  Second-harmonic (SH) generation is tremendously important for nonlinear
sensing, microscopy and communication system. One of the great challenges of
current designs is to enhance the SH signal and simultaneously tune its
radiation direction with a high directivity. In contrast to the linear
plasmonic scattering dominated by a bulk dipolar mode, a complex
surface-induced multipolar source at the doubled frequency sets a fundamental
limit to control the SH radiation from metallic nanostructures. In this work,
we harness plasmonic hybridization mechanism together with a special selection
rule governing the SH radiation to achieve the high-intensity and
tunable-direction emission by a metallic particle-in-cavity nanoantenna
(PIC-NA). The nanoantenna is modelled with a first-principle, self-consistent
boundary element method, which considers the depletion of pump waves. The giant
SH enhancement arises from a hybridized gap plasmon resonance between the small
particle and the large cavity that functions as a concentrator and reflector.
Centrosymmetry breaking of the PIC-NA not only modifies the gap plasmon mode
boosting the SH signal, but also redirects the SH wave with a unidirectional
emission. The PIC-NA has a significantly larger SH conversion efficiency
compared to existing literature. The main beam of the radiation pattern can be
steered over a wide angle by tuning the particle's position.
