Efficient material parameters estimation with terahertz time-domain spectroscopy

Existing parameter extraction techniques in the terahertz range utilize the magnitude and phase of the transmission function at different frequencies. The number of unknowns is larger than the number of available information creating a nonuniqueness problem. The estimation of the material thickness thus suffers from inaccuracies. We propose a novel optimization technique for the estimation of material refractive index in the terahertz frequency range. The algorithm is applied for materials with arbitrary frequency dependence. Dispersive dielectric models are embedded for accurate parameter extraction of a sample with unknown thickness. Instead of solving N expensive nonlinear optimization problems with different possible material thickness, our technique obtains the optimal material thickness by solving only one optimization problem. The solution of the utilized optimization problem is accelerated by estimating both the first order derivatives (gradient) and second order derivatives (Hessian) of the objective function and supplying them to the optimizer. Our approach has been successfully illustrated through a number of examples with different dispersive models. The examples include the characterization of carbon nanotubes. The technique has also been successfully applied to materials characterized by the Cole-Cole, Debye, and Lorentz models.