Ultra-broadband material spectroscopy from scattering parameters obtained from time domain measurements

Scattering parameter measurements can provide a key insight towards understanding material properties, pertaining to permittivity. The relaxation phenomena (e.g. free and bond water relaxation) and the frequencies at which they occur can convey valuable information in dielectric spectroscopy for material process monitoring and biology research. These relaxations can range from kHz to GHz range. Extracting the reflection/transmission coefficients or scattering parameters from time domain measurements over a broad range of frequencies, from kHz to GHz, can be challenging. The current approach often employed by material scientists involves performing Laplace transform, through a numerical integration, on the time domain data. On the other hand, the more computationally efficient fast Fourier transform (FFT) techniques have been well-developed and widely used in the engineering community. In this study, we propose a method, based on fast Fourier transform (FFT) of non-uniformly sampled time domain reflectometry (TDR) data, to obtain the frequency domain information in an ultra-broadband range from kHz to GHz. We test this method to known lossy materials.