A method for evaluating a complex permittivity of dielectric material by using whispering gallery modes on a spherical resonator

We have developed a new method for evaluating a complex permittivity of a dielectric material by using whispering gallery mode on a spherical dielectric resonator. As eigenvalue equations of the spherical resonator can be derived correctly without any approximations, we can expect a precise evaluation of the complex permittivity. In our estimation, the Newton method is used. Not only numerical resonance frequencies and unloaded quality factors derived from the eigenvalue equation but also these resulted from our experiments in millimeter wave region are substituted into the Newton method formula. We have also iterated the formula to converge the complex permittivity of the dielectric materials. Comparing our complex permittivity with a conventional value, it shows good agreement each other.