Analysis of losses in a double‐negative metamaterial composed of magnetodielectric spheres embedded in a matrix

A simple‐cubic lattice of identical, magnetodielectric spheres exhibiting double‐negative (DNG) behavior is analyzed.An analytic expression for the threshold loss angle δth of the spheres, above which DNG behavior is extinguished, is derived by utilizing the Möbius transformation. The formula is valid for either dielectric or magnetic loss exhibited by the particles, and is derived based on the dipole approximation of Mie's theory of scattering by a sphere. For spheres with equal real relative permittivity and permeability, it is shown that δth increases as particle volume fraction increases. It is also shown that the loss angle of the effective medium can be controlled by appropriate choice of frequency.