Negative Refractive Index in Left-Handed Materials

The real part of the refractive index n(ω) of a nearly transparent and passive medium is usually taken to have only positive values. Through an analysis of a current source radiating into a 1D “left-handed” material (LHM)—where the permittivity and permeability are simultaneously less than zero—we determine the analytic structure of n(ω), demonstrating frequency regions where the sign of Re[n(ω)] must, in fact, be negative. The regime of negative index, made relevant by a recent demonstration of an effective LHM, leads to unusual electromagnetic wave propagation and merits further exploration.