Eigenfunction Expansion (EFE) Analysis of Cylindrical Metasurfaces—Part I: Zero Thickness Tensorial Surface Susceptibility Model

We present a rigorous semianalytical formulation for the analysis of electromagnetic (EM) scattering from a cylinder constructed from a metasurface (MS) represented using surface susceptibilities. The formulation uses the generalized sheet transition conditions (GSTCs) to represent the surface and eigenfunction expansion (EFE) of the incident and scattered fields, by exploiting their angular periodicity. This article illustrates the methodology with a number of examples; including two formed from a finite sized practical unit cell exhibiting a normally oriented magnetic resonance which is compared with commercial EM full-wave solver; other examples present surfaces that have a modulated gain/loss profile (i.e., amplitude modulation) and polarization conversion. It is found that for all cases, the EFE solution very accurately captures the scattered fields in both the interior and exterior regions of the surface. Detailed convergence studies are further presented, including the effect of susceptibility modulation on the number of terms needed in the EFEs, to reach a correct field solution. The proposed EFE approach is, thus, a quick, rigorous methodology, which, although limited in the geometry it can model, has many advantages for an investigation into the use of GSTCs, application development, and providing a baseline for simulation studies.