Point dipole and quadrupole scattering approximation to collectively responding resonator systems

Abstract

We develop a theoretical formalism for collectively responding point scatterers where the radiating electromagnetic fields from each emitter are considered in the electric dipole, magnetic dipole, and electric quadrupole approximation. The contributions of the electric quadrupole moment to electromagnetically-mediated interactions between the scatterers are derived in detail for a system where each scatterer represents a linear $RLC$ circuit resonator, representing common metamaterial resonators in radiofrequency, microwave, and optical regimes. The resulting theory includes a closed set of equations for an ensemble of discrete resonators that are radiatively coupled to each other by propagating electromagnetic fields, incorporating potentially strong interactions and recurrent scattering processes. The effective model is illustrated and tested for examples of pairs of interacting point electric dipoles, where each pair can be qualitatively replaced by a model point emitter with different multipole radiation moments.

References in corpus (5)

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Cited by in corpus (4)

• Describing meta-atoms using the exact higher-order polarizability tensors
• Strong radiative interactions and subradiance in disordered metamaterials
• Cooperative field localization and excitation eigenmodes in disordered metamaterials
• Point-dipole approximation for small systems of strongly coupled radiating nanorods