Extended Data Fig. 2: Cavity swept lock on molecular and mirror dispersion.

a, A simulation of ambient air absorption spectrum over 2,700–3,330 cm⁻¹, considering only the three most intense absorbers, HDO, CH₄ and H₂O, at concentrations of 1.6 ppm, 2.1 ppm and 0.2%, respectively, matched to our measured data presented in the main text. b, The corresponding intracavity refractive index spectrum calculated from a based on the Kramers–Kronig relations. It is non-rigorously assumed that molecular absorption is zero outside the plotted spectral range. Variation in the refractive index of more than 4 × 10⁻⁷ can be seen. c, Phase delay per reflection from a mirror surface. The data are obtained from the vendor for the 3-μm cavity used in this work. We arbitrarily vertically offset the entire curve by a constant so that the phase delay is zero at the rightmost wavenumber (3,330 cm⁻¹). d, Cavity resonance frequency distribution calculated on the basis of the molecular dispersion data in b and mirror dispersion data in c, using equation (2) shown in Methods. For our comb-cavity main resonance at cavity length equal to 0.548737 m, which allows all comb lines on cavity resonance simultaneously if intracavity dispersion is absent, detuning the cavity length by about λ/2 allows one to go to the side resonance, in which λ is the laser wavelength. Owing to the presence of intracavity dispersion, neither the main nor the side cavity resonances are a vertical straight line that will allow the comb instantaneous bandwidth to be coupled into the cavity simultaneously. In our presented data, molecular dispersion spreads the resonance cavity length either left or right every time a strong absorption line is scanned across, whereas mirror dispersion shifts the resonance cavity length to the left, which is slowly increasing with the decrease in wavenumber. At this level of dispersion, a swept lock must be used: a particular comb line is guaranteed to be coupled through the cavity if the modulation depth is no less than λ/2. For example, when modulating around the main cavity resonance, the modulation depth should be set sufficiently larger than the variation in the resonance cavity length caused by dispersion, but less than λ/2 to avoid comb on cavity resonance from the side resonance. This is indicated by the purple shaded box. In actual experiments, it is not necessarily required to engage cavity swept lock to the main resonance. Side resonances can be used as well. This can be used as a strategy to counter the mirror dispersion effect to reduce the variation in resonance cavity length.