Double-Negativity Issue for Dissipative Negative-Index Media

An original criterion defining the sign of the acoustic refractive index from those of the real and imaginary parts of the constitutive parameters of dissipative isotropic media sustaining acoustic plane wave propagation, is established. We observe that the double negativity required for perfect (non dissipative) media with a negative index is not necessary for passive (dissipative) metamaterials, for which single negativity of one of the two constitutive parameters may be sufficient. Finally, a novel valid demonstration is supported by considering soft 3D locally-resonant ultrasonic metafluids (composed of "ultra-slow" porous micro-beads), having a negative acoustic index while being single-or double-negative media.