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Dual-comb spectroscopy (DCS) is a powerful method for the characterization of materials. It enables the rapid measurements of broad absorption spectra with high spectral resolution. However, dual-comb spectroscopy has a low duty cycle especially when used to study semiconductor materials whose excited states’ dephasing rates are much shorter than the spacing between the comb pulses. When DCS is applied to these systems, a vast majority of energy and acquisition time is wasted. Here, we demonstrate a simple approach that can aid efforts to solve this issue. In our approach, we use two frequency combs that have the same repetition frequencies and we digitally control the relative locking phase between the combs. This allows us to control the delay with very high precision and take the data rapidly and continuously only in the region where the signal is non-zero. We demonstrate the concept on a Neodymium-doped yttrium orthovanadate (Nd:YVO₄) sample. We show that, we could scan the delay between the signal and local oscillator comb pulses up to ∼ 6 ps in under 150 µs. We compare an absorption spectrum of (Nd:YVO₄) obtained using our approach to an absorption spectrum obtained using conventional DCS and they are in good agreement. This approach now makes DCS relevant for a wide range of materials. 

Frequency-comb-based multidimensional coherent spectroscopy is a powerful optical method for studying nonlinear optical properties of samples with narrow resonances. It enables the measurement of multidimensional coherent spectra rapidly and with high spectral resolution. However, for some samples (especially cold atoms and molecules) the dephasing times are longer than the repetition periods of the excitation lasers and hence the nonlinear signals generated in the sample by the subsequent laser pulses will interfere with each other. Here we investigate this behavior and show its effect on multidimensional coherent spectra by solving the optical Bloch equations. *The material is based upon work supported by the National Science Foundation under Grant No. [1904704] 

We experimentally investigate a fixed point of a bi-directional dual-comb ring laser and the behavior of dual-comb signals in different spectral regions. We show that the results are quite different from those obtained with traditional dual-comb spectroscopy. We explain the difference using the elastic tape formalism that we apply to a bi-directional ring laser. We also discuss how the results can aid efforts to synchronize two bi-directional laser systems to enable rapid and high-resolution multidimensional coherent spectroscopy with a compact apparatus.