Quantitative modeling of complex molecular response in coherent cavity-enhanced dual-comb spectroscopy

Abstract

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 CO${}_2$ by an electro-optic frequency comb coherently coupled to an enhancement cavity of finesse $F=19600$. Following validation, we measure the $30012\leftarrow 00001$ ${}^{12}$C${}^{16}$O${}_2$ vibrational band origin with a combined standard uncertainty of 770 kHz (fractional uncertainty of $4\times 10^{-9}$).

36 pages, 8 figures, 1 table, 95 references