Interferometric description of optical metamaterials

Abstract

We introduce a simple theoretical model that describes the interaction of light with optical metamaterials in terms of interfering optical plane waves. In this model, a metamaterial is considered to consist of planar arrays of densely packed nanoparticles. In the analysis, each such array reduces to an infinitely thin homogeneous sheet. The transmission and reflection coefficients of this sheet are found to be equal to those of an isolated nanoparticle array and, therefore, they are easy to evaluate numerically for arbitrary shapes and arrangements of the particles. The presented theory enables fast calculation of electromagnetic fields interacting with a metamaterial slab of an arbitrary size, which, for example, can be used to retrieve the effective refractive index and wave impedance in the material. The model is also shown to accurately describe optically anisotropic metamaterials that in addition exhibit strong spatial dispersion, such as bifacial metamaterials.

Bifacial Metasurface with Quadrupole Optical Response

“…The disc-dimer geometry (see the inset of Fig. 1) is chosen because it is a generic asymmetric configuration for controlling the two most significant lowest-order multipole moments, the electric-current quadrupole and electric dipole moments, independently of the polarization of the incident field [19,[29][30][31]. Similar interaction effects, such as asymmetric optical scattering and reflection, have been reported in regard to asymmetric nanoscatterers [32][33][34][35] and metasurfaces in the infrared [36][37][38] and microwave [39] spectral ranges.…”

Optical wave parameters for spatially dispersive and anisotropic nanomaterials

“…(3)- (6). All the necessary tangential reflection and transmission coefficients at the slab surfaces, ρ i j and τ i j , are shown in Fig.…”

“…Essentially all optical nanomaterials are spatially dispersive, because their structural units are not negligibly small compared to optical wavelengths [1][2][3][4][5][6][7][8][9][10][11]. This makes the description of such materials in terms of electric permittivity and magnetic permeability tensors impractical, because optical plane waves propagating in the material in different directions experience different material parameters even if their polarizations are the same.…”

“…When spatial dispersion is significant, conventional effective medium approximations based on Clausius-Mossotti-or Maxwell-Garnett-type spatial averaging of dipole excitations in the medium [12,13] yield incorrect results [1,14,15]. Usually, spatially dispersive materials, such as metamaterials, are described in terms of plane-wave parameters, such as refractive index and impedance, that depend on both the polarization and the propagation direction of the wave [1][2][3][4][5][6][7][8][9][10][11]. The parameters should therefore be given as functions of the wave propagation angles.…”

“…It is customary to divide the considered plane waves into transverse electric and transverse magnetic modes, for which either the electric or magnetic field vector is perpendicular to a certain symmetry plane of the field-matter system. However, when the wave parameters are retrieved from the transmission and reflection coefficients of a nanostructured material, it is common to assume that both the electric and magnetic fields in the material are transverse with respect to the wave vector [2,3,[5][6][7][8]. This approximation gives relatively accurate results, if the effects of spatial dispersion and optical anisotropy in the material are weak.…”