Abstract

The effective constitutive parameters of a three-dimensional periodic structure are calculated using its Bloch modes. These modes and their propagation constants are obtained from eigenvectors and eigenvalues of the generalized transfer matrix of a unit layer of the structure. Effective bulk permittivity and permeability tensors of the medium are obtained when two of the Bloch modes are dominant, i.e., propagate without significant decay inside the medium. The effect of the strongly decaying Bloch modes, which are excited at the interface with a conventional medium, are included by means of surface impedance matrices. The results are in excellent agreement with full-wave electromagnetic simulations.

© 2019 Optical Society of America

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