Extended Data Fig. 1: Coherence and phase of the ring frequency combs.

a, Schematic of the Shifted Wave Interference Fourier Transform Spectroscopy (SWIFTS) setup. The inset shows a microscope image of the QCL ring. LNA, low-noise amplifier; FTIR, Fourier transform infrared spectrometer; LO, local oscillator; QWIP, quantum well infrared photodetector. b, Comparison of the simulations with the experimental results obtained by SWIFTS. The displayed simulation results show the spectral amplitudes (top), the intermodal difference phases (middle) and the corresponding time-domain signals (bottom). Different seeds for spontaneous emission noise were used in the two simulations. The experimental data show the spectrum (top), the measured intermodal difference phases (middle) and the SWIFTS amplitudes (bottom). The red crosses on top of the SWIFTS amplitudes are given by |A_n||A_n−1|, that is, the geometric average of adjacent modes of the intensity spectrum. The red crosses agree well with the expected values for full phase coherence.