Abstract

A new technique is presented for obtaining gas concentration by measuring the slope of the anomalous dispersion at a resonance. We describe the equations that govern this process using a Lorentz model and show that the slope of the anomalous dispersion is directly related to the absorption coefficient. The slope is obtained from an interferometric setup and a frequency modulation spectroscopy technique. Experimental data are presented that illustrate this technique for two different sample cells containing water vapor.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Reid, D. Labrie, “Second-harmonic detection with tunable diode lasers—comparison of experiment and theory,” Appl. Phys. B 26, 203–210 (1981).
    [CrossRef]
  2. C. Carlisle, D. Cooper, “Tunable-diode-laser frequency-modulation spectroscopy using balanced homodyne detection,” Opt. Lett. 14, 1306–1308 (1989).
    [CrossRef] [PubMed]
  3. N. Goldstein, S. Adler-Golden, “Long-atmospheric-path measurements of near-visible absorption lines of O2 isotopes and H2O with a prototype AlGaAs laser transceiver system,” Appl. Opt. 32, 5849–5855 (1993).
    [CrossRef] [PubMed]
  4. D. Hovde, C. Parsons, “Wavelength modulation detection of water vapor with a vertical cavity surface-emitting laser,” Appl. Opt. 36, 1135–1138 (1997).
    [CrossRef] [PubMed]
  5. D. Bomse, “Dual-modulation laser line-locking scheme,” Appl. Opt. 30, 2922–2925 (1991).
    [CrossRef] [PubMed]
  6. N. Goldstein, S. Adler-Golden, J. Lee, F. Bien, “Measurement of molecular concentrations and line parameters using line-locked second harmonic spectroscopy with an AlGaAs diode laser,” Appl. Opt. 31, 3409–3415 (1992).
    [CrossRef] [PubMed]
  7. J. Leonelli, ed., Conference Proceedings of Optical Sensing for Environmental and Process Monitoring (Air & Waste Management Association, Pittsburgh, Pa., 1996).
  8. A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).
  9. J. Stone, Radiation and Optics (McGraw-Hill, New York, 1963).
  10. Ontar Corporation, 9 Village Way, North Andover, Mass. 01845-2000.

1997 (1)

1993 (1)

1992 (1)

1991 (1)

1989 (1)

1981 (1)

J. Reid, D. Labrie, “Second-harmonic detection with tunable diode lasers—comparison of experiment and theory,” Appl. Phys. B 26, 203–210 (1981).
[CrossRef]

Adler-Golden, S.

Bien, F.

Bomse, D.

Carlisle, C.

Cooper, D.

Goldstein, N.

Hovde, D.

Labrie, D.

J. Reid, D. Labrie, “Second-harmonic detection with tunable diode lasers—comparison of experiment and theory,” Appl. Phys. B 26, 203–210 (1981).
[CrossRef]

Lee, J.

Parsons, C.

Reid, J.

J. Reid, D. Labrie, “Second-harmonic detection with tunable diode lasers—comparison of experiment and theory,” Appl. Phys. B 26, 203–210 (1981).
[CrossRef]

Stone, J.

J. Stone, Radiation and Optics (McGraw-Hill, New York, 1963).

Yariv, A.

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).

Appl. Opt. (4)

Appl. Phys. B (1)

J. Reid, D. Labrie, “Second-harmonic detection with tunable diode lasers—comparison of experiment and theory,” Appl. Phys. B 26, 203–210 (1981).
[CrossRef]

Opt. Lett. (1)

Other (4)

J. Leonelli, ed., Conference Proceedings of Optical Sensing for Environmental and Process Monitoring (Air & Waste Management Association, Pittsburgh, Pa., 1996).

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).

J. Stone, Radiation and Optics (McGraw-Hill, New York, 1963).

Ontar Corporation, 9 Village Way, North Andover, Mass. 01845-2000.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Pair of plots that show the relationship between absorption and anomalous dispersion for a spectral line with a Lorentzian profile. On the left-hand side the plots are for the extinction coefficient κ and the index (n - 1) by use of the variables of Eqs. (6) and (7). On the right-hand side the ordinates are the absorption coefficient α and a normalized anomalous dispersion 2π(n - 1)/λ0. This normalized dispersion is the differential interferometric phase incurred by transmission through a unit length of the absorbing medium and is analogous to α which is the attenuation incurred by transmission through the same distance.

Fig. 2
Fig. 2

Illustrations showing how an input optical frequency modulation with amplitude Δω is converted by absorption into an intensity modulation at the second harmonic of the modulation frequency (upper figure) and by anomalous dispersion into an interferometric phase modulation at the fundamental frequency (lower figure).

Fig. 3
Fig. 3

Schematic of the experimental setup for measuring the 1392.53-nm water-vapor line by use of a phase measurement technique. The laser diode wavelength is temperature tuned to within the transition, and a small sinusoidal current dither is applied to modulate the optical frequency to approximately FWHM of the transition. The light in the sample arm develops a phase shift with respect to light in the reference arm because of the anomalous dispersion of water vapor. The resulting intensity modulation at the fundamental frequency is detected by photodiodes and recovered with the lock-in amplifier. The optical elements used to initialize the system are not shown. BS, beam splitter.

Fig. 4
Fig. 4

Data collected for the high-concentration cell. The concentration used in the model was 2.6 × 1015.

Fig. 5
Fig. 5

Data collected for the low-concentration cell. The concentration used in the model was 5.5 × 1014.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

E r ,   t = E 0 exp i n c k 0 · r - ω t ,
E r ,   t = E 0 exp i nk 0 r - ω t exp - κ k 0 r ,
α ω = 4 π κ ω / λ 0 ,
n - 1 = - π Ne 2 ω - ω 0 / m ω 0 / ω - ω 0 2 + γ 2 ,
κ = π Ne 2 γ / m ω 0 / ω - ω 0 2 + γ 2 ,
n - 1 = - ax / x 2 + γ 2 ,
κ = a γ / x 2 + γ 2 .
κ max κ 0 = a / γ ;   FWHM   of   κ   versus   ω = 2 γ ;
n - 1 max / min = ± a / 2 γ ,   occurring   at   x = ω - ω 0 = ± γ .
α 0 = 4 π a / γ λ 0
n - 1 = - α 0 γ λ 0 x / 4 π / x 2 + γ 2 ; n - 1 max / min = α 0 λ 0 / 8 π .
s 0 = - α 0 λ 0 / 4 π γ .
Δ α α 0 Δ ω / γ 2 / 1 + Δ ω / γ 2 α 0 Δ ω / γ 2   for   γ     Δ ω ,
Δ 2 π n - 1 / λ 0 α 0 Δ ω / γ / 1 + Δ ω / γ 2 α 0 Δ ω / γ   for   γ     Δ ω .
I = I 0 + η I 1 cos ϕ ,
ϕ = 2 π / λ nL ,
Δ φ = 2 π / λ Δ n L + Δ L n ,
ρ = PA / RT ,

Metrics