Negative index materials: at the frontier of macroscopic electromagnetism

Spatial dispersion and the sign of the imaginary part of the permeability

“…1, left part). Indeed, the simplicity of such a structure makes it possible to define exactely, using the retrieval method [15], effective anisotropic permittivity ε eff (k , ω) and permeability µ eff (k , ω) for all frequencies ω and wave vectors k parallel to the interfaces (see Fig. 1, right part).…”

“…In this paper, the exact expressions of these effective anisotropic parameters are derived and their properties are analyzed [15]. In particular, it is shown that the parameters ε eff (k , ω) and µ eff (k , ω) are analytic functions in the half plane of complex frequencies ω with positive imaginary part [15]. Then, a relation similar to the equations ( 4) and ( 8) is derived for the effective permeability µ eff (k , ω) at k = 0:…”

“…Next, using that the starting multilayered structure is non-magnetic, the quasistatic limit provides µ eff (0, 0) = µ 0 and the relation ( 9) becomes [15]…”

“…In this paper, arguments are provided to support that, in passive media, the imaginary part of the magnetic permeability µ(ω) can take both positive and negative values, i.e. that the relation ( 3) is not valid [15]. These arguments are based on the analysis of two different situations: i) the hydrodynamical model and ii) the spatially dispersive effective anisotropic permeability of a multilayered structure.…”