Generation of phase-stable sub-mJ ultrashort laser pulse bursts with extremely high scalable pulse number

. We demonstrate generation of bursts that consist of up to 40 ultrashort pulses with 10 μ J pulse energy, 250 fs pulse duration and an ultrashort tunable spacing, from picoseconds to nanoseconds, corresponding to a terahertz intraburst repetition rate. This was achieved by the build-up of a novel thermally-stable sub-mJ Vernier Regenerative Amplifier (RA), whose round-trip detuning is similar to its master oscillator round-trip time. The RA includes two cavities pumped from a common diode, and is able to provide for either 2 bursts (one burst out of each cavity), or for one burst and a synchronous reference pulse for characterization.


Introduction
Bursts with spacings at the nanosecond scale or larger became useful sources in materials processing [1,2], several spectroscopic applications, such as laser-induced breakdown spectroscopy (LIBS) [3], or seeding of free electron lasers [4].Recently, there is a growing effort to also provide bursts of ultrashort pulses at the highest intraburst repetition rates, corresponding to spacings comparable to sub-picosecond pulse durations, motivated by the fact that ultrahigh-repetition-rate bursts are a useful tool for the coherent control of (ro-)vibrational wavepackets.Regarding nonlinear spectroscopy, the amplification of bursts is another aspect.For bursts with a pulse spacing of a nanosecond or larger, the amplification of ultrashort pulses by chirped-pulse amplification (CPA) is a well applicable technique and allows for the reduction of the temporal intensity by chirping a single pulse.This concept does not apply however to multiple strongly chirped, but closely spaced burst pulses due to interference effects of the pulses inside the amplifier.Nonetheless, the breakdown of the CPA concept in this regime could be recently shown to be avoided by burst pulse phase modulation prior amplification [5].

Master-Oscillator Power-Amplifer Burst System
In this work, we demonstrate a novel master-oscillator power-amplifier (MOPA) Vernier burst system.The amplifier shows good thermal stability, allows for reference-free pulse-to-pulse phase-slip stabilization and includes two cavities within a monolithic design for low relative drift.The pulse spacing is tunable from subpicoseconds to several nanoseconds.The system is able to amplify bursts up to 1 mJ of total burst energy, which is also its maximum energy for a single pulse.

Vernier Twin Amplification Setup
A master oscillator (Yb:KGW) generates <100 fs pulses with nJ energies at a 76 MHz repetition rate, corresponding to a 13.2 ns initial spacing.The pulses are stretched by a common grating stretcher to 300 ps duration.To separate the beam into two synchronous beams for the two cavities of the Twin Regenerative Amplifier (RA) (Yb:CaF2, 1kHz repepetition rate), an acousto-optical modulator is used.We use the diffracted beam for the burst channel, because it allows for individual amplitude-and phase-modulation of the burst seed pulses.The reference seed pulse is acquired from the non-diffracted pulses.Between the AOM and the Twin RA we apply optical isolation for each cavity by a combination of polarizers and a Faraday Rotator.The cavity design is x-shaped, in order to minimize the amplifier size while keeping roughly the cavity round-trip time comparable to the master oscillator round-trip time of 13.2 ns.A sufficiently small absolute difference in round-trip times allows for picosecond spacings in the burst (Vernier effect).Both cavities are dual-pumped from the same CW pump diode, which, in addition to the common monolithic design, minimizes relative drifts.To achieve good thermal stability, the residual light of the pump after the second pass through the crystal is directed on a water-cooled heat dump.The bursts can be built up by applying a suitable intermediate voltage to the Pockels cell in the RA.By this, burst seed pulses can couple into the cavity, while already acquired pulses are kept inside with an effective gain of about zero.The constant pulseto-pulse phase slip that is imprinted on the burst during accumulation is stabilized by a slow feedback loop: the spectrum of the leakage signal through one of the end mirrors shows a spectral modulation according to the THz intraburst repetition rate.By Fourier-processing methods, we are able to retrieve and stabilize the phase by piezotuning the other end mirror accordingly.In contrast to our past work, this new stabilization approach requires no additional pilot beam for stabilization.
The phase-stable burst is amplified in our demonstration up to 10 uJ for each burst pulse and we demonstrate bursts with up to 40 pulses, resulting into a total burst energy of about 400 uJ.The reference pulse is amplified up to an energy required by the characterization measurement, which is about 10 uJ.Pulses of both channels are compressed in a single-grating compressor to 250 fs pulse duration.Fig. 1.Full Master-Oscillator Power-Amplifer system with a twin Vernier Regenerative Amplifier including the characterization via autocorrelation and cross-correlation.The cavity design is the same for both cavities in the Twin RA and is shown in the bottom, including the stabilization concept for pulse-to-pulse burst phase slip stabilization.OSC: Oscillator.STR: Stretcher.AOM: Acousto-Optical Modulator.RA: Regenerative Amplifier.AC: Autocorrelation.XCORR: Cross-Correlation

Burst Time-Domain Characterization Methods
We show two ways how to characterize the amplified burst of compressed pulses in this regime, where each of the approaches is suitable for different use cases.

Burst Autocorrelation
The most practical approach to characterize the amplified burst is to perform an autocorrelation, due to its simplicity and also because it can be peformed without any reference pulse.For a large number of picosecond-spaced pulses, a mechanical delay stage with few centimeters of travel range is enough.We used the autocorrelation to determine the optimal intermediate voltage of the Pockels Cell during burst buildup and achieved generation of an amplified burst of 40 pulses with a pulse spacing of about 1.8 ps.

Single-Shot Cross Correlation
For a shorter number of 4 pulses, we performed a crosscorrelation of the burst with the reference pulse under a large angle, such that the temporal characteristics of the burst were mapped into the spatial domain and retrieved on a shot-to-shot basis the cross-correlation intensity with a fast line camera.

Fig. 3 .
Fig. 3. Single-shot cross-correlation of a burst with 3 pulses with about 1 ps spacing by using a single synchronous reference pulse.