40-µJ passively CEP-stable seed source for ytterbium-based high-energy optical waveform synthesizers

: We demonstrate experimentally for the first time a ~40-µJ two-octave-wide passively carrier-envelope phase (CEP)-stable parametric front-end for seeding an ytterbium (Yb)-pump-based, few-optical-cycle, high-energy optical parametric waveform synthesizer. The system includes a CEP-stable white-light continuum and two-channel optical parametric chirped pulse amplifiers (OPCPAs) in the near- and mid-infrared spectral regions spanning altogether a two-octave-wide spectrum driven by a regenerative amplifier. The output pulses are compressed and fully characterized to demonstrate the well-behaved spectral phase of this seed source.


Introduction
Optical waveform electronics is one of the rapidly expanding fields in the optical sciences over the last decades. This emerging research field ultimately aims at the complete control of intensity and phase at each frequency component of high-energy, multi-octave-spanning, subcycle optical pulses, similarly to what can be achieved at microwave frequencies and below (e.g., for music synthesizers), but at much higher optical frequencies. Besides the importance for optical science, the versatility and the peculiarities of such pulses will allow for a number of physics experiments, ranging from the studies of the interaction of solids with such extreme light transients [1,2] to the high harmonic generation (HHG) in gases using sub-cycle pulses. HHG in particular will allow for the production of isolated attosecond pulses without any gating technique [3], and for the enhancement of the efficiency at high cutoff energies [4][5][6][7][8], i.e. for the efficient production of coherent short pulses in the water window.
Our and other groups have been active in the field of pulse synthesis for a long time, first with the synchronization of independent lasers [9] and laser amplifiers derived from the same oscillator [10], then with the synchronization of parametric sources (optical parametric amplifiers, OPAs, and optical parametric chirped pulse amplifiers, OPCPAs) which allow for higher flexibility as their bandwidth is not constrained to the energy levels of a laser-gain material. For better initial synchronization, the OP(CP)As were seeded by the same source. Other possible schemes for pulse synthesis are the Fourier-plane optical parametric amplifier [11] and the synthesis of different channels from the output of hollow-core fibers [12][13][14].
The broadband seed can be directly from the laser [3], or from white-light continuum (WLC) [13,[16][17][18][21][22][23][24] which allows for higher flexibility. CEP stabilization can be achieved either actively [3] or passively [13,[16][17][18][21][22][23][24]. The parametric amplifiers can be either in a sequential fashion, in which the seed goes through differently tuned OP(CP)As [25,26], or in a parallel fashion, in which the seed is split, amplified in parallel in differently tuned OP(CP)As and recombined [3,13,17,18]. The parallel scheme has the disadvantage of requiring active timing and phase stabilization, and the advantage of an independent dispersion compensation in each channel, and therefore better prospects for bandwidth scalability. The most energy-and bandwidth-scalable, versatile and flexible scheme for an optical parametric synthesizer is the parallel amplification of a passively-CEP-stabilized seed starting from a 1-μm source, which has been first proposed in our previous works [21][22][23][24]27] and later in a conceptual design study by the Krausz group at MPQ [20].
In this paper we present a 40-µJ, passively CEP-stable pulse source for seeding an Ybpump-based, high-energy optical parametric synthesizer. The presented system comprises CEP-stable WLC (details in section 2), and two-channel OPCPAs (details in section 3) in the near-infrared (NIR) and mid-infrared (MIR) spectral regions spanning altogether a twooctave-wide spectrum. The µJ-pulses are recompressed and spectro-temporally characterized to demonstrate the compressibility of the seed source. This is the first experimental demonstration of a passively CEP-stable two-octave-wide seed source at the µJ pulse energy level based on Yb pump-laser technology. Such a source can readily be used for strong field physics in solids and CEP dependent ionization studies in gases.

Passively CEP-stable white-light seed
Figure 1(a) shows the block diagram of the experimental setup. The system is driven by a high-energy Yb:KYW regenerative amplifier, delivering 5.4-mJ pulses at 1 kHz. The pulses are compressed down to 650 fs nearly transform-limit in a multilayer, dielectric Treacy compressor [28]. The 1.4-mJ uncompressed output from the regenerative amplifier is reserved for further amplification in a cryogenically cooled Yb:YAG thin-disk amplifier [29]. A part of the pulse, 2.55-mJ of the 3.2-mJ compressed output is hereafter used to pump the OPCPA stages to amplify the CEP-stable seed-source. Here only 0.65-mJ pulses are used to generate the CEP-stable white-light continuum.
First, a white-light continuum (WLC1 in Fig. 1(a)) is generated in a 10-mm long YAG crystal by focusing part of the compressed output of the regenerative amplifier via a 10-mm focal length lens. The generation of the WLC with sub-picosecond pulses has been carefully studied for different materials such as YAG and sapphire, with different lengths, focusing conditions and pulse durations. Optimized parameters to achieve a two-octave-spanning continuum as well as excellent pulse-to-pulse energy (<1% root mean square (RMS)) stability over long-term operation was determined [30]. Then a spectral bandwidth of 210 nm centered at 2.18 µm is amplified to 7 µJ through two nearly degenerate OPCPA stages (OPA1 and OPA2) in BBO in a type-I phase matching configuration. OPA1 and OPA2 are pumped by 70 and 140 µJ, respectively. Figure 1(b) shows the signal and idler spectra at the end of the second amplification stage (OPA2). The idler has 153-nm bandwidth at 1.96 µm, corresponding to 29-fs transform-limited (TL) pulses. The pulse-to-pulse energy fluctuations (RMS) of the signal after the second stage are measured to be 1.1% by using a photodiode over thousand pulses. The passively CEP-stable idler of the second OPA centered at 1.96 µm is then used to generate WLC in a 3-mm YAG crystal (WLC2). The supercontinuum generated in the second stage (WLC2) is shown in Fig. 1(c) in the range between 510 and 1600 nm. CEP stability is confirmed by interfering the fundamental spectrum at 960 nm with the second-harmonic generated (SHG) from the remaining idler in an f-2f setup [23]. The second OPA stage (OPA2) is operated in a saturated regime, which allows low pulse-to-pulse fluctuations of the idler and thus the idler-driven white-light continuum.

CEP characterization
Figure 2(a) shows the beating of the WLC in the range ~960-990 nm with the second harmonic of the remaining idler after super-continuum generation over 15 minutes. The beat signal is averaged over 4 pulses, which corresponds to the minimum integration time of the available spectrometer. The fringes show clearly the CEP stability of the WLC between 960 and 990 nm [23]. RMS of the phase fluctuations is calculated to be 124 mrad as can be seen in Fig. 2(b), which is comparable with previously reported values in the literature [31,32]. Figure 2(c) shows the beating over 12 hours. In this case, the beat signal is averaged over 1000 pulses due to limitations in data acquisition and analysis. The fringes show clearly the CEP stability of the WLC between 960 and 980 nm over ~12 hours. The corresponding phase is shown in Fig. 2(d). Over a 12-hour acquisition time, the RMS of the phase fluctuations is calculated to be 87 mrad. After 4-hours of operation, the CEP starts to drift. That is attributed to drift in pointing of the compressed output from the regenerative amplifier resulting in drift of the idler from the second OPA stage and fading of the WLC2 at the end of the 4 hours. Later on the pointing stability of the compressed output from the regenerative amplifier has been improved by implementing a beam-pointing stabilizer after the compressor, which enables us to routinely operate the system over 24 hours (see the next section). In previous works, the phase stability of WLC in bulk has only been shown for driver pulses with durations below 550 fs [31,33,34]. The measured interferograms confirmed that the CEP of the continuum is conserved for even longer pulses up to at least 650 fs.

Modified CEP-stable white-light source
In the presented system, we prefer BBO-based OPCPAs since the growth and handling technology of this material is very mature and the BBO crystal provides a quite broad amplification bandwidth for Yb pump-laser technology [35,36]. The WLC presented above is generated at 1.97 µm in the broadband phase-matching range of the degenerate 1 µm pumped OPA. Since the spectral phase of the WLC is typically not well-behaved around the driving wavelength making compression complicated [37], the driver wavelength of the WLC2 is shifted to 1.23 µm by tuning the idler wavelength and implementing an additional secondharmonic stage after the idler. Figure 3 shows the block-diagram of the modified seed (a), the spectra of signal, idler, and second-harmonic of the idler (b). We did not conduct further CEP characterization of the modified seed source, since SHG only doubles the phase, which has been already proven to be constant with the previous scheme.
The spectral region of WLC1 with a bandwidth of 45 nm (FWHM) centered at 1.75 µm is amplified to 50 µJ in two OPA stages. The passively CEP-stable idler of OPA2 has a pulse energy of 18 µJ. The spectrum is centered at 2.45 µm and has a bandwidth of 63 nm (FWHM). The idler spectrum is supporting <120 fs TL pulse duration. OPA1 and OPA2 are pumped with 39 µJ and 370 µJ pulse energies, respectively. Then the idler is frequency doubled (SHG1) in a 2-mm-long BBO crystal. The spectrum of SHG1 has a bandwidth of 13 nm (FWHM) centered at 1.23 µm. The efficiency of SHG1 is 13% resulting in 2.4-µJ pulses. Then the output of SHG1 is used to generate WLC in a YAG crystal (WLC2). To improve the long-term stable operation of the system, two beam pointing stabilizers are implemented before and after the grating compressor of the regenerative amplifier. Figure 3(c) shows the signal energy of OPA2 measured by an energy meter for every single pulse over 1000 pulses. The signal energy of OPA2 has less than 0.7% fluctuations (RMS) over 24 hours. The maximum deviation in energy measurement is measured to be 2.93 µJ. Then the output of SHG1 is used to generate WLC in the YAG crystal (WLC2). The generated WLC2 will seed OPA channels in two different spectral regions. That requires the optimization of the WLC for both regions under the same operating conditions, which should result in sufficient seed energy and low intensity pulse-to-pulse fluctuations in both regions. The optimization of WLC1 with sub-ps pulses has been extensively explored and demonstrated in our previous publication [30] but not for WLC2, which is driven by the idler of OPA2 with shorter pulse duration. In order to find the optimum WLC generation conditions, YAG crystals with different thicknesses ranging from 2 to 5 mm are tested with two focusing conditions by using 60 and 75 mm focal length lenses. Figure 4(a) shows the pulse-to-pulse intensity fluctuations over ~1000 pulses in the NIR and MIR regions. The measurements are realized by using Si and InGaAs photodiodes coupled with several bandpass filters transmitting the spectral regions of OPAs in the NIR and MIR,, respectively. As can be seen from the graph, even if the fluctuations can be reduced below the 2.3-% level in the NIR for the 60-mm focal length and with 3, 4, 5-mm-long crystals, the fluctuations in the MIR are >3.5% except for the case with 3-mm YAG. In that case, it is slightly higher than 2.5%. The lowest pulse-to-pulse energy fluctuations (2.3%) in both regions for the same focusing condition are obtained by using a 75-mm focal length lens and a 4-mm long YAG crystal. Figure 4(b) shows the corresponding spectrum covering the spectral coverage from the visible (VIS) up to the MIR. The spectra are acquired by using two different spectrometers and are normalized independently. The spectral region of the driver pulse is eliminated by employing band-pass filters to avoid the saturation of the spectrometer in and near the pump region around 1.23 µm.
In parallel to the 24-hour energy stability measurement of OPA2 (shown in Fig. 3(c)), the pulse energy of the NIR part of the CEP-stable WLC is monitored. The signal before the detector is spectrally filtered to cut the remaining pump driving WLC2. OPA2 exhibits quite low pulse-to-pulse energy fluctuations (<0.7% RMS, as shown in Fig. 3(c)) while WLC2 has 2.3% RMS fluctuations. However, the fine structure of the OPA2 signal energy measurement has a correlation with the drift of the WLC2 pulse energy as can be seen in Fig. 3(c). It is worth to mention that the pulse-energy measurement of OPA2 is shown between 40 and 55 µJ intentionally to demonstrate the correlation between pulse energy of OPA2 and WLC2. Both changes can be attributed to thermal effects in the laboratory resulting in slight changes in the regenerative amplifier pulse duration and in the beam profile due to thermal drifts of the grating compressor during the 24-hour day period. Since OPA2 is operated in the saturation regime, the effect of these changes is less significant than in the case of WLC2. In the case of WLC2, the slight change of the pump (in our case SHG of the idler in OPA2) affects the filamentation hence influences the stability of WLC2. For OPCPA seeding purposes, this small variation is negligible since the last OPCPA stages will be operated in saturation, which is expected to reduce the pulse-to-pulse energy fluctuations. The spectra of WLC2 in NIR and MIR spectral regions. The spectra are measured by using two different spectrometers and normalized independently. The WLC2 driver centered at 1.23 µm is eliminated by using several band-pass filters. Figure 5 shows the layout of the two-channel OPCPA system driven by the Yb:KYW regenerative amplifier. The compressed output of the Yb:KYW regenerative amplifier delivering 3.2-mJ, 650-fs long pulses [3] is split between a CEP-stable WLC generating nJ-level pulses with a spectrum extending from the visible up to the MIR, and the pumping of two OPA channels in the near and MIR spectral regions. The CEP-stable white-light seed source driven by 650 µJ pulses is described in the section 2. The white-light source is then separated into two OPCPA channels by using a dichroic mirror (DM). The remaining pump of the CEP-stable WLC is suppressed by employing dichroic mirrors before the OPCPA stages in the NIR range. The MIR channel (consisting of DOPA1, DOPA2 and DOPA3) is pumped directly with the regenerative amplifier while the NIR channel (consisting of NOPA1 and NOPA2) is pumped by the second harmonic of the pump (SHG2). The frequency doubling is achieved inside a 2-mm-long LBO crystal resulting in 41% conversion efficiency. Figure 6 shows the efficiency and energy curves of the frequency doubling stage and the beam profile in the farfield, measured at the highest SHG of 0.93 mJ. The M 2 of the beam is measured to be 1.2 and 1.3 for the x and y-axes, respectively. The NIR non-collinear OPCPA (NOPA) stages are pumped with 5.7 μJ (NOPA1) and 132 μJ (NOPA2) pulse energies. The angle between the pump and the seed beams is kept at 2.3° to satisfy the non-collinear broadband phasematching condition. The CEP-stable seed is amplified to 0.42 µJ at the end of the first stage (NOPA1). The signal energy is then amplified to 24 µJ in the second stage (NOPA2) with a corresponding pump-to-signal conversion efficiency of 18%. In both stages 3-mm long BBO crystals are used. The cut angle of the crystals is 24.2° allowing type-I phase matching. The output signal energy in the first stage is kept below 0.5 µJ to avoid superfluorescence originating in the first stage, which would be amplified in the second stage [22]. The superfluorescence in the second stage is measured to be well below the 1-% level when blocking the seed in the first stage. Figure 7(a) and (b) show the amplified spectra in NOPA1 and NOPA2 stages, respectively. The amplified spectrum extends from 640 nm to 940 nm in NOPA1, while the spectrum covers a slightly larger spectrum between 640 nm and 960 nm in NOPA2 supporting 7.7-fs (FWHM) pulses. The reason for the broader bandwidth is the slight detuning of the phase-matching angle of the NOPA2 leading to the amplification of the remaining unamplified spectrum in NOPA1 in the longer wavelength region. The dispersion of the amplified pulses is compensated by bouncing 5 times on double-chirped mirror (DCM) pairs originally designed for octave-spanning Ti:sapphire laser oscillators [38]. The MIR degenerate OPA (DOPA) stages are pumped at 1030 nm. In all DOPA stages, 4mm long BBO crystals are used. The crystals are cut at the angle of 21.8° allowing broadband phase matching centered around 2.1 µm in type-I phase-matching configuration. The first DOPA stage (DOPA1) is pumped with 95-µJ pulses and results in 1-µJ amplified pulses extending from 1730 to 2500 nm as shown in Fig. 7(a). For adaptive and precise dispersion control, an acousto-optic programmable dispersive filter (AOPDF) is implemented after DOPA1, followed by a 2-mm YAG plate, which provides negative dispersion to increase the overlap of the pump and signal pulses in time for the remaining amplification stages. In the AOPDF, a 45-mm long TeO 2 crystal (Fastlite DAZZLER THR45 1450-3000 with jitter-free option) is used. The AOPDF has a limited transmission of 40% under full load of the acoustic wave into the crystal for 500 nm bandwidth. In our case, the AOPDF is operated below the highest possible efficiency due to the required dispersion to compress the pulses. In order to compensate the losses and boost the energy above the energy of DOPA1, another DOPA stage (DOPA2) is implemented. Only 35-µJ pulses are used to pump DOPA2 resulting in 2-µJ pulses covering the range between 1820 and 2460 nm (Fig. 7(b)). This narrowing of the spectrum after DOPA2 can be attributed to spatial chirp in the diffracted beam from the AOPDF [39]. The third stage DOPA (DOPA3) is implemented to boost the energy of the signal to 16 µJ with the remaining pump energy of 570 µJ. The spectrum is extending over the range 1840-2460 nm and supports 28.4-fs pulses as shown in Fig. 7(b). Even if the spectral components above 2200 nm after DOPA2 are low in energy, they are compensated in the third stage by slightly detuning the phase matching angle. Then the pulses are compressed by two anti-reflection-coated ZnSe wedges with insertion length of 1.54 mm. The superfluorescence in the third stage is measured to be well below 1-% level while the seed is blocked in the first stage.  Figures 8(a) and (b) show the calculated intensity profile of the synthesized pulse, assuming a flat spectral phase and a pulse energy ratio of 0.73 (DOPA/NOPA) and 0.10, respectively. As can be seen from both figures, by simply tuning simply the intensity ratios between the two channels, it is possible to modify the wing contrast of the pulse profile. The experimentally available pulse energy ratio between two channels after the compression is 0.73, which corresponds to the one shown in Fig. 8(a). The central peak of the pulse has 2-fs pulse width (FHWM), while together with the wings the pulse width increases to ~8.5 fs for both cases.

Spectro-temporal characterization
The spectro-temporal characterization of the pulses for both channels is performed by using SHG frequency resolved optical gating (FROG). As a nonlinear medium for SHG, a 10-µmthick BBO crystal is used for NIR channel characterization. For the MIR channel, we used a 100-µm thick BBO crystal, which is thin enough to support the pulse bandwidth for their characterization. Figures 9(a) and 9(b) show the measured FROG traces of the compressed output of the NOPA channel for the time interval of ± 100 fs. The resulting FROG error is 0.81%. As shown in Fig. 9(c), the measured and retrieved spectra are matching well except in the lower wavelength region, where the spectral phase is not compensated. That is due to the bandwidth-limitation (below 700 nm) of the group-delay characteristics of the DCMs available during the experiments. Figure 9(d) shows the corresponding retrieved pulse profile and temporal phase. The pulses are compressed down to 12.1 fs (FWHM), while the TL pulse duration is 7.7 fs. The compression can be further improved by employing adaptive dispersion management techniques such as 4-f pulse shaping with spatial light modulators or deformable mirrors [40]or AOPDFs [3], where one can tune arbitrarily the spectral phase. The FROG results are crosschecked carefully by comparing the FROG measurements with DCM several configurations. Due to limited aperture (0.5 inch) of the available DCM pairs, several curved silver mirrors are used to image the beam, resulting in a reduction of the usable pulse energy from 24 to 22 µJ. In order to estimate the dispersion originated in WLC2, the dispersion of each optical element and propagation in air are estimated by using the corresponding Sellmeier equations and subtracted from the residual dispersion retrieved from the FROG measurement in NIR. Hence, the estimated spectral phase due to WLC corresponds to approximately 1.5 mm propagation in YAG. Table 1 summarizes the group-delay dispersion (GDD) and third-order dispersion (TOD) of the materials and pulse shaper in the MIR DOPA channel. In the dispersion calculation, 1.5 mm propagation in YAG during the WLC generation is taken into account. The main dispersion contributors are the BBO crystals (OPCPA crystals) and the TeO 2 crystal of the AOPDF. During the amplification, the GDD and TOD are kept negative and then compensated with positive GDD and TOD introduced by 1.54 mm ZnSe wedges. As can be seen from Table 1, the GDD is completely compensated while a small amount of TOD remains which leads to slightly chirped pulses.  Figure 10 shows the spectro-temporal characterization of DOPA3 after 1.54 mm propagation in ZnSe for the time interval of ± 150 fs. As can be seen from the figure, the measured (a) and the retrieved FROG traces (b) match quite well (with a FROG error of 0.16%) as well as the retrieved and measured spectra (see Fig. 10(c)). The phase is retrieved without any marginal correction. The spectral and temporal phases of the pulse are almost flat resulting in 31.1 fs (FWHM) pulse duration, close to the TL pulse duration of 28.4 fs (Figs. 10(c) and (d)).

Conclusions and outlook
In summary, we demonstrated a passively CEP-stable, two-octave-wide, superfluorescencefree, two-channel pulsed light source with ~40 µJ energy at 1 kHz repetition rate, which can be used as a seed source for a mJ-level optical parametric synthesizer. We also showed the compression of each channel, demonstrating that the spectral phase is well behaved. The NIR channel is compressed down to 12.1 fs, while the MIR channel is compressed to 31.1 fs. The scheme can be further improved by implementing additional channels to enhance the bandwidth, hence shortening the supported pulses. Our current aim is to scale up the energy to the mJ-level with further OPCPA stages employing cryogenically cooled high-energy Ybbased pump amplifiers and combine them coherently to obtain sub-cycle waveforms. The demonstrated system is an ideal seed source for a two-octave-wide optical waveform synthesizer with both high-energy and high repetition rate, which will allow us to get TW peak power at high repetition rate. This unique source will allow for the exploration of new regimes of light-matter interaction both with solids and with gases.

Funding
Excellence Cluster "The Hamburg Centre for Ultrafast Imaging-Structure, Dynamics and Control of Matter at the Atomic Scale" of the Deutsche Forschungsgemeinschaft and the European Research Council by ERC-Synergy grant AXSIS with grant no. 609920. Dr. A.-L. Calendron acknowledges a grant from the Helmholtz Association.