I. Introduction
Optical devices are potentially much faster and efficient than the electronic devices, and could in principle lead to a sizable reduction in global energy consumption. All-optical gates in fact consume as little as 10 fJ per Boolean operation, against the100 fJ of the present electronic devices, yet operating at much faster rates. The difficulty in realizing all-optical components, however, arises from the fact that nonlinear optical interactions are generally very weak, limiting the possibility to control the photon flows. Nonlinear optical process of frequency conversion such as second- and third-harmonic generation offer great opportunities for applications in nanophotonics [1] and optical microscopy [2]. However, nonlinear optical components in such devices are often bulky and rely on complex phase-matching techniques to compensate for the momentum mismatch between the pump and generated signals, for efficient frequency conversion processes.