Negative Refractive Index in Left-Handed Materials

The real part of the refractive index n({omega}) 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({omega}) , demonstrating frequency regions where the sign of Re[n({omega})] 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.