Electric field-induced second-order nonlinear optical effects in silicon waveguides

The symmetry of crystalline silicon inhibits a second-order optical nonlinear susceptibility, chi((2)), in complementary metal-oxide- semiconductor-compatible silicon photonic platforms. However, chi((2)) is required for important processes such as phase-only modulation, second-harmonic generation (SHG) and sum/difference frequency generation. Here, we break the crystalline symmetry by applying direct-current fields across p-i-n junctions in silicon ridge waveguides and induce a chi((2)) proportional to the large chi((3)) of silicon. The obtained chi((2)) is first used to perturb the permittivity (the direct-current Kerr effect) and achieve phase-only modulation. Second, the spatial distribution of chi((2)) is altered by periodically patterning p-i-n junctions to quasi-phase-match pump and second-harmonic modes and realize SHG. We measure a maximum SHG efficiency of P-2 omega/P-omega(2) = 13 +/- 0.5% W-1 at lambda(omega) = 2.29 mu m and with field-induced chi((2)) = 41 +/- 1.5 pmV(-1). We expect such field-induced chi((2)) in silicon to lead to a new class of complex integrated devices such as carrier-envelope offset frequency stabilizers, terahertz generators, optical parametric oscillators and chirp-free modulators.