Probing the dynamic response of a ring-down cavity with heterodyne detection to measure sample absorption and dispersion
Most cavity ring-down spectroscopy applications involve measurements of single-mode intensity decay rates at zero frequency (dc). These decay rates are proportional to the total cavity intensity losses but are independent of dispersion effects. Notable exceptions include experiments using ac heterodyne beat signals between a local oscillator and cavity mode1 or two cavity modes2. Building on this prior work, I will discuss a new heterodyne-detected cavity buildup/ring-down technique, collaboratively developed by D. Lisak and coworkers at Nicolaus Copernicus University (Torun, Poland) and members of the Optical Measurements Group at the National Institute of Standards and Technology (Gaithersburg Maryland, U.S.A.). This approach, referred to as dynamic mode-resolved heterodyne spectroscopy (DMHRS), yields the widths and positions of cavity modes to quantify sample absorption and dispersion, respectively. I will discuss how the cavity response can be described as a first-order linear system3 in which mode fields are induced by driven or random variations in the probe laser amplitude and/or phase. Fourier analysis of heterodyne-detected buildup and decay signals yields spectrally distinct Lorentzian resonances caused by beating between probe-mode and local oscillator-mode fields. Importantly, all spectral information is encoded in terms of measured optical frequencies and radio frequencies, with strong immunity to amplitude variations, allowable frequency mismatch between probe and cavity, and no need for path length calibration. Specific examples and related work presented include cavity buildup spectroscopy4 enabling measurements on time scales much less than the decay time, Cs-clock-referenced line positions in Doppler-broadened spectra5 providing relative uncertainties at the 10-12 level for near-IR transitions of carbon dioxide, and parallel dual-comb cavity ring-down spectroscopy for broadband measurements of absorption and dispersion in methane6.
 M. D. Levenson, B. A. Paldus, T. G. Spence, C. C. Harb, J. S. Harris Jr. R. N. Zare, Chem. Phys. Lett. 290, 335 (1998).\
 J. Ye, J. L. Hall, Phys. Rev. A 61, 061802 (2000).
 K. K. Lehmann, D. Romani, J. Chem. Phys. 105, 10263 (1996).
 A. Cygan, A. J. Fleisher, R. Ciurylo, K. A. Gillis, J. T. Hodges, D. Lisak, Comm. Phys. 4, 14 (2021).
 Z. D. Reed, D. A. Long, H. Fleurbaey, J. T. Hodges, Optica 7, 1209 (2020).
 D. Lisak, D. Charczun, A. Nishiyama, T. Voumard, T. Wildi, G. Kowzan, V. Brasch, T. Herr, A. J. Fleisher, J. T. Hodges, R. Ciurylo, A. Cygan, P. Maslowski, arXiv:2106.07730v1 [physics.optics] (2021).