Entire-domain basis functions for scattering from large curved surfaces formulated by transformation optics

A complete set of entire-domain basis functions are introduced for the analysis of scattering from bodies with curved surfaces; they are defined via the application of a generalization of the Shannon sampling theorem. These basis functions are defined for curved patches with arbitrary contours, via a three-step procedure. First, the curved patch is mapped, via Transformation Optics, onto a flat parametric domain surrounded by a virtual anisotropic inhomogeneous space. Next, linear-phase functions are defined on the parametric flat domain; the sufficient and non-redundant number of functions is found by using a spectral domain “completeness relationship” of the delta function. Finally, the back-transformation from flat anisotropic to curved isotropic space yields the basis functions for the curved patch. The number of basis functions so obtained matches the degrees of freedom of the field known in the literature. Numerical results show the effectiveness of the representation for both fields and currents.