High frequency electro-optic measurement of strained silicon racetrack resonators

TL;DR

This study uses high-frequency measurements to investigate the electro-optic effect in strained silicon resonators, revealing plasma carrier dispersion as the main cause and setting a new upper limit on the induced non-linearity.

Contribution

It provides the first high-frequency analysis of strained silicon resonators, demonstrating that plasma effects dominate the electro-optic response and establishing a lower upper limit for induced non-linearity.

Findings

Electro-optic modulation vanishes at high frequencies regardless of strain.

Plasma carrier dispersion is responsible for the observed electro-optic effect.

Upper limit of 8 pm/V for induced $oldsymbol{ ext{chi}}^{(2)}$ tensor element at -0.5 GPa stress.

Abstract

The observation of the electro-optic effect in strained silicon waveguides has been considered as a direct manifestation of an induced $\chi^{(2)}$ non-linearity in the material. In this work, we perform high frequency measurements on strained silicon racetrack resonators. Strain is controlled by a mechanical deformation of the waveguide. It is shown that any optical modulation vanishes independently of the applied strain when the applied voltage varies much faster than the carrier effective lifetime, and that the DC modulation is also largely independent of the applied strain. This demonstrates that plasma carrier dispersion is responsible for the observed electro-optic effect. After normalizing out free carrier effects, our results set an upper limit of $8\,pm/V$ to the induced high-speed $\chi^{(2)}_{eff,zzz}$ tensor element at an applied stress of $-0.5\,GPa$. This upper limit is about one order of magnitude lower than the previously reported values for static electro-optic measurements.