We present a complex-valued electric field model for experimentally observed cavity transmission in coherent cavity-enhanced (CE) multiplexed spectroscopy (i.e., dual-comb spectroscopy, DCS). The transmission model for CE-DCS differs from that previously derived for Fourier-transform CE direct frequency comb spectroscopy [Foltynowicz et al., Appl. Phys. B 110, 163-175 (2013)] by the treatment of the local oscillator which, in the case of CE-DCS, does not interact with the enhancement cavity. Validation is performed by measurements of complex-valued near-infrared spectra of CO and CO2 by an electro-optic frequency comb coherently coupled to an enhancement cavity of finesse F = 19600. Following validation, we measure the 30012 ← 00001 12C16O2 vibrational band origin with a combined standard uncertainty of 770 kHz (fractional uncertainty of 4 × 10-9).
Keywords: Frequency-comb spectroscopy; carbon dioxide; cavity-enhanced spectroscopy; electro-optic modulators; heterodyne spectroscopy; transition frequencies.