Excitation of Complex Modes of Periodic Structures Using Inhomogeneous Plane Wave Scattering in Fast and Slow Wave Regions

Periodic metamaterial unit cells are analyzed by using inhomogeneous plane wave scattering. The complex modes of the unit cell are derived using either the poles or the zeroes of the complex reflection coefficient of the fundamental Floquet mode. The required reflection coefficients are computed by a doubly periodic finite element boundary integral technique. The search for the eigenvalues is accelerated by the nonlinear Nelder-Mead method. Usually, pairs of eigenvalues are observed, which can be both, real or conjugate complex. Also, the eigenvalues correspond either to proper or improper modes. By selecting the proper or the improper modes during field computation, the other type of modes is removed from the observed response and, instead, zeroes are found in the reflection coefficient. This can explain the absorption behavior of single-sided open periodic leaky structures by investigating their reflection coefficient with the proposed inhomogeneous plane wave excitation approach. The obtained results for various single-sided open periodic unit cells are in good agreement with the results of other methods, where in the presented excitation based method there is no need to solve any dispersion equation in the complex plane.