Non-integer harmonics generation by photon acceleration in rapidly evolving nonlinear semiconductor metasurfaces

Optical harmonics generation is one of the most fundamental nonlinear frequency conversion effects, whereby an integer number of low-energy photons merge into a single high-energy photon inside a nonlinear material. Here, we report an experimental demonstration of non-integer harmonics generation from mid-infrared light in a resonant silicon metasurface. We show that the acceleration of mid-infrared photons trapped inside the metasurface, triggered by the rapid evolution of the metasurface resonance due to free carrier generation, is responsible for the generation of upconverted photons with peak frequencies of up to $approx 3.1omega$. A simple model of resonant photon acceleration is in good agreement with experimental results, and shows a clear path for higher photon acceleration efficiency, which is estimated to be around 22% in our experiments.