  Nonlinear optical phenomena in nanostructured materials have been challenging
our perceptions of nonlinear optical processes that have been explored since
the invention of lasers. For example, the ability to control optical field
confinement, enhancement, and scattering almost independently, allows nonlinear
frequency conversion efficiencies to be enhanced by many orders of magnitude
compared to bulk materials. Also, the subwavelength length scale renders phase
matching issues irrelevant. Compared with plasmonic nanostructures, dielectric
resonator metamaterials show great promise for enhanced nonlinear optical
processes due to their larger mode volumes. Here, we present, for the first
time, resonantly enhanced second-harmonic generation (SHG) using Gallium
Arsenide (GaAs) based dielectric metasurfaces. Using arrays of cylindrical
resonators we observe SHG enhancement factors as large as 104 relative to
unpatterned GaAs. At the magnetic dipole resonance we measure an absolute
nonlinear conversion efficiency of ~2X10^(-5) with ~3.4 GW/cm2 pump intensity.
The polarization properties of the SHG reveal that both bulk and surface
nonlinearities play important roles in the observed nonlinear process.
