  Terahertz (THz) Time domain spectroscopy (THz-TDS) is a broadband
spectroscopic technique spreading its uses in multiple fields: in science from
material science to biology, in industry where it measures the thickness of a
paint layer during the painting operation. Using such practical commercial
apparatus with broad spectrum for gas spectroscopy could be a major asset for
air quality monitoring and tracking of atmospheric composition. However, gas
spectroscopy needs high resolution and the usual approach in THz-TDS, where the
recorded time trace is Fourier transform, suffers from resolution limitation
due to the size of the delay line in the system. In this letter, we introduce
the concept of constraint reconstruction for super-resolution spectroscopy
based on the modeling of the spectroscopic lines in a sparse spectrum. Light
molecule gas typically shows sparse and narrow lines on a broad spectrum and we
propose an algorithm reconstructing these lines with a resolution improvement
of 10 the ultimate resolution reachable by the apparatus. We envision the
proposed technique to lead to broadband, selective, rapid and cheap gas
monitoring applications.
