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Silicon nitride (Si$_3$N$_4$) is an ever-maturing integrated platform fornonlinear optics. Yet, due to the absence of second-order ($\chi^{(2)}$)nonlinearity, Si$_3$N$_4$ is mostly considered for third-order ($\chi^{(3)}$)nonlinear interactions. Recently, this limitation was overcome by opticalpoling in both Si$_3$N$_4$ waveguides and microresonators via the photogalvaniceffect, resulting in the inscription of quasi-phase-matched $\chi^{(2)}$gratings. Here, we report cascaded nonlinear effects in a normal dispersionSi$_3$N$_4$ microresonator with combined $\chi^{(2)}$ and $\chi^{(3)}$nonlinearities. We demonstrate that the photo-induced $\chi^{(2)}$ grating alsoprovides phase-matching for the sum-frequency generation process, enabling theinitiation and successive switching of primary combs at pump wavelength.Additionally, the doubly resonant pump and second-harmonic fields allow forcascaded third-harmonic generation, where a secondary optically written$\chi^{(2)}$ grating is identified. Finally, we reach a low-noise, broadbandmicrocomb state evolved from the sum-frequency coupled primary comb. Theseresults expand the scope of cascaded effects in $\chi^{(2)}$ and $\chi^{(3)}$microresonators.

Photo-induced cascaded harmonic and comb generation in silicon nitride microresonators