Electric Field-Induced Second Order Nonlinear Optical Effects in Silicon   Waveguides
  The demand for nonlinear effects within a silicon platform to support photonic circuits requiring phase-only modulation, frequency doubling, and/or difference frequency generation, is becoming increasingly clear. However, the symmetry of the silicon crystal inhibits second order optical nonlinear susceptibility, $\chi^{(2)}$. Here, we show that the crystalline symmetry is broken when a DC field is present, inducing a $\chi^{(2)}$ in a silicon waveguide that is proportional to the large $\chi^{(3)}$ of silicon. First, Mach-Zehnder interferometers using the DC Kerr effect optical phase shifters in silicon ridge waveguides with p-i-n junctions are demonstrated with a $V_{\pi}L$ of $2.4Vcm$ in telecom bands $({\lambda}_{\omega}=1.58{\mu}m)$ without requiring to dope the silicon core. Second, the pump and second harmonic modes in silicon ridge waveguides are quasi-phase matched when the magnitude, spatial distribution of the DC field and $\chi^{(2)}$ are controlled with p-i-n junctions. Using these waveguides, second harmonic generation at multiple pump wavelengths are observed with a maximum efficiency of $P_{2{\omega}}/P_{\omega}^2$=12%/W at ${\lambda}_{\omega}=2.29{\mu}m$ in a 1mm long waveguide. This corresponds to a field-induced $\chi^{(2)}=41pm/V$, comparable to non-centrosymmetric media (LiNbO3, GaAs, GaN). The field-induced nonlinear silicon photonics will lead to a new class of CMOS compatible integrated devices spanning from near to mid infrared spectrum. 
E. Timurdogan, Christopher V. Poulton and M. R. Watts
physics.optics