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Electromagnetic Scattering by a Cluster of Hybrid Dielectric-Plasmonic Dimers

We consider time-harmonic electromagnetic scattering by a cluster of hybrid dielectric-plasmonic dimers in $\mathbb{R}^3$. Each dimer consists of a high-contrast dielectric nanoparticle and a moderately contrasting plasmonic nanoparticle separated by a subwavelength distance. The cluster is assumed to contain many such dimers whose size $a$ is small compared to the wavelength, with intra-dimer and inter-dimer distances scaling like $a^{t_1}$ and $a^{t_2}$, and the frequency is tuned near suitable electric and magnetic resonances of the associated Newtonian and magnetization operators on the reference shapes. Under these geometric, contrast and spectral assumptions, we derive a Foldy--Lax type approximation for the Maxwell system. We show that the scattered field and its far field admit asymptotic expansions in terms of four moments attached to each dimer, which solve an explicit finite-dimensional linear system. We prove invertibility of this system under quantitative smallness conditions on the contrast and the dimer density, and we obtain error estimates uniform in the number of dimers. By extracting the dominant components, we further show that each hybrid dimer behaves, at leading order, as a co-located electric and magnetic dipole driven by the local fields, and we identify the corresponding $6\times 6$ polarizability matrix. This provides a discrete model for clusters of hybrid dimers that is suitable for fast forward simulations, inverse schemes, and as input for effective-medium descriptions. In particular, it suggests parameter regimes where clusters of hybrid dimers can generate (double) negative effective permittivity and permeability and bi-anisotropic constitutive laws and eventually hyperbolic media.