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wavelength (nm) Spectrograms −1000 −500 0 500 1000 520 540 560 580 600 620 0 0.2 0.4 0.6 0.8 1 01500 2000 2500 0.5 1 Wavelength (nm)

Intensity (arb. un.)

Retrieved spectrum 1500 2000 25000 5 10 Phase (rad) −4000 −200 0 200 400 0.2 0.4 0.6 0.8 1 Time (fs)

Intensity (arb. un.)

Retrieved pulse, FWHM = 13.3 fs

Figure 5.6: SFG XFROG spectrogram and retrieval of the compressed pulse out of the second amplification stage.

stage, the behavior improved, which leads to the suspicion that the next stage act as a spatial filter for the seed. In both the near-field (shown on the right of fig. 7.3) and far-field profiles (fig. 6.2) no irregularities could be observed. However, a more homogeneous aperture crystal is to be wished for in the future, as it would allow power scaling using the remaining ≈ 50 W of pump light.

5.4

Compression

As mentioned before, the compression of the pulses is performed with 1.5 mm bulk silicon. Using the existing XFROG setup, a retrieved spectrogram yielded the residual spectral phase. This was then feed back to the AOPDF for complete compression. Already the very first try (to the surprise of the author) compressed the pulse, as shown in the spectrograms of fig. 5.6. However, the elevated background is obvious. Later, the source was found in the insufficiently smoothed feedback files, that led to a slightly distorted acoustic wave in the AOPDF. This wave then generated a background of satellite pulses all over the diffracted spectrum. As the XFROG technique shows linear response (when based on SFG), it is well suited for detecting such issues. Better feedback (fitting polynomials to the retrieved phase, as shown in fig. 5.8) yielded a much improved background later.

Apart from the AOPDF-induced distortions, the retrieved spectrum shows good agreement with the amplified on-axis spectrum and the retrieved pulse duration is 13.3 fs, which is just below two cycles. The transform limit for the spectrum is calculated to be 12.4 fs.

Despite being close to that limit, the spectrogram shows an S-shape, because the reference pulse is not transform limited itself. Also the delay path for the XFROG was very long and therefore, a compressed pulse directly after the compressor is very hard to achieve. Because of some

78 5. Building an infrared few-cycle OPCPA Time (fs) wavelength (nm) Spectrograms −400 −200 0 200 400 700 800 900 1000 1100 1200 1300 0 0.2 0.4 0.6 0.8 1 01500 2000 2500 3000 0.5 1 Wavelength (nm)

Intensity (arb. un.)

Retrieved spectrum 1500 2000 2500 30000 2 4 Phase (rad) −100 0 100 0 0.2 0.4 0.6 0.8 1 Time (fs)

Intensity (arb. un.)

Retrieved pulse, FWHM = 13.8 fs

Figure 5.7: SHG FROG of the compressed OPCPA pulses.

uncertainty in the reference (through dispersion of air, etc.) also limits the ability to characterize the very shortest pulses, another (self-referenced) pulse characterization method was needed. The transient grating method was evaluated, but given up due to the weak IR signal, that was covered by too much stronger NIR stray light on the detectors. Also no IR viewer could be used to find the diffracted signal.

Third harmonic generation (THG) on a surface proved to be hampered by the early onset of con- tinuum generation in the material. Since this artificially shortened the pulse to be characterized in the THG FROG the signal was very limited and only a small fraction of the pulse energy could be used, resulting in very long scan times. Also a third harmonic process is less suited for pulses with bad contrast (or weak spectral wings), as its SNR and dynamic range are low (using standard linear detectors).

To prevent the onset of continuum generation, extremely thin samples of SiO2 were used that

showed surprisingly strong second harmonic generation. Also the supported bandwidth seemed sufficient. Therefore, a second harmonic FROG was used as pulse characterization method. It needs to be mentioned that the second harmonic leads to a problem with detectors, as the frequency-doubled spectrum overlaps only partly with the working bandwidth of InGaAs and silicon detectors respectively. Therefore ideally, both detectors are needed. However, with the limited output intensity of our process, we needed to couple inside a spectrometer slit (or at least its delivery fiber). No method was found to calibrate two spectrometers coupled to one (bifurcated) fiber in a reliable fashion. While the solution of this problem (eventually maybe using piezo-driven fiber switches) is work in progress, for now an InGaAs spectrometer ranging from 800-1700 nm was used, which did cut the blue part of our spectrum slightly and did not allow it to be fully compressed. This results in slightly longer pulses for now.

In the SH FROG the effect of delay smear [138] was minimized by using as large as possible spot sizes with a significant separation on the focusing parabola. The result of the SH FROG is shown

5.4 Compression 79

in fig. 5.7. The retrieved spectrum is less modulated than in fig. 5.6, which can be attributed to the corrected AOPDF feedback, preserving the good contrast of the seed pulse. The retrieved pulse duration is 13.8 fs and 83% of the energy is contained in the main pulse. Since the setup is much smaller than the XFROG equivalent, we can provide a short pulse for the experiment of chapter 6. However, with a part of the spectrum cut, the retrieval of this unphysical pulse is not excellent any more. Still, it indicates a pulse duration below two optical cycles.

Most interesting is the dip in the spectrum, here at longer wavelengths compared to fig. 5.5, owing to slightly different second harmonic phase-matching. The reconstructed phase shows a discontinuity at the same position, both can be explained by a cascaded second-order effect. The generated signal and idler are degenerate in the OPA, so both signal and idler frequency

ωidler = ωsignal = ω and the respective polarizations are equal. This results in ωpump = 2ω,

and since we use QPM in the two stages described in section 5.3, the polarization of the pump is also equal. So not only the process of OPA (2ω− ω = ω) is phase-matched, but also SHG (ω+ω=2ω), following eq. (1.19). As both effects can occur at the same time, they are cascaded. The SH of the signal (or SH of the idler, or SFG between both) has the same photon energy and polarization as the pump. These back-converted photons then pump the OPA process, so signal and idler are regenerated. As the combined processes mimic degenerate four-wave mixing (it may be called SPM or XPM here, but is really degenerate) (ω = ω+ ω −ω), this leads to a phase modulation according to eq. (1.29), in the frequency domain1_{. This e}ff_{ect (also called}

self-diffraction in the literature [26]) is in fact a limitation for short pump pulses using QPM at degeneracy. A simulation by Nicholas Karpowicz in appendix D illustrates the process.

With more chirped signal and idler pulses (longer pump pulses), this behavior was not observed before in a similar setup using identical phase-matching [46]. Also the small phase-mismatch using short crystals in a collinear geometry is to blame, that will always lead to some second harmonic inside the amplified spectrum. In fact, by using different PPLN gratings (periods), we could observe a shift of the dip in the spectrum on the right of fig. 5.5.

In a non-collinear geometry (NOPA), idler and signal travel in different directions, so a spatial walk-offis given. Additionally, both can be adjusted to not phase-match SHG (as discussed in [15]). However, for amplified spectra close to one octave SFG between idler and signal can still lead to unwanted interference inside the amplified spectrum, even taking these precautions [111]. Also the bandwidth and gain of QPM is unrivaled by angle phase-matching for our wave- length regime (see section 1.2.2), so longer pump pulses in fact seem like the only option to suppress these phase modulations. As an intermediate measure, a strong depletion of the pump was avoided, to limit the effective crystal length for parasitic second order processes.

Note how (spectral and CE) phase modulation can also be caused by elevated SPM (because of nearby TPA) in the silicon compressor. Using telescopes before and after the compressor to expand the beam, this was avoided as much as possible.

The modulated phase of the spectrum does limit the compressibility, since the transform limit

80 5. Building an infrared few-cycle OPCPA 1500 2000 2500 3000 -6 -4 -2 0 2 4 6 8 10 phase (r ad) wavelength (nm) 1500 2000 2500 30000 1 2 3 4 5 in tensit y (ar b.un.)

applied measured phase retrieved phase

Figure 5.8: The (retrieved) additional phase applied to the AOPDF in order to compress, after analytically compensating for the large bulk dispersion.

of the reconstructed spectrum is 11.7 fs. This is shorter than from the XFROG measurement, because more red components are retrieved, which cannot be measured by the exInGaAs spec- trometer used for fig. 5.5 and do also not appear in the measurement of fig. 5.6. However, since we cannot check this spectral range on a daily basis, there may just not be any amplification from day to day. Also these components are weak and do not significantly shorten the pulse.

Note that the compressed pulse shown in fig. 5.7 does not posses a completely flat phase, as the AOPDF only allows one to modulate the phase before amplification. Nonlinear effects (like those mentioned above) can then modulate this phase and lead to a longer pulse. Also repeated feedback did not shorten the pulses any more. As no suitable high-energy adaptive compression method with high efficiency is known to the author, these nonlinear effects rather have to be suppressed to achieve even better compression.

The phase that was applied to compress the pulse was in fact very slight. Analytically calculated phases did already compress the pulse to a large extent, while a single FROG retrieval (and fitting of the retrieved spectral phase using low-order polynomials, shown red in fig. 5.8) shortened it to the above mentioned pulse durations.

As a side-note, efficient compression of the pulses could be observed by eye when using small (unexpanded) beam diameters on the silicon compressor. While being opaque up to 1050 nm (see appendix B.3), the bulk silicon did emit visible (broadband) red light, that could be identi- fied as the third harmonic (TH). Since the absorption coefficient of silicon at 700 nm and room temperature isα = 1890 cm−1 _{[43], the TH must be generated in the last ≈ 5µm of the back}

surface. The dispersion of this thickness leads to less than 3 fs of pulse broadening, so a strong red light did indicate a well-compressed pulse. Also propagation in air lead to build-up of TH for small beams. Unless helpful in alignment of optical setups (like the SH FROG used in this section), the beam was usually expanded to avoid this behavior in chapter 6 and chapter 7. The