Photogalvanic second harmonic generation in Si3N4 for 1 Hz level on-chip metrology and spectroscopy

Abstract

The coherent photogalvanic (PG) effect induces an effective $\chi^{(2)}$ nonlinearity in natively $\chi^{(3)}$ silicon nitride integrated photonics, unlocking pathways toward chip-scale precision spectroscopy and optical clockworks via second harmonic generation (SHG). While quasi-phase-matched PG-SHG using spatially varying internal electric fields offers tuning flexibility, it is often accompanied by pump-power- and detuning-dependent frequency offsets. Here, we investigate whether direct phase-matching---utilizing an intermodal scheme that generates a spatially uniform electric field---can support metrologically compatible SHG. By comparing the fundamental and doubled optical frequencies in a silicon nitride microresonator, we test the preservation of the (2:1) frequency ratio in directly phase-matched PG-SHG. We observe a frequency offset of $< 1\mathrm{~Hz}$, contrasting with previous limitations in quasi-phase-matched configurations. Furthermore, we measure a residual fractional frequency instability of $2\times 10^{-15}$ at $1\mathrm{~s}$, averaging down to the $10^{-16}$ level at $1000\mathrm{~s}$, with multi-hour deviations remaining below $1\mathrm{~Hz}$. These results establish directly phase-matched PG-SHG as a robust, metrologically compatible route to effective $\chi^{(2)}$ functionality, combining sub-Hz frequency-ratio fidelity and high coherence on a mature integrated platform for optical clockworks, self-referencing, and precision spectroscopy.