Measurement of the Hydrogen Cyanide Absorption Lines’ Centers with the Potential for Mise en Pratique

We built a linear absorption spectroscopy setup to measure hydrogen cyanide (H13C14N) 2ν3 rotational-vibrational band. The laser’s frequency was locked to the minimum of the absorption line by using the 1f technique. We used a commercially available lock-in amplifier combined with a custom-made PID controller allowing for the short-term frequency stability of about 10-10. The laser frequency was determined by measuring the beat-note between the laser and the optical frequency comb. The laser was locked to each absorption line for about 8 hours and the final time record allowed us to determine the absorption line central frequency with the uncertainty of about 40 kHz. This shows significant improvement compared to the data already available for HCN. Our work can potentially lead to the acceptance of HCN for Mise en Pratique (MeP), which means that laser locked to one of the HCN lines can become the official source of the one-meter unit.


INTRODUCTION
The main goal of the LaVA project (Large Volume Metrology Applications), which the presented work is part of, is to improve the metrology capability of FSI (frequency scanning interferometry) instrumentation developed at NPL (National Physical Laboratory). One of the prerequisites for this method is the gas cell and the knowledge of its absorption lines' frequencies. Currently, the absorption media used in 1.55 µm absorption band is acetylene (C2H2), which is recognized in the MeP for the SI meter. The main benefit of hydrogen cyanide (HCN) over C2H2 is its broader absorption spectrum. 12 C2H2 has an absorption spectrum of about 25 nm broad, 13 C2H2 about 30 nm and H 13 C 14 N about 40 nm broad that again can improve the FSI measurement accuracy. The available data for HCN [1] does not provide comparable accuracy to C2H2 [2], [3] mainly due to the use of not so precise measurement methods. Concretely, authors in [1] measured the lines' positions by scanning laser frequency over the profile of HCN absorption line and fitting it by Voight profile.
We firstly reported on our progress in [4]. Here we show that with the linear absorption spectroscopy method combined with the measurement of beat-note frequency between laser and optical frequency comb the HCN's absorption lines' centers can be determined more accurately by a factor of 100 in comparison with the previous results [1].

II. METHODS
The laser source we used in our experiment is a continuously tunable laser (CTL), allowing the wavelength of the laser to be tuned from 1510 nm to 1630 nm, which is more than sufficient for the measurement of HCN 2ν3 rotational-vibrational band that spreads from 1525 nm to 1565 nm.
The linear absorption spectroscopy setup shown in Fig. 1., consists of two distinct parts. In the first part, the laser beam goes through a voltage-driven attenuator and Glan-Taylor crystal, which ensures that laser beam power and polarization are stable during the whole measurement. The beam is then split into three parts. Two of them are used in the lock of laser frequency and the last one in the beat-note measurement, which will be described later in this paragraph. The two beams used for the laser lock hit the Nirvana balanced optical receiver. One of them goes through a commercially available 0.4 m long HCN gas cell filled to 0.4 Torr (~ 53 Pa). Windows of the cell are wedged, AR coated and fitted to the tubes at a small tilt to minimize the interference effects. The gas cell was put in a  temperature-controlling device, ensuring there are no temperature-induced changes of pressure in the cell during the measurement. We used a three-pass arrangement in order to improve the signal to noise ratio.
The signal from the Nirvana photodetector goes to the lockin amplifier, which, combined with the PID controller, locks the laser frequency and closes the feedback loop. The lock-in amplifier referenced to active hydrogen maser produced the modulation frequency of 10 kHz and the modulation depth of about 6 MHz.
In the beat-note part of the experimental setup, the laser beam is combined with the optical frequency comb beam, and then hits the photodetector. The signal from the photodetector goes through a set of filters and amplifiers and then it is combined with the signal from the generator, which allows subtracting the modulation from beat-note. After the next filtering, the signal goes through a limiter that changes the shape of the beat-note, so it is more recognizable by a counter. The counter is referenced to 10 MHz coming from an H-maser.

III. RESULTS
We measured the frequency of the absorption lines' centers in the 2ν3 rotational-vibrational band of H 13 C 14 N (see line profile in Fig. 2.). All the lines were about 400 MHz broad, and the line intensity was varying from 50 % for the strongest lines down to 30 %. The main broadening mechanism is the Doppler broadening which can be eliminated by using saturated absorption spectroscopy. On the other hand, this method makes the experimental setup much more complex.
The position of every single line was measured by locking the laser frequency to its minimum and keeping it locked typically for 8 hours. The example can be seen in Fig. 3, where the length of a time record is about 18 hours. The Allan deviations show the short term stability of the laser locked to absorption line minimum in 10 -10 order. Calculation of histogram then shows the unwanted trend in time record if there is any, and ideally, it should correspond to the Normal distribution. In our case, the histogram corresponds to the Normal distribution very well (Fig. 4), and the 2σ calculations gives the uncertainty of about 40 kHz for the strongest lines.
You can see the summarizing tables with positions of absorption lines' centers in Table 1 for R branch of 2ν3 rotational-vibrational band and in Table 2 for P branch. In our measurement, the most important sources of uncertainty for the positions of lines are the 2σ uncertainty of time record and the repeatability, which is more or less equal to it. Other sources of uncertainty are much less significant.

IV. CONCLUSION
The results described in the last section show great potential for HCN to become an alternative absorption medium to C2H2 in 1.5 µm absorption band (so-called C-band). All measured lines' positions, if calculated to zero pressure using pressure shift coefficients from [1], land well in the uncertainty interval of the previous results in [1] and [5].
Much work on this topic is still to be done, namely, e.g., evaluating the pressure shift coefficients of all HCN absorption lines to improve uncertainty from [1]. The results will then be compared with the same measurements done by other groups, and this set of results will hopefully lead to the application and the acceptance of HCN for MeP.

ACKNOWLEDGMENT
The work has been performed within the project 17IND03 LaVA. This project 17IND03 LaVA has received funding from the EMPIR programme co-financed by the Participating States and from the European Union's Horizon 2020 research and innovation programme. The research was also supported by projects: 19-14988S (GA CR) and CZ.02.1.01/0.0/0.0/16_026/0008460 (MEYS CR).