Tracing part-per-billion line shifts with direct-frequency-comb Vernier spectroscopy

Accurate frequency measurements of molecular transitions around $2 \mu \mathrm{m}$ are performed by using a direct-frequency-comb spectroscopy approach that combines an ${\mathrm{Er}}^{+}$ frequency-comb oscillator at $1.5 \mu \mathrm{m}$, a Tm-Ho fiber amplifier, and a Fabry-Perot-filter, high-resolution dispersive spectrometer optical multiplex-detection system. This apparatus has unique performances in terms of a wide dynamic range to integrate the intensity per comb mode, which allows one to measure molecular absorption profiles with high precision. Spectroscopic information about transition frequencies and linewidths is very accurately determined. Relative frequency uncertainties of the order of a few parts in ${10}^{-9}$ are achieved for rovibrational transitions of the ${\mathrm{CO}}_2$ molecule around $5100 {\mathrm{cm}}^{-1}$. Moreover, tiny frequency shifts due to molecular collisions and interacting laser power using direct comb spectroscopy are investigated in a systematic way.

Figure 1

Experimental setup for DCS around $2 \mu \mathrm{m}$.

Figure 2

Top: Image of the eight resolved modes of the filtered comb around $2 \mu \mathrm{m}$. Bottom: Intensity of the comb modes of the above image, integrated in the vertical CCD direction (blue dots) and fit to a FP-SOPRA instrumental function (red line) (see text for details). As shown, the optical configuration of the commercial camera reduces the field of view in direct CCD illumination to 150 pixels instead of the nominal 320 ones.

Figure 3

FP filtered FCL spectrum (black dots) of the P(34)-($20{}^{0}11-00{}^{0}01) {\mathrm{CO}}_2$ transition at $5070.14 {\mathrm{cm}}^{-1}$ and $P=10$ mbar, and fit (red line) to the function (2) plus linear background. Residuals (blue dots) are also shown. The values of the fixed parameters are ${\sigma }_T=282.359$ MHz, $\mathrm{FSR}=4.5$ GHz, $F_{\mathrm{vac}}=105$, and $m=18$. The fitted values of the line center ${\nu }_o=151999035.3\left(1.6\right)$ MHz, line strength $S=1.32\left(5\right)\times {10}^{-22}$ cm/mol, and collisional linewidth ${\Gamma }_o^{\mathrm{FWHM}}=52.0\left(9\right)$ MHz agree with the values reported in the HITRAN database [29] for this transition, i.e., ${\nu }_o^{\mathrm{Hitran}}=151999038.7\left(3.0\right)$ MHz, $S^{\mathrm{Hitran}}=1.40\left(3\right)\times {10}^{-22}$ cm/mol, and ${\Gamma }_o^{\mathrm{Hitran}}=52.2\left(2.6\right)$ MHz. (See Supplemental Material for video movie of the spectrum scan.)

Figure 4

Behavior of the fitted spectroscopic parameters for the P(18)-($20{}^{0}11-00{}^{0}01) {\mathrm{CO}}_2$ transition at $5084.79 {\mathrm{cm}}^{-1}$ as a function of pressure and amplified FCL power. Top left: Homogeneous linewidth vs ${\mathrm{CO}}_2$ pressure (blue dots) and linear fit (blue line). Top right: Line center frequency vs pressure (blue dots) and linear fit (blue line). Bottom left: Homogeneous linewidth vs mean FCL power (blue dots) and linear fit (blue line). Bottom right: Line center frequency vs mean FCL power (blue dots) and linear fit (blue line). On the left panels, the Hitran data (red dots) [29] and line fit (red dashed line) are also shown for comparison.