Fig. 2. Characterizing the integrated hybrid heterogeneous Si₃N₄–LiNbO₃ platform.

a, Transmission (T, blue) and reflection (R, orange) spectra of a heterogeneous Si₃N₄–LiNbO₃ 102-GHz-FSR microresonator (see Extended Data Fig. 2 for the full dataset). b, The histogram shows the distribution of linewidths of 532 resonances for the fundamental transverse electric mode TE₀₀ of the 102-GHz-FSR device with a median linewidth of about 100 MHz, corresponding to a quality factor of 1.9 × 10⁶ (κ₀ is the intrinsic cavity decay rate). c, Optical spectrum of the free-running DFB laser diode with 50 dB side mode suppression ratio (SMSR). d, Experimental set-up for linewidth measurements with the hybrid integrated laser using the heterodyne beatnote method. AFG, arbitrary function generator; DSO, digital storage oscilloscope. The forward pump wave a⁺ is marked by a solid red line, and the reflected backward wave a⁻ by a dashed red line. e, Comparison of the laser linewidth for the free-running DFB case and the case where the DFB is self-injection-locked to a heterogeneous Si₃N₄–LiNbO₃ microresonator. f, Time–frequency map of the beatnote showing the laser frequency change on linear modulation of the diode current. The white dashed lines mark the boundaries of the self-injection locking bandwidth, where almost no laser frequency change is observed. g, Time–frequency map of the beatnote showing the laser frequency change upon linear tuning of the cavity resonance by applying voltage to the electrodes. The DFB current remained fixed in the self-injection locking range. h, Frequency noise spectra of the free-running DFB (blue) and the DFB self-injection-locked to the 102-GHz-FSR heterogeneous Si₃N₄–LiNbO₃ microresonator (orange). The evaluated thermo-refractive noise (TRN) limit and the beta-line are given for reference (orange dash-dotted and red dashed lines, respectively).