We report Doppler-free two-photon absorption of ${\mathrm{N}}_2\mathrm{O}$ at $\lambda =4.53\mu \mathrm{m}$, measured by cavity ring-down spectroscopy. High power was achieved by optical self-locking of a quantum cascade laser to a linear resonator of finesse $\mathcal{F}=22730$, and accurate laser detuning over a 400-MHz range was measured relative to an optical frequency comb. At a sample pressure of $p=0.13\mathrm{kPa}$, we report a large two-photon cross section per molecule of ${\sigma }_{13}^{\left(2\right)}=8.0\times {10}^{-41}\mathrm{c}{\mathrm{m}}^4\mathrm{s}$ for the $Q\left(18\right)$ rovibrational transition at a resonant frequency of ${\nu }_0=66179400.8\mathrm{MHz}$.

• Received 27 March 2020
• Accepted 14 May 2020

DOI:https://doi.org/10.1103/PhysRevA.101.062509