Theoretical Model for Pattern Engineering of Harmonic Generation in All-Dielectric Nanoantennas

We develop a novel theoretical model for the study of harmonic generation in cylindrical structures of finite height. Our technique is based on the decomposition of the electromagnetic field over the complete set of modes of the corresponding infinite cylinder. Differently from previous works, in our model no constraints are given neither on the cross section nor on the refractive index of the cylinder. We then apply our approach in the special case of frequency doubling in tall AlGaAs nanodisks, where radiative modes can be neglected. Our results open new perspectives for optimization and engineering of the radiation pattern in harmonic generation processes at the nanoscale.