Characterisation of multi-layered structures using a vector-based gradient descent algorithm at terahertz frequencies

Material characterisation and imaging applications using terahertz radiation have gained interest in the past few years due to their enormous potential for industrial applications. The availability of fast terahertz spectrometers or multi-pixel terahertz cameras has accelerated research in this domain. In this work, we present a novel vector-based implementation of the gradient descent algorithm to fit the measured transmission and reflection coefficients of multilayered objects to a scattering parameter-based model, without requiring any analytical formulation of the error function. We thereby extract thicknesses and refractive indices of the layers within a maximum 2% error margin. Using the precise thickness estimates, we further image a 50 nm-thick Siemens star deposited on a silicon substrate using wavelengths larger than 300 µm. The vector-based algorithm heuristically finds the error minimum where the optimisation problem cannot be analytically formulated, which can be utilised also for applications outside the terahertz domain.