Negative-index metamaterials: is double negativity a real issue for dissipative media?

One way to obtain materials with a negative index is to achieve media with doubly negative constitutive parameters. We show that the double negativity required for perfect (non-dissipative) media is not necessary for real passive (lossy) metamaterials, for which single negativity of one of the two constitutive parameters may be sufficient. The analysis is presented through original diagrammatic representations involving both the real and imaginary parts of the dynamic constitutive parameters for isotropic media. A valid demonstration for acoustic and electromagnetic metamaterials is supported by considering an actual soft 3D locally-resonant ultrasonic metafluid having a negative acoustic index while being a single-negative medium. The crucial role of the imaginary parts of the constitutive parameters is then discussed through its impact on the figure of merit. Finally, the analysis is extended to an example of an electromagnetic negative-index metamaterial exhibiting both single and double negativity