Poles and Residues of Electromagnetic Fields in Metamaterials

This paper proposes a system-based approach to classify metamaterials based on the behavior of the complex poles and residues of the electromagnetic fields in the materials. Metamaterials are classified into 12 types, depending on their nature as double-positive permittivity and permeability (DPS), double-negative permittivity and permeability (DNG), epsilon-negative (ENG), or mu-negative (MNG) metamaterials. The presented method expands the metamaterials’ reflection and transmission impulse responses as a superposition of damped sinusoids using the singular expansion method (SEM). The matrix pencil method is then employed to efficiently extract the SEM poles and residues of the transmitted and reflected impulse responses for each investigated metamaterial. The damping factor of the transmitted wave response and the real part of the residues of the reflected wave response differentiate between DPS and DNG metamaterials. Both the real and imaginary parts of the residues of the transmitted wave response and the damping factors of the reflected wave response are utilized to differentiate between ENG and MNG metamaterials. The results demonstrate this classification procedure, which is further described in a flow chart.