Understanding the Second-Harmonic Generation Enhancement and Behavior in Metal Core Dielectric Shell Nanoparticles

To explain recently observed up to 50-fold enhancement of the second harmonic (SH) signal from gold nanoparticles after depositing of a thin dielectric layer, we perform an analytical study of the SH generation by metal core-dielectric shell spherical nanoparticles (NPs). We derive analytical expressions for the SH intensity accounting for electric dipole and quadrupole impacts. On this basis, we discuss the SH response spectrum of coated gold and silver nanoparticles. The possibility of adjusting the SH scattering 1 regime to dipole or quadrupole resonant mode by varying the shell thickness is shown. We demonstrate that the thin, up to several NPs radii, dielectric cover of the NPs gives a significant advantage in the SH intensity in a line with the resonant enhancement. This effect is most pronounced in gold nanoparticles and even dominates resonant enhancement of the SH generation. This new result in nonlinear plasmonics provides a simple recipe for gold nanoparticles: thicker dielectric coating higher the second harmonic signal. Consideration of thicker (order of optical wavelength) coatings shows that spatial Mie resonances can result in additional several orders enhancement of the SH signal generated by metal core-dielectric shell spherical NPs.