Abstract
We introduce a technique to decompose the scattered near field of two-dimensional arbitrary metaatoms into its multipole contributions. To this end we expand the scattered field upon plane wave illumination into cylindrical harmonics as known from Mie's theory. By relating these cylindrical harmonics to the field radiated by Cartesian multipoles, the contribution of the lowest order electric and magnetic multipoles can be identified. Revealing these multipoles is essential for the design of metamaterials because they largely determine the character of light propagation. In particular, having this information at hand it is straightforward to distinguish between effects that result either from the arrangement of the metaatoms or from their particular design.
Highlights
Metamaterials may be understood as a kind of artificial matter that allows to control the mould of light predominantly by the geometry of their building blocks rather by their intrinsic material properties
The key ingredient is an expansion of the scattered field of the metaatoms upon plane wave illumination into cylindrical harmonics, i.e., we are restricting the current analysis to two-dimensional metaatoms
Since we focus here on two-dimensional structures, cylindrical harmonics are an appropriate system of eigenfunctions
Summary
Metamaterials may be understood as a kind of artificial matter that allows to control the mould of light predominantly by the geometry of their building blocks rather by their intrinsic material properties. The optical response contains a strong magnetic dipole field contribution leading to an appreciable dispersion in the effective permeability Such understanding of metamaterials is very versatile as it provides the possibility to optimize metaatoms for different spectral domains [12]. Either by optimizing the magnitude of the different multipolar contributions to match a certain angular scattering response or by probing for the scattering strength in certain directions where some multipole moments do not radiate, the multipolar response can be revealed It remains an open question how unique the assignments based on the far fields are. The key ingredient is an expansion of the scattered field of the metaatoms upon plane wave illumination into cylindrical harmonics, i.e., we are restricting the current analysis to two-dimensional metaatoms By relating these cylindrical harmonics to the field of Cartesian multipoles, it is possible to calculate their spectrally resolved amplitudes. This will be of particular importance for the prediction of effective properties of self-organized, bottom-up metamaterials which might not allow for a perfectly periodic metaatom arrangement
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