In recent years, significant progress has been made regarding scaling of the performance of femtosecond fiber systems. However, there are issues that currently limit both the achievable peak and the average power of a linear amplifier chain. For example, the onset of mode instabilities [1] sets an upper limit to the average power that can be obtained from a single fiber amplifier. Typically, the power threshold of this effect lies in the range of some hundreds of watts up to the kilowatt level, strongly depending on the properties of the fiber and other system parameters. Furthermore, the pulse energy is ultimately limited by the extractable energy of the fiber, nonlinear pulse distortions, and damage issues [2].

Different theoretical models have been investigated in order to understand the physical origin of mode instabilities [3–5], and advanced fiber designs, such as large-pitch fiber (LPF) [6], chirally coupled core (CCC) fiber [7], and distributed mode filtering (DMF) fiber [8], have been developed to increase the average power threshold. In order to increase the achievable pulse energies, spatial and temporal scaling techniques are employed to reduce the peak intensity inside the fiber. Examples of those techniques include the chirped-pulse amplification (CPA) concept [9] and the use of large-mode-area fibers. Furthermore, nonlinear pulse distortions can be either reduced by employing circular polarization [10] or compensated by an active shaping of the spectral phase [11]. With these techniques, in systems with a single main amplifier, femtosecond pulses have been demonstrated at average powers of up to 830 W [12] and pulse energies of up to 2.2 mJ [13].

Despite the vast progress that has been made in scaling the average output power and the pulse energy, the performance of a single laser amplifier (independently of its architecture) will always be limited. Therefore, in spite of all the progress, the ultimate performance of a single laser amplifier might still not be sufficient to reach the desired laser parameters required for high-intensity physics at high repetition rates [14,15]. Hence, additional approaches for scaling of the performance should be considered. One example is the coherent combination of spatially separated amplifiers. In this concept, pulses emitted from a preamplifier are split into a number of channels; they are amplified in each channel independently and then, finally, a recombination of the pulses into one takes place. With this approach, an improvement of the average power and pulse energy by a factor equaling the total number of channels is possible in the ideal case. While coherent combination is especially suitable for fiber lasers due to their very high and reproducible beam quality, it might also be adapted to other laser architectures, such as innoslab [16] or thin disks [17].

This concept has been applied to systems working in continuous-wave operation for some time [18,19], but it was only quite recently applied to the ultrashort-pulse regime [20,21]. So far, by combining two rod-type fibers, pulse energies and, therewith, peak powers exceeding the single-amplifier limit can already be demonstrated [22]. The usability of the coherent combination approach depends strongly on the achievable combination efficiency, especially when the number of channels becomes large. This efficiency is determined by the quality of the beam overlap, as well as by the spectral phase and amplitude differences of the pulses, which can be caused by dissimilar nonlinear effects and dispersion in the different channels. However, according to theoretical investigations with realistic assumptions of these differences, it should be possible to increase the number of channels with only a modest drop in total efficiency [23,24]. Furthermore, the first experiment regarding the combination of four single-mode fibers at low power has recently been demonstrated [25]. However, in the experiment described herein, we increase the number of channels from two to four and demonstrate a combination of very high average powers and pulse energies to show the viability of the coherent combination concept at these parameters. A schematic picture of the experimental setup is shown in Fig. 1. A mode-locked solid-state oscillator generates femtosecond pulses with a repetition rate of 40 MHz, a bandwidth of 6 nm, and an average power of 150 mW. These pulses are stretched in a grating stretcher to about 2 ns. The stretcher uses $1740\mathrm{lines}/\mathrm{mm}$ gratings and imposes a spectral hard cut of 7 nm. The system includes three preamplifiers, whereby the last two are based on an LPF design [6]. The output of the preamplifiers provides sufficient pulse energy and average power to seed all four main amplifiers. In our experiment, the seed power for every main amplifier is about 1 W. Additionally, a phase shaper is included in the setup to compensate for spectral phase distortions that may occur due to nonlinearities or uncompensated higher-order dispersion. This way, the phase shaper improves the pulse quality at the output of the system. Two acousto-optic modulators (AOMs) are used to reduce the repetition rate to the desired value. The main-amplification stage comprises four LPF fibers in a parallel configuration with a mode-field diameter of 59 μm and a length of 1.2 m each. These fibers are especially suitable for coherent combination due to the high stability and quality of the output beam at high average powers. Waveplates are placed in front of each fiber in order to achieve the required polarization direction after amplification. The splitting of the seed beam is realized with polarization-dependent beamsplitter cubes in a cascaded setup. A delay line ($\mathrm{\Delta }\phi$ in Fig. 1) consisting of a piezo-mounted mirror is inserted at the output of one of the ports of each cube in order to actively stabilize the path lengths of the different channels and to compensate for fluctuations due to air movement, vibrations, and thermal changes. On the other hand, combination of the output beams of the amplifiers can no longer be realized with polarization-dependent beamsplitter cubes due to the very high average powers causing thermal lensing on these elements. The issue is not inherent to coherent combination, but occurs while handling very high average powers. To mitigate this problem, we employed thin-film polarizers (TFPs) and other low absorbing components, i.e., specifically selected lenses. Behind every TFP, an antireflection coated laser window is inserted. This way, a small reflected fraction of the beam is routed to a Hänsch–Couillaud detector [26], which can detect the polarization state of the combined beam. This detector is then connected to the corresponding delay line using an electronic control device. The regulator in this device stabilizes the linear polarization state of every combined laser beam at every combination step. This allows for further combination steps and for the compression of the final beam with polarization-dependent dielectric gratings. The advantage of this stabilization technique is that no phase modulation is necessary to calculate an error signal for the piezo-electric actuators. The total stabilization system has a bandwidth close to 1 kHz, which turned out to be more than enough to stabilize almost all typical fluctuations present in such a system [27]. In the referenced publication, the short- and long-term stability of a coherently combined laser system were thoroughly investigated. Because we use a stabilization scheme based on the same technique, a similar behavior is expected for this system. After combination, the pulses are recompressed in a grating compressor that shares one of its gratings with the stretcher. The compressor efficiency was measured to be around 80%.

 

Fig. 1. Schematic overview of the experimental setup.

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In the present experiment, the AOMs are configured to deliver a repetition rate of 400 kHz. The average powers of the individual amplifiers are set to a value at which no mode instabilities could be observed. The compressed output powers could be estimated to be between 126 and 137 W. With this optimized setup, we are able to achieve a combined and compressed average power of 530 W and a pulse energy of 1.3 mJ. Together with a pulse duration of 670 fs (autocorrelation trace with a duration of 940 fs shown in Fig. 2; pulse duration estimated with a deconvolution factor derived from simulations), this corresponds to a peak power of about 1.8 GW. The spectrum has a bandwidth (FWHM) of 2.7 nm, as shown in Fig. 3. It should be noted that this pulse duration could be improved by employing spectral amplitude shaping and a larger bandwidth in the stretcher/compressor. By measuring the output power and losses at various points of the system, we can estimate a system efficiency as high as 93%. The system efficiency is the combined compressed average power divided by the total power that the system emits (calculated by measuring the compressed average power of all channels independently and adding the nonpolarized output of every amplifier), assuming a compressor efficiency of about 80%. The losses take place at the first stage of combination due to imperfect linear polarizations at the output of the channels, at the second stage due to the imperfect combination of two channels, and, finally, at the compressor due to the imperfect combination of the final beam. The efficiency of the combination process compares very well with previous results of two-channel systems, as predicted by the theoretical investigations mentioned in [23,24]. The observed high efficiency can be related to the low number of components in the channels (the final collimation through the compressor is handled by a common telescope) so that possible mismatches of the individual beams are kept to a minimum. The measurement of the beam quality resulted in a value of $M^2$ of lower than $1.1\times 1.2$ (Fig. 4).

 

Fig. 2. Autocorrelation trace of the combined pulse at an average power of 530 W.

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Fig. 3. Spectrum of the combined beam with a band width of 2.7 nm.

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Fig. 4. Caustic of the beam for the $M^2$ measurement at 530 W.

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In conclusion, we have demonstrated a femtosecond fiber CPA system consisting of four coherently combined amplifiers. It delivers an average power of 530 W and pulse energies of 1.3 mJ. With the aid of coherent combination, it is possible to achieve system parameters that are currently not achievable with a serial amplifier system. These experiments demonstrated an excellent beam quality and a very high combination efficiency of the total system of 93%. Additionally, we have already seen that the system can be used together with hollow-core compression as a driver for high-harmonic generation. Depending on the fiber type, we expect to be able to improve the performance of this system even further. We think that with the coherent combination concept and further progress in fiber laser technology, average powers in the range of 1 kW and pulse energies of 10 mJ are realistic parameters in the future.