© 2008 OSA / CLEO/QELS 2008 a1334_1.pdf CMEE1.pdf
Precision Measurement of Refractive Indices of the Atmospheric Gases Using a Frequency Comb J. Zhang, Z. H. Lu, and L. J. Wang Institute of Optics, Information and Photonics, Max-Planck Research Group and University Erlangen-Nuremberg, 91058 Erlangen, Germany
[email protected] Abstract: We report high precision refractive indices measurement of air and its constitute gases using an unbalanced Mach-Zehnder interferometer with frequency combs. Our experiments demonstrate sensitivities in levels of 10-9. © 2008 Optical Society of America OCIS codes: (120.3180) Interferometry; (120.3940) Metrology.
We developed a high precision technique to measure the absolute refractive indices of gases, taking advantage of the accuracy of a frequency- and phase-stabilized frequency comb system [1, 2]. The absolute refractive indices and the dispersion curves are obtained in the wavelength range of 740 nm – 860 nm simultaneously. Here we report results for air and its constitute gases. For air refractive index, our experiment has a sensitivity of 5.7×10-9. The deviation of our result with Edlén’s formula is 2.5×10-9 at 800 nm with a standard error of 4.3×10-9 [3]. The nitrogen measurement has a standard error of 1.9×10-8 at 800 nm. The oxygen measurement is reported for the first time with a standard error of 6.6×10-9. The CO2 result shows a considerable deviation from the commonly quoted result of Old et al. by 6.4×10-7 at 800 nm [2, 4]. We believe this is due to the incorrect usage of density factor in Old et al.’s result. The experimental setup is shown in Fig. 1. The light source is a Ti:sapphire laser frequency comb whose repetition rate and offset are both locked to a Cs frequency standard. The center wavelength is 800 nm with a bandwidth of approximately 50 nm. A multipass cell, which can be filled with different gases or pump down to vacuum, is used as the long arm of a Mach-Zehnder interferometer, while the other arm is a short, adjustable reference arm. The total path-length inside the mutlipass cell is approximately 30 m. One output from the interferometer is sent into a fast photodiode as the time domain signal, recorded by a fast oscilloscope. The other output as the frequency domain signal is coupled into an optical spectrum analyzer through a single-mode fiber.
Fig. 1: Experimental setup. BS1, BS2, cube beam splitters; MPC, multipass cell; RR, retroreflector; L, lens; PD1, PD2, photodiodes; FC, fiber coupler; OSA, optical spectrum analyzer. The dashed line corresponds to the He-Ne laser optical path.
In order to determine the absolute values of the refractive indices of gases, we perform our experiment under well controlled conditions. The temperature of the multipass cell is controlled with a digital PID controller. The RMS temperature fluctuations during the experiment are less than 0.5 mK, and a long term temperature fluctuation is 0.6 mK over 90 hours. This corresponds to the multipass cell length change of 0.3 Pm for a total length of 30 m. All used temperature sensors are calibrated with a NIST traceable thermistor and thermometer. The pressure of the multipass cell is measured with a Paroscientific 760-45A pressure gauge (calibrated by PTB). The uncertainty of the absolute pressure measurement is 2 Pa. The interferometer path-length change outside the multipass cell is controlled by locking a copropagating He-Ne laser interferometer. The optical path of the He-Ne laser is shown as dashed line in Fig. 1. An RMS path-length change of 7 nm is obtained.
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© 2008 OSA / CLEO/QELS 2008 a1334_1.pdf CMEE1.pdf
In the experiment we first evacuate the multipass cell to vacuum and then fill it with different gases to a preset pressure around 1 bar. In both cases, the laser repetition rate is scanned while the laser remains frequency and phase locked. The repetition rate difference for the peaks of the envelopes of the two interferograms can be measured, from which we can calculate the group delay. In the frequency domain we measure the phases of two interference signals in gases or in vacuum. The phase difference can be written as (1) ')(O ) 2S [n(O ) 1]lcell / O. From Eq. (1), the refractive index of different gases can be determined: n(O ) 1 O') /( 2Slcell ) . We first measure the refractive index of air and convert results into the standard dry air conditions (20oC, 1 bar, 400ppm CO2) [1]. The result is compared with Edlén’s formula, and the difference is approximately 2.5×10-9 at 800 nm with a standard error of 4.3×10-9 [3]. The fitting result is 2337630 18836.05 (2) (n Air 1) u 108 7910.655 . 128.7459 1 / O2 50.01974 1 / O2 Here, and throughout this paper, is in units of micrometers. A compilation of the major measurement results of the refractive index of air is shown in the left panel of Fig. 2. We further measured the refractive indices of major atmospheric gases based on the excellent result for air. Instead of using the spectral phase difference, we use its derivative for fitting to avoid the ambiguity of an integer 2 between the phase difference [2]. The CO2 fitting result is given as 7466051 367244.7 (3) (nCO2 1) u 108 7670.524 . 2 248.5560 1 / O 57.75340 1 / O2 The result is shown in the right panel of Fig. 2, together with Old et al.’s result [4]. The deviation at 800 nm is 6.4×10-7, with a standard error of 7.8×10-8. It is found out that this deviation is due to an unsuitable compressibility factor they used for pressure at 1 atm.
Fig. 2: Left: The compilation of the refractive index of air measurements with corresponding standard error since 1966. Right: Wavelength dependence of the refractive index of CO2. The red curve is our result, and the black curve is from Old et al.
We have also performed measurements on nitrogen and oxygen. The preliminary results are expressed as 2405295 (4) (n N 2 1) u 108 8685.396 , 128.7459 1 / O2 457532.0 (5) (nO2 1) u 108 15511.93 . 50.01974 1 / O2 With the knowledge of dispersion equations for the major atmospheric gases, we are working on to develop techniques for trace gases detection. It is also possible to develop a sensitive technique for monitoring “green house” gases emission, global carbon cycle, and air pollution. [1] J. Zhang, Z. H. Lu, B. Menegozzi, and L. J. Wang, “Application of frequency combs in the measurement of the refractive index of air,” Rev. Sci. Instrum. 77, 083104 (2006). [2] J. Zhang, Z. H. Lu, and L. J. Wang, “Precision measurement of the refractive index of carbon diode with a frequency comb,” Opt. Lett. 32, 3212 (2007). [3] G. Bönsch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlén’s formulae,” Metrologia 35, 133 (1998). [4] J. G. Old, K. L. Gentill, and E. R. Peck, “Dispersion of carbon dioxide,” J. Opt. Soc. Am. 61, 89 (1971).
