Fig. 1: Diagram of photo-induced quasi-phase-matching in Si₃N₄ microresonators.

a, Illustration of SH generation by AOP. The fundamental TE mode of the pump FH1 (ω) inside the waveguide is coupled to the microresonator. AOP inscribes a nonlinear grating on the circumference of the microresonator and provides QPM for efficient SH (2ω) generation. b, Dynamics of the AOP process. λ_P, pump wavelength; λ_SH, SH wavelength; λ_a, pump resonance wavelength; λ_b, SH resonance wavelength. In region I neither pump nor SH is resonant. In region II, as λ_P is tuned into pump resonance λ_a (resonant for pump), both λ_a and λ_b redshift due to the thermal and Kerr effects, compensating the mismatch between the virtual λ_SH and λ_b (still not resonant for SH). In region III, once being doubly resonant for pump and SH, efficient AOP takes place. A nonlinear grating is inscribed and SH at λ_SH is generated. In region IV, SH generation is sustained, albeit λ_b walks off from λ_SH. c, Artistic representation of χ⁽²⁾ grating structures inscribed in the 146-GHz microresonator. The shapes and periods of the χ⁽²⁾ gratings are given by the interference between the fundamental TE mode at the pump and several TE modes at the SH (SH1 to SH5 are depicted). d, An experimentally obtained TP image of the entire microresonator, reconstructed from the superposition of several depth-scanned TP measurements. Eleven QPM grating periods are clearly recognized in the 146-GHz microresonator poled at 1,543.00 nm.