Finite element modal analysis of wave propagation in homogeneous and periodic waveguides

In this paper, we demonstrate how conventional finite element modal analysis of a slice of an infinite homogeneous or periodic waveguide provides essential information on its properties. The novelty aspects are the rigorous derivation of requested boundary conditions from the analytical bi-orthogonality relation for free waves in a waveguide and conversion of these ‘class consistent’ conditions to the finite element format. Eigenfrequencies and mode shapes obtained from the modal analysis are used to reconstruct dispersion diagram for propagating waves in a homogeneous waveguide. A novel method is proposed to assess their decay rates in the presence of material losses. For a periodic waveguide, the modal analysis of a symmetric unit periodicity cell with the ‘class consistent’ boundary conditions is innovatively used to identify partial (modal) and full stop-bands. Computational efficiency of the proposed modal analysis-based methodology as compared with standard Wave (and) Finite Element method is discussed.