Extreme coupling: A route towards local magnetic metamaterials

Abstract

Genuinely homogeneous metamaterials, which may be characterized by local effective constitutive relations, are required for many spectacular metamaterial applications. Such metamaterials have to be made of meta-atoms, i.e., subwavelength resonators, which exhibit only electric and or magnetic dipole and negligible higher-order multipolar polarizabilities in the spectral range of interest. Here, we show that these desired meta-atoms can be designed by exploiting the extreme coupling regime. Appropriate meta-atoms are identified by performing a multipole analysis of the field scattered from the respective meta-atom. To design those particular meta-atoms it is important to disclose the frequency and angular-dependent polarizability of both dipole moments. We demonstrate the applicability of a purely analytical model to accurately calculate for a normally incident plane wave reflection and transmission from meta-surfaces made of periodically arranged meta-atoms. With our work we identify a possible route towards the engineering of artificial materials while only considering the response from its constituents. Our approach is generally applicable to all spectral domains and can be used to evaluate and design metamaterials made from different constituting materials, e.g., metals, dielectrics, or semiconductors.

Tailoring dielectric resonator geometries for directional scattering and Huygens’ metasurfaces

“…quadrupoles, octupoles, etc.). This fact was very recently emphasized in [14] where the authors achieved local magnetic metamaterials through the use of the extreme coupling regime of cut-plate pairs or split ring resonators. In this paper we will make use of geometries based on perturbation theory, previously introduced in [15,16], as an alternative route to obtain resonators that exhibit dominant dipole resonances in certain frequency bands.…”

“…A common way to identify the multipoles that dominate the scattering response of isolated resonators is through the use of multipolar analysis or multipolar expansion [14,[17][18][19][20][21][22][23]. According to [17], the scattered field s E produced by a sphere can in general be written as an infinite series in the vector spherical harmonics emn N and omn M (where the subscripts e and o stand for even and odd, respectively), the so-called electromagnetic normal modes of the spherical particle, weighted by appropriate coefficients (1) In Eq.…”

On the deviation of metamaterial spheres from effective medium

“…The effects outlined above are particularly prominent in metamaterials with strongly interacting elements [12], such as those based on ring resonators. It also appears that having a resonance is essential for boundary effects to spread through the structure.…”

Ultracompact meta-pixels for high colour depth generation using a bi-layered hybrid metasurface

“…When the nanorods are anisotropic and small enough compared to the wavelength of interest, electric dipole (ED) and magnetic dipole (MD) are dominantly induced and the polarizability tensors can be reduced to , and . For the nanorods smaller than the wavelengths of the incident light, the nanorod layer can be modeled as the effective surface with averaged transverse polarization currents 19 , and their transmission and reflection matrices can be calculated as the following equations:where p x and p y are periods, ω is angular frequency, η 0 is the free space impedance, C is an interaction coefficient, and the superscript e and m mean electric and magnetic, respectively. As shown in Eqs 1 and 2, the transmission and reflection coefficients are combinations of ED and MD derived components.…”