Phase diagram of lossy negative index metamaterials

For lossy metamaterials, there exist the negative index of refraction regimes that may originate from double negative or single negative of the real parts of complex permittivity and permeability. To represent the regimes of negative index, a material quality factor space is proposed. Within the space the different negative index regimes are found located in the different regions. The contour map of the complex index of refraction in the space show that the negative index can be always possible to realize in three ways, and the loss of single negative metamaterials is greater than that of double negative metamaterials.