Evaluation of equivalent sheet impedance from isofrequency curves

Metasurfaces are structures made of one or several layers of subwavelength metallic patches printed on a grounded dielectric substrate. To ease the design and modeling of metasurfaces, the array of patches is genearlly homogenized under the local periodicity assumption and described using an equivalent sheet impedance or isofrequency curve. Recently, a fast fullwave method based on the Method of Moments (MoM) has been proposed to rapidly and accurately compute the isofrequency curves of metasurface-like periodic array of patches. In this work, we extract an equivalent sheet impedance from the isofrequency curve of a given array of patches by imposing the transverse resonance condition. If the metasurface involves several metallizations, the equivalent surface impedances of each sheet is computed independently and the different sheets are combined afterward. The proposed method is validated through numerical examples. Interestingly, the equivalent sheet impedance extracted from the isofrequency curve of the fundamental TM mode can also accurately reproduce the isofrequency curve of the fundamental TE mode.