Saturated absorption and crossover resonances in a high-finesse cavity: Formalism and application to the hyperfine structure of jet-cooled NO2by saturated-absorption cavity-ring-down spectroscopy

Abstract

The ${}^{q}{R}_{0}(0)$ rotational transition in the $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{A}{\phantom{\rule{0.16em}{0ex}}}^{2}{B}_{2}\ensuremath{\leftarrow}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{X}{\phantom{\rule{0.16em}{0ex}}}^{2}{A}_{1}$ system of jet-cooled ${\mathit{NO}}_{2}$ located around $12\phantom{\rule{0.16em}{0ex}}536\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ is analyzed using a nonlinear-susceptibility formalism designed to describe the saturated absorption due to two identical counter-propagating radiations in an $n$-level system. An analytical solution of the equations of motion is obtained in the frequency space by considering the pertinent experimental conditions, mainly a high-finesse cavity and a slit-shaped supersonic expansion. Calculation of the nonlinear absorption coefficient requires the summing of all Zeeman-component contributions and a final numerical integration over the frequency detuning assuming a Maxwell-Boltzmann speed distribution. Determination of the experimental absorption coefficients is obtained by converting the shape of the temporal decay of the electromagnetic field amplitude initially captured inside the cavity. The molecular Hamiltonian includes both spin-rotation and hyperfine interactions. Molecular constants relative to the upper level are derived by exploiting Doppler-broadening-free so-called saturated-absorption cavity-ring-down spectroscopy. The dipole moment of the partially assigned hot band is obtained [${\ensuremath{\mu}}_{\mathrm{band}}=0.0047(12)$ D] together with the number density and the effective population relaxation rates. The model is validated by varying the intracavity power from 0 to 230 W (i.e., up to a maximum peak irradiance of $240\ifmmode\times\else\texttimes\fi{}{10}^{3}\phantom{\rule{0.28em}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$), representing saturation coefficients up to 120. The experimental position, shape, and width of the Lamb and crossover dips are well reproduced. The spatial shape and modulation of the electromagnetic field are discussed.