Second Harmonic Emission from Dielectric Nanoresonators in the Absorption Regime

We study second harmonic generation in dielectric nanocylinders as a function of the wavelength of the incident field and geometrical dimensions. Uncommonly, we consider a spectral range in which the emitted nonlinear signal is partially absorbed by the dielectric. Surprisingly, we reveal that the second harmonic efficiency does not decrease as the imaginary part of the complex dielectric refractive index increases. Indeed, the presence of higher order multipoles supported by the resonators at the fundamental wavelength can significantly boost the generated second harmonic signal even in the dielectric absorption spectral region achieving nonlinear efficiency of the same order of magnitude with respect to the lossless case.