Fast analysis of spherical metasurfaces using vector wave function expansion

Modeling of spherical metasurfaces using Generalized Sheet Transition Conditions (GSTCs) and Vector Wave Function (VWF) expansion is presented. The fields internal and external to the metasurface is expanded in terms of spherical VWFs and unknown coefficients. GSTCs are used to obtain linear relationships between the unknown coefficients. An overdetermined system of equations are then solved by point matching. The method is quasi-analytical and hence there is no need for meshing which is encountered in conventional computational electromagnetic methods. This results in the method being extremely fast and hence useful for metasurface optimization. The method is validated by two examples. The formulations presented here can be easily extended to multilayered spherical metasurfaces.