Fig. 1. Ultralow-loss Si3N4 7 m spiral resonator: (a) cross-sectional view showing that the thickness of the waveguide is 100 nm, (b) spiral resonator layout (through and drop ports are shown), (c) mode profile from the propagating mode inside the 10 μm wide and 100 nm thick resonator, (d) photograph of the spiral resonator in comparison with US 1 cent, (e) intrinsic and loaded quality factors of the spiral resonator.

Fig. 2. (a) Concept of the modulated swept method to determine the FSR and resonance linewidth of the spiral resonator. The laser is locked to the central peak, while the modulation sideband is swept over the adjacent resonances. The heterodyne interference between the central peak and the sideband is used to deduce the FSR. (b) Transmission spectrum from the spiral resonator. Red line: Lorentzian curve fitting. (c) Error signal for three sweeps over the resonance, which shows the signal used for locking the laser to the resonance. (d) FSR measurement setup based on the modulated-wave sweeping method. FL, fiber laser; EOM, electro-optic modulator; PC, polarization controller; SPR, spiral resonator; PD, photodetector; LIA, lock-in-amplifier; PID, servo-controller; SA, spectrum analyzer with frequency tracking generator.

Fig. 3. (a) Chromatic dispersion measurement setup with reference to the calibrated FRR. TL, tunable laser; PC, polarization controller; PD, photodetector; FRR, calibrated fiber ring resonator; SPR, spiral resonator under measurement; scope, large record length oscilloscope (6.25 million). (b) The integrated dispersion of the spiral resonator over a wavelength range of 10 nm centered at 1565 nm and the calculated dispersion parameters. (c) Dispersion coefficient (left) and group velocity dispersion (right) calculated from the integrated dispersions measured at each center wavelength. (d) A resonance frequency shift introduced as per SPR temperature change of 1.6 K that is used to calculate the thermo-optic coefficient.

Fig. 4. Correction of laser sweeping nonlinearity using the drop port of the spiral resonator (SPR). (a) Setup implemented for correction of the sweeping nonlinearity of a tunable laser (TL) during measurement of the FSR of a Mach–Zehnder interferometer (MZI) using the SPR. PD, photodetector; PC, polarization controller. (b) Oscilloscope traces for the MZI (upper) at CH1 and the spiral resonator (lower) at CH2 that are acquired during laser is sweeping (parts of the traces are shown). (c) FFT of the swept trace before nonlinearity correction, and (d) FFT of the swept trace after applying the nonlinearity correction. The center frequency represents the FSR of the interferometer.

Fig. 5. (a) LiDAR experiment of round-trip distance of up to 40 m. PC, polarization controller; PD, photodetector; CR, circulator; CL, collimator; RR, retro-reflector; SPR, 7 m spiral resonator. (b) Standard deviation of measurement of 8 m with different laser sweeping ranges from 1 nm to 30 nm. (c) Standard deviation of the measured round-trip distances up to 40 m by sweeping the wavelength of a tunable laser over 10 nm without correcting the sweeping nonlinearity. (d) Standard deviation of the measured round-trip distances up to 40 m after correcting the sweeping nonlinearity with the SPR which shows enhancement of 4 orders of magnitude in precision.