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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 38, Iss. 27 — Sep. 20, 1999
  • pp: 5803–5815

Theoretical description based on Fourier analysis of wavelength-modulation spectrometry in terms of analytical and background signals

Pawel Kluczynski and Ove Axner  »View Author Affiliations


Applied Optics, Vol. 38, Issue 27, pp. 5803-5815 (1999)
http://dx.doi.org/10.1364/AO.38.005803


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Abstract

A theoretical description of the wavelength-modulation (WM) spectrometry technique is given. The formalism is based on Fourier analysis and can therefore correctly handle arbitrary large frequency-modulation amplitudes. It can also deal with associated intensity modulations as well as wavelength-dependent transmission effects. It elucidates clearly how various Fourier components of these entities combine with those of the line-shape function to yield separately the final analytical and background nf WM signals. Explicit expressions are given for the 2f and the 4f signals. It is shown, among other things, that the 4f technique in general gives rise to smaller background signals (and therefore larger signal-to-background ratios) than does the 2f technique when the background is dominated by etalon effects from short cavities and that a finite intensity modulation necessarily leads to an out-of-phase nf WM signal. The formalism is also able to elucidate clearly that a linear intensity modulation is not sufficient to cause any 2f background residual–amplitude–modulation signals (as was the general consensus until recently in the literature) but that 2f background signals instead can exist only in systems with either wavelength-dependent transmission or a laser with nonlinear intensity modulation.

© 1999 Optical Society of America

OCIS Codes
(020.3690) Atomic and molecular physics : Line shapes and shifts
(300.1030) Spectroscopy : Absorption
(300.6260) Spectroscopy : Spectroscopy, diode lasers

History
Original Manuscript: December 8, 1998
Revised Manuscript: May 21, 1999
Published: September 20, 1999

Citation
Pawel Kluczynski and Ove Axner, "Theoretical description based on Fourier analysis of wavelength-modulation spectrometry in terms of analytical and background signals," Appl. Opt. 38, 5803-5815 (1999)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-38-27-5803


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References

  1. J. C. Camparo, C. M. Klimack, “Laser spectroscopy on a ‘shoestring’,” Am. J. Phys. 51, 1077–1081 (1983). [CrossRef]
  2. J. C. Camparo, “The diode laser in atomic physics,” Contemp. Phys. 26, 443–477 (1985). [CrossRef]
  3. T. Imasaka, “Analytical molecular spectroscopy with diode lasers,” Spectrochim. Acta Rev. 15, 329–348 (1993).
  4. J. Franzke, A. Schnell, K. Niemax, “Spectroscopic properties of commercial laser diodes,” Spectrochim. Acta Rev. 15, 379–395 (1993).
  5. A. W. Mantz, “A review of the applicability of tunable diode-laser spectroscopy at high sensitivity,” Microchem. J. 50, 351–364 (1994). [CrossRef]
  6. P. C. D. Hobbs, “Ultrasensitive laser measurements without tears,” Appl. Opt. 36, 903–920 (1997). [CrossRef] [PubMed]
  7. D. S. Bomse, A. C. Stanton, J. A. Silver, “Frequency modulation and wavelength modulation spectroscopies: comparison of experimental methods using a lead-salt diode laser,” Appl. Opt. 31, 718–731 (1992). [CrossRef] [PubMed]
  8. K. Niemax, H. Groll, C. Schnürer-Patschan, “Element analysis by diode laser spectroscopy,” Spectrochim. Acta Rev. 15, 349–377 (1993).
  9. P. Werle, “Spectroscopic trace gas analysis using semiconductor diode lasers,” Spectrochim. Acta Part A 52, 805–822 (1996). [CrossRef]
  10. J. A. Silver, “Frequency-modulation spectroscopy for trace species detection: theory and comparison among experimental methods,” Appl. Opt. 31, 707–717 (1992). [CrossRef] [PubMed]
  11. D. T. Cassidy, J. Reid, “Atmospheric pressure monitoring of trace gases using tunable diode lasers,” Appl. Opt. 21, 1185–1190 (1982). [CrossRef] [PubMed]
  12. E. I. Moses, C. L. Tang, “High-sensitivity laser wavelength-modulation spectroscopy,” Opt. Lett. 1, 115–117 (1977). [CrossRef] [PubMed]
  13. F. Slemr, G. W. Harris, D. R. Hastie, G. I. Mackay, H. I. Schiff, “Measurement of gas phase hydrogen peroxide in air by tunable diode laser absorption spectrometry,” J. Geophys. Res. 91, 5371–5378 (1986). [CrossRef]
  14. D. M. Bruce, D. T. Cassidy, “Detection of oxygen using short external cavity GaAs semiconductor diode lasers,” Appl. Opt. 29, 1327–1332 (1990). [CrossRef] [PubMed]
  15. C. Schnürer-Patschan, A. Zybin, H. Groll, K. Niemax, “Improvement in detection limit in graphite furnace diode laser atomic absorption spectrometry by wavelength modulation technique,” J. Anal. At. Spectrom. 8, 1103–1107 (1993). [CrossRef]
  16. A. Zybin, C. Schnürer-Patschan, K. Niemax, “Wavelength modulation diode laser atomic spectrometry in modulated low-pressure helium plasmas for element-selective detection in gas chromatography,” J. Anal. At. Spectrom. 10, 563–567 (1995). [CrossRef]
  17. L.-G. Wang, D. A. Tate, H. Riris, T. F. Gallagher, “High-sensitivity frequency-modulation spectroscopy with a GaAlAs diode laser,” J. Opt. Soc. Am. B 6, 871–876 (1989). [CrossRef]
  18. J. A. Silver, A. C. Stanton, “Optical interference fringe reduction in laser absorption experiments,” Appl. Opt. 27, 1914–1916 (1988). [CrossRef] [PubMed]
  19. V. Liger, A. Zybin, Y. Kuritsyn, K. Niemax, “Diode-laser atomic-absorption spectrometry by the double-beam–double-modulation technique,” Spectrochim. Acta Part B 52, 1125–1138 (1997). [CrossRef]
  20. P. C. D. Hobbs, “Shot noise limited optical measurements at baseband with noisy lasers,” in Laser Noise, R. Roy, ed., Proc. SPIE1376, 216–221 (1990). [CrossRef]
  21. G. C. Bjorklund, “Frequency-modulation spectroscopy: a new method for measuring weak absorption and dispersion line shapes,” Opt. Lett. 5, 15–17 (1980). [CrossRef]
  22. J. L. Hall, L. Hollberg, T. Baer, H. G. Robinson, “Optical heterodyne saturation spectroscopy,” Appl. Phys. Lett. 39, 680–682 (1981). [CrossRef]
  23. W. Lenth, “High frequency heterodyne spectroscopy with current-modulated diode lasers,” IEEE J. Quantum Electron. QE-20, 1045–1050 (1984). [CrossRef]
  24. M. Gehrtz, W. Lenth, A. T. Young, H. S. Johnston, “High-frequency-modulation spectroscopy with a lead-salt diode laser,” Opt. Lett. 11, 132–134 (1986). [CrossRef] [PubMed]
  25. M. Gehrtz, G. C. Bjorklund, E. A. Whittaker, “Quantum-limited laser frequency-modulation spectroscopy,” J. Opt. Soc. Am. B 2, 1510–1526 (1985). [CrossRef]
  26. C. B. Carlisle, D. E. Cooper, H. Preier, “Quantum noise-limited FM spectroscopy with a lead-salt diode laser,” Appl. Opt. 28, 2567–2576 (1989). [CrossRef] [PubMed]
  27. P. Werle, F. Slemr, M. Gehrtz, C. Bräuchle, “Quantum-limited FM-spectroscopy with a lead-salt diode laser,” Appl. Phys. B 49, 99–108 (1989). [CrossRef]
  28. J. M. Supplee, E. A. Whittaker, W. Lenth, “Theoretical description of frequency-modulation and wavelength-modulation spectroscopy,” Appl. Opt. 33, 6294–6302 (1994). [CrossRef] [PubMed]
  29. G. R. Janik, C. B. Carlisle, T. F. Gallagher, “Two-tone frequency-modulation spectroscopy,” J. Opt. Soc. Am. B 3, 1070–1074 (1986). [CrossRef]
  30. O. E. Myers, E. J. Putzer, “Measurement broadening in magnetic resonance,” J. Appl. Phys. 30, 1987–1991 (1959). [CrossRef]
  31. A. M. Russel, D. A. Torchia, “Harmonic analysis in systems using phase sensitive detectors,” Rev. Sci. Instrum. 33, 442–444 (1962). [CrossRef]
  32. G. V. H. Wilson, “Modulation broadening of NMR and ESR line shapes,” J. Appl. Phys. 34, 3276–3285 (1963). [CrossRef]
  33. R. Arndt, “Analytical line shapes for Lorentzian signals broadened by modulation,” J. Appl. Phys. 36, 2522–2524 (1965). [CrossRef]
  34. J. Reid, D. Labrie, “Second-harmonic detection with tunable diode lasers—comparison of experiment and theory,” Appl. Phys. B 26, 203–210 (1981). [CrossRef]
  35. M. L. Olsen, D. L. Grieble, P. R. Griffiths, “Second derivative tunable diode laser spectrometry for line profile determination I. Theory,” Appl. Spectrosc. 34, 50–56 (1980). [CrossRef]
  36. D. Rojas, P. Ljung, O. Axner, “An investigation of the 2f-wavelength modulation technique for detection of atoms under optically thin as well as thick conditions,” Spectrochim. Acta Part B 52, 1663–1686 (1997). [CrossRef]
  37. J. Gustafsson, D. Rojas, O. Axner, “The influence of hyperfine structure and isotope shift on the detection of Rb atoms in atmospheric pressure atomizers by the 2f-wavelength modulation technique,” Spectrochim. Acta Part B 52, 1937–1953 (1997). [CrossRef]
  38. J. Gustafsson, O. Axner, “The influence of hyperfine structure and isotope shift on the detection of Rb by 2f-wavelength modulation diode laser absorption spectrometry—experimental verification of simulations,” Spectrochim. Acta Part B 53, 1895–1905 (1998). [CrossRef]
  39. J. Gustafsson, O. Axner, “Theoretical investigation of the temperature dependence of the 2f-wavelength modulated diode laser absorption signal,” Spectrochim. Acta Part B 53, 1827–1846 (1998). [CrossRef]
  40. J. Gustafsson, N. Chekalin, D. Rojas, O. Axner have submitted a paper to be called “Extension of the dynamic range of the 2f-wavelength modulated diode laser absorption spectrometry technique—detection of atoms under optically thick conditions” to Spectrochim. Acta Part B.
  41. L. C. Philippe, R. K. Hanson, “Laser diode wavelength-modulation spectroscopy for simultaneous measurement of temperature, pressure, and velocity in shock-heated oxygen flows,” Appl. Opt. 32, 6090–6103 (1993). [CrossRef] [PubMed]
  42. X. Zhu, D. T. Cassidy, “Modulation spectroscopy with a semiconductor diode laser by injection-current modulation,” J. Opt. Soc. Am. B 14, 1945–1950 (1997). [CrossRef]
  43. D. E. Cooper, R. E. Warren, “Frequency modulation spectroscopy with lead-salt diode lasers: a comparison of single-tone and two-tone techniques,” Appl. Opt. 26, 3726–3732 (1987). [CrossRef] [PubMed]
  44. D. E. Cooper, R. E. Warren, “Two-tone optical heterodyne spectroscopy with diode lasers: theory of line shapes and experimental results,” J. Opt. Soc. Am. B 4, 470–480 (1987). [CrossRef]
  45. N.-Y. Chou, G. W. Sachse, “Single-tone and two-tone AM–FM spectral calculations for tunable diode laser absorption spectroscopy,” Appl. Opt. 26, 3584–3587 (1987). [CrossRef] [PubMed]
  46. H. C. Sun, E. A. Whittaker, “Novel etalon fringe rejection technique for laser absorption spectroscopy,” Appl. Opt. 31, 4998–5002 (1992). [CrossRef] [PubMed]
  47. C. R. Webster, “Brewster-plate spoiler: a novel method for reducing the amplitude of interference fringes that limit tunable-laser absorption sensitivities,” J. Opt. Soc. Am. B 2, 1464–1470 (1985). [CrossRef]
  48. An alternative definition of the 2f and the 4f WM-signal fractions, which can be considered more convenient under some experimental conditions, is to relate the actually measured nth signal component to the zeroth signal component rather than to the unmodulated signal, as was done in Eqs. (18)–(21), i.e., as SAS,neven(ν̅d, ν̅a) = ΓAS,neven(ν̅d, ν̅a)SAS,0even(ν̅d, ν̅a). This will, however, give the same expression for the nf WM-signal fractions as do expressions (48) and (49) under the conditions considered [i.e., when T0e ≫ Tkk>0e and IL,0e > IL,1e ≫ IL,2e].
  49. Our choice of expression for the modulated laser intensity [Eq. (6)] however, suggests that the linear intensity modulation, given by IL,0(νc)κ1νa cos(ϕ1), should depend on the laser intensity at the center frequency. This is, however, not the case in reality but rather an artifact from our method of writing the intensity modulation. To correct for this artifact when calculating the nf WM spectra, we use the following expression for the wavelength dependence of the intensity-modulation coefficient: κ1(νd) = κ1(0)/[1 + κ1(0)νd].

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