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Quasi-phase-matching (QPM) is a widely adopted technique for mitigating stringent momentum conservation in nonlinear optical processes such as second-harmonic generation (SHG). It effectively compensates for the phase velocity mismatch between optical harmonics by introducing a periodic spatial modulation to the nonlinear optical medium. Such a mechanism has been further generalized to the spatiotemporal domain, where a non-stationary spatial QPM can induce a frequency shift of the generated light. Here we demonstrate how a spatiotemporal QPM grating, consisting in a concurrent spatial and temporal modulation of the nonlinear response, naturally emerges through all-optical poling in silicon nitride microresonators. Mediated by the coherent photogalvanic effect, a traveling space-charge grating is self-organized, affecting momentum and energy conservation, resulting in a quasi-phase-matched and Doppler-shifted second harmonic. Our observation of the photoinduced spatiotemporal QPM expands the scope of phase matching conditions in nonlinear photonics.

Second-harmonic generation allows for coherently bridging distant regions of the optical spectrum, with applications ranging from laser technology to self-referencing of frequency combs. However, accessing the nonlinear response of a medium typically requires high-power bulk sources, specific nonlinear crystals, and complex optical setups, hindering the path toward large-scale integration. Here we address all of these issues by engineering a chip-scale second-harmonic (SH) source based on the frequency doubling of a semiconductor laser self-injection-locked to a silicon nitride microresonator. The injection-locking mechanism, combined with a high-Q microresonator, results in an ultra-narrow intrinsic linewidth at the fundamental harmonic frequency as small as 57 Hz. Owing to the extreme resonant field enhancement, quasi-phase-matched second-order nonlinearity is photoinduced through the coherent photogalvanic effect and the high coherence is mapped on the generated SH field. We show how such optical poling technique can be engineered to provide efficient SH generation across the whole C and L telecom bands, in a reconfigurable fashion, overcoming the need for poling electrodes. Our device operates with milliwatt-level pumping and outputs SH power exceeding 2 mW, for an efficiency as high as 280%/W under electrical driving. Our findings suggest that standalone, highly-coherent, and efficient SH sources can be integrated in current silicon nitride photonics, unlocking the potential of $\chi^{(2)}$ processes in the next generation of integrated photonic devices.

Quasi-phase-matching for efficient backward second-harmonic generation (BSHG) requires sub-$\rm\mu$m poling periods, a non-trivial fabrication feat. For the first time, we report integrated first-order quasi-phase-matched BSHG enabled by seeded all-optical poling. The self-organized grating inscription circumvents all fabrication challenges. We compare backward and forward processes and explain how grating period influences the conversion efficiency. These results showcase unique properties of the coherent photogalvanic effect and how it can bring new nonlinear functionalities to integrated photonics.

Silicon nitride (Si$_3$N$_4$) is an ever-maturing integrated platform for nonlinear 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 optical poling in both Si$_3$N$_4$ waveguides and microresonators via the photogalvanic effect, resulting in the inscription of quasi-phase-matched $\chi^{(2)}$ gratings. Here, we report cascaded nonlinear effects in a normal dispersion Si$_3$N$_4$ microresonator with combined $\chi^{(2)}$ and $\chi^{(3)}$ nonlinearities. We demonstrate that the photo-induced $\chi^{(2)}$ grating also provides phase-matching for the sum-frequency generation process, enabling the initiation and successive switching of primary combs at pump wavelength. Additionally, the doubly resonant pump and second-harmonic fields allow for cascaded third-harmonic generation, where a secondary optically written $\chi^{(2)}$ grating is identified. Finally, we reach a low-noise, broadband microcomb state evolved from the sum-frequency coupled primary comb. These results expand the scope of cascaded effects in $\chi^{(2)}$ and $\chi^{(3)}$ microresonators.

The coherent photogalvanic effect leads to the generation of a current under the absorption interference of coherent beams and allows for the inscription of space-charge gratings leading to an effective second-order susceptibility ($\chi^{(2)}$). The inscribed grating automatically results in quasi-phase-matching between the interfering beams. Theoretical and experimental studies have been carried out, mostly focusing on the degenerate case of second-harmonic generation, showing significant conversion efficiency enhancements. However, the link between the theory and experiment was not fully established such that general guidelines and achievable conversion efficiency for a given material platform are still unclear. In this work, we theoretically analyze the phenomenological model of coherent photogalvanic effect in optical waveguides. Our model predicts the existence of non-degenerate sum-frequency generation quasi-phase-matching gratings, which is confirmed experimentally for the first time. In addition, we rigorously formulate the time dynamics of the space-charge grating inscription in coherent photogalvanic process. Based on developed theoretical equations for the time dynamics of the space-charge grating formation, we extract the material parameters governing the process for our experimental platform, stoichiometric silicon nitride. The results obtained provides a basis to compare the performances and potentials of different platforms. This work not only supplements the theory of coherent photogalvanic effect, but also enables us to identify critical parameters and limiting factors for the inscription of $\chi^{(2)}$ gratings.

Integrated entangled photon-pair sources are key elements for enabling large-scale quantum photonic solutions, and addresses the challenges of both scaling-up and stability. Here we report the first demonstration of an energy-time entangled photon-pair source based on spontaneous parametric down-conversion in silicon-based platform through an optically induced second-order ($\chi^{(2)}$) nonlinearity, ensuring type-0 quasi-phase-matching of fundamental harmonic and its second-harmonic inside the waveguide. The developed source shows a coincidence-to-accidental ratio of 1635 at 8 of $\mu$W pump power. Remarkably, we report two-photon interference with near-perfect visibility of 99.36$\pm1.94\%$, showing high-quality photonic entanglement without excess background noise. This opens a new horizon for quantum technologies requiring the integration of a large variety of building functionalities on single chips.

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.