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Part 2 – Eigenfunction Expansion (EFE) Analysis of Cylindrical and Sectorial Metasurfaces
  • Tom J. Smy ,
  • Shulabh Gupta
Tom J. Smy
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Shulabh Gupta
Carleton University

Corresponding Author:[email protected]

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Abstract

This paper presents a formulation of an eigenfunction expansion (EFE) technique for the analysis of multi-shell cylindrical metasurface configurations and tests the validity of zero thickness sheet models for simulating practical structures. The formulation homogenizes the metasurface, modeling the surface as a zero-thickness discontinuity characterized by surface susceptibilities and allows for the incorporation of Perfect Electric Conductor (PEC) cores and partial cylindrical surfaces (arcs/sectors). A primary advantage of the method is that it is a fully rigorous semi-analytical approach and is well suited for investigating the limits of the zero thickness sheet models model via the Generalized Sheet Transition Conditions (GSTCs). Comparison to full-wave simulations in commercial solvers show that, for a thin deep sub-wavelength 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 off 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 multi-shell field distributions accurately when compared to 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. Using a relatively thick unit cell (?7% of the excitation wavelength) and two different extraction models (cell edge and center) comparison to full-wave simulation shows that for resonant structures errors in field prediction are present. This is a clear indication that the zero-thickness assumption will break down for thick cells for some surface configurations. This paper demonstrates some clear advantages of the EFE approach; it is fast, rigorous and can accommodate a large range of geometric structures.