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\title{CAVITY RING-DOWN SPECTROSCOPY WITH HETERODYNE DETECTION OF DECAYS}

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\author{\FirstName A. \LastName CYGAN, \FirstName S. \LastName W\'OJTEWICZ, \FirstName H. \LastName J\'O\'ZWIAK, \FirstName G. \LastName KOWZAN, \\ \FirstName N. \LastName STOLARCZYK, \FirstName K. \LastName BIELSKA, \FirstName P. \LastName WCIS\L{}O, \FirstName R. \LastName CIURY\L{}O, \underline{\FirstName D. \LastName LISAK}}
\address{Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toru\'n, Grudziadzka 5, 87-100 Toru\'n, Poland}

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\fancyhead[C]{{\footnotesize \textit{HRMS, 28th Colloquium, Dijon, France,
  Aug. 28 - Sept. 1, 2023}}}
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\category {15,3}
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We present a new approach to the cavity ring-down spectroscopy (CRDS), allowing for fast measurement of both absorption and dispersion of the medium. 
The dispersion spectra are obtained from a heterodyne measurement of the cavity mode frequency relative to a reference optical frequency locked to the same cavity. 
This enables high accuracy, in particular, insensitivity to non-linearity of the light detection system, unlike CRDS, which requires linearity calibration at relative uncertainty of absorption of $10^{-3}$. 
Compared to the previously used cavity mode dispersion spectroscopy (CMDS)\footnote{\href{http://dx.doi.org/10.1364/OE.23.014472}{doi:10.1364/OE.23.014472}, 
A. Cygan, et al., "One-dimensional frequency-based spectroscopy", Opt. Expr. {\bf 23}, 14472 (2015).}, 
which uses a static measurement of the cavity transmission spectrum, the new approach is much faster and does not require fine frequency tuning of the sampling laser through the cavity modes. 
This allows to combine the high accuracy of CMDS\footnote{\href{http://dx.doi.org/10.1364/OE.27.021810}{doi:10.1364/OE.27.021810}, 
A. Cygan, et al., "High-accuracy and wide dynamic range frequency-based dispersion spectroscopy in an optical cavity", Opt. Expr. {\bf 27}, 21810 (2019).}$^,$\footnote{\href{http://dx.doi.org/10.1103/PhysRevLett.129.043002}{doi:10.1103/PhysRevLett.129.043002}, 
K. Bielska, et al., "Subpromille Measurements and Calculations of CO (3-0) Overtone Line Intensities", Phys. Rev. Lett. {\bf 129}, 043002 (2022).} 
with the speed of CRDS in a relatively simple optoelectronic system. Moreover, compared to the cavity buildup dispersion spectroscopy (CBDS)\footnote{\href{http://dx.doi.org/10.1038/s42005-021-00517-3}{doi:10.1038/s42005-021-00517-3}, 
A. Cygan et al., "Cavity buildup dispersion spectroscopy", Commun. Phys. {\bf 4}, 14 (2021).} our new approach requires lower laser power.

We present the new spectroscopic method on the example of precise measurements of the transition frequencies and intensities of the R23 line from the (3-0) band of CO molecule and P(3) line from the (2-0) band of the HD molecule. 
To interpret the complex shape of the Doppler broadened and perturbed by collisions HD line, we use the speed-dependent billiard-ball (SDBB) line shape model\footnote{\href{http://dx.doi.org/10.1103/PhysRevA.65.012502}{doi:10.1103/PhysRevA.65.012502}, 
R. Ciury\l{}o, et al., "Solving the line shape problem with speed-dependent, broadening and shifting, and Dicke narrowing - Part II: Application", Phys. Rev. A {\bf 65}, 012502 (2002).} 
with calculated ab initio parameters of Dicke narrowing and speed-dependence of the collision broadening and shift\footnote{\href{http://dx.doi.org/10.1016/j.jqsrt.2018.04.011}{doi:10.1016/j.jqsrt.2018.04.011}, 
P. Wcis\l{}o, et al., "Accurate deuterium spectroscopy for fundamental studies", J. Quant. Spectrosc. Radiat. Transfer {\bf 213}, 41 (2018).}.

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