Terahertz waves are nondestructive and non-ionizing to synthetic and natural materials, including polymeric and biological materials. As a result, terahertz-based spectroscopy has emerged as a suitable technique to uncover fundamental molecular mechanisms and material properties in this electromagnetic spectrum regime. In terahertz time-domain spectroscopy (THz-TDS), the material's optical properties are resolved using the raw time-domain signals collected from the sample and air reference data depending on accurate prior knowledge of the sample geometry. Alternatively, different spectral analysis algorithms can extract the complex index of refraction of optically thick or optically thin samples without specific thickness knowledge. A THz-TDS signal without apparent Fabry-Pérot oscillations is commonly associated with optically thin samples, whereas the terahertz signal of optically thick samples exhibits distinct Fabry-Pérot oscillations. While several extraction algorithms have been reported a priori, the steps from reducing the time-domain signal to calculating the complex index of refraction and resolving the correct thickness can be daunting and intimidating while obscuring important steps. Therefore, the objective is to decipher, demystify, and demonstrate the extraction algorithms for Fabry-Pérot-absent and -present terahertz signals for various polymers with different molecular structure classifications and nonlinear optical crystal zinc telluride. The experimental results were in good agreement with previously published values while elucidating the contributions of the molecular structure to the stability of the algorithms. Finally, the necessary condition for manifesting Fabry-Pérot oscillations was delineated.
Keywords: data extraction; material parameters; terahertz time-domain spectroscopy.