Another current trend is to design systems with built-in passive mutual coherence 5, 14. Alternatively, schemes correcting the relative fluctuations with analog electronics 6, digital processing 12, or computer algorithms 13 permit measurements, even with free-running lasers. In this way, mutual coherence times of the order of 1 s, determined by the linewidth of the continuous-wave lasers, have been achieved and linear-phase correction enhances the effective averaging times to tens of minutes 7. The most powerful approach for establishing mutual coherence between two frequency combs has been to lock, with fast intra-cavity actuators, each comb to the same pair of cavity-stabilized continuous-wave lasers with hertz-level linewidth. Conversely, the precise control of the phase difference in a two-beam interferometer involving a moveable mirror has indeed been perfected over decades and the mutual coherence between the two arms of the interferometer can be maintained over tens of hours 11 in standard laboratory environments. Unfortunately, it is still challenging to control the relative timing and phase fluctuations between the two combs and therefore to keep them coherent over extended measurement times. Although such systems have a potential for precisions directly set by atomic clocks, they still fail in many aspects to compete with mechanical interferometers. With a dual-comb system, a type of two-beam interferometer, the phase difference is in most of the implementations automatically and periodically scanned by means of two asynchronous trains of pulses. For about a decade, novel applications involving time-domain interference between the two frequency combs have emerged and hold promise for enhancing the precision of interferometric measurements, as encountered in spectroscopy and sensing 4, 5, 6, 7, distance metrology 8, tomography 9, telecommunications 10, etc. The performance of laser frequency combs 1 has been constantly perfected to meet scientific challenges such as optical-clock comparisons 2 or low-noise microwave generation 3. Our technique without phase correction can be implemented with any frequency comb generator including microresonators or semiconductor lasers. An illustration is given with near-infrared Fourier transform molecular spectroscopy with two combs of slightly different repetition frequencies. Here with feed-forward relative stabilization of the carrier-envelope offset frequencies, we experimentally realize a mutual coherence over times approaching 2000 s, more than three orders of magnitude longer than that of state-of-the-art dual-comb systems. Computer-based phase-correction techniques, which often lead to artifacts and worsened precision, must be implemented for longer averaging times. ![]() At best, the mutual coherence reaches about 1 s. Mutual coherence between the two combs over the measurement time is a pre-requisite to interferometry, although it is instrumentally challenging. A comb-enabled instrument, the dual-comb interferometer, exploits interference between two frequency combs and attracts considerable interest in precision spectroscopy and sensing, distance metrology, tomography, telecommunications, etc. Laser frequency combs emit a spectrum with hundreds of thousands of evenly spaced phase-coherent narrow lines.
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