Three dimensional resonator mode computation by finite difference method

A discretization of the Maxwellian eigenvalue problem in three dimensions is described that yields a symmetric band matrix with only positive eigenvalues. In contrast to previously published methods the algorithm assures that all numerical solutions are physically correct and that unphysical "ghost modes" do not appear. This unique property is achieved by first solving all the four Maxwell's equations one by one separately using a consistent discretization method and second combining the resulting four matrix equations to a single eigenvalue problem on the grid space. Also, this method is more general than previous ones and allows an arbitrary distribution of material which can be dielectric and permeable. A computer code has been written that realizes the method in its full generality. Various examples prove the practical applicability and the correctness of the numerical solutions in comparison with measurements.