## 6 Probe Compression  
The detection bandwidth of electro-optic sampling and the temporal resolution of the resulting measurement are limited by the finite duration of the probing pulse. The finite nature of the probe pulse's duration results in a frequency response [43]  
\[F(\Omega)=A_{opt}(\Omega)\chi^{(2)}(\Omega)\Delta\Phi(\Omega) \tag{1}\]  
where  
\[A_{opt}(\Omega) =\frac{\sqrt{\pi}}{\tau_{probe}}exp\left(-\frac{\Omega^{2}\tau_{ probe}^{2}}{4}\right) \tag{2a}\] \[\Delta\Phi =\frac{exp(-i\Delta k(\Omega)L_{det})-1}{i\Delta k(\Omega)} \tag{2b}\]  
are the autocorrelation of the Gaussian probe pulse with duration \(\tau_{probe}\) and the frequency-dependent mismatch factor, respectively. Here, \(\Omega\) is the THz frequency, \(\chi^{(2)}\) is the second-order susceptibility of the electro-optic crystal, \(L_{det}\) is the crystal thickness, and \(\Delta k=k(\omega_{probe})+k(\Omega)-\hat{k}(\omega_{probe}-\Omega)\) is the mismatch term between the probe field, the THz field, and the frequency-difference wave vectors [43]. \(A_{opt}\) acts as a low-pass filter whose cutoff frequency depends on the probe pulse duration \(\tau_{probe}\). As such, shorter probe pulse durations result in a broader passband, thus increasing the detection bandwidth. It is therefore desirable to compress the probe pulse to achieve an optimal detection bandwidth, increasing the usable spectrum of the THz-TDS system. While this has been carried out in previous experiments using, e.g., hollow-core fibers [15] or multi-pass cell compressor [32], we decided to generate a compressed probe pulse using a two-stage compression technique allowed by the resources already available in the lab. First, an optical parametric amplifier (OPA; Orpheus-F, Light Conversion) is used to generate 2060 nm light; later, a second harmonic generation in a BBO crystal up-converts it back to 1030 nm. Our OPA generates a 2060 nm idler beam with a FWHM bandwidth of around 123 nm, which, under transform-limited conditions, results in a pulse duration of \(\simeq\)50 fs. Unfortunately, the OPA's idler output is not transform-limited but is instead chirped upon emission from the OPA system. To compensate for this, we introduced two Zinc Selenide (ZnSe) windows in the beam path,angling these to change the path length through the windows until optimal dispersion compensation was reached. The beam is then focused into a 0.5 mm thick BBO crystal, and the 2060 nm pump light is separated from the generated 1030 nm light using suitably coated separators (Layertec, Mellingen, Germany). We judge when optimal dispersion compensation is achieved by observing the power of the 1030 nm generated. The angle of the ZnSe windows is tuned to maximum SHG output is achieved.  
Following generation, the temporally compressed 1030 nm pulse's duration is measured using the frequency-resolved optical gating technique (FROG). This measurement resulted in a pulse duration of \(\simeq\)56 fs, showing that we have achieved a compression ratio of \(\simeq\)3. The results of the FROG pulse measurement are shown in Figure 8. The FWHM bandwidth of the pulse is \(\simeq\)29 nm, corresponding to a transform-limited pulse duration of 53 fs. This confirms that the compressed pulse is indeed very close to the transform limit.  
THz measurements taken using this compressed pulse to probe the THz show finer temporal resolution and a wider detected THz bandwidth when compared to traces taken with an uncompressed probe (Figure 9). From the increased THz bandwidth in the measurement with the compressed probe pulse it is clear that a probe duration of 245 fs is not sufficient to detect the full generated THz spectrum. Also shown are results from simulations performed by following the method described in [43], confirming the relationship found in our experiments.  
Other experimental parameters were kept identical in both measurements. Improvements in temporal resolution are desirable in spectroscopic applications as they allow for the detection of spectral features across a broader bandwidth.