Uncertainty and Ambiguity in Terahertz Parameter Extraction and Data Analysis

Phase sensitive measurement techniques, such as THz time-domain spectroscopy or dispersive Fourier transform spectroscopy, are very useful tools to obtain a complete set of optical material parameters. When recording the electric field as a function of time delay between THz and optical pulse, the absorption coefficient and the index of refraction can be extracted. However, the analysis shows ambiguity. Here, we describe an analysis which yields a complete set of mathematical solutions and show how the physically relevant can be deduced. We present a comprehensive mathematical survey for parameter extraction. We have recorded the THz spectra of anthracene and the fatty acid capric acid as examples for weakly absorbing solid samples, and an ionic liquid as an example for a strongly absorbing liquid sample. Finally, we discuss the uncertainty of the obtained optical parameters using error propagation of the Fourier transformation with a simple model and a rigorous mathematical procedure.