A recursive formula for the general scattering analysis of electrically small multilayer spherical scatterers

• A recursive formula of the Mie scattering coefficients for the quasistatic analysis of multilayer spherical scatterers • General conditions for the resonance and transparency of electrically small multilayer spherical scatterers • Some special cases where the resonance or transparency can be achieved for arbitrary thickness of the outermost layer The electromagnetic scattering characteristics of single-layer and multilayer spherical scatterers are obtained through the calculation of Mie scattering coefficients. However, the physically interpretable mathematical forms of Mie coefficients are acquired through different approximation methods. This paper presents a concise recursive formula achieved by Taylor approximants of Mie scattering coefficients for electrically small multilayer spherical scatterers. This formula determines the general conditions in attaining resonant or transparent inclusions; the features that are of the essence in designing metasurfaces with unconventional electromagnetic properties. Also, it is unveiled by this formula that the occurrence of some special cases is probable, where the thickness of the outermost layer does not affect the resonance and transparency conditions. These special cases are examined for the classical core-shell structure.