Hardware-based feedback loop

After assessing the slow software feedback loop, for high frequency timing jitter a faster delay stabilization proved to be desirable. There we no longer use a commercial spectrometer read out in software, but need to build up a fast optical detection system that can ideally yield a single-shot directional error signal.

Since photo diodes are available with large bandwidths, intensity-based measurements like the BOC can be advantageous in case of high regulation bandwidths, achievable by acousto-optic or electro-optic modulators. However our sampling rate is limited to the repetition rate of the laser at 3 kHz. While this is still too fast for a standard CCD-array to be read out for each shot, a position sensitive detector (PSD, or lateral effect detector) can be read out continuously and offers enough bandwidth (typicallyτRC ≈ 70µs, depending on the detector size and read-out electronics) for

our application. As its outputs allow the fast calculation of the center of mass independent of the beam shape of the intensity on the detector, this is ideal for our application. Also the spatial resolution can be on the order of sub-µm (depending on the noise in the associated electronics and on the optical signal itself), which clearly trumps a CCD array. However, the sensitivity is somewhat lower compared to CCDs or photo diodes and the position is calculated by normalizing to the integrated intensity, making it susceptible to intensity fluctuations.

4.3 Optical synchronization 63 Piezo translation stage stepper motor dela y t SFG g_rating

PSD

Aligna 4D

Aligna 4D

PID

uController

SF57 Ti:Sa multipass amplifier

Ti:Sa oscillator Yb:YAG regenerative amplifier

Figure 4.10: Setup of the hardware-based synchronization

As a diffraction grating can resolve our spectrally encoded delay information in space, the SFG setup only needs to be upgraded with a spectrometer-like detection setup. Imaging provides the frequency-space mapping and the strong chirp of the seed pulse achieves the time-frequency mapping, resulting in time-space mapping of temporal delay between pump and seed. The center of mass then yields this delay and provides a direct error signal.

This is realized in the lab by splitting small fractions of pump (10 mW) and seed amplifier (2 mW). Next, the seed pulses are stretched using a AR-coated block of SF57 glass. This proved to be advantageous, as a grating stretcher can easily introduce angular dispersion, if not aligned properly. Spatial chirp in the focus then showed to be problematic in the frequency resolved SF stage. As the spot sizes are rather large to avoid B-integral issues (see section 3.2.1), telescope arrangements are used for optimizing the intensity for the SFG process. Both collimated and parallel beams are then sent trough a f = 100 mm plano-convex lens, to overlap their foci in a 1 mm long BBO crystal, cut atθ= 29 deg. As the telescopes allowed close matching of the spot sizes in the crystal (approximately 90µm), the sum frequency at 450 nm output is rather high at 0.2 mW, especially given the stretched seed. While the fundamental beams are blocked, the SF is collimated and sent onto a diffraction grating (1200 lines/mm) that showed a diffraction efficiency of 45%. The angular dispersion is then translated to spatial chirp by use of another lens that focuses on the PSD (Hamamatsu S599-01). This results in a very elliptical intensity profile, where beam position along the fast axis (xPS D in the following) indicates the pump-seed

64 4. Synchronizing OPCPA delayτaccording to dxPSD dτ = ∂xPSD ∂λSF |{z} I ∂λSF ∂ωseed |{z} II dωseed dτ |{z} III (4.2)

where I is given by the imaging system of lens and grating, II by the wavelength of the pump laser and III is proportional to the chirp of the seed pulse. I and III allow tuning of the system for higher resolution or longer temporal range. Limiting however is the size (4 mm) and the signal-to-noise ratio (SNR) of the PSD, as well as the finite pump pulse duration.

While a larger stretching factor III increases the sensitivity, it limits the temporal overlap and therefore also the generated SF signal. This then decreases the SNR (and consequently the resolution) of the PSD. A similar argument forI can be made.

In the perpendicular direction yPS D, the jitter from beam pointing amounted to 0.7µm, which

is equivalent to 6 fs for our configuration. This is larger than the theoretical (no sample & hold noise) resolution of the PSD (0.2µm). A similar beam pointing is also expected along xPS D,

leading to some cross talk with the beam stabilization in our jitter stabilization. Equation (4.2) provides the solution if this cross talk is too severe. Note that beam pointing here does not necessarily mean the focus position is moving (which could be improved usingI), but the PSD could vibrate as well.

The refined setup is shown in fig. 4.10. To minimize the engineering effort, a commercial beam stabilization (Aligna 4D, TEM Messtechnik Hannover) like in section 3.2.3 was employed. In- stead of four spatial dimensions, it now stabilizes one temporal (appearing as a spatial) dimension in the following manner: The PSD signals are fed to sample & hold stages (S&H), before the position is calculated. Given this error signal, a PID controller tries to center the delay by mov- ing a fast piezo stage (nanoX 200 with 30V300 amplifier, open-loop, Piezosystems Jena, 240µm range). A micro-controller uses a linear translation stage (LIMES 84-120-HMS, OWIS) to center the piezo voltage at about 75 V for better linearity and range. This way the piezo stage (with a resonance frequency of 500 Hz at a retro-reflector weight of 40 g) can compensate for fast jitter, while the slower stepper motor stage is ensuring long-term temporal overlap.

Measuring the jitter with this solution yielded the data shown in fig. 4.11 and fig. 4.12 in temporal and frequency domain, respectively. While the free-running jitter amounted toσ= 127 fs (shown in blue), the stepper motor stage alone could only compensate for frequency components below 1 Hz, similar to section 4.3.4, which resulted in comparableσ = 45 fs. Using the faster PID- regulated piezo stage, the effective regulation bandwidth was increased by more than one order of magnitude, as shown in fig. 4.12. This enables jitter compensation down to 24 fs, a small fraction of the pump pulse duration. The right axis of fig. 4.12 shows the integrated timing jitter, given by σ = pP

f Pf, wherePf is the power spectral density plotted on the left axis. We see

that the piezo can limit the jitter below 220 Hz to around 10 fs. However, there we experience vibrations on the optical table. Devices like turbomolecular pumps work in this frequency range and increase the timing jitter significantly. It should be considered, that the significant shot- to-shot jitter of 15 fs derived from the data shown in fig. 4.11, is located beyond the Nyquist

4.3 Optical synchronization 65

Figure 4.11: Temporal jitter as measured from the PSD error signal. Curves are offset by 100 fs for better visibility.

frequency and is mirrored onto lower frequency components (aliasing). The strong perturbation at 220 Hz could therefore be located at 2780 Hz (or further above) and be of electro-magnetic origin. In fact, in chapter 6 an elevated noise floor was observed in this frequency range. For the measurement of fig. 4.11, this was already reduced by a simple home-made low-pass filter at 10 kHz.

When tuning the PID loop more aggressively (less I and more P), the high-frequency components can even increase, since the perturbations drive the loop into oscillation or even resonance. Also the limited sturdiness (due to weight limitations) of the retro reflector mounted on the piezo stage can lead to oscillations in the regulation loop. This may even be fostered by cross-talk, since coupling of the error signal to beam pointing or intensity is to be expected to a certain extent in our detection scheme.