Finite-Element Modeling of Evanescent Modes in the Stopband of Periodic Structures

A novel implementation of periodic boundary conditions in the finite-element method is presented that is applicable to complex eigenmode analysis of the electromagnetic waves in infinite periodic media. A weighted residual finite-element (FE) model is employed to obtain the attenuation constant of evanescent/complex modes within bandgaps by analyzing only one unit cell of the structure. Plots of the imaginary and the real parts of the propagation constants versus frequency are shown which confirms the capability of the developed FE code in capturing complex modes.