  Optical frequency-comb-based-high-resolution spectrometers offer enormous
potential for spectroscopic applications. Although various implementations have
been demonstrated, the lack of suitable mid-infrared comb sources has impeded
explorations of molecular fingerprinting. Here we present for the first time a
frequency-comb Fourier transform spectrometer operating in the
2100-to-3700-cm-1 spectral region that allows fast and simultaneous
acquisitions of broadband absorption spectra with up to 0.0056 cm-1 resolution.
We demonstrate part-per-billion detection limits in 30 seconds of integration
time for various important molecules including methane, ethane, isoprene, and
nitrous oxide. Our system enables precise concentration measurements even in
gas mixtures that exhibit continuous absorption bands, and it allows detection
of molecules at levels below the noise floor via simultaneous analysis of
multiple spectral features. This system represents a near real-time,
high-resolution, high-bandwidth mid-infrared spectrometer which is ready to
replace traditional Fourier transform spectrometers for many applications in
trace gas detection, atmospheric science, and medical diagnostics.
