Eigenmode Solution for TE-Wave Propagation Through Anisotropic Metamaterial Particle 3-D Arrays via Dipole Approximation

The wavenumbers for an obliquely propagating transverse electromagnetic mode via a 3-D array of anisotropic scatterers are theoretically studied and numerically derived through a consistent method based on the dipole approximation. First, it is assumed that the anisotropic particle can be replaced with a set of dipole moments, and, in terms of its polarizabilities and the array interaction coefficients, the dispersion equation of the system is efficiently extracted. Then, the eigenmodes are rapidly retrieved using a computational non-linear equation solver scheme. The proposed technique is applied to two well-known anisotropic metamaterial scatterers, and the desired wavenumbers are accurately evaluated and successfully validated for various angles of propagation.