Broadband Electromagnetic Transparency by Graded Metamaterial Sphere

We have investigated the scattering of electromagnetic waves from a radially inhomogeneous metamaterial sphere whose dielectric permittivity is described by the graded Drude model $\epsilon_{s}(r)=1-\omega_p^2(r)/\omega^2$. The radial position dependent plasma frequency depends on $r$ as $\omega_p^2=1/2-c(r/r_{0})^n$, where $c$ and $n$ are positive constants and $r_{0}$ is the radius of the sphere. The electromagnetic field distribution has been calculated within the full-wave Mie scattering theory. When $n=2$, exact analytic solutions can be obtained in terms of confluent Heun function and confluent hypergeometric function of Kummer. This allows us to obtain the full-wave total scattering cross section analytically from the scattering field amplitudes. While the total scattering cross section $Q_{s}$ depends on both the graded plasma frequency profile and the frequency of the incident electromagnetic wave, it is found that $Q_{s}$ can achieve extremely small values over a broad frequency band and graded parameters. The analytic solutions allow us to assess the conditions for achieving broadband electromagnetic transparency in the metamaterial sphere and make tunable electromagnetic transparency feasible.