Spaces of electromagnetic and mechanical constitutive parameters for dissipative media with either positive or negative index

Abstract

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

“…However, although double negativity clearly implies a negative index [5], the opposite is not true [3]. It has been shown in dissipative isotropic homogeneous metamaterials that the 2D space of constitutive parameters should be carefully considered [17]. In terms of the sign of the real-valued parameters j and q [18], the conventional twoaxis diagrammatic representation that is often used to identify NIMs [19] is not appropriate for dissipative media.…”

“…0 (the passivity condition for harmonic waves with time-dependence e Àixt ) and c 0 as the reference phase speed, i.e., the sound speed in the background medium. NIMs therefore refer to media with n 0 < 0 and are often related with double-negative media [17]. When energy losses can be neglected (j 00 /j 0~q00 /q 0~n00 /n 0~0 ), the acoustic index n 0 is negative for j 0 < 0 and q 0 < 0 (for example, see Figure 9 in [18]).…”

“…A clear picture of the constitutive-parameter combinations (j, q) ensuring a positive or negative acoustic index in dissipative media has been recently established by analyzing the Poynting vector P (average energy flux density) and the complex-valued wave vector k (= k 0 + ik 00 ) of the acoustic plane waves propagating in these media [17]. This diagrammatic representation has been reported in Figure 2 of [17] in terms of the phase angles h j and h q of the constitutive parameters j ¼ j j j e ih j ; ð q ¼ jqje ihq Þ, which are the key values for analyzing the index sign of a given material. To increase the overall readability of the sign of all the different parameters, another type of display involving the ratios j 00 /j 0 (= tan h j ) and q 00 /q 0 (= tan h q ) is proposed.…”

“…To increase the overall readability of the sign of all the different parameters, another type of display involving the ratios j 00 /j 0 (= tan h j ) and q 00 /q 0 (= tan h q ) is proposed. The key criteria for characterizing dissipative NIMs, originally established with h j and h q in [17], can be expressed with the real and imaginary parts of the constitutive parameters (j, q):…”

“…Therefore, for the sake of completeness and full understanding of the positive/negative-index regimes of dissipative isotropic metamaterials, the (former) four quadrants must be enriched by sub-diagrams invoking the signs of the imaginary parts of j and q. Following on from recent works [17], we propose here insightful diagrammatic representations, based on more readable criteria (valid for acoustics and electromagnetism), for the characterization of dissipative NIMs.…”