Near-to mid-IR spectral purity transfer with a tunable frequency comb: methanol frequency metrology over a record frequency span

We report the upgrade and operation of a frequency-comb-assisted high-resolution mid-infrared molecular spectrometer allowing us to combine high spectral purity, SI-traceability, wide tunability and high sensitivity. An optical frequency comb is used to transfer the spectral purity of a SI-traceable 1.54 $\mu$m metrology-grade frequency reference to a 10.3 $\mu$m quantum cascade laser (QCL). The near-infrared reference is operated at the French time/frequency metrology institute, calibrated there to primary frequency standards, and transferred to Laboratoire de Physique des Lasers via the REFIMEVE fiber network. The QCL exhibits a line width of $\delta\nu\sim 0.1$ Hz, a sub-$10^{-15}$ relative frequency stability from 0.1 to 10 s and its frequency is traceable to the SI with a total relative uncertainty better than $4\times10^{-14}$ after 1-s averaging time. We have developed the instrumentation allowing comb modes to be continuously tuned over 9 GHz resulting in a QCL of record spectral purity uninterruptedly tunable at the precision of the reference over an unprecedented span of $\Delta\nu$ = 1.4 GHz. We have used our apparatus to conduct sub-Doppler spectroscopy of methanol in a multi-pass cell, demonstrating state-of-art frequency uncertainties down to the few kilohertz level ($\sim10^{-10}$ in relative value). We have observed weak intensity resonances unreported so far, resolved subtle doublets never seen before and brought to light discrepancies with the HITRAN database. This demonstrates the potential of our apparatus for probing subtle internal molecular processes, building accurate spectroscopic models of polyatomic molecules of atmospheric or astrophysical interest, and carrying out precise spectroscopic tests of fundamental physics.