Modal analysis of anapoles, internal fields, and Fano resonances in dielectric particles

All-dielectric nanostructures have aroused strong interest because of their potential to trap light at subwavelength scales and to yield strong internal electric or magnetic field enhancements. Optimizing the internal fields appears as a crucial challenge for enhancing light matter interactions in all-dielectric nanostructures. Mie resonators host radiationless states called anapoles associated to a pronounced minimum of light scattering. However, the question is to know whether these radiationless states maximize the internal field intensities. Here we use a modal expansion of the internal and external fields to demonstrate that anapoles in dielectric Mie resonators result from a Fano resonance produced by the interference between two mode contributions with low and high quality factors plus an additional non-resonant term. A modal expansion of the internal field enhancement averaged over the whole scatterer volume shows that the maximum of the internal field enhancement does not occur at the anapole frequency but at the real part of the eigenfrequency associated with the high quality factor. This analysis is carried out for both electric and magnetic modes of the dielectric scatterer and evinces that a larger internal field enhancement is found for the first magnetic dipole resonance, even though this resonance does not feature an anapole behavior.