Abstract
We study second harmonic generation (SHG) by high-index dielectric nanoparticles and possessing bulk quadratic nonlinearity of a tensorial form. The nanoparticles exhibit Mie resonances in infrared and optical regions. We theoretically show how the polarization structure of the Mie modes governs the SHG process, and demonstrate that the superposition of two resonances at the incident light wavelength and at the SH wavelength provides us the enhancement of SHG. We also perform the multipolar decomposition of second harmonic radiation, and show that it is governed by the selection rules, defined by the symmetry of the nanoparticle shape, incident wave polarization and crystalline symmetry of the lattice.
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