Analysis of Double-Negative (DNG) Bandwidth for a Metamaterial Composed of Magnetodielectric Spheres Embedded in a Matrix

Based on Mie scattering theory and effective medium theory, the percentage bandwidth in which permittivity and permeability of a simple cubic lattice of identical, nonmetallic mag neto-dielectric spheres are simultaneously negative (double-negative, or DNG) is analyzed. Relaxing the restriction of previous work, that k₁a → 0 where k₁ is the wavenumber in the matrix and α is the particle radius, new analytical formulas are obtained for k₁a <; π/10, from which the DNG bandwidth can be easily computed. As an example, a contour map of DNG bandwidth for a wide range of values of particle permittivity and permeability is plotted for particle volume fraction f = 0.3. From the analytical formulas, it is shown that the maximum achievable DNG band width for a simple cubic lattice of spheres with particle volume fraction f = 0.3 is 7.4%, when the particle permittivity and permeability are both approximately 14 times greater than those of the matrix.