Cavities for electron spin resonance: predicting the resonant frequency

Microwave cavities are used in electron spin resonance to enhance magnetic fields. Dielectric resonators (DRs), pieces of high dielectric material, can be used to tailor the resonant frequency of a cavity. However, designing cavities with DRs to obtain desired frequencies is challenging and in general can only be done numerically with expensive software packages. We present a new method for calculating the resonant frequencies and corresponding field modes for cylindrically symmetric cavities and apply it to a cavity with vertically stacked DRs. The modes of an arbitrary cavity are expressed as an expansion of empty cavity modes. The wave equation for D gives rise to an eigenvalue equation whose eigenvalues are the resonant frequencies and whose eigenvectors yield the electric and magnetic fields of the mode. A test against theory for an infinitely long dielectric cylinder inside an infinite cavity yields an accuracy better than 0.4\% for nearly all modes. Calculated resonant frequencies are also compared against experiment for quasi-TE011 modes in resonant cavities with ten different configurations of DRs; experimental results agree with predicted values with an accuracy better than 1.0\%. MATLAB code is provided at http://www.physics.byu.edu/research/coltonlab/cavityresonance.