RLC Circuit Model for the Scattering of Light by Small Negative Refractive Index Spheres

We study the scattering properties of very small spheres made of a negative refractive index (NRI) using circuit network principles. The Lorenz-Mie theory is used to represent the transverse magnetic and transverse electric scattering coefficients based on resistor, inductor, and capacitor (RLC) ladder circuit models derived from continued fractions. The lumped elements are then analyzed and a comparison is made between these new elements and those expected for conventional positive refractive index spheres. This provides an alternative interpretation for the fact that the scattering efficiency Q_sca for NRI spheres with size parameters x <;<; 1 does not always obey Rayleigh´s formula Q_sca ~ x⁴. The RLC circuits obtained here, besides being very simple, provide accurate physical insights into the problem of the scattering of light by NRI spheres, therefore serving as a new theoretical background for studying the scattering properties of negative refractive index metamaterials.