  Bringing efficient second-order nonlinear effects in integrated photonics is
an important task motivated by the prospect of enabling all possible optical
functionalities on chip. Such task has proved particularly challenging in
silicon photonics, as materials best suited for photonic integration lack
second-order susceptibility ($\chi^{(2)}$). Methods for inducing effective
$\chi^{(2)}$ in such materials have recently opened new opportunities. Here, we
present optically reconfigurable quasi-phase-matching in large radius
Si$_3$N$_4$ microresonators resulting in mW level on-chip second-harmonic
generated powers. Most importantly we show that such all-optical poling can
occur unconstrained from intermodal phase-matching, leading to widely tunable
second-harmonic generation. We confirm the phenomenon by two-photon imaging of
the inscribed $\chi^{(2)}$ grating structures within the microresonators as
well as by dynamic tracking of both the pump and second-harmonic mode
resonances. These results unambiguously establish that the photogalvanic
effect, responsible for all-optical poling, can overcome phase mismatch
constraints even in resonant systems, and simultaneously allow for the combined
record of output power and tunability.
