  Light-matter interactions at the nanoscale constitute a fundamental
ingredient for engineering applications in nanophotonics and quantum optics. To
this regard electromagnetic Mie resonances excited in high-refractive index
dielectric nanoparticles have recently attracted interest because of their
lower losses and better control over the scattering patterns compared to their
plasmonic metallic counterparts. The emergence of several resonances in those
systems results in an overall high complexity, where the electric and magnetic
dipoles have significant overlap in the case of spherical symmetry, thus
concealing the contributions of each resonance separately. Here we show,
experimentally and theoretically, the emergence of strong light-matter coupling
between the magnetic and electric-dipole resonances of individual silicon
nanodisks coupled to a J-aggregated organic semiconductor resonating at optical
frequencies, evidencing how the different properties of the two resonances
results in two different coupling strengths. The energy splittings observed are
of the same order of magnitude as in similar plasmonic systems, thus confirming
dielectric nanoparticles as promising alternatives for localized strong
coupling studies. The coupling of both the electric and magnetic dipole
resonances can offer interesting possibilities for the control of directional
light scattering in the strong-coupling regime and the dynamic tuning of
nanoscale light-matter coupled states by external fields.
