Accurate Characterization of Resonant Samples in the Terahertz Regime Through a Technique Combining Time-Domain Spectroscopy and Kramers–Kronig Analysis

We propose and experimentally demonstrate an original method, combining terahertz time-domain spectroscopy (THz-TDS) and Kramers-Kronig relations (KKR), in order to characterize in transmission materials exhibiting high absorption peaks. At these frequencies, the modulus of transmittance of a sample could be null, or at least smaller than the detector noise, and consequently the signal phase is lost, not only at the peak frequency, but also at higher frequencies. Thus, for these high frequencies, the value of the refractive index estimated from the measured THz-TDS data could be strongly erroneous. Using an optimized version of KKR, namely singly subtractive KKR, we are able to retrieve the phase of the THz transmittance over the whole studied bandwidth and thus to correct the THz-TDS data to precisely determine the refractive index as well as the absorption coefficient of the material over almost the whole THz range.