Terahertz Time-Domain Spectroscopy for the Characterization of Dielectrics and Foams Using Amplitude and Phase in Reflection Mode

Abstract

Amplitude-only measurements have recently been proposed to avoid phase sensitivity issues in terahertz (THz) time-domain spectroscopy (TDS) in reflection mode. These methods, however, are typically applied to open-boundary setups and may fail in scenarios where the Fabry–Perot interference is weak or absent. Here, we show that phase information can be essential in the characterization of low-index materials, such as dielectric foams. We address this limitation by focusing on a grounded Fabry–Perot configuration (i.e., a reflective backplane geometry), which enhances spectral features and allows for full exploitation of both amplitude and phase information. To this end, two effective protocols are developed here to accurately determine the complex permittivity of dielectric materials by exploiting both the amplitude and the phase of THz-TDS measurements. The first method fits directly the physical parameters of established permittivity dispersion models describing the unknown material by minimizing the weighted Euclidean norms of the amplitude and phase errors. This convex fitting approach improves convergence stability, especially when interference fringes are weak. The second method first estimates the optimal real permittivity values from the phase measurements, and then the loss tangent from the amplitude measurements. These mathematical values are then fitted through a suitable permittivity model to ensure causality. Both techniques are tested against materials with different dielectric properties, highlighting the case scenarios in which phase measurements significantly improve the accuracy of material dielectric characterization.