Eigenvalue computation of open periodically composed waveguides by series expansion

Eigenvalues of periodically constituted waveguides with complicated material distribution are efficiently determined, where eigensolvers in software packages show difficulties in finding the eigensolutions. Moreover, the treated waveguide structures are open, causing even more trouble with available numerical solvers or rather demanding procedures within analytical approaches. Since open configurations are essential for the evaluation of radiating structures, we suggest to convert the open problem setting into a closed equivalent configuration but without disturbing the actual field behaviour. Thus, the original continuous mode spectrum is turned into a discrete and proper set of eigenmodes. The field solution of the periodically modified waveguide is obtained by series expansion with the eigensolutions of the homogeneous background waveguide as basis functions. An eigenproblem is still to solve, but it is considerably reduced in size and easy to solve by the use of a-priori information.