Interferogram-based determination of the absolute mode numbers of optical frequency combs in dual-comb spectroscopy

Dual-comb spectroscopy (DCS), which uses two optical frequency combs (OFCs), requires an accurate knowledge of the mode number of each comb line to determine spectral features. We demonstrate a fast evaluation method of the absolute mode numbers of both OFCs used in DCS system. By measuring the interval between the peaks in the time-domain interferogram, it is possible to accurately determine the ratio of one OFC repetition frequency ( f rep ) to the difference between the f rep values of the two OFCs (Δ f rep ). The absolute mode numbers can then be straightforwardly calculated using this ratio. This method is applicable to a broad range of Δ f rep values down to several Hz without any additional instruments. For instance, the minimum required measurement time is estimated to be about 1 s for Δ f rep ≈ 5.6 Hz and f rep ≈ 60 MHz. The optical frequencies of the absorption lines of acetylene gas obtained by DCS with our method of mode number determination shows good agreement with the data from the HITRAN database.