A negative index will occur for waves of one circular polarization if κ κ > ϵ ϵ r μ μ r . In this case, it is not necessary that either or both ϵ ϵ r and μ μ r be negative to achieve a negative index of refraction. A negative refractive index due to chirality was predicted by Pendry and Tretyakov et al., and first observed simultaneously and independently by Plum et al. and Zhang et al. in 2009.