Measurement of permittivity by means of an open resonator. I. Theoretical

Abstract

The objective of this paper is to provide a reliable theoretical foundation for the open-resonator method of measuring permittivity and loss-tangent of dielectric materials. From an exact solution of Maxwell’s equations obtained by means of the complex-source-point method, simplified formulae for the six Cartesian components of the electromagnetic field are obtained. These are then used in a variational formula to obtain an accurate formula for the resonant frequency of an open resonator with spherical mirrors (of equal radius of curvature) having a parallel-plane slab of dielectric material located centrally between the two mirrors. It is assumed that the mirrors are sufficiently large for diffraction effects to be negligible. In the following companion paper II, experimental results are presented which verify the accuracy, within the usual limits of practical measurement, of the simple correction formulae deduced here.