On the unique numerical solution of Maxwellian eigenvalue problems in three dimensions

The numerical computation of eigensolutions of Maxwell's equations does not necessarily yield unique solutions - especially when applied to three dimensional problems. Thus an accurate calculation can become extremely difficult and the results uncertain. This problem can be overcome by using a special finite difference method that solves all the four Maxwell equations in a consistent way, so that the properties of the differential equations and their solutions are still exhibited in the grid space for the corresponding matrix equations and their discrete solutions. By utilizing a simple combination of Maxwell's equations in the grid space we find a matrix representation with non-vanishing eigenvalues and thus unique solutions. This matrix equation corresponds to the wave equation in free space. Numerical examples prove the stability and simplicity of the algorithm as well as the accuracy in comparison with measurements. (orig.)