  Plasmonic enhancement of nonlinear optical processes confront severe
limitations arising from the strong dispersion of metal susceptibilities and
small interaction volumes that hamper desirable phase-matching-like conditions.
Maximizing nonlinear interactions in nanoscale systems require simultaneous
excitation of resonant modes that spatially and constructively overlap at all
wavelengths involved in the process. Here, we present a hybrid rectangular
patch antenna design for optimal second harmonic generation (SHG) that is
characterized by a non-centrosymmetric dielectric/ferroelectric material at the
plasmonic hot spot. The optimization of the rectangular patch allows for the
independent tuning of various modes of resonances that can be used to enhance
the SHG process. We explore the angular dependence of SHG in these hybrid
structures and highlight conditions necessary for maximal SHG efficiency.
Furthermore, we propose a novel configuration with a periodically-poled
ferroelectric layer for orders-of-magnitude enhanced SHG at normal incidence.
Such a platform may enable the development of integrated nanoscale light
sources and on-chip frequency converters.
