Unit Cell Polarizability and Sheet Impedance Extraction in Aperiodic Environments

A technique for the extraction of the polarizability of a particle or equivalent sheet impedance of printed circuit elements in aperiodic metasurface environments is presented. The technique does not rely on local periodic assumptions that are commonly made in metasurface sheet impedance extraction techniques. Instead, the local electric field and induced surface current on each of the homogenized sheet impedance elements in the aperiodic array is extracted from a solved linear system representing the electromagnetics problem. The ratio of local electric field to induced surface current density defines the element impedance in the true aperiodic environment. This impedance is used to find a printed circuit element which generates the same current when excited by the local electric field. Geometrical parameters are varied until agreement between the homogenized sheet impedance and the printed circuit element is observed. An example of an aperiodic 10-element metasurface is provided.