The electromagnetic fields of a triaxial ellipsoid calculated by modal superposition

The electromagnetic fields and eigen-frequencies of triaxially ellipsoidal resonators have been calculated. The method used is modal superposition, based on the decomposition of the fields inside the resonator into a series expansion, with unknown coefficients, of the eigen-states of a spherical resonator. The coefficients and eigen-frequencies have then been calculated by minimizing the rms electric field at the resonator surface using software designed within MatLab®. Accuracies of parts in 1010 have been obtained for the eigen-frequencies, and the dependence of the calculations on the ellipsoidal eccentricities and the resonator modes has been analysed. The results are compared with those of Mehl (2009 Metrologia 46 554–9), who used a second-order approximation. The method of modal superposition has the potential for solving many similar problems in resonators of arbitrary shapes.