Modeling the cavity dispersion in cavity-enhanced optical frequency comb Fourier transform spectroscopy

Abstract: Cavity enhanced optical frequency comb spectroscopy is a technique that allows for quick and sensitive measurements of molecular absorption spectra. Locking the comb lines of an optical frequency comb to the cavity modes of an enhancement cavity and then extracting the spectral information with a Fourier transform spectrometer grants easy access to wide segments of absorption spectra. One of the main obstacles complicating the analysis of the measurements is the inevitable dispersion occurring inside the cavity. In this project, absorption measurements of CO2 were performed using an existing and well established setup consisting of a near-infrared optical frequency comb locked to a Fabry- Pérot enhancement cavity using the Pound-Drever-Hall technique, and a Fourier transform spectrometer. The purpose was to improve theoretical models of the measured absorption spectra by creating and verifying a model for the cavity dispersion, stemming mostly from the cavity mirrors but also from the normal dispersion of the intracavity medium. Until now, the cavity dispersion has been treated as an unknown and was included as a fitting parameter together with the CO2 concentration when applying fits to the absorption measurements. The dispersion model was based on previously performed precise measurements of the positions of the cavity modes. The model was found to agree well with measurements. In addition, pre-calculating the dispersion drastically reduced computation time and seemed to improve the overall robustness of the fitting routine. A complicating factor was found to be small discrepancies between the locking frequencies as determined prior to the measurements and the values yielding optimum agreement with the model. These apparent shifts of the locking points were found to have a systematic dependence on the distance between the locking points. The exact cause of this was not determined but the results indicate that with the locking points separated by more than about 10nm the shifts are negligible.