Optimizing Aperture Geometry in THz-TDS for Accurate Spectroscopy of Quantum Materials

TL;DR

This study systematically quantifies how circular aperture geometry in a free-space THz-TDS setup distorts transmitted signals, particularly attenuating low-frequency components when apertures are small. By combining time- and frequency-domain measurements with a dielectric-slab transmission model, the authors extract effective optical parameters and demonstrate how aperture size biases parameter retrieval, including in a representative quantum material. They show that aperture thickness has negligible impact within the tested range, validating the slab-model assumption, and provide a practical method to estimate the beam waist from transmitted intensity. The findings yield actionable guidelines for aperture selection and beam characterization to preserve low-frequency information essential for accurate spectroscopy of quantum materials.

Abstract

Terahertz time-domain spectroscopy (THz-TDS) provides a powerful platform for investigating low-energy excitations in quantum materials. Because these materials are often limited in size, experimental setups typically rely on tightly focused beams and metallic holders with small apertures. In this work, we perform a systematic study of how aperture geometry influences THz signal transmission in a standard free-space configuration. By analyzing time- and frequency-domain data for circular apertures of varying diameters and thicknesses, we quantify the spatial and spectral filtering effects imposed by aperture size. We show that small apertures progressively attenuate low-frequency components of the transmitted signal, while higher-frequency content remains comparatively unaffected. These effects become especially significant for apertures smaller than typical THz beam waists, resulting in amplitude suppression and phase distortions that compromise the accuracy of frequency-domain analysis and optical parameter retrieval. To validate these observations, additional measurements were performed on a representative quantum material, confirming the practical relevance of the identified aperture effects. The transmitted intensity as a function of aperture diameter also provides a straightforward method for estimating the beam waist at the focus. In contrast, standard aperture thicknesses do not introduce measurable distortions, confirming the adequacy of treating thick, non-resonant apertures as dielectric slabs. These findings establish practical guidelines for aperture selection in THz-TDS and underscore the importance of preserving low-frequency response for reliable characterization of quantum materials.

Figures (7)

• Figure 1: Schematic diagram of the THz-TDS setup. Infrared laser pulses are split into two optical paths: one directed to a PCA emitter, which generates broadband THz radiation, and the other routed through a mechanical delay line for temporal scanning. The THz pulse passes through the sample region---where aperture holders are positioned---and is detected by a second PCA. The transmitted electric field is recorded as a function of time.
• Figure 2: (a) Time-domain electric field pulses acquired via THz-TDS for different circular aperture diameters $D$, along with a reference measurement without an aperture (black). A systematic reduction in pulse amplitude is observed with decreasing aperture size. (b) Corresponding amplitude (solid) and phase (dashed) spectra obtained via Fourier transform. Smaller apertures cause substantial attenuation of low-frequency components and induce phase errors. The shaded region highlights the spectral range from 0.40.8.
• Figure 3: Transmitted intensity as a function of aperture diameter. The experimental points (orange squares) represent the squared peak electric field amplitudes obtained from time-domain THz measurements, serving as a proxy for relative transmitted power. The solid black line is a fit based on the analytical model for Gaussian beam power transmission through a circular aperture [Eq. \ref{['eq:power']}]. The inset illustrates the Gaussian beam profile near the focal plane, with the beam waist $w_0$ indicated, along with its relation to the full width at half maximum (FWHM). The fit yields $w_0 = \qty{2.36(21)}{\mm}$ and a corresponding FWHM of 2.78(25).
• Figure 4: Transmitted spectral intensity as a function of frequency and aperture diameter. The colormap is derived from Fourier transforms of the time-domain signals [Fig. \ref{['fig2']}]. As the aperture diameter decreases, low-frequency components are progressively attenuated, while high-frequency components remain comparatively unaffected. Two dashed green lines are overlaid as visual guides: the left-hand curve traces the shifting low-frequency boundary of the transmitted spectrum, and the right-hand curve marks the nearly constant high-frequency edge. These features reflect the frequency-dependent spatial confinement of the focused THz beam and the corresponding filtering effect imposed by the apertures.
• Figure 5: Extracted optical parameters as a function of frequency for different aperture diameters. (a) Transmittance, defined as the squared modulus of the complex transmission coefficient. (b) Real refractive index and (c) extinction coefficient, both retrieved by analytically inverting the transmission model described in the Methods section. For large apertures, the extracted values converge toward the expected free-space limits ($n = 1$, $\kappa = 0$). As the diameter decreases, both parameters deviate significantly, particularly at low frequencies, reflecting the influence of beam truncation and spectral distortion on parameter retrieval in THz-TDS.