Double-resonance spectroscopy determines highly excited vibrational energy of 13CO2 with kilohertz accuracy

We present a comb-referenced mid-infrared to near-infrared double-resonance (MIR-NIR DR) scheme applied to 13CO2 to achieve high-accuracy rovibrational term values for highly excited, optically dark vibrational states. A single-pass MIR pump drives the strong ν3 = 1 ← 0 fundamental transition, while a cavity-enhanced NIR probe interrogates the weak ν3 = 4 ← 1 hot band via ring-down detection. Using a ladder (Ξ)-type excitation scheme that links the ground state directly to the 4ν3 manifold, the sum of the two transition frequencies yields the pure vibrational energy of the dark (00 041) state with an uncertainty of 4.0 kHz, providing metrology-grade constraints for theoretical models and line lists. The demonstrated approach offers a practical route to access dark or ultra-weak vibrational manifolds in molecules of atmospheric and astrophysical relevance.