Phase-stable, multi-µJ femtosecond pulses from a repetition-rate tunable Ti:Sa-oscillator-seeded Yb-fiber amplifier
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We present a high-power, MHz-repetition-rate, phase-stable femtosecond laser system based on a phase-stabilized Ti:Sa oscillator and a multi-stage Yb-fiber chirped-pulse power amplifier. A 10-nm band around 1030 nm is split from the 7-fs oscillator output and serves as the seed for subsequent amplification by 54 dB to 80 W of average power. The µJ-level output is spectrally broadened in a solid-core fiber and compressed to ~30 fs with chirped mirrors. A pulse picker prior to power amplification allows for decreasing the repetition rate from 74 MHz by a factor of up to 4 without affecting the pulse parameters. To compensate for phase jitter added by the amplifier to the feed-forward phase-stabilized seeding pulses, a self-referencing feed-back loop is implemented at the system output. An integrated out-of-loop phase noise of less than 100 mrad was measured in the band from 0.4 Hz to 400 kHz, which to the best of our knowledge corresponds to the highest phase stability ever demonstrated for high-power, multi-MHz-repetition-rate ultrafast lasers. This system will enable experiments in attosecond physics at unprecedented repetition rates, it offers ideal prerequisites for the generation and field-resolved electro-optical sampling of high-power, broadband infrared pulses, and it is suitable for phase-stable white light generation.
KeywordsPhase Noise Frequency Comb Master Oscillator Power Amplifier Attosecond Pulse Phase Jitter
Around the turn of the last century, the generation of visible/near-infrared few-cycle pulses became a matter of course in laser laboratories. The ability to control the electric field of such pulses enabled ground-breaking applications like high-precision frequency comb spectroscopy  and led to the establishment of new research fields like attosecond science [2, 3]. Titanium-sapphire (Ti:Sa) oscillators can be considered the workhorse in this field, since they are the most widespread technology employed to seed laser systems generating phase-stable few-cycle pulses. Important contributions to the success of these oscillators are their large optical bandwidth, leading to the direct generation of few-cycle pulses, and the excellent phase stability achievable with feed-back  and feed-forward stabilization schemes . However, a major drawback of Ti:Sa amplifiers is the high thermal absorption and thermal lensing in the gain medium, which restricts the average powers to a few tens of Watts even with cryogenic cooling , thus limiting high-pulse-energy operation to repetition rates significantly lower than 1 MHz. Recently, Yb-based laser technology has rapidly progressed as a powerful competitor to the well-established Ti:Sa technology. The superior thermal properties of Yb-doped active media enable an improvement of several orders of magnitude in terms of average power [7, 8, 9, 10, 11]. To overcome the disadvantage of a significantly narrower gain bandwidth, several post-amplification nonlinear pulse compression techniques have been developed [9, 10, 11, 12, 13, 14]. Recently, from an Yb:YAG thin-disk oscillator followed by two nonlinear compression stages, pulses of 2.2 cycles with 6 W of average power at a repetition rate of 38 MHz and with a phase jitter of 270 mrad (out-of-loop phase noise integrated in the band between 1 Hz and 500 kHz) were demonstrated .
In this study, we combine a feed-forward stabilized Ti:Sa master oscillator with an Yb-fiber power amplifier, resulting in a high-power, ultrashort-pulse laser system with several unique advantages for electric-field-resolved metrology. First, the high phase stability achieved with the Ti:Sa frontend is largely preserved upon amplification of a 10-nm band around 1030 nm by about 54 dB to 80 W. Additional phase fluctuations introduced by the multi-stage, chirped-pulse amplifier (CPA) and by subsequent nonlinear compression to about 30 fs were compensated for by a feed-back loop, resulting in an unprecedentedly small overall phase jitter of the high-power pulse train of less than 100 mrad (out-of-loop phase noise, integrated in the band between 0.4 Hz and 400 kHz). Due to its phase stability, this source is particularly well suited to drive cavity-enhanced high-order harmonic generation (HHG) for the generation of extreme ultraviolet (XUV) frequency combs [15, 16] and of XUV attosecond pulses [16, 17, 18]. Second, the master oscillator power amplifier (MOPA) approach readily enables the use of a high-frequency pulse picker after the low-power oscillator , allowing for a tunable repetition frequency (18.5, 24.7, 37 and 74 MHz). And third, the Ti:Sa oscillator produces a 74-MHz train of 7-fs pulses, inherently synchronized with the pulses amplified in the Yb-fiber CPA. These could be used for instance as a pump in time-resolved photoelectron emission microscopy , where attosecond XUV probe pulses are generated with the CPA output. Another application could be electro-optical sampling of broadband infrared radiation  generated with the CPA output, where a repetition-rate ratio of a factor of 2 between the sampling pulses and the long-wavelength field enables ultralow-noise lock-in detection .
2 Experimental setup
To fine-tune the pulse duration at the CPA output, the pre-compressor is motorized to control the distance of the gratings. It only influences the pulse duration of the stretched pulses by up to 10 ps and allows for stable and precise control of the output pulse duration. The estimated B-integral of the system amounts to around 0.1 rad irrespective of the setting of the pre-compressor. The dispersion of the gratings is matched up to the sixth order.
The overall phase noise at the exit of the system is measured with two independent f – 2f interferometers . The first interferometer (in-loop) is used to generate a feed-back error signal which is combined with the original feed-forward stabilization by adding a frequency modulation to the RF signal used to drive the AOFS (signal 3 in Fig. 1) and thus also a phase modulation (see phase along the black lines in Fig. 1b, c). The second (out-of-loop) interferometer is used to determine the actual phase noise outside of the locking loop.
The amplification process contains several potential phase noise sources, including amplification noise , grating jitter (mechanical and air fluctuations)  and residual noise during the pulse picking in the AOM . Furthermore, the mechanical jitter in the interferometers themselves and the supercontinuum generation necessary for f − 2f detection add to the measured phase noise .
The value of the carrier-envelope offset frequency f ceo of the amplified pulse train can be adjusted by manipulating the signal used for the stabilization in the AOFS, which consists of three contributions, as shown in Fig. 1b, c. Signal 1 is the feed-forward signal consisting of the repetition frequency and the carrier-envelope offset frequency of the oscillator (f rep + f ceo,osc) which, in normal operation, shifts f ceo to 0 MHz in the -first diffraction order of the AOFS. The value of f ceo can optionally be tuned by mixing an additional frequency with an RF mixer and a signal generator (signal 2). The combined signal is then band-pass filtered, amplified and fed to the AOFS (signal 3).
3.1 Carrier-envelope-offset frequency of 11 MHz
In a first configuration, we set the driving frequency of the AOFS to f rep + f ceo,osc-11 MHz (a value of 71 MHz, the free running oscillator offset frequency f ceo,osc is kept around 8 MHz by means of intracavity wedges and crystal temperature). This is depicted in Fig. 1b. Using this scheme, any value of the carrier-envelope-offset frequency of the output pulse train can be chosen, provided that the AOFS is suited for that frequency.
3.2 Carrier-envelope-offset frequency of 0 MHz
By adapting the AOFS signal generation and phase detection in the f − 2f interferometer, the value of the comb offset can also be set to 0 MHz, as shown in Fig. 1c. The main difference in the f − 2f interferometer setup is the spectrally resolved detection and the signal processing. The interferometer delivers an interferogram which is digitally evaluated and fed to a PDI controller. The feed-back loop consists of two stages, a faster loop using a 360° phase shifter  and a slower one to compensate for drifts over several radians (see red trace in Fig. 4). The slow drift compensation is accomplished by decreasing the AOFS frequency by 22 MHz and afterwards increasing it by the same synchronized frequency with a small additional modulation, corresponding to the feed-back signal. Due to the digital evaluation of the interferogram, the lock was limited to a bandwidth of 167 Hz. The previous measurements at 11-MHz offset frequency, however, showed that the bandwidth of 167 Hz is sufficient as there was no major difference when using a locking bandwidth of 11 kHz (Fig. 3). The results for the long-term measurements are shown in Fig. 4. As no second spectrally resolved 0-MHz f − 2f interferometer was available, only in-loop measurements can be shown. However, the 11-MHz measurements corroborate that the out-of-loop performance should be on the same order. The necessity of a slow drift compensation for more than 2 rad presents itself in the open-loop trace (red) as the phase drift is larger than 30 rad during 7.5 min. This drift is not possible to lock with only a single 360° phase shifter as demonstrated in . The in-loop closed-loop measurement is shown in black and manifests an extraordinary value of 53 mrad within a bandwidth of 167 Hz which is consistent with the in-loop value of 60 mrad measured at f ceo = 11 MHz (magenta trace, bandwidth 4 kHz). This operation is stable over tens of minutes.
4 Conclusion and outlook
In conclusion, we have demonstrated an Yb-fiber MOPA system seeded by a Ti:Sa oscillator, achieving excellent phase stability. The repetition rate of the 0.7-µJ, ~32-fs output pulses can be reduced from 74 MHz (fundamental repetition rate of the oscillator) by an integer factor of up to 4 without affecting the pulse parameters. In principle, the repetition rate can be further reduced at the same average power by stronger pulse stretching in the CPA  and the pulse duration can be further compressed with alternative, pulse-energy-scalable schemes [9, 10, 11, 12, 13, 14]. For all repetition rates, an integrated phase noise of 60-mrad in-loop and 225-mrad out-of-loop was measured in a bandwidth from 2 mHz to 4 kHz. These results have a threefold significance for ultrafast laser technology. First, they demonstrate that the residual phase noise introduced by Yb-fiber amplifiers (including CPA), even for an amplification factor of > 50 dB, is low enough to be readily compensated by a simple feed-back scheme. On the other hand, they indicate that for a high phase stability, a feed-back loop is necessary for the compensation of these phase fluctuations. Second, these results prove that feed-forward-stabilized Ti:Sa oscillators are well suited as low-phase-noise seeders for Yb:fiber systems. Third, they show that a fast AOM pulse picker after the low-power frontend mostly preserves the phase stability irrespective of the picking factor.
The laser system demonstrated here opens up new opportunities in several fields. For instance, the zero-offset-frequency pulse train can be used to drive HHG in a suitable femtosecond enhancement cavity [16, 17] for the generation of attosecond pulse trains and, ultimately, for the generation of isolated attosecond pulses at multi-MHz repetition rates . This will dramatically decrease the measurement times in photoelectron emission microscopy and spectroscopy, in particular allowing for the study of plasmonic fields with a unique combination of nm-scale spatial resolution with sub-femtosecond temporal resolution . Furthermore, the adjustable repetition rate allows for direct studies of cumulative effects such as those observed in HHG in gases at high repetition rates . Another application which will tremendously profit from this MOPA is field-resolved detection of broadband infrared pulses , employing the 7-fs pulses generated by the Ti:Sa oscillator for electro-optical sampling with a lock-in detection at half the fundamental oscillator repetition rate . Furthermore, the phase-stable output could be employed as a frequency comb or to drive the generation of ultrabroadband supercontinua, which can be used to obtain high-energy field-synthesized femtosecond transients .
Open access funding provided by Max Planck Society. This work was funded by the Fraunhofer and Max-Planck cooperation within the project “MEGAS” and the Deutsche Forschungsgemeinschaft (DFG) (MAP). I.P. acknowledges funding by European Research Council (Grant Agreement No. 617173, “ACOPS”). We thank Ferenc Krausz and Fabian Lücking for fruitful discussions.
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