SOLVING PERIODIC EIGENPROBLEMS BY SOLVING CORRESPONDING EXCITATION PROBLEMS IN THE DOMAIN OF THE EIGENVALUE

Periodic eigenproblems describing the dispersion behavior of periodically loaded waveguiding structures are considered as resonating systems. In analogy to resonators, their eigenvalues and eigensolutions are determined by solving corresponding excitation problems directly in the domain of the eigenvalue. Arbitrary excitations can be chosen in order to excite the desired modal solutions, where in particular lumped ports and volumetric current distributions are considered. The method is employed together with a doubly periodic hybrid finite element boundary integral technique, which is able to consider complex propagation constants in the periodic boundary conditions and the Greenʹs functions. Other numerical solvers such as commercial simulation packages can also be employed with the proposed procedure, where complex propagation constants are typically not directly supported. However, for propagating waves with relatively small attenuation, it is shown that the attenuation constant can be determined by perturbation methods. Numerical results for composite right/left-handed waveguides and for the leaky modes of a grounded dielectric slab are presented.