Relaxed dispersion constraints and metamaterial effective parameters with physical meaning for all frequencies

Abstract

Metamaterial effective parameters may exhibit freedom from typical dispersion constraints. For instance, the emergence of a magnetic response in arrays of split-ring resonators for long wavelengths cannot be attained in a passive continuous system obeying the Kramers-Kronig relations. We characterize such freedom by identifying the three possible asymptotes which effective parameters can approach when analytically continued. Apart from their dispersion freedom, we also demonstrate that the effective parameters may be redefined in such a way that they have a certain physical meaning for all frequencies. There exists several possible definitions for the effective permittivity and permeability whereby this is achieved, thereby giving several possible frequency variations for high frequencies, while nevertheless converging to the same dispersion for long wavelengths.

Hierarchical self-assembly of a bulk metamaterial enables isotropic magnetic permeability at optical frequencies

“…Although negative values of the imaginary part m 00 of the magnetic permeability were already reported in theoretical and numerical studies of metamaterials, it is an unusual result that deserves some comment. 33,34 The whole electromagnetic response of the MNCs arises from plasmonic resonant modes generated by a unique driving force, namely the electric field of the light wave. The (e,m) approach is an approximation that formally splits the unique spatially dispersive electric response into a pair of more familiar electric-like and magnetic-like responses, the latter deriving from second order spatial derivatives of the electric field.…”

Instantaneous modulations in time-varying complex optical potentials

“…We should mention that our choice of the permittivity suggests that the causality principle is not fulfilled, i.e., the parameters of the permittivity do not follow conventional dispersion constraints, as represented by the Kramers-Kronig relations. Given the known inconsistencies with the Kramers-Kronig relations for  -symmetric systems [60][61][62][63] and other artificial metamaterials with complex-valued permittivity [64][65][66][67][68], analogous relations must be constructed for various types of  -symmetric time-varying dielectric permittivities, relaxing the strict assumptions made for causality.…”

An introduction to spatial dispersion: revisiting the basic concepts

“…Following that the next three sections address each of geometric (III), structural (IV), and dynamic (V) spatial dispersions in turn. Note that the idea of spatial dispersion as being grounded in spatial properties as opposed to (spectral) wavevector ones is mirrored in the various treatments of temporal dispersion: although sometimes seen as a consequence of a dynamic time-domain process [8] particularly when implemented in FDTD algorithms [9], temporal dispersion is more often discussed in solely terms of a (spectral) frequency response [10,11].…”