  In the developing field of nonlinear plasmonics, it is important to
understand the fundamental relationship between properties of the localized
surface plasmon resonance (LSPR) of metallic nanostructures and their nonlinear
optical responses. A detailed understanding of nonlinear responses from
nanostructures with well characterized LSPRs is an essential prerequisite for
the future design of sophisticated plasmonic systems with advanced functions to
control light. In this article, we investigate the second order harmonic (SH)
responses from gold nanocrescent (Au NC) antennas which have wavelength and
polarization sensitive LSPRs in the visible and near-infrared wavelength range.
The wavelength dependence of the SH intensity exhibits spectral profiles
different from dipole LSPR bands in absorbance spectra. The incident
polarization angle dependence was found to vary significantly when the
excitation wavelength was tuned over the dipole band. Finite-difference
time-domain calculations coupled with a nonlinear hydrodynamic model were
carried out for Au NC arrays to investigate the local field enhancement of the
incoming fundamental and emitting SH light. The experimental and theoretical
results indicate that the effects of higher order LSPRs, such as quadrupole and
multipole resonances, occurring at SH wavelengths are important in governing
the SH generation process. Also, it is shown that the incident polarization
angle dependence of SH signals is very strongly sensitive to nanoscale
variations in the NC shape.
