  Plasmonic nanostructures that support surface plasmon (SP) resonance
potentially provide a route for the development of nanoengineered nonlinear
optical devices. In this work, second-order nonlinear light scattering,
specifically sum-frequency generation (SFG) and second-harmonic generation
(SHG), from plasmonic nanoantennas is modeled by the boundary element method
(BEM). Far-field scattering patterns are compared with the results calculated
by the Mie theory to validate the accuracy of the developed nonlinear solver.
The SFG from a multi-resonant nanoantenna (MR-NA) and the SHG from a
particle-in-cavity nanoantenna (PIC-NA) are analyzed by using the developed
method. Enhancements of the scattering signals due to double-resonance of the
MR-NA and gap plasmonic mode of the PIC-NA are observed. Unidirectional
nonlinear radiation for the PIC-NA is realized. Moreover, its emission
direction can be controlled by the location of the nanosphere. This work
provides new theoretical tools and design guidelines for plasmonic nonlinear
nanoantennas.
