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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 16 — Aug. 2, 2010
  • pp: 16460–16473
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Laser absorption spectroscopy of water vapor confined in nanoporous alumina: wall collision line broadening and gas diffusion dynamics

Tomas Svensson, Märta Lewander, and Sune Svanberg  »View Author Affiliations


Optics Express, Vol. 18, Issue 16, pp. 16460-16473 (2010)
http://dx.doi.org/10.1364/OE.18.016460


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Abstract

We demonstrate high-resolution tunable diode laser absorption spectroscopy (TDLAS) of water vapor confined in nanoporous alumina. Strong multiple light scattering results in long photon pathlengths (1 m through a 6 mm sample). We report on strong line broadening due to frequent wall collisions (gas-surface interactions). For the water vapor line at 935.685 nm, the HWHM of confined molecules are about 4.3 GHz as compared to 2.9 GHz for free molecules (atmospheric pressure). Gas diffusion is also investigated, and in contrast to molecular oxygen (that moves rapidly in and out of the alumina), the exchange of water vapor is found very slow.

© 2010 Optical Society of America

1. Introduction

High-resolution tunable diode laser absorption spectroscopy (TDLAS) is a well established method for selective and sensitive gas sensing and accurate measurements of gas concentration, pressure, and temperature. The technique is widely used, e.g. in atmospherical sciences, for combustion diagnostics, and for industrial process monitoring. The use of TDLAS for analysis of gas located inside turbid solids [1–3

1. M. Sjöholm, G. Somesfalean, J. Alnis, S. Andersson-Engels, and S. Svanberg, “Analysis of gas dispersed in scattering media,” Opt. Lett. 26, 16–18 (2001). [CrossRef]

] is an emerging subfield with numerous interesting application areas. The approach, often referred to as gas in scattering media absorption spectroscopy (GASMAS), has been applied in, e.g. medical diagnostics of the human paranasal sinuses [4–6

4. L. Persson, M. Andersson, T. Svensson, M. Cassel-Engquist, K. Svanberg, and S. Svanberg, “Non-intrusive optical study of gas and its exchange in human maxillary sinuses,” Proc. SPIE 6628, 662804 (2007). [CrossRef]

], characterization and optical porosimetry of pharmaceutical tablets and ceramics [7–9

7. T. Svensson, L. Persson, M. Andersson, S. Svanberg, S. Andersson-Engels, J. Johansson, and S. Folestad, “Non-invasive characterization of pharmaceutical solids by diode laser oxygen spectroscopy,” Appl. Spectrosc. 61, 784–786 (2007). [CrossRef] [PubMed]

], as well as for monitoring of drying processes [10

10. M. Andersson, L. Persson, M. Sjöholm, and S. Svanberg, “Spectroscopic studies of wood-drying processes,” Opt. Express 14, 3641–3653 (2006). [CrossRef] [PubMed]

] and food packaging [11

11. M. Lewander, Z. G. Guan, L. Persson, A. Olsson, and S. Svanberg, “Food monitoring based on diode laser gas spectroscopy,” Appl. Phys. B 93, 619–625 (2008). [CrossRef]

].

More recently, it has also been shown that GASMAS can be used to study gases in nanoporous materials [12

12. T. Svensson and Z. Shen, “Laser spectroscopy of gas confined in nanoporous materials,” Appl. Phys. Lett. 96, 021107 (2010). [CrossRef]

]. Besides having potential applications in material science for, e.g. studies of heterogenous catalysis, molecular sieving, adsorption and gas dynamics in nanoporous materials, this new domain of laser spectroscopy is also of fundamental spectroscopic interest. In particular, the absorption lines of gases are strongly broadened by frequent wall collisions (gas-surface interactions). For oxygen molecules confined in 20 nm pores of nanoporous bulk alumina, it was found that wall collision broadening is the dominating source of line broadening - even at atmospheric pressure [12

12. T. Svensson and Z. Shen, “Laser spectroscopy of gas confined in nanoporous materials,” Appl. Phys. Lett. 96, 021107 (2010). [CrossRef]

]. Normally, pressure broadening due to intermolecular collisions is the main broadening mechanism during measurements at atmospheric pressure. However, considering that the mean free path (i.e. distance between subsequent collisions) of many gases at atmospheric pressure is 50–100 nm [13

13. Hirschfelder, Curtiss, and Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954).

], it is not surprising that nano-confinement also will be a major source of line broadening. In addition, as wall collision line broadening strongly depends on the pore size, the phenomenon opens for a new, non-destructive method for pore size assessment.

fwall=1τwall=AVkTK2πm=A4V×vavg
(1)

where τ wall is the average time between wall collisions, A the container area, V the container volume, k the Boltzmann constant, TK the temperature, m the molecular mass, and ν avg the average speed of the molecules. Assuming that collisions cause complete relaxation, the halfwidth of wall collision broadening is approximately Γwall = (2πτ wall)−1. For some time, it was assumed that the lineshape due to wall collisions was Lorentzian, and that the resulting collisional linewidth Γcoll was given by Γcoll=Γgas2+Γwall2gas and Γwall refering to the HWHM linewidths due to intermolecular and wall collisions, respectively) [20

20. W. Gordy, “Microwave spectroscopy,” Rev. Mod. Phys. 20, 668–717 (1948). [CrossRef]

]. It was later theoretically shown that the lineshape due to wall collisions indeed is not Lorentzian [14

14. R. H. Johnson and M. W. P. Strandberg, “Broadening of microwave absorption lines by collisions with the cell walls,” Phys. Rev. 86, 811–812 (1952). [CrossRef]

,15

15. M. Danos and S. Geschwind, “Broadening of microwave absorption lines due to wall collisions,” Phys. Rev. 91, 1159–1162 (1953). [CrossRef]

], and that it depends on the container shape. Furthermore, for a parallell plate geometry, it was found that the combined linewidth follows Γcoll = Γgas + r 0(r) × Γwall, where r 0(r) is a coefficient that depends on the relative contribution ratio r = Γgaswall and should be close to unity as long as r > 1 [16

16. S. C. M. Luijendijk, “Effect of wall collisions on shape of microwave-absorption lines,” J. Phys. B. 8, 2995–3000 (1975). [CrossRef]

] (in this context, it can be mentioned that also sub-Doppler effects have been demonstrated for gases in thin pillbox-type cells [21

21. R. H. Romer and R. H. Dicke “New technique for high-resolution microwave spectroscopy,” Phys. Rev. 99, 532–536 (1955). [CrossRef]

,22

22. G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy “Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy,” Europhys. Lett. 63, 35–41 (2003). [CrossRef]

]). However, little is known about other geometries and cases where wall collision broadening dominates. Nor have any direct experimental studies of wall collision lineshapes been published. In microwave spectroscopy, wall collisions have mainly been considered a phenomenon accounted for by minor corrections. The impact of wall collisions has recently also been noted in connection with optical spectroscopy of gases at low pressure gas confined inside the 10 µm core of hollow photonic band-gap fibers [23

23. S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005). [CrossRef] [PubMed]

,24

24. J. Hald, J. C. Petersen, and J. Henningsen, “Saturated optical absorption by slow molecules in hollow-core photonic band-gap fibers,” Phys. Rev. Lett. 98, 213902 (2007). [CrossRef] [PubMed]

]. High-resolution laser spectroscopy of gases confined in nanoporous materials is thus a new topic. In contrast to the microwave spectroscopy discussed above, wall collision line broadening is here a very prominent effect. So far, the only study involves a near-infrared transition of molecular oxygen (at 760 nm) confined in alumina [12

12. T. Svensson and Z. Shen, “Laser spectroscopy of gas confined in nanoporous materials,” Appl. Phys. Lett. 96, 021107 (2010). [CrossRef]

]. While wall collision broadening in the microwave region was in the kHz regime, that study reports on GHz line broadening for molecular confined in nano-cavities. Much is yet to learn about line broadening and lineshapes of confined molecules, and the area constitutes a new challenge for the theory of collisions and spectroscopic lineshapes. In addition, potential applications needs to be identified and explored.

In this work, we demonstrate high-resolution laser spectroscopy of water vapor (H2O) confined in nanoporous alumina (Al2O3) with a pore size of about 70 nm (as given by mercury intrusion porosimetry). The strong multiple scattering of the alumina results in long interaction pathlengths, and allows direct absorption spectroscopy with peak absorption fractions of about 1–3%. For a 6 mm thick sample, the average optical pathlength through pores of the material is almost half a meter. Speckle interference is a major problem in GASMAS in general [2

2. T. Svensson, M. Andersson, L. Rippe, J. Johansson, S. Folestad, and S. Andersson-Engels, “High sensitivity gas spectroscopy of porous, highly scattering solids,” Opt. Lett. 33, 80–82 (2008). [CrossRef]

], and is in this work suppressed by means of laser beam dithering (as suggested in [2

2. T. Svensson, M. Andersson, L. Rippe, J. Johansson, S. Folestad, and S. Andersson-Engels, “High sensitivity gas spectroscopy of porous, highly scattering solids,” Opt. Lett. 33, 80–82 (2008). [CrossRef]

]). We then investigate line broadening due to the tight confinement by studying near-infrared transitions around 935 nm. Since the utilized TDLAS system has not been used for lineshape analysis previously, we also report on its basic performance in this respect (spectroscopy of water vapor at ambient conditions). Furthermore, we report on gas exchange by studying the gas diffusion dynamics after having stored the sample in 100% relative humidity, and also by simultaneously monitor water vapour and molecular oxygen during nitrogen flushing.

2. Experimental details

2.1. High-resolution laser spectroscopy

High-resolution spectra are recorded by employing tunable diode laser absorption spectroscopy (TDLAS). The TDLAS instrument utilized is a fiber-based dual beam system for near-infrared sensing of molecular oxygen (around 760 nm) and water vapor (around 935 nm) [6

6. M. Lewander, Z. G. Guan, K. Svanberg, S. Svanberg, and T. Svensson, “Clinical system for non-invasive in situ monitoring of gases in the human paranasal sinuses,” Opt. Express 17, 10849–10863 (2009). [CrossRef] [PubMed]

]. The system was originally designed and used for simultaneous measurements of path integrated O2 and H2O absorption by means of wavelength modulation spectroscopy (WMS). A detailed description of the TDLAS system is found in [6

6. M. Lewander, Z. G. Guan, K. Svanberg, S. Svanberg, and T. Svensson, “Clinical system for non-invasive in situ monitoring of gases in the human paranasal sinuses,” Opt. Express 17, 10849–10863 (2009). [CrossRef] [PubMed]

], and a schematic of the experimental configuration is given in Fig. 1. Briefly, the system is based on two distributed feedback (DFB) diode lasers (Nanoplus). Along the lines described in, e.g. [8

8. T. Svensson, M. Andersson, L. Rippe, S. Svanberg, S. Andersson-Engels, J. Johansson, and S. Folestad, “VCSEL-based oxygen spectroscopy for structural analysis of pharmaceutical solids,” Appl. Phys. B 90, 345–354 (2008). [CrossRef]

,25

25. M. Andersson, L. Persson, T. Svensson, and S. Svanberg, “Flexible lock-in detection system based on synchronized computer plug-in boards applied in sensitive gas spectroscopy,” Rev. Sci. Instrum. 78, 113107 (2007). [CrossRef] [PubMed]

], both diode laser tuning and data acquisition are controlled by a computer card (NI-6120, National Instruments) with internally synchronized analog outputs (AO) and inputs (AI). The tuning is realized by imposing linear ramps (5 Hz repetition rate) on the diode laser operation current supplied by conventional diode laser drivers. The two DFB diode lasers are pigtailed to single-mode optical fibers (SMF), and in order to allow simultaneous sensing of two gases these are combined into one single fiber. Unfortunately, the early part of the optical system cause unwanted interference noise. To be able to remove these detrimental effects, a beam splitter (BS) is used to create a dual beam configuration. The reference arm allows baseline recordi ngs and is crucial for analysis of sample arm data. Light in both arms are detected by large-area photodiodes (PD), and the resulting photocurrents are amplified and converted to voltage by low-noise transimpedance amplifiers (TIA). The voltage signals corresponding to the reference and sample arms are denoted ur and us, respectively. A relative optical frequency scale is determined by recording the etalon fringes of a solid BK7 etalon (40.75 mm long, having a 2.44 GHz free spectral range at 935 nm).

Fig. 1. Schematic of the TDLAS instrumentation (see text for details).

In the present work, we conduct direct absorption measurements with only the 935 nm diode laser (except for the nitrogen flushing experiment where WMS is used for simultaneous monitoring of both oxygen and water vapor; see Section 3.3). Measurements on porous samples are conducted in transmission. Light is injected into the sample by means of a divergent output of a single-mode optical fiber, and a 5.6 × 5.6 mm2 large-area photodiode (S1337-66BR, Hamamatsu) is used to collect the diffuse light transmitted through the sample.

Since GASMAS deals with spectroscopy of gas located inside porous, highly scattering solids, one needs to handle detection of weak diffuse light, unknown interaction pathlengths and severe speckle interference. As described in [2

2. T. Svensson, M. Andersson, L. Rippe, J. Johansson, S. Folestad, and S. Andersson-Engels, “High sensitivity gas spectroscopy of porous, highly scattering solids,” Opt. Lett. 33, 80–82 (2008). [CrossRef]

], speckle interference is suppressed by means of laser beam dithering. A lens mounted on tracking coils (TC-L) is inserted between the sample and the output of the single-mode fiber (the path through ambient air is about 1 cm, and the corresponding absorption is negligible compared to that from the nanoporous alumina). By feeding the tracking coils with low-frequency noise, the speckle interference is converted into noise that can be averaged out.

2.2. Spectral lines

We study water vapor by utilizing the strongest absorption line in the 940 nm region. This particular line is located at 935.684 nm (10687.36209 cm−1, vacuum wavelength), and is due to the (000) → (201) vibrational transition with the rotational change given by (J,Ka,Kc): (303) → (404). There are four neighboring lines of importance, but these are at least five times weaker. The strongest of them is the line located at 935.608 nm (10688.233710 cm−1). Relevant line parameters of these two transitions are given in Table 1.

2.3. Analysis of high-resolution spectra

The sample arm signal us(ν), where ν denotes relative optical frequency, can be written as a product of a baseline u 0(ν) and a transmission profile T(ν)

us(ν)=u0(ν)×T(ν)
(2)

Accordingly, experimental data is evaluated by simultaneously fitting a baseline and a transmission profile to us (using non-linear Levenberg-Marquardt optimization). In this work, the baseline model is based on the reference arm signal, ur(ν). Differences in offset and intensity between the two arms are taken into account by introducing two free fit parameters a 0 and a 1. The baseline model is explicitly stated in Eq. 3.

u0(ν)a0+a1×ur(ν)
(3)

Table 1. Line parameters of the two strongest lines investigated in this work. Except for the Doppler and Voigt widths (ΓD and ΓV), values are taken from the HITRAN 2008 compilation [26]. An important original source of line parameters is [27]. ΓD and ΓV are calculated theoretically for atmospheric conditions (1 atm and 296 K) [28].

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When a HITRAN simulation, Tsim(ν), is used to model the transmission profile, the complete model is given by

us(ν)(a0+a1×ur(ν))×(1+k×(Tsim(νν0)1))
(4)

Due to strong wall collision line broadening [12

12. T. Svensson and Z. Shen, “Laser spectroscopy of gas confined in nanoporous materials,” Appl. Phys. Lett. 96, 021107 (2010). [CrossRef]

], spectra originating from gas confined in the nanoporous alumina cannot be simulated by HITRAN. In such cases, the transmission profile is instead modeled by a certain number of independent Lorentz lineshapes:

T(ν)exp(Σiαi×g¯(Γi,νν0i))
(5)

Here, denotes a peak normalized Lorentzian lineshape, and the free fit parameters in this model are: αi being the peak absorbance, Γi being the Lorentz HWHM, and ν 0,i being the line center on the relative optical frequency scale. Using the same baseline model as in Eq. 4, the complete model then beomes

us(ν)(a0+a1×ur(ν))×exp(Σiαi×g¯(Γi,νν0i))
(6)

In order to make fitting robust, an initial guess is constructed based on (i) the expected positions of absorption lines, and (ii) the observed peak absorption fraction of the strongest line.

2.4. Calculations of water vapor concentration

The concentration of water vapor in air is calculated using the Arden-Buck equation, [29

29. A. Buck, “New equations for computing vapor-pressure and enhancement factor,” J. Appl. Meteorol. 20, 1527–1532 (1981). [CrossRef]

]

p=6.0326×103exp(17.502(TK273.15)TK32.18)
(7)

where TK (K) is the temperature and p (atm) the saturation pressure. A measurement of the relative humidity is needed in order to estimate the actual partial pressure of water vapor. For this purpose, we employ a Testo 608-H1 hygrometer (accuracy of ±3% RH units).

2.5. Nanoporous alumina

The alumina investigated in this work is a nanoporous bulk alumina manufactured by sintering a monodispersive 0.3 µm α-alumina powder at 1000 °C. The sample is 13 mm in diameter and about 6 mm thick. It has previously been used in connection with spectroscopy of confined oxygen molecules [12

12. T. Svensson and Z. Shen, “Laser spectroscopy of gas confined in nanoporous materials,” Appl. Phys. Lett. 96, 021107 (2010). [CrossRef]

]. The pore structure has been characterized by mercury intrusion porosimetry, a porosimetry standard [30

30. J. Rouquerol, D. Avnir, C. W. Fairbridge, D. H. Everett, J. H. Haynes, N. Pernicone, J. D. F. Ramsay, K. S. W. Sing, and K. K. Unger, “Recommendations for the characterization of porous solids,” Pure Appl. Chem. 66, 1739–1758 (1994). [CrossRef]

]. The sample is then put in a container with liquid mercury, and the intruded volume is recorded as the pressure is gradually increased. Larger pores are filled first, and smaller and smaller pores are filled as the pressure is increased (the relation between pressure and pore size is modeled by the Washburn equation [31

31. E. W. Washburn, “The dynamics of capillary flow.” Phys. Rev. 17, 273–283 (1921). [CrossRef]

]). As shown in Fig. 2, the total porosity is ϕ = 35.4%, and the mercury intrusion data suggest a narrow (±10 nm) pore size distribution around 70 nm. It should, however, be noted that the pore size given by mercury intrusion porosimetry refers to the most narrow dimension of the pore structure, i.e. the pore neck size. In addition, the method assumes sequential filling of pores in decreasing order of size. This means that the effective pore size most likely is underestimated, and that 70 nm cannot be regarded as an absolute truth (the effective pore size is most likely above 100 nm).

Fig. 2. Results of mercury intrusion porosimetry. In (a), the cumulative intrusion is plotted versus pore diameter (not versus mercury pressure). Note that the pressure increase towards the right, while the pore diameter decrease (smaller pores are filled at higher pressures). The intrusion comes a halt at 0.317 mL. Since the measurement was performed on a sample with a volume of 0.8948 mL, the porosity is approximately 35.4%. The pore size distribution is shown in (b), and is the derivative of the cumulative intrusion.

The optical properties have been studied with photon time-of-flight spectroscopy (PTOFS) [12

12. T. Svensson and Z. Shen, “Laser spectroscopy of gas confined in nanoporous materials,” Appl. Phys. Lett. 96, 021107 (2010). [CrossRef]

,32

32. T. Svensson, E. Alerstam, D. Khoptyar, J. Johansson, S. Folestad, and S. Andersson-Engels, “Near infrared photon time-of-flight spectroscopy of turbid materials up to 1400 nm,” Rev. Sci. Instrum. 80, 063105 (2009). [CrossRef] [PubMed]

]. The material is extremely scattering and exhibits a λ −4 Rayleigh-type scattering dependency, where the reduced scattering coefficient µs approximately follows 596 cm−1 × (λ/µm)−3.9 (improved expression based on re-evaluation of data from [12

12. T. Svensson and Z. Shen, “Laser spectroscopy of gas confined in nanoporous materials,” Appl. Phys. Lett. 96, 021107 (2010). [CrossRef]

] using a more accurate measure of the sample thickness). The reduced scattering coefficient is thus about 770 cm−1 at 935 nm (i.e. a 1/µs ~ 13 µm transport mean free path for photons), while absorption is low (< 0.01 cm−1). The distribution of photon pathlengths for transmission measurements of the alumina material is shown in Fig. 3. The pathlength is calculated from the time-of-flight by assuming a volume-averaged refractive index 1.76 × (1 − ϕ) + 1 × ϕ ≃ 1.49. The experimental data was recorded for a 2.25 mm thick sample at 940 nm, where diffusion-based evaluation [32

32. T. Svensson, E. Alerstam, D. Khoptyar, J. Johansson, S. Folestad, and S. Andersson-Engels, “Near infrared photon time-of-flight spectroscopy of turbid materials up to 1400 nm,” Rev. Sci. Instrum. 80, 063105 (2009). [CrossRef] [PubMed]

,33

33. D. Contini, F. Martelli, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation: I. Theory,” Appl. Opt. 36, 4587–4599 (1997). [CrossRef] [PubMed]

] yields a reduced scattering coefficient of about 750 cm−1. The reason why measurements were not performed on the 6 mm thick sample used for gas spectroscopy is that the corresponding time-of-flight (TOF) distribution would not fit within the 12.5 ns window offered by our 80 MHz repetition rate pulsed laser [32

32. T. Svensson, E. Alerstam, D. Khoptyar, J. Johansson, S. Folestad, and S. Andersson-Engels, “Near infrared photon time-of-flight spectroscopy of turbid materials up to 1400 nm,” Rev. Sci. Instrum. 80, 063105 (2009). [CrossRef] [PubMed]

]. Instead, the TOF distribution expected for the 6 mm sample is calculated theoretically [33

33. D. Contini, F. Martelli, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation: I. Theory,” Appl. Opt. 36, 4587–4599 (1997). [CrossRef] [PubMed]

] for 935 nm light (770 cm−1 in reduced scattering), taking the experimental arrangement into account (a ~2 mm diameter injection spot size and a 5.6 × 5.6 mm2 square detector). The simulation results in an average photon pathlength of about 105 cm (average TOF of 5 ns). It may appear surprising that transmission through a few millimeters of the investigated alumina gives rise to pathlengths of more than one meter. However, the scattering of the alumina is only moderate when comparing it to the extreme scattering of various disordered materials used in fundamental science of light localization (transport mean free paths of photons down to 0.1 µm have been reported) [34

34. D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997). [CrossRef]

,35

35. M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett. 96 (2006).

].

Fig. 3. Distribution of pathlengths for photons detected after transmission through the alumina material. Experimental data (black) was recorded for a 2.25 mm thick sample at 940 nm, while the simulated data (red) corresponds to transmission through a 6 mm thick sample for light at 935 nm.

3. Experimental results

3.1. System test on ambient air

In order to test how well the utilized system is suited for lineshape investigation, we studied high-resolution spectra obtained under well known (ambient) conditions. The raw data generated by the system are shown in Fig. 4.

HITRAN-based evaluation of the data, as described in Section 2.3, is presented in Fig. 5(a). The evaluation is based on a HITRAN simulation for 983 mbar, 295.5 K, a pathlength of 100 cm, and a H2O volume mixing ratio of 5000 ppm. The fitted value of k was 0.977, and suggests a path integrated concentration of about 4900 ppm·m. The Arden-Buck equation for a 295.5 K and 19.8±3% RH results in H2O partial pressure in the 0.0044 to 0.0060 atm range, and path integrated concentrations between 4600 and 6200 ppm·m (for 983 mbar = 0.97 atm). The experimental result is thus well within accuracy of the utilized hygrometer. Furthermore, the good agreement in spectral shape between our experiment and HITRAN shows that our system can be used for lineshape assessment. Note, however, that the residual pattern exhibit non-random structures, indicating non-canceled interference, inaccurate reference values for pressure and temperature, and/or slight inaccuracy in the the frequency scale. On the other hand, the maximum residual is not more than 2 × 10−4 and the signal-to-residual ratio is well above 100.

Since HITRAN cannot take wall collision broadening into account, we will later evaluate measurements on confined water vapor by fitting multiple Lorentzian lines to our data. In order to verify the performance of this procedure, we tested it on the ambient air data. The result is presented in Fig. 5(b), where 5 Lorentzians are simultaneously fitted to the data. Fitted line parameters are given in Table 2. The fact that the lines should exhibit Voigt lineshapes is not of major importance, since the Lorentzian contribution is dominating at atmospheric pressure. For the three strongest lines, fitted spectral positions and linewidths agree well with line parameters stated in HITRAN. The two weakest lines have peak absorption fractions that are not much larger than the residual background. This is reflected by a fairly large deviation in fitted and expected parameters.

Fig. 4. Experimental data from measurement over a 100 cm path through ambient air at about 983 mbar, 296 K and 19% relative humidity. Analysis of the etalon fringes gives a tuning coefficient of −3.8 GHz/mA (0.01 nm/mA).
Fig. 5. Spectral evaluation of the 100 cm ambient air data shown in Fig. 4 based on HITRAN-based fitting (left) and Lorentzian fitting (right). The fitted spectra (red solid) overlays experimental data (black solid).

Table 2. Comparison of expected and measured spectral position and linewidths. Spectral positions are given relative to the position of the strongest line. Expected linewidth, ΓV, refers to Voigt HWHM the calculated for 983 mbar (0.97 atm) and 295.5 K [28]. ΓfitL refers to the linewidth of fitted Lorentzian lineshapes, and αfit to fitted peak absorbance.

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3.2. Gas confined in nanoporous alumina

It is very important to note that interference suppression is crucial during laser spectroscopy of gas in turbid media [2

2. T. Svensson, M. Andersson, L. Rippe, J. Johansson, S. Folestad, and S. Andersson-Engels, “High sensitivity gas spectroscopy of porous, highly scattering solids,” Opt. Lett. 33, 80–82 (2008). [CrossRef]

]. If our experiments are performed under static conditions (tracking coils turned off), the transmittance spectrum is distorted by a 5 × 10−3 (peak-to-peak) random interference structure (c.f. Fig. 6). This noise is detrimental to spectral analysis, even for the strongest absorption line in our experiments.

Fig. 6. Example of the speckle-type interference encountered during measurement on the porous alumina (ambient conditions). The transmittance spectra is heavily distorted if interference suppression is turned off. The acquisition time was 60 s in both measurements. The bottom graph states the normalized difference in detector signals when tracking coils are switched on and off, i.e. (u off su on s)/u on s. The peak-to-peak interference level is on the order of 5 × 10−3.

Fig. 7. Experimental spectrum of water vapor confined in the nanoporous alumina (black solid) together with a fit based on four Lorentzian peaks (red solid). The acquisition time was 60 s. In order to visualize the strong line broadening due to nano-confinenment, a peak normalized HITRAN simulation for water vapor (1 atm, 296 K) is shown for reference.

Table 3. Experimentally determined spectral parameters of water vapor confined in the nanoporous alumina (spectral data shown in Fig. 7). ΓfitL refers to the linewidth of fitted Lorentzian lineshapes, and αfit to fitted peak absorbance. For spectral position and HWHM, the uncertainty is given as one standard deviation (three measurements, different days). Since the time between measurement and removal from 100% RH differs, only the mean peak absorbance can be given. HITRAN-based values (ν0 and ΓV) for free ambient H2O (1 atm, 296 K) are stated for reference.

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T(ν)=exp(Sg(νν0)NL)
(8)

where S cm2Hz is the integrated linestrength, g(ν) the area-normalized lineshape function (a function of optical frequency), and N the number density of the absorber. For the strongest water vapor line, as stated in Table 1, we have S = 1.936 × 10−11 cm2Hz. The peak value of a Lorentzian lineshape function is g max = 1=(πΓ), i.e. 7.4026 × 10−11 Hz−1 for the molecules confined in the alumina (Γ = 4.3 GHz). The number density of water vapor is given by c × N 0, where c is the concentration and N 0 the Loschmidt number. The Loschmidt number states the total number density of an ideal gas and depends on temperature (TK) and pressure (p), N 0 = p/(kBTK), where kB is the Boltzmann constant. For our case, TK = 296 K and p = 1 atm, we have N 0 = 2.4794 × 1019 cm−3. Turning to the water vapor concentration, some reasoning is needed. The absorption measurement was made soon after the sample was taken from a sealed environment (100% RH and a temperature of about 296 K). According to Eq. 7, the corresponding saturation pressure of water vapor is 0.0275 atm (a concentration of 27500 ppm, at atmospheric pressure). Given the experiences from investigations of gas dynamics (c.f. Fig. 8), we expect that the effective concentration in the material during our measurement is approximately 3/4 of the saturation pressure (i.e. a concentration of about 21000 ppm). The resulting number density is thus N = 0.021N 0 ≃ 5.2 × 1017 cm−3. We may now estimate the interaction pathlength by solving

0.97=Tmin=exp(SgmaxNL)
(9)

Doing so, we find that L is approximately 41 cm. This is in good agreement with the measurement of the photon time-of-flight distribution (c.f. Section 2.5), in which the total photon pathlength was estimated to 105 cm. Given the 35.4% porosity of the alumina, we should thus expect that about 37 cm is through the pores (i.e. close to the 41 cm derived from gas absorption). Note that this reasoning assumes that light has no significant preference to travel in the solid when the heterogeneity is smaller than the wavelength of light. In contrast, recent work on light propagation in macroporous materials show that light is predominantly confined to the solid [9

9. T. Svensson, E. Alerstam, J. Johansson, and S. Andersson-Engels, “Optical porosimetry and investigations of the porosity experienced by light interacting with porous media,” Opt. Lett. 35, 1740–1742 (2010). [CrossRef] [PubMed]

]. The issue thus deserve further attention.

3.3. Gas exchange dynamics

In order to study water vapor transport in the nanoporous alumina, we studied how the water vapor concentration in the alumina relaxes to ambient conditions after the material has been stored in a sealed environment with 100% RH. Fig. 8(a) shows how the water vapour absorption signal slowly decreases with time. The process exhibits non-trivial features and cannot be modeled by a single exponential decay. This is illustrated by the outcome of exponential fitting over the complete data series. On the other hand, the process from 20 minutes and onwards appears to be well modeled by a single exponential. Note also that the relative absorption does not drop to 0.25, as expected from the ambient air relative humidity. This may be explained by an initial rapid decay that is not captured (the insertion of the sample into the setup takes up to one minute), or that 100% RH was not reached within the sample.

The results of the relaxation experiment stand in great contrast to the experiences from spectroscopy of molecular oxygen confined in the alumina. Oxygen has been found to enter and exit the alumina very quickly [12

12. T. Svensson and Z. Shen, “Laser spectroscopy of gas confined in nanoporous materials,” Appl. Phys. Lett. 96, 021107 (2010). [CrossRef]

]. In order to further illustrate this difference, we conducted simultaneous sensing of water vapor and oxygen in the nanoporous alumina during a nitrogen flushing experiment. In order to readily be able to separate absorption of the two gases, we employ WMS and use different modulation frequencies at the two wavelengths used. The result of the experiment is given in Fig. 8(b). There, the absorption imprint of the gases are measured by the peak-to-peak value of the intensity-corrected first harmonic WMS signal (1f IC-WMS). The sample was flushed with nitrogen approximately from t = 0 to t = 4 min. The flushing was conducted in open air by directing a ~12 l/min flow of nitrogen towards the sample. The decay in water vapor concentration is clearly very slow, while the decay in oxygen concentration is extremely fast and cannot be resolved by our instrument. Note that the flushing method utilized here was not able to completely replace the air surrounding the sample (previous measurements on the same material show that the signal indeed can be completely removed within seconds [12

12. T. Svensson and Z. Shen, “Laser spectroscopy of gas confined in nanoporous materials,” Appl. Phys. Lett. 96, 021107 (2010). [CrossRef]

]). Despite non-optimal nitrogen flushing, the experiment clearly illustrates the significant difference in gas exchange characteristics. Water vapor is clearly a “sticky gas”.

Fig. 8. Part (a) shows gas exchange dynamics during relaxation from 100% RH to ambient conditions (23% RH). Part (b) shows simultaneous monitoring of water vapor and oxygen during a nitrogen flushing experiment. The nitrogen flushing is started at t = 0 and stopped at t = 4 min (range marked in grey), and the time-resolution is 4 s (interference suppression via beam dithering requires some averaging time). In contrast to the slow exchange of water vapor, as seen also in part (a), the response for oxygen is rapid.

4. Discussion

4.1. Regarding wall collision line broadening

In order to progress, two things are important. The first thing is to perform measurements at reduced pressures. This will eliminate the impact of intermolecular collisions, while wall collision broadening should remain equally strong. It will allow investigations of the wall collision lineshape, as well as studies of how it adds to traditional collisional broadening. Secondly, better information about the shape and size of pores must be gathered. The pore neck size, as provided by mercury intrusion porosimetry, may be far from the effective pore size. When interpreting lineshapes of gases tightly confined in porous materials, one should also keep in mind that the lineshape can be influenced also by Dicke narrowing [37

37. R. Dicke, “The effect of collisions upon the Doppler width of spectral lines,” Phys. Rev. 89, 472–473 (1953). [CrossRef]

,38

38. R. P. Frueholz and J. C. Camparo, “Implications of the trapping-desorption and direct inelastic-scattering channels on Dicke-narrowed line-shapes,” Phys. Rev. A 35, 3768–3774 (1987). [CrossRef] [PubMed]

] as well as by, e.g. van der Waals interactions [39

39. V. Sandoghdar, C. I. Sukenik, E. A. Hinds, and S. Haroche, “Direct measurement of the van der Waals interaction between an atom and its images in a micron-sized cavity,” Phys. Rev. Lett. 68, 3432–3435 (1992). [CrossRef] [PubMed]

,40

40. M. Fichet, G. Dutier, A. Yarovitsky, P. Todorov, I. Hamdi, I. Maurin, S. Saltiel, D. Sarkisyan, M. P. Gorza, D. Bloch, and M. Ducloy, “Exploring the van der Waals atom-surface attraction in the nanometric range,” Euro-phys. Lett. 77, 54001 (2007). [CrossRef]

].

4.2. Regarding gas diffusion

Despite the fairly simple pore structure (a narrow distribution around 70 nm), the gas exchange process appears non-trivial, and cannot be explained by a single exponential decay. The minor plateau occurring after 6 min is reproducible, and is thus not a measurement error. It is important to realize that the measured absorption is a product of the photon sampling distribution and the gas concentration distribution. This fact complicates interpretation, and needs further attention. Another question is whether adsorption/desorption processes can influence the internal gas concentration. A key in resolving these issues is to construct a GASMAS instrumentation that allows measurements of samples while kept in controlled atmospheres (avoiding manual moving of samples from controlled conditions to ambient conditions, as in the present work).

Acknowledgement

The authors are grateful to Karin Lindqvist at SWEREA IVF for manufacturing of the alumina, and to Erik Alerstam, Dmitry Khoptyar and Stefan Andersson-Engels for collaboration on PTOFS. This work was supported by the Swedish Research Council through a direct grant and a Linnaeus grant to the Lund Laser Centre.

References and links

1.

M. Sjöholm, G. Somesfalean, J. Alnis, S. Andersson-Engels, and S. Svanberg, “Analysis of gas dispersed in scattering media,” Opt. Lett. 26, 16–18 (2001). [CrossRef]

2.

T. Svensson, M. Andersson, L. Rippe, J. Johansson, S. Folestad, and S. Andersson-Engels, “High sensitivity gas spectroscopy of porous, highly scattering solids,” Opt. Lett. 33, 80–82 (2008). [CrossRef]

3.

S. Svanberg, “Optical analysis of trapped gas-Gas in scattering media absorption spectroscopy,” Laser Phys. 20, 68–77 (2010). [CrossRef]

4.

L. Persson, M. Andersson, T. Svensson, M. Cassel-Engquist, K. Svanberg, and S. Svanberg, “Non-intrusive optical study of gas and its exchange in human maxillary sinuses,” Proc. SPIE 6628, 662804 (2007). [CrossRef]

5.

L. Persson, M. Andersson, M. Cassel-Engquist, K. Svanberg, and S. Svanberg, “Gas monitoring in human sinuses using tunable diode laser spectroscopy,” J. Biomed. Opt. 12, 054001 (2007). [CrossRef] [PubMed]

6.

M. Lewander, Z. G. Guan, K. Svanberg, S. Svanberg, and T. Svensson, “Clinical system for non-invasive in situ monitoring of gases in the human paranasal sinuses,” Opt. Express 17, 10849–10863 (2009). [CrossRef] [PubMed]

7.

T. Svensson, L. Persson, M. Andersson, S. Svanberg, S. Andersson-Engels, J. Johansson, and S. Folestad, “Non-invasive characterization of pharmaceutical solids by diode laser oxygen spectroscopy,” Appl. Spectrosc. 61, 784–786 (2007). [CrossRef] [PubMed]

8.

T. Svensson, M. Andersson, L. Rippe, S. Svanberg, S. Andersson-Engels, J. Johansson, and S. Folestad, “VCSEL-based oxygen spectroscopy for structural analysis of pharmaceutical solids,” Appl. Phys. B 90, 345–354 (2008). [CrossRef]

9.

T. Svensson, E. Alerstam, J. Johansson, and S. Andersson-Engels, “Optical porosimetry and investigations of the porosity experienced by light interacting with porous media,” Opt. Lett. 35, 1740–1742 (2010). [CrossRef] [PubMed]

10.

M. Andersson, L. Persson, M. Sjöholm, and S. Svanberg, “Spectroscopic studies of wood-drying processes,” Opt. Express 14, 3641–3653 (2006). [CrossRef] [PubMed]

11.

M. Lewander, Z. G. Guan, L. Persson, A. Olsson, and S. Svanberg, “Food monitoring based on diode laser gas spectroscopy,” Appl. Phys. B 93, 619–625 (2008). [CrossRef]

12.

T. Svensson and Z. Shen, “Laser spectroscopy of gas confined in nanoporous materials,” Appl. Phys. Lett. 96, 021107 (2010). [CrossRef]

13.

Hirschfelder, Curtiss, and Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954).

14.

R. H. Johnson and M. W. P. Strandberg, “Broadening of microwave absorption lines by collisions with the cell walls,” Phys. Rev. 86, 811–812 (1952). [CrossRef]

15.

M. Danos and S. Geschwind, “Broadening of microwave absorption lines due to wall collisions,” Phys. Rev. 91, 1159–1162 (1953). [CrossRef]

16.

S. C. M. Luijendijk, “Effect of wall collisions on shape of microwave-absorption lines,” J. Phys. B. 8, 2995–3000 (1975). [CrossRef]

17.

P. E. Wagner, R. M. Somers, and J. L. Jenkins, “Line broadening and relaxation of 3 microwave transitions in ammonia by wall and intermolecular collisions,” J. Phys. B. 14, 4763–4770 (1981). [CrossRef]

18.

S. L. Coy, “Speed dependence of microwave rotational relaxation rates,” J. Chem. Phys. 73, 5531–5555 (1980). [CrossRef]

19.

G. R. Gunthermohr, R. L. White, A. L. Schawlow, W. E. Good, and D. K. Coles, “Hyperfine structure in the spectrum of N14H3. I. Experimental results,” Phys. Rev. 94, 1184–1191 (1954). [CrossRef]

20.

W. Gordy, “Microwave spectroscopy,” Rev. Mod. Phys. 20, 668–717 (1948). [CrossRef]

21.

R. H. Romer and R. H. Dicke “New technique for high-resolution microwave spectroscopy,” Phys. Rev. 99, 532–536 (1955). [CrossRef]

22.

G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy “Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy,” Europhys. Lett. 63, 35–41 (2003). [CrossRef]

23.

S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005). [CrossRef] [PubMed]

24.

J. Hald, J. C. Petersen, and J. Henningsen, “Saturated optical absorption by slow molecules in hollow-core photonic band-gap fibers,” Phys. Rev. Lett. 98, 213902 (2007). [CrossRef] [PubMed]

25.

M. Andersson, L. Persson, T. Svensson, and S. Svanberg, “Flexible lock-in detection system based on synchronized computer plug-in boards applied in sensitive gas spectroscopy,” Rev. Sci. Instrum. 78, 113107 (2007). [CrossRef] [PubMed]

26.

L. S. Rothman, I. E. Gordon, A. Barbe, D. C. Benner, P. E. Bernath, M. Birk, V. Boudon, L. R. Brown, A. Campargue, J. P. Champion, K. Chance, L. H. Coudert, V. Dana, V. M. Devi, S. Fally, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, I. Kleiner, N. Lacome, W. J. Lafferty, J. Y. Mandin, S. T. Massie, S. N. Mikhailenko, C. E. Miller, N. Moazzen-Ahmadi, O. V. Naumenko, A. V. Nikitin, J. Orphal, V. I. Perevalov, A. Perrin, A. Predoi-Cross, C. P. Rinsland, M. Rotger, M. Simeckova, M. A. H. Smith, K. Sung, S. A. Tashkun, J. Tennyson, R. A. Toth, A. C. Vandaele, and J. Vander Auwera, “The HITRAN 2008 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 110, 533–572 (2009). [CrossRef]

27.

L. R. Brown, R. A. Toth, and M. Dulick, “Empirical line parameters of H162O near 0.94 µm: Positions, intensities and air-broadening coefficients,” J. Mol. Spectrosc. 212, 57–82 (2002). [CrossRef]

28.

J. Olivero and R. Longbothum, “Empirical fits to Voigt line-width - brief review,” J. Quant. Spectrosc. Radiat. Transfer 17, 233–236 (1977). [CrossRef]

29.

A. Buck, “New equations for computing vapor-pressure and enhancement factor,” J. Appl. Meteorol. 20, 1527–1532 (1981). [CrossRef]

30.

J. Rouquerol, D. Avnir, C. W. Fairbridge, D. H. Everett, J. H. Haynes, N. Pernicone, J. D. F. Ramsay, K. S. W. Sing, and K. K. Unger, “Recommendations for the characterization of porous solids,” Pure Appl. Chem. 66, 1739–1758 (1994). [CrossRef]

31.

E. W. Washburn, “The dynamics of capillary flow.” Phys. Rev. 17, 273–283 (1921). [CrossRef]

32.

T. Svensson, E. Alerstam, D. Khoptyar, J. Johansson, S. Folestad, and S. Andersson-Engels, “Near infrared photon time-of-flight spectroscopy of turbid materials up to 1400 nm,” Rev. Sci. Instrum. 80, 063105 (2009). [CrossRef] [PubMed]

33.

D. Contini, F. Martelli, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation: I. Theory,” Appl. Opt. 36, 4587–4599 (1997). [CrossRef] [PubMed]

34.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997). [CrossRef]

35.

M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett. 96 (2006).

36.

G. Banerjee and K. Sengupta, “Pore size optimisation of humidity sensor - a probabilistic approach,” Sens. Actuators B 86, 34–41 (2002). [CrossRef]

37.

R. Dicke, “The effect of collisions upon the Doppler width of spectral lines,” Phys. Rev. 89, 472–473 (1953). [CrossRef]

38.

R. P. Frueholz and J. C. Camparo, “Implications of the trapping-desorption and direct inelastic-scattering channels on Dicke-narrowed line-shapes,” Phys. Rev. A 35, 3768–3774 (1987). [CrossRef] [PubMed]

39.

V. Sandoghdar, C. I. Sukenik, E. A. Hinds, and S. Haroche, “Direct measurement of the van der Waals interaction between an atom and its images in a micron-sized cavity,” Phys. Rev. Lett. 68, 3432–3435 (1992). [CrossRef] [PubMed]

40.

M. Fichet, G. Dutier, A. Yarovitsky, P. Todorov, I. Hamdi, I. Maurin, S. Saltiel, D. Sarkisyan, M. P. Gorza, D. Bloch, and M. Ducloy, “Exploring the van der Waals atom-surface attraction in the nanometric range,” Euro-phys. Lett. 77, 54001 (2007). [CrossRef]

OCIS Codes
(020.3690) Atomic and molecular physics : Line shapes and shifts
(290.4210) Scattering : Multiple scattering
(290.7050) Scattering : Turbid media
(300.6260) Spectroscopy : Spectroscopy, diode lasers
(300.6320) Spectroscopy : Spectroscopy, high-resolution
(160.4236) Materials : Nanomaterials

ToC Category:
Spectroscopy

History
Original Manuscript: May 18, 2010
Revised Manuscript: July 1, 2010
Manuscript Accepted: July 1, 2010
Published: July 21, 2010

Citation
Tomas Svensson, Märta Lewander, and Sune Svanberg, "Laser absorption spectroscopy of water vapor confined in nanoporous alumina: wall collision line broadening and gas diffusion dynamics," Opt. Express 18, 16460-16473 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-16-16460


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References

  1. M. Sjöholm, G. Somesfalean, J. Alnis, S. Andersson-Engels, and S. Svanberg, “Analysis of gas dispersed in scattering media,” Opt. Lett. 26, 16–18 (2001). [CrossRef]
  2. T. Svensson, M. Andersson, L. Rippe, J. Johansson, S. Folestad, and S. Andersson-Engels, “High sensitivity gas spectroscopy of porous, highly scattering solids,” Opt. Lett. 33, 80–82 (2008). [CrossRef]
  3. S. Svanberg, “Optical analysis of trapped gas-Gas in scattering media absorption spectroscopy,” Laser Phys. 20, 68–77 (2010). [CrossRef]
  4. L. Persson, M. Andersson, T. Svensson, M. Cassel-Engquist, K. Svanberg, and S. Svanberg, “Non-intrusive optical study of gas and its exchange in human maxillary sinuses,” Proc. SPIE 6628, 662804 (2007). [CrossRef]
  5. L. Persson, M. Andersson, M. Cassel-Engquist, K. Svanberg, and S. Svanberg, “Gas monitoring in human sinuses using tunable diode laser spectroscopy,” J. Biomed. Opt. 12, 054001 (2007). [CrossRef] [PubMed]
  6. M. Lewander, Z. G. Guan, K. Svanberg, S. Svanberg, and T. Svensson, “Clinical system for non-invasive in situ monitoring of gases in the human paranasal sinuses,” Opt. Express 17, 10849–10863 (2009). [CrossRef] [PubMed]
  7. T. Svensson, L. Persson, M. Andersson, S. Svanberg, S. Andersson-Engels, J. Johansson, and S. Folestad, “Noninvasive characterization of pharmaceutical solids by diode laser oxygen spectroscopy,” Appl. Spectrosc. 61, 784–786 (2007). [CrossRef] [PubMed]
  8. T. Svensson, M. Andersson, L. Rippe, S. Svanberg, S. Andersson-Engels, J. Johansson, and S. Folestad, “VCSEL based oxygen spectroscopy for structural analysis of pharmaceutical solids,” Appl. Phys. B 90, 345–354 (2008). [CrossRef]
  9. T. Svensson, E. Alerstam, J. Johansson, and S. Andersson-Engels, “Optical porosimetry and investigations of the porosity experienced by light interacting with porous media,” Opt. Lett. 35, 1740–1742 (2010). [CrossRef] [PubMed]
  10. M. Andersson, L. Persson, M. Sjöholm, and S. Svanberg, “Spectroscopic studies of wood-drying processes,” Opt. Express 14, 3641–3653 (2006). [CrossRef] [PubMed]
  11. M. Lewander, Z. G. Guan, L. Persson, A. Olsson, and S. Svanberg, “Food monitoring based on diode laser gas spectroscopy,” Appl. Phys. B 93, 619–625 (2008). [CrossRef]
  12. T. Svensson, and Z. Shen, “Laser spectroscopy of gas confined in nanoporous materials,” Appl. Phys. Lett. 96, 021107 (2010). [CrossRef]
  13. Hirschfelder, Curtiss, and Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954).
  14. R. H. Johnson, and M. W. P. Strandberg, “Broadening of microwave absorption lines by collisions with the cell walls,” Phys. Rev. 86, 811–812 (1952). [CrossRef]
  15. M. Danos, and S. Geschwind, “Broadening of microwave absorption lines due to wall collisions,” Phys. Rev. 91, 1159–1162 (1953). [CrossRef]
  16. S. C. M. Luijendijk, “Effect of wall collisions on shape of microwave-absorption lines,” J. Phys. B 8, 2995–3000 (1975). [CrossRef]
  17. P. E. Wagner, R. M. Somers, and J. L. Jenkins, “Line broadening and relaxation of 3 microwave transitions in ammonia by wall and intermolecular collisions,” J. Phys. B 14, 4763–4770 (1981). [CrossRef]
  18. S. L. Coy, “Speed dependence of microwave rotational relaxation rates,” J. Chem. Phys. 73, 5531–5555 (1980). [CrossRef]
  19. G. R. Gunthermohr, R. L. White, A. L. Schawlow, W. E. Good, and D. K. Coles, “Hyperfine structure in the spectrum of N14H3. I. Experimental results,” Phys. Rev. 94, 1184–1191 (1954). [CrossRef]
  20. W. Gordy, “Microwave spectroscopy,” Rev. Mod. Phys. 20, 668–717 (1948). [CrossRef]
  21. R. H. Romer, and R. H. Dicke, “New technique for high-resolution microwave spectroscopy,” Phys. Rev. 99, 532–536 (1955). [CrossRef]
  22. G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy, “Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy,” Europhys. Lett. 63, 35–41 (2003). [CrossRef]
  23. S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005). [CrossRef] [PubMed]
  24. J. Hald, J. C. Petersen, and J. Henningsen, “Saturated optical absorption by slow molecules in hollow-core photonic band-gap fibers,” Phys. Rev. Lett. 98, 213902 (2007). [CrossRef] [PubMed]
  25. M. Andersson, L. Persson, T. Svensson, and S. Svanberg, “Flexible lock-in detection system based on synchronized computer plug-in boards applied in sensitive gas spectroscopy,” Rev. Sci. Instrum. 78, 113107 (2007). [CrossRef] [PubMed]
  26. L. S. Rothman, I. E. Gordon, A. Barbe, D. C. Benner, P. E. Bernath, M. Birk, V. Boudon, L. R. Brown, A. Campargue, J. P. Champion, K. Chance, L. H. Coudert, V. Dana, V. M. Devi, S. Fally, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, I. Kleiner, N. Lacome, W. J. Lafferty, J. Y. Mandin, S. T. Massie, S. N. Mikhailenko, C. E. Miller, N. Moazzen-Ahmadi, O. V. Naumenko, A. V. Nikitin, J. Orphal, V. I. Perevalov, A. Perrin, A. Predoi-Cross, C. P. Rinsland, M. Rotger, M. Simeckova, M. A. H. Smith, K. Sung, S. A. Tashkun, J. Tennyson, R. A. Toth, A. C. Vandaele, and J. Vander Auwera, “The HITRAN 2008 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transf. 110, 533–572 (2009). [CrossRef]
  27. L. R. Brown, R. A. Toth, and M. Dulick, “Empirical line parameters of H16 2 O near 0.94 1m: Positions, intensities and air-broadening coefficients,” J. Mol. Spectrosc. 212, 57–82 (2002). [CrossRef]
  28. J. Olivero, and R. Longbothum, “Empirical fits to Voigt line-width - brief review,” J. Quant. Spectrosc. Radiat. Transf. 17, 233–236 (1977). [CrossRef]
  29. A. Buck, “New equations for computing vapor-pressure and enhancement factor,” J. Appl. Meteorol. 20, 1527–1532 (1981). [CrossRef]
  30. J. Rouquerol, D. Avnir, C. W. Fairbridge, D. H. Everett, J. H. Haynes, N. Pernicone, J. D. F. Ramsay, K. S. W. Sing, and K. K. Unger, “Recommendations for the characterization of porous solids,” Pure Appl. Chem. 66, 1739–1758 (1994). [CrossRef]
  31. E. W. Washburn, “The dynamics of capillary flow,” Phys. Rev. 17, 273–283 (1921). [CrossRef]
  32. T. Svensson, E. Alerstam, D. Khoptyar, J. Johansson, S. Folestad, and S. Andersson-Engels, “Near infrared photon time-of-flight spectroscopy of turbid materials up to 1400 nm,” Rev. Sci. Instrum. 80, 063105 (2009). [CrossRef] [PubMed]
  33. D. Contini, F. Martelli, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation: I. Theory,” Appl. Opt. 36, 4587–4599 (1997). [CrossRef] [PubMed]
  34. D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997). [CrossRef]
  35. M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett. 96, 96 (2006).
  36. G. Banerjee, and K. Sengupta, “Pore size optimisation of humidity sensor - a probabilistic approach,” Sens. Actuators B Chem. 86, 34–41 (2002). [CrossRef]
  37. R. Dicke, “The effect of collisions upon the Doppler width of spectral lines,” Phys. Rev. 89, 472–473 (1953). [CrossRef]
  38. R. P. Frueholz, and J. C. Camparo, “Implications of the trapping-desorption and direct inelastic-scattering channels on Dicke-narrowed line-shapes,” Phys. Rev. A 35, 3768–3774 (1987). [CrossRef] [PubMed]
  39. V. Sandoghdar, C. I. Sukenik, E. A. Hinds, and S. Haroche, “Direct measurement of the van der Waals interaction between an atom and its images in a micron-sized cavity,” Phys. Rev. Lett. 68, 3432–3435 (1992). [CrossRef] [PubMed]
  40. M. Fichet, G. Dutier, A. Yarovitsky, P. Todorov, I. Hamdi, I. Maurin, S. Saltiel, D. Sarkisyan, M. P. Gorza, D. Bloch, and M. Ducloy, “Exploring the van der Waals atom-surface attraction in the nanometric range,” Europhys. Lett. 77, 54001 (2007). [CrossRef]

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