Tutorial: accurate determination of refractive index and absorption coefficient in terahertz time-domain spectroscopy

Abstract

This tutorial presents an up-to-date methodology primarily for determining the refractive index and absorption coefficient of strongly terahertz-absorbing solid materials, with principles extended to other sample types. The accurate and straightforward methodology requires three terahertz time-domain spectroscopy (THz-TDS) measurements: baseline, reference and sample. The baseline is a measurement of the terahertz time-domain spectrometer's empty beam path. The reference consists of a weakly terahertz-absorbing material and the sample is a well-mixed binary mixture of a weakly and a strongly terahertz-absorbing material. During THz-TDS data processing, the concept of half-width is introduced, defining the time span over which half of a symmetric apodisation function is applied. The half-width ensures consistent application of the apodisation function across all THz-TDS measurements and facilitates the automatic specification of a uniform time-delay range for fast Fourier transform. Complex transfer functions for the reference and sample are derived with respect to the baseline, enabling the extraction of their respective refractive index and absorption coefficient spectra. The reference provides the closest possible experimental estimate of the weakly terahertz-absorbing material's actual optical constants within the sample, and where applicable, also incorporates the effects of sample porosity by approximation. Utilising effective medium theories, the refractive index and absorption coefficient spectra of the strongly terahertz-absorbing material can be accurately determined. This tutorial additionally discusses the conventional approaches, addresses cases with limited time-delay ranges and different experimental configurations, identifies simplification strategies, highlights potential pitfalls in the derivation process and discusses their implications, ensuring robust analysis of THz-TDS data.