A calculation of the absorption cross section of some molecules (NH3, C2H4, CO2, O3, NO2, PH3, HNO3, SF6, CH3OH, HCOOH, OCS, CH3CN, C2H6, SO2, and H2O) at the wavelengths transmitted by a CO2 laser filled with different isotopes (12C16O2, 13C16O2, 12C18O2, 14C16O2, 14C18O2, 13C18O2, and 12C16O18O) is presented. The spectroscopical parameters for the molecules from GEISA database have been used. Hence the selection of the molecules was substantially based on the availability of the parameters in the database. The results of the calculations may be used in designing the differential absorption technique for remote monitoring of these molecules. The pressure and temperature dependence of the cross sections are described by and coefficients; these coefficients were calculated for the largest absorption cross sections for each molecule. The absorption cross sections of CH3OH and HCOOH at low pressures for all these CO2 lasers are also presented. These calculations are provided for design of new CO2-laser-pumped far-infrared lasers.

1. Introduction

In this paper we report molecular absorption cross sections at CO2-laser emission frequencies for several selected gases of atmospheric relevance (M = NH3, C2H4, CO2, O3, NO2, PH3, HNO3, SF6, CH3OH, HCOOH, OCS, CH3CN, C2H6, SO2, and H2O). This information may be useful mainly in the differential absorption (Light Detection and Ranging) LIDAR technique for remote measurement of the gas species [18] and also may be used to monitor the CO2 content in fuel combustion products [9], remote sensing of gases in human breath [10], or multiphoton dissociation processes or to measure water vapor concentration and wind speed vector in the plume of volcano [11, 12]. Note that the LIDAR technique sometimes is used for remote sensing of some exotic gases, like, for example, chemical warfare [13].

In some cases (CH3OH and HCOOH) it also may be used in designing optically pumped FIR (far infrared=THz) lasers where CO2 laser is used as a source of a pump radiation [14]. Also, the absorption of CO2-laser radiation by a cell with a mixture of some of these gases is used in our lab for quick check and assignment of the CO2-laser lines.

The focus of the present study is to predict absorption cross section in pure air at wavelengths of seven isotopic CO2 lasers: 12C16O2 (normal), 13C16O2, 12C18O2, 14C16O2, 14C18O2, 13C18O2, and 12C16O18O, which we hereafter denote as 26-, 36-, 28-, 46-, 48-, 38-, and 268-lasers.

In the clear atmosphere, absorption at 9–11 μm is due primarily to water vapor and carbon dioxide. Since the fraction of CO2 in the atmosphere is about 3.8 × 10−4 and (CO2)~10−22 cm2, the resonant absorption of 50% of the 26-laser radiation by atmospheric molecules occurs at the distance about 7 km. This distance may be not large enough for typical LIDAR applications, like monitoring of air pollution over the large town or early detection of small forest fires [15, 16]. Also, the fluctuations of the CO2 concentration in the atmosphere decrease strongly the accuracy of the LIDAR based on the 26-laser. Hence the first advantage of latter six CO2 lasers over conventional 26-laser is low attenuation from atmospheric CO2, which may extend strongly the detection distance and/or the accuracy of the LIDAR. Moreover, these isotopically substituted CO2 lasers may be used to detect the concentration of CO2 in the atmosphere or, more simply, to monitor the CO2 content in fuel combustion products [9].

Another advantage is another set of wavelengths; sometimes it makes it possible to detect molecules, unavailable for conventional 26-laser LIDAR.

It is important to note that the use of CO2 lasers for LIDAR remote sensing offers some advantages over that of the more current LIDAR experiments being conducted using the fundamental absorption transitions of hydrocarbons near 3 to 4 μm and CW Quantum Cascade Lasers, in that the absorption values near 10 μm are not too high and not too low for remote sensing at ranges of a few hundred meters, and the output power of the CO2 laser is high offering good detection ranges.

Note that commercially available CO2 lasers often may be filled with different isotopic gases (e.g., PL3 series from Edinburgh Photonics). Also, CO2 lasers make up to 108 shots without changing of the gas mixture (e.g., InfraLight series of CO2 lasers); hence there is no large difference, which isotopic modification of CO2 gas to use.

This work was greatly facilitated by usage of GEISA spectroscopical database [17], and only the molecules from the database were involved in calculations. We have not included several gases (N2H4, C6H6, C2Cl4, C2HCl3, C2H3Cl, C2H5SH, C2H4Cl2, CF2Cl2, and CFCl3) which may be detected by CO2 lasers [18], since no information is available on their absorption cross sections in the GEISA and HITRAN databases.

There were a lot of experimental measurements of the absorption coefficients at 26-laser frequencies. The most popular molecules are SF6 [1921], C2H4 [2224], and NH3 [2226], and the list of references here is very large. A lot of for more complicated molecules are also reported in the literature, for example, for acetonitrile, benzene, cyclohexane, 1,2-dichloroethane, ethyl acetate, freon-12, freon-113, furan, isopropanol, methyl chloroform, methyl ethyl ketone, -butanol, vinyl chloride, and iodopropane [27]; seven hydrazine fuel gases [28]; hydrazine, unsymmetrical dimethylhydrazine, and monomethylhydrazine [29]; C2H4, C2H3Cl3, C2HCl3, and Freon-113 [3]; and triacetone triperoxide [8].

However, much less information is available regarding of CO2 lasers other than 26-laser. For example, we know the measurements of (H2O) at 26-, 36-, and 46-laser wavelengths [30], (ClO2) at 28-laser wavelengths [31], (NH3) at a 36-laser [32]. Also, the photoacoustic spectroscopy has been used to determine for M = NH3, CCl2F2, CHClF2, CFCl3, and CClF3 at 36-laser wavelengths [33].

To the best of our knowledge, the FIR lasers normally are pumped by 26-lasers or, much rarely, by 36-laser [3437]; the other CO2 lasers are used very rarely [38, 39]. Note that while 26-laser has about 100 laser lines, using different isotopic CO2 lasers gives up to 1000 lines; hence the amount of different FIR-lasers pumped by CO2 lasers should increase accordingly.

With this in mind, we performed the calculation which hopefully provides the information of the quality comparable with that of the experimental studies. We hope that it will stimulate using isotopically different CO2 lasers for different applications.

2. Results

Assuming Lorentzian line shapes, we calculated the absorption cross sections at all possible CO2-laser frequencies. Tables 1, 2, and 3 show for 26-, 36-, and 28-lasers, respectively, for CO2-laser lines between P(40) and R(40), excluding the range P(6)–R(6). Atmospheric pressure bar and temperature  K are assumed everywhere, and the self-broadening is neglected (i.e., [M]≪[air]). The following expressions were used: where the index labels all transitions in molecule , is intensity of the th spectral line, , is Lorentzian width, , is the absorption maximum frequency of the th spectral line, is the pressure shift of the line transition, is the energy of the lower state for th transition, for linear molecules like CO2 and for nonlinear molecules, and are air pressure and temperature, respectively, and is Boltzmann constant.

The parameters , , , , , and are taken from GEISA database for each transition of each M molecule. Note that the pressure shifts are given in the database only for CH3CN and NO2 molecules. All of them are rather small (10−3 cm−1/atm), and they change only the third digit in calculated absorption cross sections. We hope that there is the same situation with all other molecules; hence we present the cross sections with three-digit accuracy; the last digit may be wrong due to the pressure shifts. All CO2-laser frequencies were taken from Freed et al. [40].

In Table 4 we present the “best” laser transitions for each isotopic variation of CO2 laser and for each molecule M. The pressure and temperature dependence of the cross sections are described by and coefficients as , , and the coefficients have been calculated from (1) and presented in Table 4 also.

It is not easy task to point out the “best” CO2-laser line for detection of molecule M. Normally the “best” CO2-laser line should lie in the ranges R(10)–R(40), P(10)–P(40) and has the largest absorption by M molecules; if the largest values occur outside these ranges, we mark it by asterisk shown in the table also. However, if the largest values occur at marginal lines of CO2 laser and are much larger than all other cross sections, we present this marginal line only.

3. Discussion

Some of our results are compared with the experimental literature data in Table 5. As one can see from the table, the present results agree favorably with the experimental data of Patty et al. [24] and Persson et al. [22], who have determined , , and coefficients for 26-laser absorption by NH3, O3, and C2H4 molecules.

Note that only in several cases our M molecules are important as “standard” air pollutant (NH3, C2H4, PH3, and O3) and in other cases our M molecules may happen in the air only near special industrial objects. As one can see from Tables 14, 26-laser is a good choice for all these four gases.

There are several advantages of the other CO2 lasers: monitoring of HNO3, NO2, C2H6, and CO2 molecules requires 46-/48-/36-, 36-, 36-/46-/48-, and 38-/268-lasers, respectively, instead of 26-laser.

We included in Table 4 several molecules with low cross sections (OCS, CH3CN, C2H6, SO2, and NO2). Although CO2 laser is not the best choice to detect these molecules, these data may be useful in special cases, for example, when CO2 LIDAR is used to monitor the leakage of these gases from industrial areas.

Surely, the data in all our tables are only starting points in discussion about applicability of particular CO2-laser transitions for remote sensing under atmospheric conditions, because at many wavenumbers, the absorption by H2O may be much stronger than absorption by the gases of interest. Hence one always should find the tradeoff between the absorption of H2O and the absorption of these gases.

For example, the “best” line for NH3 detection by 26-laser in Table 4 is 10R(30) with (NH3) = 303 × 10−20 cm2. However, at this wavelength, the ratio (NH3)/(H2O) is only 4.4 × 105. If we choose another 26-laser line for NH3 detection, P(34) (931.0014 cm−1) with (NH3) = 55.2 × 10−20 cm2 and (H2O) = 0.0023 × 10−23 cm2, the ratio will be much higher: (NH3)/(H2O) = 2.4 × 107. Hence, this another 26-laser line is better for NH3 detection, although the value (NH3) is lower.

Therefore, we included H2O in our calculations; see the results in Tables 1, 2, and 3. Our (H2O) data in the tables should help to choose the “best” pairs of CO2-laser lines (absorbing and nonabsorbing) for remote sensing of the gases of interest. Note that the pair of CO2-laser wavenumbers may originate from two isotopically different CO2 lasers; therefore the possibility to use many isotopic variations of CO2 laser simplifies strongly the choice of such pairs.

4. Application to FIR Lasers

There are several important benchmark molecules which are normally used in CO2-laser-pumped FIR lasers: CH3OH, CH2F2, HCOOH, 15NH3, CD3OD, CD3 OH, CD3Cl, 13CD3I, and 13CH3F. The absorption of CO2 radiation by these molecules results in FIR-laser emission. Table 6 lists our values for CH3OH and HCOOH at low pressures, where the shapes of spectral lines of these molecules are given by Doppler effect. As one can see, there are a lot of interesting possibilities to obtain new strong sources of FIR radiation. One of them may be 9R(19) line of 268-laser, which has very large (HCOOH) value.

Although there is no direct relation between intensities of CO2 absorption and FIR emission, it is clear that using 1000 CO2-laser lines instead of 100–200 should increase strongly the amount of strong FIR-laser transitions.

5. Conclusion

The absorption cross sections and and parameters of some molecules (NH3, C2H4, CO2, O3, NO2, PH3, HNO3, SF6, CH3OH, HCOOH, OCS, CH3CN, C2H6, SO2, and H2O) at CO2 laser frequencies (12C16O2,13C16O2, 12C18O2, 14C16O2, 14C18O2, 13C18O2, and 12C16O18O) have been calculated with the use of spectroscopical parameters from GEISA database. The present results are in reasonable agreement with other experimental measurements for NH3, O3, and C2H4. The results of the calculations may be used in designing the differential absorption technique for remote monitoring of these molecules.