Resonance enhanced two-photon cavity ring-down spectroscopy of vibrational overtone bands: A proposal

This paper presents an analysis of near-resonant, rovibrational two-photon spectroscopy and the use of cavity ring-down spectroscopy for its detection. Expressions are derived for the photon absorption rate of a three-level system, correct to all orders and the simpler expressions that result from various approximations. The analysis includes the angular momentum projection degeneracies and linear or circular polarization of the exciting field. Expressions are derived for the rate of two-photon power loss for light inside a resonant cavity. Explicit calculations are made for excitation of the ν₃ mode of ¹²C¹⁶O₂ for which the two-photon excitation spectrum is dominated by a single v₃ = 0 → 2, Q(16) line at ν̃=2335.826 cm^-1. This transition has an intermediate v₃ = 0 → 1, P(16) one-photon transition that is off resonance by 0.093 cm^-1 (2.8 GHz). At 1 Torr total pressure, the Q(16) two-photon transition is calculated to have a cross section of 2.99 × 10^-38 cm⁴ s per CO₂ molecule in the J = 16 state or 2.24 × 10^-39 cm⁴ s per CO₂ molecule at 300 K. The analysis of the sensitivity limits for 2-photon cavity ring-down spectroscopy predicts a theoretical detection limit of 32 ppq (10^-15) Hz^-1/2 for ¹²C¹⁶O₂, higher sensitivity than has been realized using one-photon absorption. The analysis predicts that most polyatomic molecules will have sparse, Doppler-free two-photon absorption spectra, which will dramatically increase the selectivity of trace gas detection of samples with multiple components with overlapping absorption bands. This is demonstrated by the predicted mid-IR two-photon absorption spectrum of butadiene using theoretical spectroscopic constants.