Selection Rules In Second Harmonic Generation Process Supported By Mie Resonances – METAMATERIALS 2018

In the paper we discuss the second harmonic generation (SHG) from dielectric nanoparticles possessing bulk nonlinear tensor χ (2) . Having high refractive index subwave-length nanoparticle demonstrate Mie resonances in the optical spectrum. We theoretically study how the polarization structure of Mie modes govern the SHG process. We identify the allowed transitions by building the selection rules for spherical nanoparticles basing on the Mie theory. Moreover, one can develop a group theory approach, extrapolating it over nanoparticles of more complicated shape.