Due to their extraordinary plasmonic properties, gold nanoparticles have been widely used for a variety of applications and localized surface plasmon resonance (LSPR) has become a powerful biosensing technique. This technique allows for label-free, rapid and real time detection, which makes it one of the first candidate for medical diagnostics, environmental monitoring, and food safety. Unfortunately, metallic nanoparticles present high dissipative losses and optical heating. To overcome this problem, in the last decade the use of high index dielectric materials, instead that metallic ones, have been proposed. These materials, like Si, do not support plasmons but they support the so-called Mie resonances, or geometrical resonances.