  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 neglects the excitation of
higher-order multipoles. 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 is significantly 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. As we prove, such nonlocal response is
especially pronounced in the vicinity of anapole minimum in the scattering
cross-section. We examine the excitation of high-index dielectric disk in
microwave domain and silicon nanodisk in near infrared applying
group-theoretical analysis and retrieving the nonlocal corrections to the
dipole moments. Extending the discrete dipole model to include nonlocality of
the dipole response, we demonstrate an improved agreement with 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.
