Eigenfunction Expansion (EFE) Analysis of Cylindrical Metasurfaces—Part II: Sectors and Multishells

This article presents a formulation of an eigenfunction expansion (EFE) technique for the analysis of multishell cylindrical metasurface (MS) configurations and tests the validity of zero-thickness sheet models for simulating practical structures. The formulation homogenizes the MS, modeling the surface as a zero-thickness discontinuity via the generalized sheet transition conditions (GSTCs) characterized by surface susceptibilities. Comparison with full-wave simulations in commercial solvers show that, for a thin deep subwavelength unit cell, single-shell arcs with increasing curvatures (up to at least half of a wavelength in radius) are accurately captured by the use of the model. The simulations also show that the edge diffraction ff the finite length arcs are well modeled. This is an important result as it indicates that susceptibilities extracted from full-wave unit-cell simulations assuming a flat periodic infinite surface are appropriate for use in high curvature finite surfaces. A second set of simulations showed that the EFE predicted multishell field distributions accurately when compared with unit-cell-based simulations. A final set of simulations for single- and double-shell configurations is used to demonstrate the limitations of the GSTC approach for unit cells of appreciable thickness.