  Parametric oscillation is a fundamental concept that underlies nonlinear
wave-matter interactions, leading to generation or amplification of new
frequency components. Using a temporal modulation generated by the heterodyne
interference of a control direct current (dc) electric field and an optical
field, we resonantly drive large-amplitude oscillations of amorphous silicon
meta-atoms - nanoscale building blocks of an optical metasurface. We observed
gigantically enhanced second harmonic generation (SHG) with an
electric-field-controlled on off ratio over 10000 and an ultra-high modulation
depth of 405 per volt. A simple Mathieu equation involving a time-dependent
resonance captures most features of experiment data (for example, SHG intensity
has super-quadratic dc field dependence), and provides insight into SHG
efficiency enhancement through parametric modulations. Our work provides a
compact, electric-tunable and CMOS (Complementary Metal-Oxide Semiconductor)
compatible approach to boosting and dynamically controlling nonlinear light
generations on a chip. It holds great potential for applications in optical
communications and signal processing.
