Scattering properties of an impedance-matched, ideal, homogeneous, causal "left-handed" sphere

The plane-wave scattering properties of a sphere of material having an ideal, homogeneous, and causal permittivity epsilon(f), and permeability mu(f) were investigated through detailed three-dimensional finite-difference time-domain, method-of-moments, and series-solution simulations. A Lorentzian functional form was chosen for epsilon(f) and mu( f), as it yields causal responses and allows us to study the physics of the left-handed-medium (LHM) regime. Our interest lies mainly in the frequency range where negative refraction [Re(n) < 0] is observed. We found that when operating in the LHM regime, an impedance-matched sphere responds with scattering features strikingly different from those found in ordinary materials. In particular, we found zero back-scattering and forward scattering that exceeds that of a metal sphere of similar size. The equality of E- and H-plane patterns was proved analytically and numerically, and the possibility of internal subwavelength focusing with a zero index sphere is also reported.