Eigenmode Solution of 2-D and 3-D Electromagnetic Cavities Containing Absorbing Materials Using the Jacobi–Davidson Algorithm

Eigenmodes of electromagnetic cavities containing absorbing dielectric materials are determined using an adaptation of the Jacobi–Davidson technique to solve discrete matrix eigenequations derived from Maxwellʹs equations. The discretisations, obtained using finite difference and finite integration methods, give rise to non-Hermitian matrices, having complex eigenvalues, and the Jacobi–Davidson method is shown to be applicable even when very low-Q cavity eigenmodes exist in the presence of highly lossy dielectric or permeable materials. Examples are given of eigensolutions for both 2-D (cylindrically symmetric) and 3-D electromagnetic operators.