Effective optical response of metamaterials

Abstract

We use a homogenization procedure for Maxwell's equations in order to obtain in the local limit the frequency-dependent macroscopic dielectric-response tensor ⑀ ij M ͑͒ of metamaterials made of a matrix with inclusions of any geometrical shape repeated periodically with any lattice structure. We illustrate the formalism calculating ⑀ ij M ͑͒ for several structures. For dielectric rectangular inclusions within a conducting material we obtain an anisotropic response that may change from conductorlike at low to dielectriclike with resonances at large , attaining a very small reflectance at intermediate frequencies which can be tuned through geometrical tailoring. A simple explanation allowed us to predict and confirm similar behavior for other shapes, even isotropic, close to the percolation threshold.

Optical properties of nanostructured metamaterials

“…When l 0 $ L with L the size of the unit cell, R as obtained in Ref. [18] disagrees with our current calculation. This is not surprising, as here we have neglected retardation.…”

“…We first compare our results to the previous formalism of Ortiz et al [18] where a homogenization of Maxwell's equations was done without neglecting retardation. The retarded results do depend on the relative size of the unit cell and the wavelength of the incoming light.…”

“…Besides the average dielectric function, the formalism above incorporates the effects that the rapidly varying Fourier components of the microscopic response has on the macroscopic response, i.e., the localfield effect. Similar homogenization procedures are also found in [18,[21][22][23][24]. However, here we show how the homogenization of Maxwell's equations may be done by using Haydock's recursive Scheme [25].…”

“…Besides the single coupling to SPP modes, double resonant conditions, [15] and waveguide modes [16] seem to play an important role in the optical enhancement for metallic gratings with very narrow slits and for compound [17]. On the other hand, a very strong polarization dependence in the optical response of periodic arrays of oriented sub-wavelength holes on metal hosts [6,7,18] and single rectangular inclusion within a perfect conductor [19] have been recently reported. These studies did not rely on SPP excitation as a mechanism to explain their optical results.…”

Nonlocal homogenization theory in metamaterials: Effective electromagnetic spatial dispersion and artificial chirality

“…Two different homogenization techniques are obtained by assuming one of these two ingredients and subsequently incorporating the other. Therefore, starting from the photonic-crystal description of the structure where the spatial periodicity is fully taken into account, the effective medium response can be extracted in the long wavelength regime [19][20][21][22][23][24][25]. Conversely, the spatial rapidly-varying metamaterial features allows an asymptotic multi-scale analysis of the sample electromagnetic response which combined with the array periodicity yields the effective medium response [26][27][28][29][30][31][32].…”