Efficient Second Harmonic Generation by Mode Phase Matching in a Silicon Waveguide

Bulk silicon possesses no second-order susceptibility (χ
⁽²⁾
), inhibiting second-order nonlinear processes in the emerging silicon photonic platform. Here, we propose a method to overcome this limitation by enabling a third-order (χ
⁽³⁾
) nonlinear mixing scheme between optical waves and an externally applied static electric field inside a silicon waveguide. We show in theory that facilitated by a modal phase-matching scheme efficient second-harmonic generation can be realized under an applied voltage of 65 V, giving rise to an equivalent χ
⁽²⁾
= 4.7 pm/V. We also show that unlike the classical second-harmonic generation, the wavelengths of phase-matched pump and second-harmonic waves are pump-power dependent due to the χ
⁽³⁾
nature of this process.