## 4 Beamline Design  
One of the main technical challenges associated with a THz-TDS driven by a medium-energy, high-power pump laser is the rejection of the optical pump from the generated THz beam-path. While custom-designed parabolic mirrors associated with geometrical filtering and further filtering with paper foils, as carried out, e.g., [32], provide a potential solution to the problem, we sought to build our THz-TDS with off-the-shelf components--specifically 2-inch-diameter off-axis parabolic mirrors (Thorlabs, Newton, NJ, USA) and flat copper mirrors (LBP-Optics, Biggleswade, UK) and only minimal customization, with the two-fold objective of removing the optical pump while preserving as much as possible the generated THz power. We designed the THz-TDS beamline to allow for geometrical pump rejection with limited THz losses. Given our pump beam's size and the results of knife-edge measurements of the generated THz beam, we concluded that a propagation distance of \(\simeq\)450 mm would be required to expand the THz beam to a diameter of 50.8 mm, filling the aperture of the parabolic mirrors. The best matching off-the-shelf product we could source was a \(15^{\circ}\) off-axis parabolic mirror with an equivalent focal length of \(15^{\prime\prime}\) (381 mm). Figure 2: Generation efficiency for increasing pump power. The optimal condition in our experiment was reached with a 3.5 mm \(1/e^{2}\) diameter pump beam (red curve), for which the conversion efficiency was saturated at 30 W, the maximum laser power available for pumping the rectification process. As a comparison, we show that the conversion efficiency saturates at lower powers for smaller beam sizes (blue and green data). We numerically investigated the effect of such a choice on the focused THz beam quality, resulting in the design shown in Figure 3. The expected beam size for a 1.5 THz beam is \(330\times 316\,\mathrm{\SIUnitSymbolMicro m}\) in the detection plane, with phase profile variations of a few tenths of a radian across the beam, confirmed by physical optics propagation simulations performed on the beamline design and shown in Figure 4.  
The design of the beamline was completed using Zemax OpticStudio (2022 R2.02), allowing us to design and optimize the layout. This enabled us to confirm the expected pump beam size at the point of incidence with the pump rejection mirror, informing the required diameter of the rejection hole, as well as assessing the phase curvature in the EO detection plane. OpticStudio was also used to generate Figure 4 using the physical optics propagation (POP) simulation engine. This simulation method performs diffraction calculations to sequentially propagate the wavefront through the optical system surface by surface, taking into account the coherent nature of the propagating light, diffraction from small or fine features such as mirror edges, and wavefront phase. A Gaussian beam source with the same divergence of the experimental THz beam (\(\sim\)6.36\({}^{\circ}\)) was defined, and POP simulations were run with \(1024\times 1024\) resolution; the results shown in Figure 4 are zoomed in 2\(\times\) for clearer presentation. Our beamline also utilizes four off-axis parabolic mirrors as well as an additional flat THz mirror. The first mirror is the 15\({}^{\circ}\) off-axis parabolic mentioned before, which allows the THz beam to diverge and fill the 50.8 mm aperture of the parabolic mirrors. This mirror collimates the THz beam and focuses the pump beam. The second mirror is a flat mirror  
Figure 4: Simulated intensity (**a**) and phase (**b**) profiles of the THz beam in the plane of the EO crystal. The beam measures \(330\times 316\,\mathrm{\SIUnitSymbolMicro m}\). Figure 3: A schematic of our low-loss THz-TDS beamline utilizing a long focal length parabolic and a flat pump rejection mirror. with a 1 mm hole drilled in the center. This hole allows for the rejection of the tightly focused pump beam with minimal clipping; a water-cooled beam dump safely disposes of the pump light.