A Rigorous Numerical Solution for Characterization of Low-loss Dielectric Materials from Cavity Measurements

The cavity perturbation method is currently widely used for the characterization of the complex dielectric constant of material samples. This method provides a simple analytical solution by relating the real and imaginary parts of the dielectric constant of the sample to the changes in the measured resonant frequency and the quality factor of the loaded cavity. The validity of this method, however, is contingent upon the small size of the dielectric sample. For low-loss dielectric materials, relatively large samples are needed to measure the change in the Q-factor accurately. Therefore, a full-wave numerical technique must be used to model the cavity problem. The persent proposal will conduct a thorough study of three rigorous techniques: the integral equation technique, the finite element method, and the finite element method, and the finite difference time domain method, as applied to the problem at hand. A novel inversion algorithm for the solution of the associated inverse problem will be implemented. The numerical tehniques will be compared, and the code that provides the highest accuracy, while computationally efficient, will be selected for the estimation of the dielectric constant using the cavity method. The accuracy of the numerical code will be verified using experimental data collected from various low-loss dielectric samples.