Saturated absorption spectroscopy of $M1$ transitions of ${\mathrm{O}}_2$ near 764 nm

Magnetic dipole transitions of oxygen molecules, which span the microwave-to-infrared region, play a crucial role in remote sensing applications. However, accurately determining the parameters of these weak transitions has long been a challenge. In this work, we present a saturated absorption spectroscopy measurement of magnetic dipole transitions of ${}^{16}\mathrm{O}_2$ near 764 nm using a comb-locked cavity ring-down spectrometer. The Line positions of eight transitions in the P branch of the $b{}^1{\mathrm{\Sigma }}_g^{+}\leftarrow X{}^3{\mathrm{\Sigma }}_g^{-}(0,0)$ band were determined with an accuracy of better than 3.5 kHz under zero magnetic field, an improvement of two orders of magnitude over previous studies. Zeeman splittings induced by the Earth's geomagnetic field were partially resolved, and their influence on the spectral line profile was meticulously analyzed using the Stokes matrix formalism. The results of this study also indicate the potential for the experimental determination of the Landé $g$ factors of the energies of ${\mathrm{O}}_2$ with better accuracy.

Figure 1

Configuration of the saturated cavity ring-down spectroscopy apparatus. BS: beam splitter; PBS: polarized beam splitter; HWP: half-wave plate; AOM: acoustic-optic modulator; EOM: electro-optic modulator; PZT: piezoelectric ceramic actuator; PD: photodiode; APD: Avalanche photodiode.

Figure 2

(a) Energy level diagram of the $A$ band transitions of ${}^{16}\mathrm{O}_2$. (b) Overview of the $A$ band of ${\mathrm{O}}_2$ near 760 nm. The rectangle indicates eight lines studied in this work.

Figure 3

Saturated absorption spectra of the ${}^{P}Q\left(10\right)$ and ${}^{P}P\left(11\right)$ transitions. Red points are experimental data recorded with magnetic shielding, and they were fitted with the following function: $\frac{1}{c\tau }=A+B(\nu -{\nu }_0)+\frac{2C}{\pi }\frac{w}{4{(\nu -{\nu }_0)}^2+w^2}$, where $A$ and $B$ represent the intercept and slope of the baseline, $C$ is the integral of the absorption coefficient, $w$ is the full width at half maximum (FWHM) of the peak, and ${\nu }_0$ is the central frequency of the line. Solid black lines are simulated spectra and the fitting residuals are shown in the lower panels. Blue points show the experimental data recorded under the geomagnetic field (${31}^{\circ }{50}^{\prime }{34}^{\prime \prime }\mathrm{N}, {117}^{\circ }{15}^{\prime }{12}^{\prime \prime }\mathrm{E}$) on April 9, 2022, 0.55 Gauss, without using magnetic shielding. Oxygen sample pressure: 2 Pa. Number of scan: 518.

Figure 4

Upper panels: Cavity ring-down saturation spectra of the ${}^{P}P\left(11\right)$ line retrieved with (a) various laser powers (Sample pressure: 3.0 Pa) and (b) at different sample pressures. Spectra were vertically shifted for a better illustration. Lower panels: (c) Line centers obtained at different effective saturated coefficients $S$, (d) line centers obtained at different sample pressures. Red shadows show the 68% confidence intervals of the linear fit. Note that the effective $S$ value was derived using the average laser power of the ring-down curve used in the single-exponential decay fitting, and all frequencies are shifted by 392 254 548 991.1 kHz.

Figure 5

Definition of the reference frame. The laser propagates along the $z$ axis, which is linearly polarized along the $x$ axis. The local geomagnetic vector $\vec{B}$ is 0.55 Gauss with $\theta ={56}^{\circ }$ and $\eta ={157}^{\circ }$.

Figure 6

Absorption spectra of ${}^{P}Q\left(10\right)$ under magnetic fields in different directions with the same amplitude of 0.55 Gauss. Bold solid lines show sums of all simulated Zeeman components (thin lines). (a) The magnetic field is parallel to the laser propagation direction ($z$), $\theta =0^{\circ }$ and $\eta ={90}^{\circ }$. (b) The magnetic field is perpendicular to the laser beam and parallel to the $y$ direction, $\theta ={90}^{\circ }$ and $\eta ={180}^{\circ }$. The distance between two nearby Zeeman components is indicated as “d.” (c) The local geomagnetic field, $\theta ={56}^{\circ }$, and $\eta ={157}^{\circ }$. Red scattering points with error bars are experimental data. Definition of the direction of the magnetic field is given in Fig. 5.

Figure 7

(a) Calculated Zeeman splittings $d$ under the magnetic field of 1.0 Gauss for transitions in the $A$ band, using $g\left(J\right)$ values given by the models with [37] (red solid symbol) or without [54] (blue open symbol) corrections. (b) Differences between both values from two models.