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As in Figure 1, the 2D space of the constitutive parameters was explored for (a) acoustic metamaterials  with two volume fractions: Φ = 20% (white curve) and Φ = 45% (black curve) and for (b) electromagnetic metamaterials . Note that a scale function was used to make the ratio-axis ρ″/ρ′ and κ″/κ′ span the range]−∞, +∞[. All the values of both ratios have been mapped to the graphical display according to the following function: x′= f(x) = x/(1 + |x|), where x is an actual value of the considered ratio and x′ is its graphical position proportional to the length of the semi-axis (x′ ∈ ]−1, +1[). Thus, the origin (x′ = 0), the middle (x′ = 1/2) and the edge (x′ = 1) of the positive semi-axis correspond to ratios (x = ρ″/ρ′ or x = κ″/κ′) equal to 0, 1 and +∞, respectively. The same property holds for the negative-ratio semi-axis with x and x′ both negative.
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