Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials

Abstract

We study the frequency dependence of the effective electromagnetic parameters of left-handed and related meta-materials of the split ring resonator and wire type. We show that the reduced translational symmetry (periodic structure) inherent to these meta-materials influences their effective electromagnetic response. To anticipate this periodicity, we formulate a periodic effective medium model which enables us to distinguish the resonant behavior of electromagnetic parameters from effects of the periodicity of the structure. We use this model for the analysis of numerical data for the transmission and reflection of periodic arrays of split ring resonators, thin metallic wires, cut wires as well as the left-handed structures. The present method enables us to identify the origin of the previously observed resonance/anti-resonance coupling as well as the occurrence of negative imaginary parts in the effective permittivities and permeabilities of those materials. Our analysis shows that the periodicity of the structure can be neglected only for the wavelength of the electromagnetic wave larger than 30 space periods of the investigated structure.

Analysis and Design of an Ultra-Thin Metamaterial Absorber

“…Around the resonant frequency, the antiresonant frequency dependence of the effective permittivity is observed. According to [31,32], that phenomena is due to the finite spatial periodicity of the metamaterial. (27)).…”

Extremely Sub-Wavelength Negative Index Metamaterial

“…At this frequency, the effective permittivity is ε = −9111.7 − i5655.8, and the effective permeability is μ = −4.7 + i6.7. Negative imaginary part in ε is due to the deficiency of the HEM approximation at this wavelength (i.e., the structure is still not sufficiently subwavelength) [43][44][45][46][47][48][49].…”

“…Furthermore, it was predicted that the accuracy of the widely used effective parameter retrieval procedure [41][42][43] would be improved for extremely sub-wavelength metamaterials. The retrieved effective parameters are obtained by inverting transmission and reflection coefficients under homogeneous effective medium (HEM) approximation.…”

“…The retrieved effective parameters are obtained by inverting transmission and reflection coefficients under homogeneous effective medium (HEM) approximation. Since the HEM approximation disregards the spatial dispersion, it usually results in non-physical negative imaginary parts in the retrieved constitutive parameters [43][44][45][46][47][48][49]. However, the influence of the spatial dispersion on the extremely sub-wavelength metamaterials diminishes and the accuracy of the HEM approximation improves.…”

Electromagnetic metamaterial with built-in microstructures

“…Here, the local effective medium is extended for including high spatial frequencies. The emphasis of this paper is not on the applicability of effective medium theories when eff or eff tends to infinity or the extraction of eff and eff from an artificial structure 19 but to explore the similarities and/or differences between a microstructured medium and its corresponding homogenized counterpart. The lattice spacing here is very small compared to the wavelength.…”