Nonlocal response of Mie-resonant dielectric particles

Mie-resonant high-index dielectric particles are at the core of modern all-dielectric photonics. In many situations, their response to the external fields is well-captured by the dipole model, which incorporates electric and magnetic dipole moments of the scatterers neglecting higher-order multipole contributions. In that case, it is commonly assumed that the dipole moments induced by the external fields are given by the product of particle polarizability tensor and the field in the particle center. Here, we demonstrate that the dipole response of non-spherical subwavelength dielectric particles appears to be essentially more complex since the dipole moments are defined not only by the field in the particle center but also by the second-order spatial derivatives of the field thus giving rise to the nonlocal response of the individual scatterer which is especially pronounced in the vicinity of anapole minimum in the scattering cross-section. As an illustrative example, we examine the response of high-index dielectric disks applying group-theoretical analysis and retrieving the nonlocal corrections to the dipole response from full-wave numerical simulations. These results provide important insights into meta-optics of Mie-resonant non-spherical particles as well as metamaterials and metadevices based on them.