadening and recompression was influenced by the nonlinear phase that was already imposed by the FCPA system. With almost transform limited pulses to start the broadening process, we are now able to obtain almost pure self-phase modulation (SPM) phase that can mostly be compensated by chirped mirrors with negative group velocity dispersion. However, it has to be noted that there are remaining higher order phase terms imposed by the SPM process.

3. Nonlinear compression - experimental setup and results

Nonlinear compression in noble-gas filled hollow core fibers relies on self-phase modulation of the input, which leads to spectral broadening. When removing the imposed chirp, the pulses are shortened in time and usually the peak power is enhanced. The nonlinearity here is provided by the noble gas filling and can be adapted to the experimental conditions by the gas (Ne, Ar, Kr, Xe) and its pressure.

The major limitations for this compression arise from ionization and self-focusing effects that limit the intensity and peak power of the input pulses, respectively [26]. They depend on the gas type and pressure, which both have to be adjusted to the input parameters of our laser system. In [20] we have discussed that xenon is the only noble gas that provides the required nonlinearity for the output pulses of the FCPA system. On the other hand, ionization is facilitated due to the low ionization potential of xenon (12.1 eV) and self-focusing due to the high nonlinearity (n₂=8.1·10⁻²³ m²/(W·bar)). For a peak power of 1.8 GW the critical pressure (the pressure where self-focusing sets in) is about 1.1 bar [27].

Indeed, we observe a decreasing energy transmission that sets in at around 1 bar of xenon pressure (Fig. 2 ). This indicates that self-focusing can reduce the efficiency of the system. In addition, multiphoton ionization is expected to create free electrons due to the high intensity of 2·10¹³ W/cm² at the fiber entrance. This can cause plasma defocusing effects that eventually reduce the coupling efficiency. Both effects could be suppressed to some extend by implementing a differential pumping scheme [28].

 

Fig. 2 Output energy after propagating the 1mJ, 480 fs pulses through a 53 cm, 200 µm inner diameter fiber filled with xenon at various pressure.

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The setup used for nonlinear compression is shown in Fig. 3 . The output of the FCPA system is coupled to a 53 cm long 200 µm inner diameter hollow core fiber. For efficient coupling to the EH₁₁ mode the focal spot size is set to ~128 µm by using a f=500 mm focal length lens. The overall transmission of this fiber has been measured to be higher than 60%. The fiber with an outer diameter is kept straight by a V-groove which is placed inside a chamber containing two anti reflection coated windows. After being evacuated the chamber is filled with xenon gas serving as nonlinear medium for the occurrence of self-phase modulation. Compression is achieved by the use of chirped mirrors with a group velocity dispersion (GVD) of −250fs²/bounce. Due to the high reflectance of the chirped mirrors, the compressor efficiency is usually higher than 95% overall.

 

Fig. 3 Experimental setup used for double-stage nonlinear compression. The pulses of a fiber chirped pulse amplification (FCPA) system are coupled to a first hollow core fiber that sits on a V-groove in a chamber filled with xenon. Subsequent compression is achieved by a chirped mirror compressor. Next, the compressed pulses are coupled to a second hollow core fiber filled with argon followed by another chirped mirror compressor. The output is analyzed with an autocorrelator (AC) and an optical spectrum analyzer (OSA).

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When coupling the output pulses of the FCPA to the fiber at a xenon pressure of 0.85 bar the spectrum broadens to a −10dB bandwidth of 55 nm (Fig. 4 (a) ). The average power that has been measured after the compressor was as high as 24.5 W, which is equivalent to a pulse energy of 490 µJ at 50 kHz. To the best of our knowledge, this is the highest average power that has been extracted so far from a single stage nonlinear compression. By applying an overall GVD of −4500 fs², the pulses are compressed to an autocorrelation width of 112 fs (Fig. 4 (b)).

 

Fig. 4 (a) Measured (blue) and simulated spectrum (gray) after the first stage. (b) Measured (blue) and simulated (gray) autocorrelation of the compressed pulses after the first stage. (c) Collimated beam after the compressor of the first stage.

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Figure 4 also contains simulations of the nonlinear compression that has been performed by using the temporal pulse profile of the input pulse (Fig. 1 (c)) and a split step fourier method. For the simulation we have assumed 90% coupling efficiency that can be obtained due to the well defined beam profile of the fiber amplifier. For a 200 µm fiber the theoretical loss calculates to 0.46 m⁻¹ [29], while experimentally we observe a loss of 0.8 m⁻¹. For the simulation process we use the latter value and a mode field diameter of 143 µm. The n₂ values of the xenon gas have been adapted to n₂=6.1·10⁻²³ W/cm² such that the measured experimental spectrum and the simulation match. Since the n₂ values are not exactly known this assumption is justified. The experimental data and the simulation agree very well (Fig. 4 (a) and (b)), both for the autocorrelation and the spectrum. This allows us to extract the compressed pulse duration of 68 fs, with 60% of the pulse energy in a Gaussian like 68 fs main pulse. The peak power for the compressed pulse is 4.2 GW. Together with the excellent beam quality (Fig. 4 (c)) this first stage is already an interesting source for various applications.

However, a second stage can be used for further pulse shortening and peak power enhancement. Therefore, the output of the first stage is imaged to the second fiber with an f=200 mm lens. The second stage contains a V-groove mounted 20 cm long, 200 µm inner diameter fiber sitting in a chamber followed by a compressor utilizing chirped mirrors with a GVD of −100 fs²/bounce. The transmission of the second stage including compression is as high as 80%. Due to the peak power enhancement and pulse shortening obtained in the first stage a lower nonlinearity is required resulting in a short fiber and argon (n₂=9.8·10⁻²⁴ m²/W·bar) as nonlinear medium.

The argon pressure in the second stage is set to 2.0 bar allowing for further spectral broadening of the pulses emerging from the first stage. The broadened spectrum has a −10 dB bandwidth of 67 nm (Fig. 5 (a) ). A GVD of −800 fs² is used to compress the pulses to an autocorrelation width of 51 fs (Fig. 5 (b)). We have performed a numerical simulation for the second stage as well. We were using the output of our first simulation as input for the second stage. Again the numerical and experimental results agree very well (Fig. 5 (a) and (b)). Thus, we are able to extract pulses with a duration of 35 fs, where 54% of the energy are contained in a 35 fs Gaussian main pulse. The peak power of second stage amounts to 5.7 GW, while a good beam quality is maintained (Fig. 5 (c)). These are the shortest pulses with the highest peak power that have been obtained with high average power fiber lasers to date. The temporal pulse quality of the pulses can be improved by well known pulse cleaning techniques such as nonlinear elliptical polarization rotation (NER) [20,30] or cross-polarized wave (XPW) generation [31]. The energy outside the main pulse does not affect high harmonic generation, since the peak power of the wings is low. Calculations based on the ADK model [32] have shown that the accumulated ionization of our compressed pulse is only slighter higher than that of a transform limited Gaussian pulse with the same peak power meaning that phase matching will not be affected by the wings of the pulse. The pulse energy of the compressed pulses after the second stage was 380 µJ, which is an average power of 19 W at a repetition rate of 50 kHz. Note that the overall efficiency of the two stages including coupling, propagation and compressor loss is as high as 38%. The obtained pulse parameters (peak power, pulse duration and average power) are significantly enhanced in comparison to [20]. This high average and peak power ultrashort pulse laser system is expected to benefit e.g. EUV source development (HHG).

 

Fig. 5 (a) Measured (blue) and simulated spectrum (gray) after the second stage. (b) Measured (blue) and simulated (gray) autocorrelation of the compressed pulses after the second stage. (c) Collimated beam after the compressor of the second stage.

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4. Conclusion

A post-compression scheme for a state-of-the-art fiber chirped pulse amplification system is realized by exploiting nonlinear interaction in noble gas filled hollow-core fibers. By using a double-stage setup we compress 1 mJ, 480 fs, 50 kHz (50 W), 1.8 GW pulses to 380 µJ, 35 fs, 50 kHz (19 W), 5.7 GW pulses. This is possible by implementing a pulse shaping device into the fiber system [2], thus allowing to start with nearly transform limited pulses at mJ level pulse energies. A high nonlinearity gas (xenon) is used in a first stage to achieve significant spectral broadening. After the first compression stage another nonlinear interaction in argon further broadens the spectrum before the pulses are compressed again. This setup allows shortening of the pulses by more than one order of magnitude while enhancing the peak power by a factor of 3. Due to the high efficiency the final pulse energy is as high as 380 µJ. The source offers the required parameter for efficient high harmonic generation at high repetition rates, which will be implemented in the future.

We also believe that there is further potential for using this compression scheme. Currently, the chirped mirrors used for compression do not perfectly fit our central wavelength limiting especially the broadening of the second stage. By using broader bandwidth mirrors, further pulse shortening to about 10 fs can be expected, which will results in more than 10 GW peak power few-cycle pulses. The use of differential pumping [27] can help to minimize ionization and self-focusing issues allowing for more stable operation.