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.
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