Extraction of enhanced, ultrashort laser pulses from a passive 10-MHz stack-and-dump cavity
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Periodic dumping of ultrashort laser pulses from a passive multi-MHz repetition-rate enhancement cavity is a promising route towards multi-kHz repetition-rate pulses with Joule-level energies at an unparalleled average power. Here, we demonstrate this so-called stack-and-dump scheme with a 30-m-long cavity. Using an acousto-optic modulator, we extract pulses of 0.16 mJ at 30-kHz repetition rate, corresponding to 65 stacked input pulses, representing an improvement in three orders of magnitude over previously extracted pulse energies. The ten times longer cavity affords three essential benefits over former approaches. First, the time between subsequent pulses is increased to 100 ns, relaxing the requirements on the switch. Second, it allows for the stacking of strongly stretched pulses (here from 800 fs to 1.5 ns), thus mitigating nonlinear effects in the cavity optics. Third, the choice of a long cavity offers increased design flexibility with regard to thermal robustness, which will be crucial for future power scaling. The herein presented results constitute a necessary step towards stack-and-dump systems providing access to unprecedented laser parameter regimes.
KeywordsPulse Energy Input Pulse Diffraction Efficiency Switching Rate Nonlinear Phase
A number of visionary applications like laser wake-field acceleration of elementary particles  or space debris removal  ask for a dramatically improved performance of femtosecond laser systems with high repetition rates . In particular, Joule-level pulse energies at average powers in the multi-kilowatt regime with diffraction-limited beam quality are required. This combination of parameters greatly exceeds the capabilities of today’s laser systems, and the scalability of the average and of the pulse peak power of single-aperture amplifier solutions does not suffice these demands [4, 5, 6, 7]. Current limitations which need to be overcome are mainly caused by thermal or nonlinear effects in the amplifier media [8, 9]. Recently, multi-aperture spatial combining approaches have emerged as one possibility to circumvent these limitations [10, 11]. Additionally, temporal combining techniques aimed at artificially extending the stretched pulse duration and, thus, overcoming pulse peak power limitations have been successfully demonstrated. Among those, the most straightforward approach is the so-called divided-pulse amplification (DPA) . Here, in order to reduce the peak power-related limitations, each pulse is split into several temporally separated replicas before the final amplification stage and recombined afterwards. Alternatively, the creation of temporal replicas can be avoided, if a pulse train with a much higher repetition rate is amplified and subsequently temporally combined to achieve the repetition rate demanded by the application. Here, the general idea is to increase the pulse peak power at the cost of a reduced repetition rate by temporally stacking successive pulses after their amplification. One implementation of this approach, which we refer to as stack and dump (SND), is to superpose amplified pulses in an enhancement cavity (EC) and periodically extract them using a fast and efficient switch [13, 14].
Passive ECs have been subject to intensive research and development for several decades [15, 16, 17]. They are employed for a multitude of intracavity optical conversion processes such as high-harmonic generation [18, 19] or inverse Compton scattering . Due to the energy enhancement in such a cavity, average powers in the MW range  and multi-GW peak power levels  are achievable within the cavity at multi-MHz repetition rates. In 2002 and 2003, the extraction of pulses from such an enhancement cavity was proposed  and demonstrated at around 80-MHz with nJ-level, picosecond pulses by the Ye and Hänsch groups [24, 25]. In 2004, slightly stretched femtosecond pulses were first enhanced and then extracted from a 100-MHz cavity . Recently, concepts making use of the vast potential of ECs as stacking devices for stretched ultrashort pulses were published [13, 27].
In this paper, we demonstrate the SND scheme in a 30-m-long EC, corresponding to a length increase of a factor of 10 over the state of the art. Towards tapping the full potential of ECs as stacking devices for ultrashort pulses, this constitutes a crucial design criterion relaxing the thermal stress in the switch and in the cavity optics  and allowing for longer times between successive pulses. The EC supported a steady-state power enhancement factor exceeding 200 and was seeded with a 10-MHz repetition-rate train of 3-µJ pulses. The cavity enabled the enhancement of strongly stretched pulses (~1.5 ns). A systematic investigation of different dumping rates was performed with an intracavity acousto-optic modulator (AOM). Pulses with the accumulated energy of up to 65 input pulses, i.e. 0.2 mJ, were extracted at 30 kHz. These pulses were recompressed to the initial duration of 800 fs, demonstrating the feasibility of SND with strongly stretched pulses and energies surpassing previous results by three orders of magnitude. These results, even if not stating new laser parameter records on their own, constitute the first milestone towards a power-scalable device and, thus, are a necessary step towards the first stack-and-dump system providing truly unprecedented laser parameters. Peak power-related and thermal limitations of this technique are discussed.
2 Cavity set-up and steady-state enhancement
3 Non-steady-state operation: pulse extraction
The efficiency as well as the extracted enhancement can be further optimized by adapting the input coupler reflectivity R for each switching rate as discussed in . For a given input coupler reflectivity, the optimum working point in terms of the switching rate depends on whether the highest pulse energy or the highest efficiency is desired. The small deviations of the measured values from the ones predicted by theory (Fig. 4) are caused by variations in the alignment, slightly changing the overlap between the incoming beam and the cavity mode. It is noteworthy that the stabilization of the oscillator to the cavity was barely affected by the dumping process. Only at the highest investigated switching rates, the partial dumping occasionally leads to a collapse of the lock.
The spot size in the AOM is crucial for the peak intensity, but on the other hand it is determined by the required switching time for a given cavity length. To achieve an efficient enhancement at an increased input energy, using an AOM as a switching device, it is hence necessary to extend the cavity length. This measure offers the additional benefit that for a certain desired switching rate (i.e. output repetition rate) the required number of stacked pulses is lower for longer cavities (see Eq. 3) which decreases the magnitude of the acquired nonlinear phase due to lower average round trips of the pulses. Naturally a sweet spot has to be found in the trade-off between a high enhancement and a minimized nonlinear phase.
4 Conclusion and outlook
The experiments presented here constitute a first demonstration that pulse stacking of stretched fs pulses in a 10-MHz cavity is a promising route towards increasing the pulse peak power of high-average-power ultrafast laser systems. An extracted enhancement of 65, delivering pulse energies of 0.16 mJ at 30 kHz with a pulse duration of 800 fs, demonstrates a significant improvement over previous results [24, 25, 26, 27]. To achieve this progress, it was necessary to lengthen the cavity in order to allow for a longer switching time with the additional benefit of a cavity mode that is less sensitive to thermal effects . Other temporal pulse combining techniques, like divided-pulse amplification [31, 32], are limited in the number of combined pulses due to an increasing complexity. Stack and dump currently constitutes the most promising way for the superposition of a large number of pulses.
In the next experimental step, the AR-coated AOM will be exchanged for a Brewster-cut AOM and a state-of-the-art seed system  will be used to deliver up to 1 mJ at 2-MHz repetition rate with a spectrum enabling pulse durations below 300 fs. Our simulations under consideration of SPM-related effects in the AOM show that at the corresponding cavity length of 150 m an extracted enhancement of around 50 should be feasible by stacking 100 pulses. Together with a good management of the thermal lenses  that may occur in the cavity, these modifications will enable the extraction of 50-mJ pulses at 20-kHz repetition rate with a cavity efficiency of 50%, conserving 1 kW average power. Finally, a purely reflective switch [13, 14] overcoming AOM-related limitations is highly desirable to further increase the performance and efficiency of the system to Joule-class pulse energy and multi-kW average powers.
This work has been partly supported by the European Research Council under the ERC Grant Agreement No.  “ACOPS”, by the German Federal Ministry of Education and Research (BMBF) under contract 13N13167 “MEDUSA” and by the Fraunhofer and Max Planck cooperation program “MEGAS”.
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