Cancellation of Fabry-Perot interference effects in terahertz time-domain spectroscopy of optically thin samples

Terahertz time-domain spectroscopy is increasingly used in many fields of research. For strongly absorbing materials with refraction index close to 1, optical parameters at terahertz frequencies are most conveniently quantified using transmission measurements through thin samples. Unfortunately, extracting optical parameters from raw data implies the use and/or development of complicated numerical data processing procedures. In this work we present an efficient computational procedure for extracting the optical parameters in very thin samples (≲100μm) from transmission terahertz time-domain spectroscopy. In our procedure, we are able to successfully remove from raw data the Fabry-Perot interference effects, which are commonly recognized to be the leading cause of inaccuracy in the extracted parameters, introducing fictitious oscillations in their frequency dependence. The procedure is based on the Davidenko method to identify the roots of complex functions used to numerically solve the implicit equation obtained by equating the experimental and theoretical transfer functions. The advantage of the method is the possibility of obtaining the roots using the numerical solution of a system of real differential equations using standard mathematical packages. In addition, we show that complete removal of the Fabry-Perot oscillations is achieved by including in the computational procedure, besides the sample thickness, the instrumental error on the starting instant of the terahertz signal sampling. This error could be common to many terahertz time-domain systems, especially those using optical fibers. This correction is necessary in general to preserve the terahertz spectroscopic features in the extracted optical parameters for strongly absorbing materials with refraction index close to 1, such as water, biological matter, and several organic materials.