Abstract

Frequency-modulation (FM) spectroscopy permits high-resolution, high-sensitivity, easily calibrated absorption measurements of atomic and molecular species and narrow spectral features in solids. This paper reviews some important developments in laser FM spectroscopy, from its inception as a spectroscopic tool to the demonstration of quantum-limited absorption measurements, emphasizing the sensitivity limitations caused by residual amplitude modulation (RAM). Moreover, a detailed account is presented of a new double-beam, single-detector technique that efficiently suppresses the RAM and permits quantum-limited performance to be achieved in laser FM spectroscopy. We also include some recent results of the first reported FM spectroscopic investigations of the NO2 molecule.

© 1985 Optical Society of America

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  1. G. C. Bjorklund, IBM Invention Disclosure SA 8790135 (March1979); “Frequency-modulation spectroscopy: a new method for measuring weak absorptions and dispersions,” Opt. Lett. 5, 15 (1980); U.S. Patent4,297,035 (November1981).
    [PubMed]
  2. The FM technique was independently suggested by R. W. P. Drever as a means for servolocking a tunable laser to a high-finesse optical cavity. It was first experimentally implemented for this purpose by R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, Joint Institute for Laboratory Astrophysics, Boulder, Colo. 80303 (personal communication, September1979) and then by M. Prentiss, B. Peuse, G. Sanders, S. Ezekiel, Research Laboratory of Electronics, Progress Rep. No. 123 (Massachusetts Institute of Technology, Cambridge, Mass., January1981).
  3. The most recent applications of FM spectroscopy are described in Refs. 35, 37, and 40. For a review of the use of FM techniques covering the literature up to 1983, cf. Ref. 28 and references therein.
  4. N. Nayak, G. S. Agarwal, “Absorption and fluorescence in frequency-modulated fields under conditions of strong modulation and absorption,” Phys. Rev. A (to be published).
  5. N. H. Tran, R. Kachru, P. Pillet, H. B. van Lindenvan den Heuvell, T. F. Gallagher, J. P. Watjen, “Frequency-modulation spectroscopy with a pulsed dye laser: experimental investigations of sensitivity and useful features,” Appl. Opt. 23, 1353 (1984).
    [Crossref]
  6. D. E. Cooper, T. F. Gallagher, “Frequency-modulation spectroscopy with a multimode laser,” Opt. Lett. 9, 451 (1984).
    [Crossref] [PubMed]
  7. H. E. Hunziker, “A new technique for gas-phase kinetic spectroscopy of molecules in the triplet state,” IBM J. Res. Develop. 15, 10 (1971).
    [Crossref]
  8. M. Cardona, Modulation Spectroscopy, Supplement II of Solid State Physics, F. Seitz, D. Turnbull, eds. (Academic, New York, 1969).
  9. C. S. Gudemann, C. C. Marner, M. H. Begemann, E. Schafer, J. Pfaff, R. J. Saykally, “Velocity modulation laser absorption spectroscopy of molecular ions,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 106 (1983).
  10. J. L. Hall, T. Baer, L. Hollberg, H. G. Robinson, “Precision spectroscopy and laser frequency control using FM sideband optical heterodyne techniques,” in Laser Spectroscopy V, A. R. W. McKellar, T. Oka, B. P. Stoicheff, eds. (Springer-Verlag, Berlin, 1981), p. 16.
  11. M. Ducloy, J. J. Snyder, “High frequency optical heterodyne spectroscopy,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 87 (1983).
  12. A. L. Huston, W. E. Moerner, “Detection of persistent spectral holes using ultrasonic modulation,” J. Opt. Soc. Am. B 1, 349 (1984).
    [Crossref]
  13. A. L. Huston, W. E. Moerner, IBM Research Laboratories, San José, Calif. 95193 (personal communication).
  14. E. I. Moses, C. L. Tang, High-sensitivity laser wavelength-modulation spectroscopy, Opt. Lett. 1, 115 (1977).
    [Crossref] [PubMed]
  15. P. Pokrowsky, W. Zapka, F. Chu, G. C. Bjorklund, “High frequency wavelength modulation spectroscopy with diode lasers,” Opt. Commun. 44, 175 (1983).
    [Crossref]
  16. D. S. Kliger, ed., Ultrasensitive Laser Spectroscopy (Academic, New York, 1983).
  17. J. A. Gelbwachs, C. F. Klein, J. E. Wessel, “Saturated optical nonresonant emission spectroscopy (SONRES) for atomic detection,” Appl. Phys. Lett. 30, 489 (1977).
    [Crossref]
  18. J. Allen, W. R. Anderson, D. Crosley, “Optoacoustic pulses in a flame,” Opt. Lett. 1, 118 (1977).
    [Crossref] [PubMed]
  19. P. K. Schenk, J. W. Hastie, “Optogalvanic spectroscopy—application for combustion systems,” Opt. Eng. 20, 522 (1981).
  20. T. D. Harris, A. M. Williams, “Low absorbance measurements,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 110 (1983).
  21. T. Hirschfelder, “The choice between absorption and fluorescent techniques,” Appl. Spectrosc. 31, 245 (1977).
    [Crossref]
  22. J. D. Ingle, “Additional comments relating to the choice between absorption and fluorescent techniques,” Appl. Spectrosc. 36, 588 (1982).
    [Crossref]
  23. G. C. Bjorklund, W. Lenth, C. Ortiz, “Cryogenic frequency domain optical mass memory,” Proc. Soc. Photo-Opt. Instrum. Eng. 298, 107 (1982).
  24. W. Lenth, “Optical heterodyne spectroscopy with frequency- and amplitude-modulated semiconductor lasers,” Opt. Lett. 8, 575 (1983).
    [Crossref] [PubMed]
  25. W. Lenth, “High frequency heterodyne spectroscopy with current-modulated diode lasers,” IEEE J. Quantum Electron. QE-20, 1045 (1984).
    [Crossref]
  26. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), pp. 341–343.
  27. J. L. Hall, H. G. Robinson, T. Baer, L. Hollberg, “The line-shapes of subdoppler resonances observable with FM side-band (optical heterodyne) laser techniques,” in Advances in Laser Spectroscopy, F. T. Arecchi, F. Strumia, H. Walther, eds. (Plenum, New York, 1983), p. 99.
    [Crossref]
  28. G. C. Bjorklund, M. D. Levenson, W. Lenth, C. Ortiz, “Frequency modulation (FM) spectroscopy—theory of lineshapes and signal-to-noise analysis,” Appl. Phys. B 32, 145 (1983).
    [Crossref]
  29. E. A. Whittaker, P. Pokrowsky, W. Zapka, K. Roche, G. C. Bjorklund, “Improved laser technique for high sensitivity atomic absorption spectroscopy in flames,” J. Quantum. Spectrosc. Radiat. Transfer 30, 289 (1983).
    [Crossref]
  30. L. Hollberg, Ma Long-sheng, M. Hohenstatt, J. L. Hall, “Precision measurements by optical heterodyne techniques,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 91 (1983).
  31. When current modulated diode lasers are used for FM spectroscopy,24,25 one generally has to deal with a fairly strong RAM (R/M~ 0.1). It was recognized in Refs. 24 and 25, however, that the RAM phase difference ψ depends critically on the diode-laser operating conditions. It should thus be possible to set ψ such that the distortive term becomes small compared with the pure-FM term—at least for the Fourier component being studied (in phase or quadrature).
  32. E. A. Whittaker, M. Gehrtz, G. C. Bjorklund, “Residual amplitude modulation in laser electro-optic phase modulation,” J. Opt. Soc. Am. B 2, 1320–1326 (1985).
    [Crossref]
  33. A possible improvement on this situation has been reported by B. A. Woody, L. Lyndz (Appl. Opt., to be published) who report a sensitivity limit of ~10−6. We thank the authors for a personal communication of their preliminary results.
  34. M. D. Levenson, W. E. Moerner, D. E. Horne, “FM spectroscopy detection of stimulated Raman gain,” Opt. Lett. 8, 108 (1983).
    [Crossref] [PubMed]
  35. E. A. Whittaker, H. R. Wendt, H. E. Hunziker, G. C. Bjorklund, “Laser FM spectroscopy with photochemical modulation: a sensitive, high resolution technique for chemical intermediates,” Appl. Phys. B 35, 105 (1984).
    [Crossref]
  36. R. Vasudev, R. N. Zare, “Laser optogalvanic study of HCO A state predissociation,” J. Chem. Phys. 76, 5267 (1982).
    [Crossref]
  37. E. A. Whittaker, B. J. Sullivan, G. C. Bjorklund, H. R. Wendt, H. E. Hunziker, “ND4Schüler band absorption observed by laser FM spectroscopy in a photochemical reaction,” J. Chem. Phys. 80, 961 (1984).
    [Crossref]
  38. G. Herzberg, “Rydberg spectra of triatomic hydrogen and of the ammonium radical,” Faraday Disc. Chem. Soc. 71, 165 (1981).
    [Crossref]
  39. F. Alberti, K. P. Huber, J. K. G. Watson, “Absorption spectrum and analysis of the ND4Schüler band,” J. Mol. Spectrosc. 107, 133 (1984).
    [Crossref]
  40. J. M. Jasinski, E. A. Whittaker, G. C. Bjorklund, R. W. Dreyfus, R. D. Estes, R. E. Walkup, “Detection of SiH2in silane and disilane glow discharges by frequency modulation absorption spectroscopy,” Appl. Phys. Lett. 44, 1155 (1984).
    [Crossref]
  41. M. Romagnoli, M. D. Levenson, G. C. Bjorklund, “Frequency-modulation-polarization spectroscopy,” Opt. Lett. 8, 635 (1983).
    [Crossref] [PubMed]
  42. M. Romagnoli, M. D. Levenson, G. C. Bjorklund, “Frequency-modulation-polarization-spectroscopy detection of persistent spectral holes,” J. Opt. Soc. Am. B 1, 571 (1984).
    [Crossref]
  43. M. Gehrtz, W. E. Moerner, G. C. Bjorklund, “Shot-noise limited detection of very weak absorptions with laser FM spectroscopy,” Opt. Lett. (to be published).
  44. This is the most important difference between this method and the double-beam WMS scheme proposed in Ref. 14, where the corresponding phase shift is 90°.
  45. Cf. the much more complicated demodulation scheme used in the double-beam, one-detector WMS method proposed by M. Welkowsky, R. Braunstein, “A double-beam, single-detector wavelength modulation spectrometer,” Rev. Sci. Instrum. 43, 399 (1972).
    [Crossref]
  46. K.-H. Hellwege, ed., Landolt-Börnstein Zahlenwerte und Funktionen (Springer-Verlag, Berlin, 1960), Vol. II-2a, p. 10.
  47. As the width of the absorption line depicted in Fig. 12 is somewhat larger than the FM sideband spacing, the maximum differential absorption experienced by the sidebands is slightly smaller than the peak absorptivity of the line. Although the corresponding reduction factor could be calculated explicitly from the FM line-shape theory,28 we chose a calibration procedure29,35 that for a given linewidth relates the FM-signal voltage directly to the peak absorptivity. The values that we quote here and in Fig. 12 thus correspond to absorptivity differences taken at the absorption line peak and at a position off the absorption line.
  48. The widths of the absorption lines shown in Fig. 13 are slightly smaller than the FM sideband spacing. Thus in this case the maximum differential absorptivity experienced by the sidebands is directly given by the peak absorptivities of the iodine absorption lines, and the Δδ values that we quote here and in Fig. 13 are exactly equal to the differential absorptivities seen by the sidebands.
  49. The RAM-induced noise spectrum observed previously35(Fig. 5) shows much stronger low-frequency components, probably for two reasons: (1) A different EOM was used that caused much stronger RAM and (2) a relatively high FM index (M~ 1) was employed that also increased the RAM.
  50. J. F. Ward, C. C. Wang, C. E. Wieman, “A proposal for improved OH detection using frequency modulation sepctroscopy,” presented at the March 1985meeting of the American Physical Society, Baltimore, Maryland.
  51. L. T. Molinari, W. B. Grant, “FTIR-spectrometer-determined absorption coefficients of seven hydrazine fuel gases: implications for laser remote sensing,” Appl. Opt. 23, 3893 (1984).
    [Crossref]
  52. D. E. Cooper, T. F. Gallagher, “Frequency modulation spectroscopy with a CO2laser: results and implications for ultrasensitive point monitoring of the atmosphere,” Appl. Opt. 24, 710 (1985).
    [Crossref]
  53. P. A. Leighton, Photochemistry of Air Pollution (Academic, New York, 1961).
  54. K. A. Frederiksson, H. M. Hertz, “Evaluation of the DIAL technique for studies on NO2using a mobile lidar system,” Appl. Opt. 23, 1403 (1984).
    [Crossref]
  55. H. Levy, “Photochemistry of the troposphere,” Adv. Photochem. 9, 369 (1974).
    [Crossref]
  56. D. K. Hsu, D. L. Monts, R. N. Zare, Spectral Atlas of Nitrogen Dioxide 5530 Å to 6480 Å (Academic, New York, 1978).
  57. J. C. D. Brand, W. H. Chan, J. L. Hardwick, “Rotational analysis of the 8000–9000 Å bands of nitrogen dioxide,” J. Mol. Spectrosc. 56, 309 (1975).
    [Crossref]

1985 (2)

1984 (11)

K. A. Frederiksson, H. M. Hertz, “Evaluation of the DIAL technique for studies on NO2using a mobile lidar system,” Appl. Opt. 23, 1403 (1984).
[Crossref]

L. T. Molinari, W. B. Grant, “FTIR-spectrometer-determined absorption coefficients of seven hydrazine fuel gases: implications for laser remote sensing,” Appl. Opt. 23, 3893 (1984).
[Crossref]

F. Alberti, K. P. Huber, J. K. G. Watson, “Absorption spectrum and analysis of the ND4Schüler band,” J. Mol. Spectrosc. 107, 133 (1984).
[Crossref]

J. M. Jasinski, E. A. Whittaker, G. C. Bjorklund, R. W. Dreyfus, R. D. Estes, R. E. Walkup, “Detection of SiH2in silane and disilane glow discharges by frequency modulation absorption spectroscopy,” Appl. Phys. Lett. 44, 1155 (1984).
[Crossref]

M. Romagnoli, M. D. Levenson, G. C. Bjorklund, “Frequency-modulation-polarization-spectroscopy detection of persistent spectral holes,” J. Opt. Soc. Am. B 1, 571 (1984).
[Crossref]

E. A. Whittaker, H. R. Wendt, H. E. Hunziker, G. C. Bjorklund, “Laser FM spectroscopy with photochemical modulation: a sensitive, high resolution technique for chemical intermediates,” Appl. Phys. B 35, 105 (1984).
[Crossref]

E. A. Whittaker, B. J. Sullivan, G. C. Bjorklund, H. R. Wendt, H. E. Hunziker, “ND4Schüler band absorption observed by laser FM spectroscopy in a photochemical reaction,” J. Chem. Phys. 80, 961 (1984).
[Crossref]

N. H. Tran, R. Kachru, P. Pillet, H. B. van Lindenvan den Heuvell, T. F. Gallagher, J. P. Watjen, “Frequency-modulation spectroscopy with a pulsed dye laser: experimental investigations of sensitivity and useful features,” Appl. Opt. 23, 1353 (1984).
[Crossref]

D. E. Cooper, T. F. Gallagher, “Frequency-modulation spectroscopy with a multimode laser,” Opt. Lett. 9, 451 (1984).
[Crossref] [PubMed]

A. L. Huston, W. E. Moerner, “Detection of persistent spectral holes using ultrasonic modulation,” J. Opt. Soc. Am. B 1, 349 (1984).
[Crossref]

W. Lenth, “High frequency heterodyne spectroscopy with current-modulated diode lasers,” IEEE J. Quantum Electron. QE-20, 1045 (1984).
[Crossref]

1983 (10)

G. C. Bjorklund, M. D. Levenson, W. Lenth, C. Ortiz, “Frequency modulation (FM) spectroscopy—theory of lineshapes and signal-to-noise analysis,” Appl. Phys. B 32, 145 (1983).
[Crossref]

E. A. Whittaker, P. Pokrowsky, W. Zapka, K. Roche, G. C. Bjorklund, “Improved laser technique for high sensitivity atomic absorption spectroscopy in flames,” J. Quantum. Spectrosc. Radiat. Transfer 30, 289 (1983).
[Crossref]

L. Hollberg, Ma Long-sheng, M. Hohenstatt, J. L. Hall, “Precision measurements by optical heterodyne techniques,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 91 (1983).

T. D. Harris, A. M. Williams, “Low absorbance measurements,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 110 (1983).

P. Pokrowsky, W. Zapka, F. Chu, G. C. Bjorklund, “High frequency wavelength modulation spectroscopy with diode lasers,” Opt. Commun. 44, 175 (1983).
[Crossref]

C. S. Gudemann, C. C. Marner, M. H. Begemann, E. Schafer, J. Pfaff, R. J. Saykally, “Velocity modulation laser absorption spectroscopy of molecular ions,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 106 (1983).

M. Ducloy, J. J. Snyder, “High frequency optical heterodyne spectroscopy,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 87 (1983).

M. D. Levenson, W. E. Moerner, D. E. Horne, “FM spectroscopy detection of stimulated Raman gain,” Opt. Lett. 8, 108 (1983).
[Crossref] [PubMed]

W. Lenth, “Optical heterodyne spectroscopy with frequency- and amplitude-modulated semiconductor lasers,” Opt. Lett. 8, 575 (1983).
[Crossref] [PubMed]

M. Romagnoli, M. D. Levenson, G. C. Bjorklund, “Frequency-modulation-polarization spectroscopy,” Opt. Lett. 8, 635 (1983).
[Crossref] [PubMed]

1982 (3)

R. Vasudev, R. N. Zare, “Laser optogalvanic study of HCO A state predissociation,” J. Chem. Phys. 76, 5267 (1982).
[Crossref]

J. D. Ingle, “Additional comments relating to the choice between absorption and fluorescent techniques,” Appl. Spectrosc. 36, 588 (1982).
[Crossref]

G. C. Bjorklund, W. Lenth, C. Ortiz, “Cryogenic frequency domain optical mass memory,” Proc. Soc. Photo-Opt. Instrum. Eng. 298, 107 (1982).

1981 (2)

G. Herzberg, “Rydberg spectra of triatomic hydrogen and of the ammonium radical,” Faraday Disc. Chem. Soc. 71, 165 (1981).
[Crossref]

P. K. Schenk, J. W. Hastie, “Optogalvanic spectroscopy—application for combustion systems,” Opt. Eng. 20, 522 (1981).

1977 (4)

1975 (1)

J. C. D. Brand, W. H. Chan, J. L. Hardwick, “Rotational analysis of the 8000–9000 Å bands of nitrogen dioxide,” J. Mol. Spectrosc. 56, 309 (1975).
[Crossref]

1974 (1)

H. Levy, “Photochemistry of the troposphere,” Adv. Photochem. 9, 369 (1974).
[Crossref]

1972 (1)

Cf. the much more complicated demodulation scheme used in the double-beam, one-detector WMS method proposed by M. Welkowsky, R. Braunstein, “A double-beam, single-detector wavelength modulation spectrometer,” Rev. Sci. Instrum. 43, 399 (1972).
[Crossref]

1971 (1)

H. E. Hunziker, “A new technique for gas-phase kinetic spectroscopy of molecules in the triplet state,” IBM J. Res. Develop. 15, 10 (1971).
[Crossref]

Agarwal, G. S.

N. Nayak, G. S. Agarwal, “Absorption and fluorescence in frequency-modulated fields under conditions of strong modulation and absorption,” Phys. Rev. A (to be published).

Alberti, F.

F. Alberti, K. P. Huber, J. K. G. Watson, “Absorption spectrum and analysis of the ND4Schüler band,” J. Mol. Spectrosc. 107, 133 (1984).
[Crossref]

Allen, J.

Anderson, W. R.

Baer, T.

J. L. Hall, H. G. Robinson, T. Baer, L. Hollberg, “The line-shapes of subdoppler resonances observable with FM side-band (optical heterodyne) laser techniques,” in Advances in Laser Spectroscopy, F. T. Arecchi, F. Strumia, H. Walther, eds. (Plenum, New York, 1983), p. 99.
[Crossref]

J. L. Hall, T. Baer, L. Hollberg, H. G. Robinson, “Precision spectroscopy and laser frequency control using FM sideband optical heterodyne techniques,” in Laser Spectroscopy V, A. R. W. McKellar, T. Oka, B. P. Stoicheff, eds. (Springer-Verlag, Berlin, 1981), p. 16.

Begemann, M. H.

C. S. Gudemann, C. C. Marner, M. H. Begemann, E. Schafer, J. Pfaff, R. J. Saykally, “Velocity modulation laser absorption spectroscopy of molecular ions,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 106 (1983).

Bjorklund, G. C.

E. A. Whittaker, M. Gehrtz, G. C. Bjorklund, “Residual amplitude modulation in laser electro-optic phase modulation,” J. Opt. Soc. Am. B 2, 1320–1326 (1985).
[Crossref]

M. Romagnoli, M. D. Levenson, G. C. Bjorklund, “Frequency-modulation-polarization-spectroscopy detection of persistent spectral holes,” J. Opt. Soc. Am. B 1, 571 (1984).
[Crossref]

J. M. Jasinski, E. A. Whittaker, G. C. Bjorklund, R. W. Dreyfus, R. D. Estes, R. E. Walkup, “Detection of SiH2in silane and disilane glow discharges by frequency modulation absorption spectroscopy,” Appl. Phys. Lett. 44, 1155 (1984).
[Crossref]

E. A. Whittaker, H. R. Wendt, H. E. Hunziker, G. C. Bjorklund, “Laser FM spectroscopy with photochemical modulation: a sensitive, high resolution technique for chemical intermediates,” Appl. Phys. B 35, 105 (1984).
[Crossref]

E. A. Whittaker, B. J. Sullivan, G. C. Bjorklund, H. R. Wendt, H. E. Hunziker, “ND4Schüler band absorption observed by laser FM spectroscopy in a photochemical reaction,” J. Chem. Phys. 80, 961 (1984).
[Crossref]

G. C. Bjorklund, M. D. Levenson, W. Lenth, C. Ortiz, “Frequency modulation (FM) spectroscopy—theory of lineshapes and signal-to-noise analysis,” Appl. Phys. B 32, 145 (1983).
[Crossref]

E. A. Whittaker, P. Pokrowsky, W. Zapka, K. Roche, G. C. Bjorklund, “Improved laser technique for high sensitivity atomic absorption spectroscopy in flames,” J. Quantum. Spectrosc. Radiat. Transfer 30, 289 (1983).
[Crossref]

P. Pokrowsky, W. Zapka, F. Chu, G. C. Bjorklund, “High frequency wavelength modulation spectroscopy with diode lasers,” Opt. Commun. 44, 175 (1983).
[Crossref]

M. Romagnoli, M. D. Levenson, G. C. Bjorklund, “Frequency-modulation-polarization spectroscopy,” Opt. Lett. 8, 635 (1983).
[Crossref] [PubMed]

G. C. Bjorklund, W. Lenth, C. Ortiz, “Cryogenic frequency domain optical mass memory,” Proc. Soc. Photo-Opt. Instrum. Eng. 298, 107 (1982).

G. C. Bjorklund, IBM Invention Disclosure SA 8790135 (March1979); “Frequency-modulation spectroscopy: a new method for measuring weak absorptions and dispersions,” Opt. Lett. 5, 15 (1980); U.S. Patent4,297,035 (November1981).
[PubMed]

M. Gehrtz, W. E. Moerner, G. C. Bjorklund, “Shot-noise limited detection of very weak absorptions with laser FM spectroscopy,” Opt. Lett. (to be published).

Brand, J. C. D.

J. C. D. Brand, W. H. Chan, J. L. Hardwick, “Rotational analysis of the 8000–9000 Å bands of nitrogen dioxide,” J. Mol. Spectrosc. 56, 309 (1975).
[Crossref]

Braunstein, R.

Cf. the much more complicated demodulation scheme used in the double-beam, one-detector WMS method proposed by M. Welkowsky, R. Braunstein, “A double-beam, single-detector wavelength modulation spectrometer,” Rev. Sci. Instrum. 43, 399 (1972).
[Crossref]

Cardona, M.

M. Cardona, Modulation Spectroscopy, Supplement II of Solid State Physics, F. Seitz, D. Turnbull, eds. (Academic, New York, 1969).

Chan, W. H.

J. C. D. Brand, W. H. Chan, J. L. Hardwick, “Rotational analysis of the 8000–9000 Å bands of nitrogen dioxide,” J. Mol. Spectrosc. 56, 309 (1975).
[Crossref]

Chu, F.

P. Pokrowsky, W. Zapka, F. Chu, G. C. Bjorklund, “High frequency wavelength modulation spectroscopy with diode lasers,” Opt. Commun. 44, 175 (1983).
[Crossref]

Cooper, D. E.

Crosley, D.

Drever, R. W. P.

The FM technique was independently suggested by R. W. P. Drever as a means for servolocking a tunable laser to a high-finesse optical cavity. It was first experimentally implemented for this purpose by R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, Joint Institute for Laboratory Astrophysics, Boulder, Colo. 80303 (personal communication, September1979) and then by M. Prentiss, B. Peuse, G. Sanders, S. Ezekiel, Research Laboratory of Electronics, Progress Rep. No. 123 (Massachusetts Institute of Technology, Cambridge, Mass., January1981).

Dreyfus, R. W.

J. M. Jasinski, E. A. Whittaker, G. C. Bjorklund, R. W. Dreyfus, R. D. Estes, R. E. Walkup, “Detection of SiH2in silane and disilane glow discharges by frequency modulation absorption spectroscopy,” Appl. Phys. Lett. 44, 1155 (1984).
[Crossref]

Ducloy, M.

M. Ducloy, J. J. Snyder, “High frequency optical heterodyne spectroscopy,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 87 (1983).

Estes, R. D.

J. M. Jasinski, E. A. Whittaker, G. C. Bjorklund, R. W. Dreyfus, R. D. Estes, R. E. Walkup, “Detection of SiH2in silane and disilane glow discharges by frequency modulation absorption spectroscopy,” Appl. Phys. Lett. 44, 1155 (1984).
[Crossref]

Ford, G. M.

The FM technique was independently suggested by R. W. P. Drever as a means for servolocking a tunable laser to a high-finesse optical cavity. It was first experimentally implemented for this purpose by R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, Joint Institute for Laboratory Astrophysics, Boulder, Colo. 80303 (personal communication, September1979) and then by M. Prentiss, B. Peuse, G. Sanders, S. Ezekiel, Research Laboratory of Electronics, Progress Rep. No. 123 (Massachusetts Institute of Technology, Cambridge, Mass., January1981).

Frederiksson, K. A.

Gallagher, T. F.

Gehrtz, M.

E. A. Whittaker, M. Gehrtz, G. C. Bjorklund, “Residual amplitude modulation in laser electro-optic phase modulation,” J. Opt. Soc. Am. B 2, 1320–1326 (1985).
[Crossref]

M. Gehrtz, W. E. Moerner, G. C. Bjorklund, “Shot-noise limited detection of very weak absorptions with laser FM spectroscopy,” Opt. Lett. (to be published).

Gelbwachs, J. A.

J. A. Gelbwachs, C. F. Klein, J. E. Wessel, “Saturated optical nonresonant emission spectroscopy (SONRES) for atomic detection,” Appl. Phys. Lett. 30, 489 (1977).
[Crossref]

Grant, W. B.

Gudemann, C. S.

C. S. Gudemann, C. C. Marner, M. H. Begemann, E. Schafer, J. Pfaff, R. J. Saykally, “Velocity modulation laser absorption spectroscopy of molecular ions,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 106 (1983).

Hall, J. L.

L. Hollberg, Ma Long-sheng, M. Hohenstatt, J. L. Hall, “Precision measurements by optical heterodyne techniques,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 91 (1983).

J. L. Hall, T. Baer, L. Hollberg, H. G. Robinson, “Precision spectroscopy and laser frequency control using FM sideband optical heterodyne techniques,” in Laser Spectroscopy V, A. R. W. McKellar, T. Oka, B. P. Stoicheff, eds. (Springer-Verlag, Berlin, 1981), p. 16.

The FM technique was independently suggested by R. W. P. Drever as a means for servolocking a tunable laser to a high-finesse optical cavity. It was first experimentally implemented for this purpose by R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, Joint Institute for Laboratory Astrophysics, Boulder, Colo. 80303 (personal communication, September1979) and then by M. Prentiss, B. Peuse, G. Sanders, S. Ezekiel, Research Laboratory of Electronics, Progress Rep. No. 123 (Massachusetts Institute of Technology, Cambridge, Mass., January1981).

J. L. Hall, H. G. Robinson, T. Baer, L. Hollberg, “The line-shapes of subdoppler resonances observable with FM side-band (optical heterodyne) laser techniques,” in Advances in Laser Spectroscopy, F. T. Arecchi, F. Strumia, H. Walther, eds. (Plenum, New York, 1983), p. 99.
[Crossref]

Hardwick, J. L.

J. C. D. Brand, W. H. Chan, J. L. Hardwick, “Rotational analysis of the 8000–9000 Å bands of nitrogen dioxide,” J. Mol. Spectrosc. 56, 309 (1975).
[Crossref]

Harris, T. D.

T. D. Harris, A. M. Williams, “Low absorbance measurements,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 110 (1983).

Hastie, J. W.

P. K. Schenk, J. W. Hastie, “Optogalvanic spectroscopy—application for combustion systems,” Opt. Eng. 20, 522 (1981).

Hertz, H. M.

Herzberg, G.

G. Herzberg, “Rydberg spectra of triatomic hydrogen and of the ammonium radical,” Faraday Disc. Chem. Soc. 71, 165 (1981).
[Crossref]

Hirschfelder, T.

Hohenstatt, M.

L. Hollberg, Ma Long-sheng, M. Hohenstatt, J. L. Hall, “Precision measurements by optical heterodyne techniques,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 91 (1983).

Hollberg, L.

L. Hollberg, Ma Long-sheng, M. Hohenstatt, J. L. Hall, “Precision measurements by optical heterodyne techniques,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 91 (1983).

J. L. Hall, H. G. Robinson, T. Baer, L. Hollberg, “The line-shapes of subdoppler resonances observable with FM side-band (optical heterodyne) laser techniques,” in Advances in Laser Spectroscopy, F. T. Arecchi, F. Strumia, H. Walther, eds. (Plenum, New York, 1983), p. 99.
[Crossref]

J. L. Hall, T. Baer, L. Hollberg, H. G. Robinson, “Precision spectroscopy and laser frequency control using FM sideband optical heterodyne techniques,” in Laser Spectroscopy V, A. R. W. McKellar, T. Oka, B. P. Stoicheff, eds. (Springer-Verlag, Berlin, 1981), p. 16.

Horne, D. E.

Hough, J.

The FM technique was independently suggested by R. W. P. Drever as a means for servolocking a tunable laser to a high-finesse optical cavity. It was first experimentally implemented for this purpose by R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, Joint Institute for Laboratory Astrophysics, Boulder, Colo. 80303 (personal communication, September1979) and then by M. Prentiss, B. Peuse, G. Sanders, S. Ezekiel, Research Laboratory of Electronics, Progress Rep. No. 123 (Massachusetts Institute of Technology, Cambridge, Mass., January1981).

Hsu, D. K.

D. K. Hsu, D. L. Monts, R. N. Zare, Spectral Atlas of Nitrogen Dioxide 5530 Å to 6480 Å (Academic, New York, 1978).

Huber, K. P.

F. Alberti, K. P. Huber, J. K. G. Watson, “Absorption spectrum and analysis of the ND4Schüler band,” J. Mol. Spectrosc. 107, 133 (1984).
[Crossref]

Hunziker, H. E.

E. A. Whittaker, B. J. Sullivan, G. C. Bjorklund, H. R. Wendt, H. E. Hunziker, “ND4Schüler band absorption observed by laser FM spectroscopy in a photochemical reaction,” J. Chem. Phys. 80, 961 (1984).
[Crossref]

E. A. Whittaker, H. R. Wendt, H. E. Hunziker, G. C. Bjorklund, “Laser FM spectroscopy with photochemical modulation: a sensitive, high resolution technique for chemical intermediates,” Appl. Phys. B 35, 105 (1984).
[Crossref]

H. E. Hunziker, “A new technique for gas-phase kinetic spectroscopy of molecules in the triplet state,” IBM J. Res. Develop. 15, 10 (1971).
[Crossref]

Huston, A. L.

A. L. Huston, W. E. Moerner, “Detection of persistent spectral holes using ultrasonic modulation,” J. Opt. Soc. Am. B 1, 349 (1984).
[Crossref]

A. L. Huston, W. E. Moerner, IBM Research Laboratories, San José, Calif. 95193 (personal communication).

Ingle, J. D.

Jasinski, J. M.

J. M. Jasinski, E. A. Whittaker, G. C. Bjorklund, R. W. Dreyfus, R. D. Estes, R. E. Walkup, “Detection of SiH2in silane and disilane glow discharges by frequency modulation absorption spectroscopy,” Appl. Phys. Lett. 44, 1155 (1984).
[Crossref]

Kachru, R.

Klein, C. F.

J. A. Gelbwachs, C. F. Klein, J. E. Wessel, “Saturated optical nonresonant emission spectroscopy (SONRES) for atomic detection,” Appl. Phys. Lett. 30, 489 (1977).
[Crossref]

Kowalski, F. V.

The FM technique was independently suggested by R. W. P. Drever as a means for servolocking a tunable laser to a high-finesse optical cavity. It was first experimentally implemented for this purpose by R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, Joint Institute for Laboratory Astrophysics, Boulder, Colo. 80303 (personal communication, September1979) and then by M. Prentiss, B. Peuse, G. Sanders, S. Ezekiel, Research Laboratory of Electronics, Progress Rep. No. 123 (Massachusetts Institute of Technology, Cambridge, Mass., January1981).

Leighton, P. A.

P. A. Leighton, Photochemistry of Air Pollution (Academic, New York, 1961).

Lenth, W.

W. Lenth, “High frequency heterodyne spectroscopy with current-modulated diode lasers,” IEEE J. Quantum Electron. QE-20, 1045 (1984).
[Crossref]

G. C. Bjorklund, M. D. Levenson, W. Lenth, C. Ortiz, “Frequency modulation (FM) spectroscopy—theory of lineshapes and signal-to-noise analysis,” Appl. Phys. B 32, 145 (1983).
[Crossref]

W. Lenth, “Optical heterodyne spectroscopy with frequency- and amplitude-modulated semiconductor lasers,” Opt. Lett. 8, 575 (1983).
[Crossref] [PubMed]

G. C. Bjorklund, W. Lenth, C. Ortiz, “Cryogenic frequency domain optical mass memory,” Proc. Soc. Photo-Opt. Instrum. Eng. 298, 107 (1982).

Levenson, M. D.

Levy, H.

H. Levy, “Photochemistry of the troposphere,” Adv. Photochem. 9, 369 (1974).
[Crossref]

Long-sheng, Ma

L. Hollberg, Ma Long-sheng, M. Hohenstatt, J. L. Hall, “Precision measurements by optical heterodyne techniques,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 91 (1983).

Lyndz, L.

A possible improvement on this situation has been reported by B. A. Woody, L. Lyndz (Appl. Opt., to be published) who report a sensitivity limit of ~10−6. We thank the authors for a personal communication of their preliminary results.

Marner, C. C.

C. S. Gudemann, C. C. Marner, M. H. Begemann, E. Schafer, J. Pfaff, R. J. Saykally, “Velocity modulation laser absorption spectroscopy of molecular ions,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 106 (1983).

Moerner, W. E.

A. L. Huston, W. E. Moerner, “Detection of persistent spectral holes using ultrasonic modulation,” J. Opt. Soc. Am. B 1, 349 (1984).
[Crossref]

M. D. Levenson, W. E. Moerner, D. E. Horne, “FM spectroscopy detection of stimulated Raman gain,” Opt. Lett. 8, 108 (1983).
[Crossref] [PubMed]

M. Gehrtz, W. E. Moerner, G. C. Bjorklund, “Shot-noise limited detection of very weak absorptions with laser FM spectroscopy,” Opt. Lett. (to be published).

A. L. Huston, W. E. Moerner, IBM Research Laboratories, San José, Calif. 95193 (personal communication).

Molinari, L. T.

Monts, D. L.

D. K. Hsu, D. L. Monts, R. N. Zare, Spectral Atlas of Nitrogen Dioxide 5530 Å to 6480 Å (Academic, New York, 1978).

Moses, E. I.

Munley, A. J.

The FM technique was independently suggested by R. W. P. Drever as a means for servolocking a tunable laser to a high-finesse optical cavity. It was first experimentally implemented for this purpose by R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, Joint Institute for Laboratory Astrophysics, Boulder, Colo. 80303 (personal communication, September1979) and then by M. Prentiss, B. Peuse, G. Sanders, S. Ezekiel, Research Laboratory of Electronics, Progress Rep. No. 123 (Massachusetts Institute of Technology, Cambridge, Mass., January1981).

Nayak, N.

N. Nayak, G. S. Agarwal, “Absorption and fluorescence in frequency-modulated fields under conditions of strong modulation and absorption,” Phys. Rev. A (to be published).

Ortiz, C.

G. C. Bjorklund, M. D. Levenson, W. Lenth, C. Ortiz, “Frequency modulation (FM) spectroscopy—theory of lineshapes and signal-to-noise analysis,” Appl. Phys. B 32, 145 (1983).
[Crossref]

G. C. Bjorklund, W. Lenth, C. Ortiz, “Cryogenic frequency domain optical mass memory,” Proc. Soc. Photo-Opt. Instrum. Eng. 298, 107 (1982).

Pfaff, J.

C. S. Gudemann, C. C. Marner, M. H. Begemann, E. Schafer, J. Pfaff, R. J. Saykally, “Velocity modulation laser absorption spectroscopy of molecular ions,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 106 (1983).

Pillet, P.

Pokrowsky, P.

P. Pokrowsky, W. Zapka, F. Chu, G. C. Bjorklund, “High frequency wavelength modulation spectroscopy with diode lasers,” Opt. Commun. 44, 175 (1983).
[Crossref]

E. A. Whittaker, P. Pokrowsky, W. Zapka, K. Roche, G. C. Bjorklund, “Improved laser technique for high sensitivity atomic absorption spectroscopy in flames,” J. Quantum. Spectrosc. Radiat. Transfer 30, 289 (1983).
[Crossref]

Robinson, H. G.

J. L. Hall, H. G. Robinson, T. Baer, L. Hollberg, “The line-shapes of subdoppler resonances observable with FM side-band (optical heterodyne) laser techniques,” in Advances in Laser Spectroscopy, F. T. Arecchi, F. Strumia, H. Walther, eds. (Plenum, New York, 1983), p. 99.
[Crossref]

J. L. Hall, T. Baer, L. Hollberg, H. G. Robinson, “Precision spectroscopy and laser frequency control using FM sideband optical heterodyne techniques,” in Laser Spectroscopy V, A. R. W. McKellar, T. Oka, B. P. Stoicheff, eds. (Springer-Verlag, Berlin, 1981), p. 16.

Roche, K.

E. A. Whittaker, P. Pokrowsky, W. Zapka, K. Roche, G. C. Bjorklund, “Improved laser technique for high sensitivity atomic absorption spectroscopy in flames,” J. Quantum. Spectrosc. Radiat. Transfer 30, 289 (1983).
[Crossref]

Romagnoli, M.

Saykally, R. J.

C. S. Gudemann, C. C. Marner, M. H. Begemann, E. Schafer, J. Pfaff, R. J. Saykally, “Velocity modulation laser absorption spectroscopy of molecular ions,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 106 (1983).

Schafer, E.

C. S. Gudemann, C. C. Marner, M. H. Begemann, E. Schafer, J. Pfaff, R. J. Saykally, “Velocity modulation laser absorption spectroscopy of molecular ions,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 106 (1983).

Schenk, P. K.

P. K. Schenk, J. W. Hastie, “Optogalvanic spectroscopy—application for combustion systems,” Opt. Eng. 20, 522 (1981).

Snyder, J. J.

M. Ducloy, J. J. Snyder, “High frequency optical heterodyne spectroscopy,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 87 (1983).

Sullivan, B. J.

E. A. Whittaker, B. J. Sullivan, G. C. Bjorklund, H. R. Wendt, H. E. Hunziker, “ND4Schüler band absorption observed by laser FM spectroscopy in a photochemical reaction,” J. Chem. Phys. 80, 961 (1984).
[Crossref]

Tang, C. L.

Tran, N. H.

van Lindenvan den Heuvell, H. B.

Vasudev, R.

R. Vasudev, R. N. Zare, “Laser optogalvanic study of HCO A state predissociation,” J. Chem. Phys. 76, 5267 (1982).
[Crossref]

Walkup, R. E.

J. M. Jasinski, E. A. Whittaker, G. C. Bjorklund, R. W. Dreyfus, R. D. Estes, R. E. Walkup, “Detection of SiH2in silane and disilane glow discharges by frequency modulation absorption spectroscopy,” Appl. Phys. Lett. 44, 1155 (1984).
[Crossref]

Wang, C. C.

J. F. Ward, C. C. Wang, C. E. Wieman, “A proposal for improved OH detection using frequency modulation sepctroscopy,” presented at the March 1985meeting of the American Physical Society, Baltimore, Maryland.

Ward, J. F.

J. F. Ward, C. C. Wang, C. E. Wieman, “A proposal for improved OH detection using frequency modulation sepctroscopy,” presented at the March 1985meeting of the American Physical Society, Baltimore, Maryland.

Watjen, J. P.

Watson, J. K. G.

F. Alberti, K. P. Huber, J. K. G. Watson, “Absorption spectrum and analysis of the ND4Schüler band,” J. Mol. Spectrosc. 107, 133 (1984).
[Crossref]

Welkowsky, M.

Cf. the much more complicated demodulation scheme used in the double-beam, one-detector WMS method proposed by M. Welkowsky, R. Braunstein, “A double-beam, single-detector wavelength modulation spectrometer,” Rev. Sci. Instrum. 43, 399 (1972).
[Crossref]

Wendt, H. R.

E. A. Whittaker, B. J. Sullivan, G. C. Bjorklund, H. R. Wendt, H. E. Hunziker, “ND4Schüler band absorption observed by laser FM spectroscopy in a photochemical reaction,” J. Chem. Phys. 80, 961 (1984).
[Crossref]

E. A. Whittaker, H. R. Wendt, H. E. Hunziker, G. C. Bjorklund, “Laser FM spectroscopy with photochemical modulation: a sensitive, high resolution technique for chemical intermediates,” Appl. Phys. B 35, 105 (1984).
[Crossref]

Wessel, J. E.

J. A. Gelbwachs, C. F. Klein, J. E. Wessel, “Saturated optical nonresonant emission spectroscopy (SONRES) for atomic detection,” Appl. Phys. Lett. 30, 489 (1977).
[Crossref]

Whittaker, E. A.

E. A. Whittaker, M. Gehrtz, G. C. Bjorklund, “Residual amplitude modulation in laser electro-optic phase modulation,” J. Opt. Soc. Am. B 2, 1320–1326 (1985).
[Crossref]

J. M. Jasinski, E. A. Whittaker, G. C. Bjorklund, R. W. Dreyfus, R. D. Estes, R. E. Walkup, “Detection of SiH2in silane and disilane glow discharges by frequency modulation absorption spectroscopy,” Appl. Phys. Lett. 44, 1155 (1984).
[Crossref]

E. A. Whittaker, H. R. Wendt, H. E. Hunziker, G. C. Bjorklund, “Laser FM spectroscopy with photochemical modulation: a sensitive, high resolution technique for chemical intermediates,” Appl. Phys. B 35, 105 (1984).
[Crossref]

E. A. Whittaker, B. J. Sullivan, G. C. Bjorklund, H. R. Wendt, H. E. Hunziker, “ND4Schüler band absorption observed by laser FM spectroscopy in a photochemical reaction,” J. Chem. Phys. 80, 961 (1984).
[Crossref]

E. A. Whittaker, P. Pokrowsky, W. Zapka, K. Roche, G. C. Bjorklund, “Improved laser technique for high sensitivity atomic absorption spectroscopy in flames,” J. Quantum. Spectrosc. Radiat. Transfer 30, 289 (1983).
[Crossref]

Wieman, C. E.

J. F. Ward, C. C. Wang, C. E. Wieman, “A proposal for improved OH detection using frequency modulation sepctroscopy,” presented at the March 1985meeting of the American Physical Society, Baltimore, Maryland.

Williams, A. M.

T. D. Harris, A. M. Williams, “Low absorbance measurements,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 110 (1983).

Woody, B. A.

A possible improvement on this situation has been reported by B. A. Woody, L. Lyndz (Appl. Opt., to be published) who report a sensitivity limit of ~10−6. We thank the authors for a personal communication of their preliminary results.

Yariv, A.

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), pp. 341–343.

Zapka, W.

P. Pokrowsky, W. Zapka, F. Chu, G. C. Bjorklund, “High frequency wavelength modulation spectroscopy with diode lasers,” Opt. Commun. 44, 175 (1983).
[Crossref]

E. A. Whittaker, P. Pokrowsky, W. Zapka, K. Roche, G. C. Bjorklund, “Improved laser technique for high sensitivity atomic absorption spectroscopy in flames,” J. Quantum. Spectrosc. Radiat. Transfer 30, 289 (1983).
[Crossref]

Zare, R. N.

R. Vasudev, R. N. Zare, “Laser optogalvanic study of HCO A state predissociation,” J. Chem. Phys. 76, 5267 (1982).
[Crossref]

D. K. Hsu, D. L. Monts, R. N. Zare, Spectral Atlas of Nitrogen Dioxide 5530 Å to 6480 Å (Academic, New York, 1978).

Adv. Photochem. (1)

H. Levy, “Photochemistry of the troposphere,” Adv. Photochem. 9, 369 (1974).
[Crossref]

Appl. Opt. (4)

Appl. Phys. B (2)

G. C. Bjorklund, M. D. Levenson, W. Lenth, C. Ortiz, “Frequency modulation (FM) spectroscopy—theory of lineshapes and signal-to-noise analysis,” Appl. Phys. B 32, 145 (1983).
[Crossref]

E. A. Whittaker, H. R. Wendt, H. E. Hunziker, G. C. Bjorklund, “Laser FM spectroscopy with photochemical modulation: a sensitive, high resolution technique for chemical intermediates,” Appl. Phys. B 35, 105 (1984).
[Crossref]

Appl. Phys. Lett. (2)

J. M. Jasinski, E. A. Whittaker, G. C. Bjorklund, R. W. Dreyfus, R. D. Estes, R. E. Walkup, “Detection of SiH2in silane and disilane glow discharges by frequency modulation absorption spectroscopy,” Appl. Phys. Lett. 44, 1155 (1984).
[Crossref]

J. A. Gelbwachs, C. F. Klein, J. E. Wessel, “Saturated optical nonresonant emission spectroscopy (SONRES) for atomic detection,” Appl. Phys. Lett. 30, 489 (1977).
[Crossref]

Appl. Spectrosc. (2)

Faraday Disc. Chem. Soc. (1)

G. Herzberg, “Rydberg spectra of triatomic hydrogen and of the ammonium radical,” Faraday Disc. Chem. Soc. 71, 165 (1981).
[Crossref]

IBM J. Res. Develop. (1)

H. E. Hunziker, “A new technique for gas-phase kinetic spectroscopy of molecules in the triplet state,” IBM J. Res. Develop. 15, 10 (1971).
[Crossref]

IEEE J. Quantum Electron. (1)

W. Lenth, “High frequency heterodyne spectroscopy with current-modulated diode lasers,” IEEE J. Quantum Electron. QE-20, 1045 (1984).
[Crossref]

J. Chem. Phys. (2)

R. Vasudev, R. N. Zare, “Laser optogalvanic study of HCO A state predissociation,” J. Chem. Phys. 76, 5267 (1982).
[Crossref]

E. A. Whittaker, B. J. Sullivan, G. C. Bjorklund, H. R. Wendt, H. E. Hunziker, “ND4Schüler band absorption observed by laser FM spectroscopy in a photochemical reaction,” J. Chem. Phys. 80, 961 (1984).
[Crossref]

J. Mol. Spectrosc. (2)

F. Alberti, K. P. Huber, J. K. G. Watson, “Absorption spectrum and analysis of the ND4Schüler band,” J. Mol. Spectrosc. 107, 133 (1984).
[Crossref]

J. C. D. Brand, W. H. Chan, J. L. Hardwick, “Rotational analysis of the 8000–9000 Å bands of nitrogen dioxide,” J. Mol. Spectrosc. 56, 309 (1975).
[Crossref]

J. Opt. Soc. Am. B (3)

J. Quantum. Spectrosc. Radiat. Transfer (1)

E. A. Whittaker, P. Pokrowsky, W. Zapka, K. Roche, G. C. Bjorklund, “Improved laser technique for high sensitivity atomic absorption spectroscopy in flames,” J. Quantum. Spectrosc. Radiat. Transfer 30, 289 (1983).
[Crossref]

Opt. Commun. (1)

P. Pokrowsky, W. Zapka, F. Chu, G. C. Bjorklund, “High frequency wavelength modulation spectroscopy with diode lasers,” Opt. Commun. 44, 175 (1983).
[Crossref]

Opt. Eng. (1)

P. K. Schenk, J. W. Hastie, “Optogalvanic spectroscopy—application for combustion systems,” Opt. Eng. 20, 522 (1981).

Opt. Lett. (6)

Proc. Soc. Photo-Opt. Instrum. Eng. (5)

M. Ducloy, J. J. Snyder, “High frequency optical heterodyne spectroscopy,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 87 (1983).

C. S. Gudemann, C. C. Marner, M. H. Begemann, E. Schafer, J. Pfaff, R. J. Saykally, “Velocity modulation laser absorption spectroscopy of molecular ions,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 106 (1983).

L. Hollberg, Ma Long-sheng, M. Hohenstatt, J. L. Hall, “Precision measurements by optical heterodyne techniques,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 91 (1983).

T. D. Harris, A. M. Williams, “Low absorbance measurements,” Proc. Soc. Photo-Opt. Instrum. Eng. 426, 110 (1983).

G. C. Bjorklund, W. Lenth, C. Ortiz, “Cryogenic frequency domain optical mass memory,” Proc. Soc. Photo-Opt. Instrum. Eng. 298, 107 (1982).

Rev. Sci. Instrum. (1)

Cf. the much more complicated demodulation scheme used in the double-beam, one-detector WMS method proposed by M. Welkowsky, R. Braunstein, “A double-beam, single-detector wavelength modulation spectrometer,” Rev. Sci. Instrum. 43, 399 (1972).
[Crossref]

Other (21)

K.-H. Hellwege, ed., Landolt-Börnstein Zahlenwerte und Funktionen (Springer-Verlag, Berlin, 1960), Vol. II-2a, p. 10.

As the width of the absorption line depicted in Fig. 12 is somewhat larger than the FM sideband spacing, the maximum differential absorption experienced by the sidebands is slightly smaller than the peak absorptivity of the line. Although the corresponding reduction factor could be calculated explicitly from the FM line-shape theory,28 we chose a calibration procedure29,35 that for a given linewidth relates the FM-signal voltage directly to the peak absorptivity. The values that we quote here and in Fig. 12 thus correspond to absorptivity differences taken at the absorption line peak and at a position off the absorption line.

The widths of the absorption lines shown in Fig. 13 are slightly smaller than the FM sideband spacing. Thus in this case the maximum differential absorptivity experienced by the sidebands is directly given by the peak absorptivities of the iodine absorption lines, and the Δδ values that we quote here and in Fig. 13 are exactly equal to the differential absorptivities seen by the sidebands.

The RAM-induced noise spectrum observed previously35(Fig. 5) shows much stronger low-frequency components, probably for two reasons: (1) A different EOM was used that caused much stronger RAM and (2) a relatively high FM index (M~ 1) was employed that also increased the RAM.

J. F. Ward, C. C. Wang, C. E. Wieman, “A proposal for improved OH detection using frequency modulation sepctroscopy,” presented at the March 1985meeting of the American Physical Society, Baltimore, Maryland.

P. A. Leighton, Photochemistry of Air Pollution (Academic, New York, 1961).

D. K. Hsu, D. L. Monts, R. N. Zare, Spectral Atlas of Nitrogen Dioxide 5530 Å to 6480 Å (Academic, New York, 1978).

M. Gehrtz, W. E. Moerner, G. C. Bjorklund, “Shot-noise limited detection of very weak absorptions with laser FM spectroscopy,” Opt. Lett. (to be published).

This is the most important difference between this method and the double-beam WMS scheme proposed in Ref. 14, where the corresponding phase shift is 90°.

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), pp. 341–343.

J. L. Hall, H. G. Robinson, T. Baer, L. Hollberg, “The line-shapes of subdoppler resonances observable with FM side-band (optical heterodyne) laser techniques,” in Advances in Laser Spectroscopy, F. T. Arecchi, F. Strumia, H. Walther, eds. (Plenum, New York, 1983), p. 99.
[Crossref]

When current modulated diode lasers are used for FM spectroscopy,24,25 one generally has to deal with a fairly strong RAM (R/M~ 0.1). It was recognized in Refs. 24 and 25, however, that the RAM phase difference ψ depends critically on the diode-laser operating conditions. It should thus be possible to set ψ such that the distortive term becomes small compared with the pure-FM term—at least for the Fourier component being studied (in phase or quadrature).

A possible improvement on this situation has been reported by B. A. Woody, L. Lyndz (Appl. Opt., to be published) who report a sensitivity limit of ~10−6. We thank the authors for a personal communication of their preliminary results.

J. L. Hall, T. Baer, L. Hollberg, H. G. Robinson, “Precision spectroscopy and laser frequency control using FM sideband optical heterodyne techniques,” in Laser Spectroscopy V, A. R. W. McKellar, T. Oka, B. P. Stoicheff, eds. (Springer-Verlag, Berlin, 1981), p. 16.

A. L. Huston, W. E. Moerner, IBM Research Laboratories, San José, Calif. 95193 (personal communication).

D. S. Kliger, ed., Ultrasensitive Laser Spectroscopy (Academic, New York, 1983).

M. Cardona, Modulation Spectroscopy, Supplement II of Solid State Physics, F. Seitz, D. Turnbull, eds. (Academic, New York, 1969).

G. C. Bjorklund, IBM Invention Disclosure SA 8790135 (March1979); “Frequency-modulation spectroscopy: a new method for measuring weak absorptions and dispersions,” Opt. Lett. 5, 15 (1980); U.S. Patent4,297,035 (November1981).
[PubMed]

The FM technique was independently suggested by R. W. P. Drever as a means for servolocking a tunable laser to a high-finesse optical cavity. It was first experimentally implemented for this purpose by R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, Joint Institute for Laboratory Astrophysics, Boulder, Colo. 80303 (personal communication, September1979) and then by M. Prentiss, B. Peuse, G. Sanders, S. Ezekiel, Research Laboratory of Electronics, Progress Rep. No. 123 (Massachusetts Institute of Technology, Cambridge, Mass., January1981).

The most recent applications of FM spectroscopy are described in Refs. 35, 37, and 40. For a review of the use of FM techniques covering the literature up to 1983, cf. Ref. 28 and references therein.

N. Nayak, G. S. Agarwal, “Absorption and fluorescence in frequency-modulated fields under conditions of strong modulation and absorption,” Phys. Rev. A (to be published).

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Figures (14)

Fig. 1
Fig. 1

Schematic diagram illustrating the principle of FM spectroscopy and the basic setup used in the experiments.

Fig. 2
Fig. 2

Minimum detectable (SNR = 1) differential absorptivity Δδmin as a function of detection bandwidth Δf. The diagram schematically illustrates the sensitivity limit of FM spectroscopy under background-limited conditions (solid line; cf. Subsection 2.D). The theoretical prediction according to Eq. (2.12) is shown as the dashed line.

Fig. 3
Fig. 3

RAM fringes obtained by scanning the laser frequency 10 GHz with no sample present. The EOM material used here was a LiTaO3 crystal. (a) Laser beam orthogonal to crystal end face and ωrf = 333 MHz. (b) Laser beam orthogonal to crystal end face and ωrf = 309 MHz (equivalent to a π/2 phase shift at the rf mixer LO port), illustrating the well-defined phase of the fringe signal. (c) Laser beam angled by ~3° from normal to crystal end face and ωrf = 309 MHz. By appropriate choice of phase and beam orientation, the fringes may be completely eliminated, leaving a contribution to the RAM that for this crystal is virtually independent of laser frequency.

Fig. 4
Fig. 4

Sketch illustrating the RAM background problem of FM spectroscopy. The figure shows the idealized power versus frequency spectrum of the photodetector signal (normalized to the zero-frequency value) in FM spectroscopy in the absence of any sample absorption. The peak at the modulation frequency ωrf comes from the AM imparted by the imperfect phase modulator.

Fig. 5
Fig. 5

Electronic power spectrum of the FM signal taken at the output of the rf mixer IF port. The modulation frrequency was 2 GHz. The laser was mechanically chopped at 2.8 kHz. No sample was in the beam. The spectrum shows the RAM signal peaking at the chopper frequency, accomplished by the low-frequency noise spectrum leaking through via the RAM.

Fig. 6
Fig. 6

Electronic power spectrum of the FM signal under the same conditions as in Fig. 5 except that now an absorbing sample of photochemically modulated HCO radicals is in the laser beam. The photochemical-modulation frequency is approximately 0.3 kHz, and the arrows in the figure point to the HCO-induced signals at 2.8 ± 0.3 kHz.

Fig. 7
Fig. 7

Laser frequency scan showing the photochemical-modulation phase relationship between the ND4 (upper part) and ND2 (lower part) absorption signal. ND2 is present as intermediate in the production of ND4. The markers show the location of the known transitions.39 FM frequency, 2 GHz; laser-chop frequency, 2.8 kHz; photochemical-modulation frequency, 12 kHz. The signal was detected at 2.8 kHz ± 12 kHz. The differential absorptivity for the ND4 was approximately 10−5.

Fig. 8
Fig. 8

Schematics illustrating the double-beam, one-detector RAM-nulling technique. R(λ) represents the modulation index of the RAM, and ψ is the phase shift between the FM and the RAM.24,25 Unimportant constant factors are omitted here for brevity. With two beam splitters (BS’s), a sample (s) and a reference (r) beam are generated and subsequently recombined onto the photodiode. A chopper (Ch) serves to chop both beams synchronously but 180° out of phase (cf. the insert in the upper left-hand corner of the figure). With both beams hitting the photodetector, the terms depending on the chopper frequency ωchop cancel one another (provided the relative power levels Ps and Pr in the two paths are made equal with a variable attenuator ND, and the path lengths ls and 1r are equalized). One is left, finally, with a dc signal at the mixer output. In effect this technique shifts the unwanted RAM signal out of the frequency band of interest at ωchop to zero frequency.

Fig. 9
Fig. 9

Schematic diagram showing the sequential steps involved in demodulating the RAM-induced photosignal; first, for each of the beams separately (single s and r) and then for the actual double-beam case (dual). Because each of the individual beams is chopped and carries the RAM signal B(t) [cf. Eqs. (3.10) and (3.12)] one obtains rf bursts at the chopper frequency even when no sample is present. After the first demodulation with the mixer, these rf bursts are converted into a square-wave signal, which is subsequently demodulated at the chopper frequency with a lock-in amplifier yielding a dc-output signal. Now, when the laser is scanned slowly (on the time scale of the chopper period), one finally obtains an output voltage U(λ), which is proportional to Ps B ^ (λ) when the reference beam path is blocked, i.e., when only the sample beam is used. Correspondingly, the output voltage for the reference beam only is proportional to −Pr B ^ (λ). Finally, both beams are allowed to impinge on the photodetector (dual), and one obtains a continuous-wave rf output signal that, after demodulation with the mixer, converts to a dc-signal. As this signal has no frequency components at the chopper frequency, the final demodulation with the lock-in amplifier yields a zero output voltage [i.e., Ltot,ns(λ) in Eq. (5.8)].

Fig. 10
Fig. 10

Demonstration of the basic features of the double-beam technique. The RAM fringe traces obtained with a, the sample and b, the reference beam separately have opposite sign as required by Eq. (5.9). With both beams impinging on the photodetector (trace c) the RAM fringes are efficiently suppressed [Eq. (5.8)].

Fig. 11
Fig. 11

FM spectra obtained with an iodine absorption cell, demonstrating the sensitivity limitations due to a, multipass RAM fringes and b, the efficient RAM nulling with the double-beam technique. Note the 10-times-increased sensitivity in b. The iodine-vapor pressure was 230 μTorr.

Fig. 12
Fig. 12

FM spectra obtained with an iodine absorption cell, demonstrating the sensitivity limitations that are due to single-pass RAM (a and c) and the efficient RAM nulling with the double-beam technique (b and d). The lock-in amplifier starts to overload (OVLD) in the single-beam recordings. The modulation index used was 0.047, and the effective-noise bandwidth was 12.5 Hz. The iodine-vapor pressure was 33 μTorr for traces a and b and 10 μTorr for traces c and d.

Fig. 13
Fig. 13

FM spectrum of weak iodine absorption lines, obtained with the double-beam technique, demonstrating shot-noise-limited sensitivity. The modulation index used was 0.11, and the effective noise bandwidth was 1 Hz. The iodine-vapor pressure was 1.6 μTorr. The frequency scale (abscissa) is offset by 17 771.48 cm−1.

Fig. 14
Fig. 14

Power spectra of the amplified mixer output (after the PMPA), showing RAM peaking at the chopper frequency and associated low-frequency noise feedthrough with a, the single-beam technique, and their suppression with b, the double-beam technique. No sample was in the s-beam path. The light levels were the same for both light-on spectra (16 mW).

Equations (54)

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S = κ I .
SNR = κ I [ N e 2 + ( β I ) 2 + ( N s I ) 2 ] 1 / 2 .
Δ ϕ ( t ) = M sin Ω t .
Ω Γ feature .
Δ ω ( t ) = Ω M cos Ω t = Δ ω 0 cos Ω t .
Δ ω 0 < Γ feature ,
Ω ~ Γ feature .
E 1 ( t ) = E 0 exp ( i ω c t ) .
E 2 F ( t ) = E 0 exp [ i ( ω c t + M sin ω rf t ) ] = E 0 n = - n = J n ( M ) exp [ i ( ω c + n ω rf ) t ] ,
I 2 F ( t ) = c E 0 2 8 π = I 0 .
E 2 F ( t ) = E 0 { M 2 exp [ i ( ω c + ω rf ) t ] + exp ( i ω c t ) - M 2 exp [ i ( ω c - ω rf ) t ] } .
T n = T ¯ exp ( - δ n - i ϕ n ) ,
δ n = α n L / 2 ,             ϕ n = η n L ( ω c + n ω rf ) / c .
T ¯ = exp ( - δ ¯ - i ϕ ¯ ) ,
E 3 F ( t ) = E 0 { T 0 exp ( i ω c t ) + T 1 M 2 exp [ i ( ω c + ω rf ) t ] - T - 1 M 2 exp [ i ( ω c - ω rf ) t ] } .
I 3 F ( t ) = F ( t ) = I 0 exp ( - 2 δ ¯ ) ( 1 - Δ δ M cos ω rf t + Δ 2 ϕ M sin ω rf t ) ,
Δ δ = δ 1 - δ - 1 ,             Δ 2 ϕ = ( ϕ 1 - ϕ 0 ) - ( ϕ 0 - ϕ - 1 ) .
F ^ ( λ ) = I 0 exp ( - 2 δ ¯ ) × { - Δ δ M ( quadrature ) Δ 2 ϕ M ( in phase ) ,
Δ δ min = 2 M [ Δ f ( I 0 / ω c ) ] 1 / 2 .
I 2 ( t ) = I 0 [ 1 + 2 R sin ( ω rf t + ψ ) ] ,
E 2 ( t ) = E 2 F ( t ) [ 1 + R sin ( ω rf t + ψ ) ] .
E 2 ( t ) = E 2 F ( t ) + E 2 A ( t ) ,
E 2 A ( t ) = E 0 { R 2 i exp [ i ( ω c - ω rf ) t + i ψ ] - R 2 i exp [ i ( ω c - ω r f ) t - i ψ ] } .
E 3 ( t ) = E 3 F ( t ) + E 3 A ( t ) ,
E 3 A ( t ) = E 0 { T 1 R 2 i exp [ i ( ω c + ω rf ) t + i ψ ] - T - 1 R 2 i exp [ i ( ω c - ω rf ) t - i ψ ] } .
I 3 ( t ) = F ( t ) + D ( t ) + exp ( - 2 δ ¯ ) B ( t ) .
D ( t ) = - I 0 exp ( - 2 δ ¯ ) [ R ( Σ δ sin ψ + Δ ϕ cos ψ ) cos ω rf t + R ( Σ δ cos ψ - Δ ϕ sin ψ ) sin ω rf t ] ,
Σ δ = 2 δ 0 + δ 1 + δ - 1 .
B ( t ) = I 0 ( 2 R sin ψ cos ω rf t + 2 R cos ψ sin ω rf t ) = I 2 2 R sin ( ω rf t + ψ ) .
I ( t ) = F ( t ) + exp ( - 2 δ ¯ ) B ( t ) .
I ns ( t ) = I 0 + B ( t ) .
M ( λ ) = F ^ ( λ + exp ( - 2 δ ¯ ) B ^ ( λ )
M ns ( λ ) = B ^ ( λ ) 0.
B ^ ( λ ) = I 0 × { 2 R sin ψ ( quadrature ) 2 R cos ψ ( in phase ) .
Ψ ( EOM ) ~ 0
ω rf 2 π ν F S R .
R ( multipass EOM ) M ~ 10 - 3 10 - 2 .
ψ ( external ) ~ π 2 ,
R ( single - pass EOM ) M ~ 10 - 5 10 - 3 .
Δ δ min ~ R M ~ 10 - 5 10 - 2 .
I r ( t ) = P r I ns ( t ) ( 1 - cos ω chop t ) ,
I s ( t ) = P s ( t ) ( 1 + cos ω chop t ) .
l r = l s .
P r = exp ( - 2 δ ¯ ) P s ,
I tot ( t ) = P r [ I 0 + 2 B ( t ) ] + P s F ( t ) ( 1 + cos ω chop t ) .
M tot ( λ ) = 2 P r B ^ ( λ ) + P S F ^ ( λ ) ( 1 + cos ω chop t ) .
L tot ( λ ) = P s F ^ ( λ ) ,
L tot , ns ( λ ) = 0.
L s , ns ( λ ) = - L r , ns ( λ ) .
Δ δ calc b = 0.63 × 10 - 4             and             Δ δ calc d = 1.97 × 10 - 5 .
Δ δ min ( exp ) = 1.7 × 10 - 7 .
Δ δ min ( calc ) = 1.9 × 10 - 7 .
NEPP ~ 0.7 μ Torr m ( path length )
REPP ~ 1000 μ Torr m ( path length ) .

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