Measurement of Dielectrics From 20 to 50 GHz With a Fabry–Pérot Open Resonator

Abstract

A novel approach to the measurement of complex permittivity of low-loss dielectric materials with the aid of an open Fabry-Pérot resonator with concave Gaussian mirrors is presented in this paper. For that purpose, a new scalar 1-D layered electromagnetic (EM) model of the resonator is proposed. The model takes the advantage of Cartesian-to-Gaussian coordinate transformation and axisymmetrical properties of the TEM modes of interest. There are several advantages of the proposed approach. The first is the use of Gaussian mirrors instead of spherical ones, which better fit to the shape of Gaussian wavefronts. Second, the model more accurately accounts for oblique incidence of the wave onto the surface of the sample, which is one of the major challenges in case of alternative models based on a characteristic equation. An automated measurement setup operating in the 20-50-GHz range has been designed and manufactured to experimentally validate the proposed measurement method. A real part of permittivity of a few well-known materials, such as silicon, quartz, polystyrene, or polyethylene terephthalate (PET) foil, has been measured with the accuracy better than 0.5%, which means a significant improvement as compared to the state of the art in this area.