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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 33, Iss. 27 — Sep. 20, 1994
  • pp: 6294–6302

Theoretical description of frequency modulation and wavelength modulation spectroscopy

James M. Supplee, Edward A. Whittaker, and Wilfried Lenth  »View Author Affiliations


Applied Optics, Vol. 33, Issue 27, pp. 6294-6302 (1994)
http://dx.doi.org/10.1364/AO.33.006294


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Abstract

We present a comprehensive theory for heterodyne absorption spectroscopy with phase-modulated light. The general equations presented allow for an arbitrary modulation index and an arbitrary modulation frequency. We use this description for three purposes: First, we review the special cases of so-called frequency modulation and wavelength modulation spectroscopy. Second, we present the additional case of large-index, high-frequency modulation. Third, we present an overview of how the absorption signal depends on the experimental parameters of modulation frequency and modulation index. This overview may be helpful to experimentalists in choosing these parameters, for it provides a systematic understanding of how moving around in parameter space changes certain features of the signal, while leaving other features invariant.

© 1994 Optical Society of America

History
Original Manuscript: July 19, 1993
Revised Manuscript: February 23, 1994
Published: September 20, 1994

Citation
James M. Supplee, Edward A. Whittaker, and Wilfried Lenth, "Theoretical description of frequency modulation and wavelength modulation spectroscopy," Appl. Opt. 33, 6294-6302 (1994)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-33-27-6294


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References

  1. M. Cardona, Modulation Spectroscopy, Suppl. 11 of Solid State Physics, F. Seitz, D. Turnbull, H. Ehrenreich, eds. (Academic, New York, 1969), Chaps. 3–4, pp. 89–115.
  2. M. Gehrtz, G. C. Bjorklund, E. A. Whittaker, “Quantum-limited laser frequency-modulation spectroscopy,” J. Opt. Soc. Am. B 2, 1510–1526 (1985). [CrossRef]
  3. E. A. Whittaker, P. Pokrowsky, W. Zapka, K. Roche, G. C. Bjorklund, “Improved laser technique for high sensitivity atomic absorption spectroscopy in flames,” J. Quant. Spectrosc. Radiat. Transfer 30, 289–296 (1983). [CrossRef]
  4. P. Pokrowsky, W. Zapka, F. Chu, G. C. Bjorklund, “High frequency wavelength modulation spectroscopy with diode lasers,” Opt. Commun. 44, 175–179 (1983). [CrossRef]
  5. G. C. Bjorklund, M. D. Levenson, “Sub-Doppler frequency-modulation spectroscopy of I2,” Phys. Rev. A 24, 166–169 (1981). [CrossRef]
  6. 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]
  7. W. Lenth, C. Ortiz, G. C. Bjorklund, “Pulsed frequency-modulation spectroscopy as a means for fast absorption measurements,” Opt. Lett. 6, 351–353 (1981). [CrossRef] [PubMed]
  8. E. I. Moses, C. L. Tang, “High-sensitivity laser wavelength-modulation spectroscopy,” Opt. Lett. 1, 115–117 (1977). [CrossRef] [PubMed]
  9. P. Pokrowsky, W. Herrmann, “Sensitive detection of hydrogen chloride by derivative spectroscopy with a diode laser,” in Laser Spectroscopy for Sensitive Detection, J. A. Gelbwachs, ed., Proc. Soc. Photo-Opt. Intrum.286, 33–38 (1981).
  10. E. D. Hinkley, P. L. Kelley, “Detection of air pollutants with tunable diode lasers,” Science 171, 635–639 (1971). [CrossRef] [PubMed]
  11. G. C. Bjorklund, “Frequency-modulation spectroscopy: a new method for measuring weak absorptions and dispersions,” Opt. Lett. 5, 15–17 (1980); >G. C. Bjorklund,, “Method and device for detecting a specific spectral feature,” U.S. patent4,297,035 (27October1981). [CrossRef] [PubMed]
  12. J. L. Hall, L. Hollberg, T. Baer, H. G. Robinson, “Optical heterodyne saturation spectroscopy,” Appl. Phys. Lett. 39, 680–682 (1981). [CrossRef]
  13. W. Lenth, “High frequency heterodyne spectroscopy with current-modulated diode lasers,” IEEE J. Quantum Electron. QE-20, 1045–1050 (1984). [CrossRef]
  14. M. Gehrtz, W. Lenth, A. Y. Young, H. S. Johnston, “High-frequency-modulation spectroscopy with a lead–salt diode laser,” Opt. Lett. 11, 132–134 (1986). [CrossRef] [PubMed]
  15. A. Schenzle, R. G. DeVoe, R. G. Brewer, “Phase-modulation laser spectroscopy,” Phys. Rev. A 25, 2606–2621 (1982). [CrossRef]
  16. G. C. Bjorklund, M. D. Levenson, W. Length, C. Ortiz, “Frequency modulation (FM) spectroscopy–theory of line-shapes and signal-to-noise analysis,” Appl. Phys. B 32, 145–152 (1983). [CrossRef]
  17. W. Lenth, “Optical heterodyne spectroscopy with frequency and amplitide-modulation semiconductor lasers,” Opt. Lett. 8, 575–577(1983). [CrossRef] [PubMed]
  18. D. Hils, J. L. Hall, “Response of a Fabry–Perot cavity to phase modulated light,” Rev. Sci. Instrum. 58, 1406–1412 (1987). [CrossRef]
  19. J. A. Silver, “Frequency-modulation spectroscopy for trace species detection: theory and comparison among experimental techniques,” Appl. Opt. 6, 707–717 (1992). [CrossRef]
  20. This Fourier expansion is commonly used in modulation spectroscopy. For background material see, e.g., C. Louis Cuccia, Harmonics, Sidebands, and Transients in Communication Engineering (McGraw-Hill, New York, 1952), Chaps. 15 and 16, pp. 255–280.
  21. Lord Rayleigh, “On approximately simple waves,” Philos. Mag., 5th Ser. 50, 135–139 (1900). [CrossRef]
  22. D. E. Coooper, 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]
  23. Here we have used Jo2+2∑n=1∞Jn2=1.
  24. M. Ducloy, “Doppler-free two-photon heterodyne spectroscopy by single-beam frequency modulation,” Opt. Lett. 7, 432–433 (1982). [CrossRef] [PubMed]
  25. N. Nayak, G. S. Agarwal, “Absorption and fluorescence in frequency-modulated fields under conditions of strong modulation and saturation,” Phys. Rev. A 31, 3175–3182 (1985). [CrossRef] [PubMed]
  26. E. A. Whittaker, G. C. Bjorklund, “Developments in the theory of frequency modulation spectroscopy,” in Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1983), p. 232.
  27. D. E. Cooper, T. F. Gallagher, “Double frequency modulation spectroscopy: high modulation frequency with low-bandwidth detectors,” Appl. Opt. 24, 1327–1334 (1985). [CrossRef] [PubMed]
  28. T. F. Gallagher, R. Kachru, F. Gounand, G. C. Bjorklund, W. Lenth, “Frequency-modulation spectroscopy with a pulsed dye laser,” Opt. Lett. 7, 28–30 (1982). [CrossRef] [PubMed]
  29. H. Lotem, “Extension of the spectral coverage range of frequency modulation spectroscopy by double frequency modulation,” J. Appl. Phys. 54, 6033–6035 (1983). [CrossRef]
  30. L-G. Wang, H. Riris, C. B. Carlisle, T. F. Gallagher, “Comparison of approaches to modulation spectroscopy with GaAlAs semiconductor lasers: application to water vapor,” Appl. Opt. 27, 2071–2077 (1988). [CrossRef] [PubMed]
  31. P. Werle, F. Slemr, M. Gehrtz, C. Brauchle, “Quantum-limited FM-spectroscopy with a lead–salt diode laser,” Appl. Phys. B 49, 99–108 (1989). [CrossRef]
  32. 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]
  33. 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]
  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. G. V. H. Wilson, “Modulation broadening of NMR and ESR line shapes,” J. Appl. Phys. 34, 3276–3285 (1963). [CrossRef]
  36. R. N. Hager, R. C. Anderson, “Theory of the derivative spectrometer,” J. Opt. Soc. Am. 60, 1444–1449 (1970). [CrossRef]
  37. G. N. Watson, A Treatise of the Theory of Bessel Functions (Cambridge U. Press, Cambridge, 1966), p. 151.
  38. N. M. Blachman, G. A. McAlpine, “The spectrum of a high-index FM waveform: Woodward’s theorem revisited,” IEEE Trans. Commun. Technol. COM-17, 201–208 (1969). [CrossRef]
  39. R. Arndt, “Analytical line shapes for Lorentzian signals broadened by modulation,” J. Appl. Phys. 36, 2522–2524 (1965). [CrossRef]
  40. H. Wahlquist, “Modulation broadening of unsaturated Lorentzian lines,” J. Chem. Phys. 35, 1708–1710 (1961). [CrossRef]

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