Frequency stabilization of a quantum cascade laser by weak resonant feedback from a Fabry-P\'{e}rot cavity

Frequency-stabilized mid-infrared lasers are valuable tools for precision molecular spectroscopy. However, their implementation remains limited by complicated stabilization schemes. Here we achieve optical self-locking of a quantum cascade laser to the resonant leak-out field of a highly mode-matched two-mirror cavity. The result is a simple approach to achieving ultra-pure frequencies from high-powered mid-infrared lasers. For short time scales (<0.1 ms), we report a linewidth reduction factor of $3\times10^{-6}$ to a linewidth of 12 Hz. Furthermore, we demonstrate two-photon cavity-enhanced absorption spectroscopy of an N$_{2}$O overtone transition near a wavelength of 4.53 $\mu$m.