Fig. 1. Principle of a hertz-level broadband spectrometer based on dual RF modulation. (a) Measurement scheme. A tunable CW laser is modulated by two RF signals (fmod1,fmod2) via an EOM. The modulated light is used to probe a reference cavity with quasi-periodic structures, such as a fiber cavity or integrated photonic cavity. The transmitted light is monitored by a PD and recorded by an oscilloscope to provide frequency reference markers for the scanning diode laser. The referenced diode laser is used to spectrally measure devices under test, such as on-chip photonic devices or gas absorption spectra. Optionally, part of the light probes a narrow linewidth atomic/molecular transition for an absolute frequency reference. (b) Principle of time-to-frequency conversion based on dual RF modulation. Dual RF modulation generates two sidebands neighboring the carrier frequency on both sides plotted on the frequency axis. While scanning the laser frequency, the generated sidebands form four additional transmission dips together with the carrier transmission dips in the time domain. The laser scan speed, laser frequency, and FSR can be precisely traced back to the modulation frequencies and their difference, and the time interval between the small sideband dips.

Fig. 2. Mode spectrum measurement of a fiber loop cavity calibrated by dual RF modulation. (a) Transmission spectrum of the 5-m fiber loop cavity. Inset, zoomed-in section showing the calibration markers around 1300 nm. The deep transmission dips are cavity resonances measured by the sweeping carrier laser while the small four dips within one FSR result from the RF modulation sidebands. (b) Measured FSR evolution (blue, upper panel) of the fiber loop cavity interrogated by the dual RF modulation scheme, together with a second-order polynomial fit (black), in contrast to the result (red, lower panel) measured by single RF modulation. (c) Frequency difference between the measured FSR by dual RF modulation and the fitted curve in panel (b). (d) Histogram of the data in panel (c) and a fitted Gaussian curve with an rms deviation of 8.3 Hz.

Fig. 3. Measured dispersion of the fiber cavity based on the fitted trace in Fig. 2(b). (a) Group velocity dispersion of a 5-m fiber cavity. (b) GDD of a 5-m-long fiber cavity (blue), 2-m-long fiber cavity (red), and 3 m of optical fiber.

Fig. 4. Si3N4 resonator mode spectrum and dispersion measurement. (a) Normalized transmission spectrum of the Si3N4 on-chip resonator with red markers on the fundamental TE mode family. (b) Zoomed-in spectrum around 1270.6 nm together with fiber cavity resonance markers. Inset, scanning electron microscope image of the 200-μm-diameter Si3N4 resonator used in the experiments. (c) Measured integrated dispersion profile (blue circles) at pump wavelength of 1310 nm together with a second-order polynomial fit (red trace). (d) Optical spectrum of a bright soliton generated in the Si3N4 resonator pumped at 1310 nm and a sech2 envelope fit (blue dashed trace). A dispersive wave (marked with an arrow) is observed at 1326 nm.

Fig. 5. Absorption spectrum of a gas cell filled with HF. (a) Transmission spectrum of the HF gas cell between 1270 and 1330 nm. (b) Spectral profile (solid black line) of the HF P(2) line together with the frequency markers (blue) from the 5-m fiber cavity. The dashed red line is a Voigt fit. (c) Fit residuals of the HF P(2) absorption line. The jumps in the fit residual are due to the discrete voltage resolution of the oscilloscope.