Frequency axis for swept dual-comb spectroscopy with quantum cascade lasers

In dual-comb spectroscopy, there is a one-to-one map between the frequencies of the measured beat notes and the frequencies of the optical comb lines. Its determination usually involves the use of one or more reference lasers with known frequencies. Quantum cascade laser frequency combs, however, are often operated in a free-running mode, and without a reference, the determination of the RF-to-optical frequency map is not trivial. Here, we propose a method by which the comb shift is measured with an unbalanced Mach-Zehnder interferometer, and the spectral point spacing is determined through the intermode beat measured on the laser electrodes. The frequency axis is accurate within ∼ 0.001 cm^-1.