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

Abstract

The symmetry of crystalline silicon inhibits a second-order optical nonlinear susceptibility, χ⁽²⁾, in complementary metal–oxide–semiconductor-compatible silicon photonic platforms. However, χ⁽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 χ⁽²⁾ proportional to the large χ⁽³⁾ of silicon. The obtained χ⁽²⁾ is first used to perturb the permittivity (the direct-current Kerr effect) and achieve phase-only modulation. Second, the spatial distribution of χ⁽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_2ω/P_ω² = 13 ± 0.5% W⁻¹ at λ_ω = 2.29 µm and with field-induced χ⁽²⁾ = 41 ± 1.5 pm V^–1. We expect such field-induced χ⁽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.