The electromagnetic waves generated by a cluster of nanoparticles with high refractive indices

• Published in: Journal of the London Mathematical Society 2023-10, Vol.108 (4), p.1531-1616
• Main Authors: Cao, Xinlin, Ghandriche, Ahcene, Sini, Mourad
• Format: Article
• Language: English
• ISSN: 0024-6107; 1469-7750
• DOI: 10.1112/jlms.12788

We estimate the electromagnetic field generated by a cluster of dielectric nanoparticles embedded into a background made up of a vacuum. The dielectric nanoparticles are small scaled but enjoy high contrast of their relative permittivity. Such scales/contrasts can be ensured using the Lorentz model with incident frequencies chosen appropriately close to the undamped resonance frequency (appearing in the Lorentz model). Under certain ratio between their size and contrast, these nanoparticles generate resonances, called dielectric resonances. These resonances are characterized and computed via the spectrum of the electric Newtonian potential operator, stated on the support of nanoparticles, and projected on the space of divergence‐free fields with vanishing boundary normal components. We characterize the dominant field generated by a cluster of such dielectric‐resonating nanoparticles. In this point‐interaction approximation, the nanoparticles can be distributed to occupy volume‐like domains or low‐dimensional hypersurfaces where periodicity is not required. The form of these approximations suggests that the effective electromagnetic medium, equivalent to the cluster of such nanoparticles, is a perturbation of the magnetic permeability and not the electric permittivity. The cluster can be tuned such that the equivalent permeability has positive or negative values (while the permittivity stays unchanged).