Abstract

The sensitivity of FM spectroscopy can be dramatically enhanced by location of the sample in a high-finesse cavity, for example, ∼5 orders of magnitude in this study. To avoid conversion of laser frequency noise into amplitude noise by the cavity, we choose the rf modulation frequency to match the cavity’s free spectral range. In this way small frequency fluctuations produce no additional noise, and a pure FM dispersion signal is recovered in transmission. We present a systematic study of the detection sensitivity, signal line shape and size, and slope at the central tuning. Experimentally, using a weakly absorbing gas such as C2H2 or C2HD placed inside an external high-finesse resonator, we obtained an integrated absorption sensitivity of 5×10-13 (1×10-14/cm) for the gas’s weak near-IR molecular overtone transitions. As an interesting application, a Nd:YAG laser was well stabilized on the P(5) line of the C2HD (ν2+3ν3) band by this technique. The high attainable sensitivity permitted selection of slow molecules with low power and gas pressure to give a linewidth 13 times below the room-temperature transit-time limit.

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Under shot-noise-limited conditions, the minimum detectable absorption is ΔαL=2[hνB/(ηP0)]1/2/[J0(β)J1(β)]= 3.2×10−7, where P0=0.1 mW, B=1 Hz, β=1, λ=790.7 nm, and η=0.8.
  2. M. Zhu and J. L. Hall, “Stabilization of optical frequency/phase of a laser system: application to a commercial dye laser with an external stabilizer,” J. Opt. Soc. Am. B 10, 802–816 (1993).
    [CrossRef]
  3. P. Jungner, S. Swartz, M. Eickhoff, J. Ye, J. L. Hall, and S. Waltman, “Absolute frequency of the molecular iodine transition R(56)32–0 near 532 nm,” IEEE Trans. Instrum. Meas. 44, 151–154 (1995); P. Jungner, M. Eickhoff, S. Swartz, J. Ye, J. L. Hall, and S. Waltman, “Stability and absolute frequency of molecular iodine transitions near 532 nm,” in Laser Frequency Stabilization and Noise Reduction, Y. Shevy, ed., Proc. SPIE 2378, 22–34 (1995); J. L. Hall, L.-S. Ma, M. Taubman, B. Tiemann, F. L. Hong, O. Pfister, and J. Ye, “Stabilization and frequency measurement of the I2-stabilized Nd:YAG laser,” IEEE Trans. Instrum. Meas.IEIMAO 48, 583–586 (1999).
    [CrossRef]
  4. M. de Labachelerie, K. Nakagawa, and M. Ohtsu, “Ultranarrow 13C2H2 saturated absorption lines at 1.5 μm,” Opt. Lett. 19, 840–842 (1994); M. de Labachelerie, K. Nakagawa, Y. Awaji, and M. Ohtsu, “High-frequency-stability laser at 1.5 μm using Doppler-free molecular lines,” Opt. Lett. 20, 572–574 (1995); K. Nakagawa, M. de Labachelerie, Y. Awaji, and M. Kurogi, “Accurate optical frequency atlas of the 1.5-μm bands of acetylene,” J. Opt. Soc. Am. B JOBPDE 13, 2708–2714 (1996).
    [CrossRef] [PubMed]
  5. L. S. Ma, P. Dubé, J. Ye, and J. L. Hall, “Saturation spectroscopy of molecular overtones for laser frequency standards in the visible and near-visible domain,” in Quantum Electronics and Laser Science Conference, Vol. 16 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), p. 18.
  6. P. Cerez, A. Brillet, C. N. Man-Pichot, and R. Felder, “He–Ne lasers stabilized by saturated absorption in iodine at 612 nm,” IEEE Trans Instrum. Meas. 29, 352–354 (1980).
    [CrossRef]
  7. L. S. Ma and J. L. Hall, “Optical heterodyne spectroscopy enhanced by an external optical cavity: toward improved working standards,” IEEE J. Quantum Electron. 26, 2006–2012 (1990).
    [CrossRef]
  8. L. S. Ma, J. Ye, P. Dubé, and J. L. Hall, “A new modulation method for sensitive nonlinear spectroscopy—application to molecular overtones as visible frequency references,” in Laser Spectroscopy XII, M. Inguscio, M. Allegrini, and A. Sasso, eds. (World Scientific, Singapore, 1995), pp. 199–203; J. L. Hall, J. Ye, L.-S. Ma, S. Swartz, P. Jungner, and S. Waltman, “Optical frequency standards—some improvements, some measurements, and some dreams,” in Fifth Symposium on Frequency Standards & Metrology, J. C. Bergquist, ed. (World Scientific, Singapore, 1995), pp. 267–276.
  9. J. Ye, L.-S. Ma, and J. L. Hall, “Sub-Doppler optical frequency reference at 1.064 μm via ultrasensitive cavity-enhanced frequency modulation spectroscopy of C2HD overtone transition,” Opt. Lett. 21, 1000–1002 (1996).
    [CrossRef] [PubMed]
  10. J. Ye, L.-S. Ma, and J. L. Hall, “Ultrastable optical frequency reference at 1.064 μm using C2HD molecular overtone reference,” IEEE Trans Instrum. Meas. 46, 178–182 (1997).
    [CrossRef]
  11. C. J. Bordé, J. L. Hall, C. V. Kunasz, and D. G. Hummer, “Saturated absorption line shape. Calculation of the transit-time broadening by a perturbation approach,” Phys. Rev. A 14, 236–263 (1976).
    [CrossRef]
  12. V. S. Letokhev and V. P. Chebotayev, Nonlinear Laser Spectroscopy (Springer-Verlag, Berlin, 1977).
  13. J. Vander Auwera, D. Hurtmans, M. Carleer, and M. Herman, “The ν3 fundamental in C2H2,” J. Mol. Spectrosc. 157, 337–357 (1993).
    [CrossRef]
  14. M. de Labachelerie, K. Nakagawa, and M. Ohtsu, “Ultranarrow 13C2H2 saturated absorption lines at 1.5 μm,” Opt. Lett. 19, 840–842 (1994).
    [CrossRef] [PubMed]
  15. M. A. Temsamani, J. V. Auwera, and M. Herman, “The absorption spectrum of C2HD between 9000 and 13 000 cm−1,” Mol. Phys. 79, 359–371 (1993).
    [CrossRef]
  16. F. S. Pavone, F. Marin, M. Inguscio, K. Ernst, and G. Di Lonardo, “Sensitive detection of acetylene absorption in the visible by using a stabilized AlGaAs diode laser,” Appl. Opt. 32, 259–262 (1993).
    [CrossRef] [PubMed]
  17. G. T. Scherer, K. K. Lehmann, and W. Klemperer, “The high resolution visible overtone spectrum of acetylene,” J. Chem. Phys. 78, 2817–2832 (1983); K. K. Lehmann, “The absolute intensity of visible overtone bands of acetylene,” J. Chem. Phys. 91, 2759–2760 (1989).
    [CrossRef]
  18. R. L. Smith, “Practical solutions of the lock-in detection problem for Lorentz and dispersion resonance signals,” J. Opt. Soc. Am. 61, 1015–1022 (1971); H. Wahlquist, “Modulation broadening of unsaturated Lorentzian lines,” J. Chem. Phys. 35, 1708–1710 (1961).
    [CrossRef]
  19. S. Stenholm, Foundation of Laser Spectroscopy (Wiley, New York, 1983).
  20. J. F. Kelly and A. Gallagher, “Efficient electro-optic modulator for optical pumping of Na beams,” Rev. Sci. Instrum. 58, 563–566 (1987).
    [CrossRef]
  21. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
    [CrossRef]
  22. J. Ye, L.-S. Ma, and J. L. Hall, “Ultrasensitive high resolution laser spectroscopy and its application to optical frequency standards,” in Proceedings of the 28th Annual Precise Time and Time Inteval (PTTI) Applications and Planning Meeting, L. A. Breakiron, ed. (U.S. Naval Observatory, Washington, D.C., 1997), pp. 289–303.
  23. M. L. Eickhoff and J. L. Hall, “Optical frequency standard at 532 nm,” IEEE Trans Instrum. Meas. 44, 155–158 (1995).
    [CrossRef]
  24. L.-S. Ma, Ph. Courteille, G. Ritter, W. Neuhauser, and R. Blatt, “Precision laser spectrometer with multiple frequency modulation,” in Digest of International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1994), p. 61; Ph. Courteille, L.-S. Ma, G. Ritter, W. Neuhauser, and R. Blatt, “Frequency measurement of Te2 resonances near 467 nm,” Appl. Phys. B 59, 187–193 (1994).
    [CrossRef]
  25. S. N. Bagayev, V. P. Chebotayev, A. K. Dmitriyev, A. E. Om, Yu. V. Nekrasov, and B. N. Skvortsov, “Second-order Doppler-free spectroscopy,” Appl. Phys. B: Photophys. Laser Chem. 52, 63–66 (1991); Ch. Chardonnet, F. Guernet, G. Charton, and Ch. J. Bordé, “Ultrahigh-resolution saturation spectroscopy using slow molecules in an external cell,” Appl. Phys. B 59, 333–343 (1994).
    [CrossRef]
  26. J. Ye, “Ultrasensitive high resolution laser spectroscopy and its application to optical frequency standards,” Ph.D. dissertation (University of Colorado at Boulder, Boulder, Colo., 1997).

1997 (1)

J. Ye, L.-S. Ma, and J. L. Hall, “Ultrastable optical frequency reference at 1.064 μm using C2HD molecular overtone reference,” IEEE Trans Instrum. Meas. 46, 178–182 (1997).
[CrossRef]

1996 (1)

1995 (1)

M. L. Eickhoff and J. L. Hall, “Optical frequency standard at 532 nm,” IEEE Trans Instrum. Meas. 44, 155–158 (1995).
[CrossRef]

1994 (1)

1993 (4)

1990 (1)

L. S. Ma and J. L. Hall, “Optical heterodyne spectroscopy enhanced by an external optical cavity: toward improved working standards,” IEEE J. Quantum Electron. 26, 2006–2012 (1990).
[CrossRef]

1987 (1)

J. F. Kelly and A. Gallagher, “Efficient electro-optic modulator for optical pumping of Na beams,” Rev. Sci. Instrum. 58, 563–566 (1987).
[CrossRef]

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

1980 (1)

P. Cerez, A. Brillet, C. N. Man-Pichot, and R. Felder, “He–Ne lasers stabilized by saturated absorption in iodine at 612 nm,” IEEE Trans Instrum. Meas. 29, 352–354 (1980).
[CrossRef]

1976 (1)

C. J. Bordé, J. L. Hall, C. V. Kunasz, and D. G. Hummer, “Saturated absorption line shape. Calculation of the transit-time broadening by a perturbation approach,” Phys. Rev. A 14, 236–263 (1976).
[CrossRef]

Auwera, J. V.

M. A. Temsamani, J. V. Auwera, and M. Herman, “The absorption spectrum of C2HD between 9000 and 13 000 cm−1,” Mol. Phys. 79, 359–371 (1993).
[CrossRef]

Bordé, C. J.

C. J. Bordé, J. L. Hall, C. V. Kunasz, and D. G. Hummer, “Saturated absorption line shape. Calculation of the transit-time broadening by a perturbation approach,” Phys. Rev. A 14, 236–263 (1976).
[CrossRef]

Brillet, A.

P. Cerez, A. Brillet, C. N. Man-Pichot, and R. Felder, “He–Ne lasers stabilized by saturated absorption in iodine at 612 nm,” IEEE Trans Instrum. Meas. 29, 352–354 (1980).
[CrossRef]

Carleer, M.

J. Vander Auwera, D. Hurtmans, M. Carleer, and M. Herman, “The ν3 fundamental in C2H2,” J. Mol. Spectrosc. 157, 337–357 (1993).
[CrossRef]

Cerez, P.

P. Cerez, A. Brillet, C. N. Man-Pichot, and R. Felder, “He–Ne lasers stabilized by saturated absorption in iodine at 612 nm,” IEEE Trans Instrum. Meas. 29, 352–354 (1980).
[CrossRef]

de Labachelerie, M.

Di Lonardo, G.

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Eickhoff, M. L.

M. L. Eickhoff and J. L. Hall, “Optical frequency standard at 532 nm,” IEEE Trans Instrum. Meas. 44, 155–158 (1995).
[CrossRef]

Ernst, K.

Felder, R.

P. Cerez, A. Brillet, C. N. Man-Pichot, and R. Felder, “He–Ne lasers stabilized by saturated absorption in iodine at 612 nm,” IEEE Trans Instrum. Meas. 29, 352–354 (1980).
[CrossRef]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Gallagher, A.

J. F. Kelly and A. Gallagher, “Efficient electro-optic modulator for optical pumping of Na beams,” Rev. Sci. Instrum. 58, 563–566 (1987).
[CrossRef]

Hall, J. L.

J. Ye, L.-S. Ma, and J. L. Hall, “Ultrastable optical frequency reference at 1.064 μm using C2HD molecular overtone reference,” IEEE Trans Instrum. Meas. 46, 178–182 (1997).
[CrossRef]

J. Ye, L.-S. Ma, and J. L. Hall, “Sub-Doppler optical frequency reference at 1.064 μm via ultrasensitive cavity-enhanced frequency modulation spectroscopy of C2HD overtone transition,” Opt. Lett. 21, 1000–1002 (1996).
[CrossRef] [PubMed]

M. L. Eickhoff and J. L. Hall, “Optical frequency standard at 532 nm,” IEEE Trans Instrum. Meas. 44, 155–158 (1995).
[CrossRef]

M. Zhu and J. L. Hall, “Stabilization of optical frequency/phase of a laser system: application to a commercial dye laser with an external stabilizer,” J. Opt. Soc. Am. B 10, 802–816 (1993).
[CrossRef]

L. S. Ma and J. L. Hall, “Optical heterodyne spectroscopy enhanced by an external optical cavity: toward improved working standards,” IEEE J. Quantum Electron. 26, 2006–2012 (1990).
[CrossRef]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

C. J. Bordé, J. L. Hall, C. V. Kunasz, and D. G. Hummer, “Saturated absorption line shape. Calculation of the transit-time broadening by a perturbation approach,” Phys. Rev. A 14, 236–263 (1976).
[CrossRef]

Herman, M.

M. A. Temsamani, J. V. Auwera, and M. Herman, “The absorption spectrum of C2HD between 9000 and 13 000 cm−1,” Mol. Phys. 79, 359–371 (1993).
[CrossRef]

J. Vander Auwera, D. Hurtmans, M. Carleer, and M. Herman, “The ν3 fundamental in C2H2,” J. Mol. Spectrosc. 157, 337–357 (1993).
[CrossRef]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Hummer, D. G.

C. J. Bordé, J. L. Hall, C. V. Kunasz, and D. G. Hummer, “Saturated absorption line shape. Calculation of the transit-time broadening by a perturbation approach,” Phys. Rev. A 14, 236–263 (1976).
[CrossRef]

Hurtmans, D.

J. Vander Auwera, D. Hurtmans, M. Carleer, and M. Herman, “The ν3 fundamental in C2H2,” J. Mol. Spectrosc. 157, 337–357 (1993).
[CrossRef]

Inguscio, M.

Kelly, J. F.

J. F. Kelly and A. Gallagher, “Efficient electro-optic modulator for optical pumping of Na beams,” Rev. Sci. Instrum. 58, 563–566 (1987).
[CrossRef]

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Kunasz, C. V.

C. J. Bordé, J. L. Hall, C. V. Kunasz, and D. G. Hummer, “Saturated absorption line shape. Calculation of the transit-time broadening by a perturbation approach,” Phys. Rev. A 14, 236–263 (1976).
[CrossRef]

Ma, L. S.

L. S. Ma and J. L. Hall, “Optical heterodyne spectroscopy enhanced by an external optical cavity: toward improved working standards,” IEEE J. Quantum Electron. 26, 2006–2012 (1990).
[CrossRef]

Ma, L.-S.

J. Ye, L.-S. Ma, and J. L. Hall, “Ultrastable optical frequency reference at 1.064 μm using C2HD molecular overtone reference,” IEEE Trans Instrum. Meas. 46, 178–182 (1997).
[CrossRef]

J. Ye, L.-S. Ma, and J. L. Hall, “Sub-Doppler optical frequency reference at 1.064 μm via ultrasensitive cavity-enhanced frequency modulation spectroscopy of C2HD overtone transition,” Opt. Lett. 21, 1000–1002 (1996).
[CrossRef] [PubMed]

Man-Pichot, C. N.

P. Cerez, A. Brillet, C. N. Man-Pichot, and R. Felder, “He–Ne lasers stabilized by saturated absorption in iodine at 612 nm,” IEEE Trans Instrum. Meas. 29, 352–354 (1980).
[CrossRef]

Marin, F.

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Nakagawa, K.

Ohtsu, M.

Pavone, F. S.

Temsamani, M. A.

M. A. Temsamani, J. V. Auwera, and M. Herman, “The absorption spectrum of C2HD between 9000 and 13 000 cm−1,” Mol. Phys. 79, 359–371 (1993).
[CrossRef]

Vander Auwera, J.

J. Vander Auwera, D. Hurtmans, M. Carleer, and M. Herman, “The ν3 fundamental in C2H2,” J. Mol. Spectrosc. 157, 337–357 (1993).
[CrossRef]

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Ye, J.

J. Ye, L.-S. Ma, and J. L. Hall, “Ultrastable optical frequency reference at 1.064 μm using C2HD molecular overtone reference,” IEEE Trans Instrum. Meas. 46, 178–182 (1997).
[CrossRef]

J. Ye, L.-S. Ma, and J. L. Hall, “Sub-Doppler optical frequency reference at 1.064 μm via ultrasensitive cavity-enhanced frequency modulation spectroscopy of C2HD overtone transition,” Opt. Lett. 21, 1000–1002 (1996).
[CrossRef] [PubMed]

Zhu, M.

Appl. Opt. (1)

Appl. Phys. B (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

IEEE J. Quantum Electron. (1)

L. S. Ma and J. L. Hall, “Optical heterodyne spectroscopy enhanced by an external optical cavity: toward improved working standards,” IEEE J. Quantum Electron. 26, 2006–2012 (1990).
[CrossRef]

IEEE Trans Instrum. Meas. (3)

P. Cerez, A. Brillet, C. N. Man-Pichot, and R. Felder, “He–Ne lasers stabilized by saturated absorption in iodine at 612 nm,” IEEE Trans Instrum. Meas. 29, 352–354 (1980).
[CrossRef]

J. Ye, L.-S. Ma, and J. L. Hall, “Ultrastable optical frequency reference at 1.064 μm using C2HD molecular overtone reference,” IEEE Trans Instrum. Meas. 46, 178–182 (1997).
[CrossRef]

M. L. Eickhoff and J. L. Hall, “Optical frequency standard at 532 nm,” IEEE Trans Instrum. Meas. 44, 155–158 (1995).
[CrossRef]

J. Mol. Spectrosc. (1)

J. Vander Auwera, D. Hurtmans, M. Carleer, and M. Herman, “The ν3 fundamental in C2H2,” J. Mol. Spectrosc. 157, 337–357 (1993).
[CrossRef]

J. Opt. Soc. Am. B (1)

Mol. Phys. (1)

M. A. Temsamani, J. V. Auwera, and M. Herman, “The absorption spectrum of C2HD between 9000 and 13 000 cm−1,” Mol. Phys. 79, 359–371 (1993).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

C. J. Bordé, J. L. Hall, C. V. Kunasz, and D. G. Hummer, “Saturated absorption line shape. Calculation of the transit-time broadening by a perturbation approach,” Phys. Rev. A 14, 236–263 (1976).
[CrossRef]

Rev. Sci. Instrum. (1)

J. F. Kelly and A. Gallagher, “Efficient electro-optic modulator for optical pumping of Na beams,” Rev. Sci. Instrum. 58, 563–566 (1987).
[CrossRef]

Other (13)

J. Ye, L.-S. Ma, and J. L. Hall, “Ultrasensitive high resolution laser spectroscopy and its application to optical frequency standards,” in Proceedings of the 28th Annual Precise Time and Time Inteval (PTTI) Applications and Planning Meeting, L. A. Breakiron, ed. (U.S. Naval Observatory, Washington, D.C., 1997), pp. 289–303.

L.-S. Ma, Ph. Courteille, G. Ritter, W. Neuhauser, and R. Blatt, “Precision laser spectrometer with multiple frequency modulation,” in Digest of International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1994), p. 61; Ph. Courteille, L.-S. Ma, G. Ritter, W. Neuhauser, and R. Blatt, “Frequency measurement of Te2 resonances near 467 nm,” Appl. Phys. B 59, 187–193 (1994).
[CrossRef]

S. N. Bagayev, V. P. Chebotayev, A. K. Dmitriyev, A. E. Om, Yu. V. Nekrasov, and B. N. Skvortsov, “Second-order Doppler-free spectroscopy,” Appl. Phys. B: Photophys. Laser Chem. 52, 63–66 (1991); Ch. Chardonnet, F. Guernet, G. Charton, and Ch. J. Bordé, “Ultrahigh-resolution saturation spectroscopy using slow molecules in an external cell,” Appl. Phys. B 59, 333–343 (1994).
[CrossRef]

J. Ye, “Ultrasensitive high resolution laser spectroscopy and its application to optical frequency standards,” Ph.D. dissertation (University of Colorado at Boulder, Boulder, Colo., 1997).

V. S. Letokhev and V. P. Chebotayev, Nonlinear Laser Spectroscopy (Springer-Verlag, Berlin, 1977).

G. T. Scherer, K. K. Lehmann, and W. Klemperer, “The high resolution visible overtone spectrum of acetylene,” J. Chem. Phys. 78, 2817–2832 (1983); K. K. Lehmann, “The absolute intensity of visible overtone bands of acetylene,” J. Chem. Phys. 91, 2759–2760 (1989).
[CrossRef]

R. L. Smith, “Practical solutions of the lock-in detection problem for Lorentz and dispersion resonance signals,” J. Opt. Soc. Am. 61, 1015–1022 (1971); H. Wahlquist, “Modulation broadening of unsaturated Lorentzian lines,” J. Chem. Phys. 35, 1708–1710 (1961).
[CrossRef]

S. Stenholm, Foundation of Laser Spectroscopy (Wiley, New York, 1983).

P. Jungner, S. Swartz, M. Eickhoff, J. Ye, J. L. Hall, and S. Waltman, “Absolute frequency of the molecular iodine transition R(56)32–0 near 532 nm,” IEEE Trans. Instrum. Meas. 44, 151–154 (1995); P. Jungner, M. Eickhoff, S. Swartz, J. Ye, J. L. Hall, and S. Waltman, “Stability and absolute frequency of molecular iodine transitions near 532 nm,” in Laser Frequency Stabilization and Noise Reduction, Y. Shevy, ed., Proc. SPIE 2378, 22–34 (1995); J. L. Hall, L.-S. Ma, M. Taubman, B. Tiemann, F. L. Hong, O. Pfister, and J. Ye, “Stabilization and frequency measurement of the I2-stabilized Nd:YAG laser,” IEEE Trans. Instrum. Meas.IEIMAO 48, 583–586 (1999).
[CrossRef]

M. de Labachelerie, K. Nakagawa, and M. Ohtsu, “Ultranarrow 13C2H2 saturated absorption lines at 1.5 μm,” Opt. Lett. 19, 840–842 (1994); M. de Labachelerie, K. Nakagawa, Y. Awaji, and M. Ohtsu, “High-frequency-stability laser at 1.5 μm using Doppler-free molecular lines,” Opt. Lett. 20, 572–574 (1995); K. Nakagawa, M. de Labachelerie, Y. Awaji, and M. Kurogi, “Accurate optical frequency atlas of the 1.5-μm bands of acetylene,” J. Opt. Soc. Am. B JOBPDE 13, 2708–2714 (1996).
[CrossRef] [PubMed]

L. S. Ma, P. Dubé, J. Ye, and J. L. Hall, “Saturation spectroscopy of molecular overtones for laser frequency standards in the visible and near-visible domain,” in Quantum Electronics and Laser Science Conference, Vol. 16 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), p. 18.

Under shot-noise-limited conditions, the minimum detectable absorption is ΔαL=2[hνB/(ηP0)]1/2/[J0(β)J1(β)]= 3.2×10−7, where P0=0.1 mW, B=1 Hz, β=1, λ=790.7 nm, and η=0.8.

L. S. Ma, J. Ye, P. Dubé, and J. L. Hall, “A new modulation method for sensitive nonlinear spectroscopy—application to molecular overtones as visible frequency references,” in Laser Spectroscopy XII, M. Inguscio, M. Allegrini, and A. Sasso, eds. (World Scientific, Singapore, 1995), pp. 199–203; J. L. Hall, J. Ye, L.-S. Ma, S. Swartz, P. Jungner, and S. Waltman, “Optical frequency standards—some improvements, some measurements, and some dreams,” in Fifth Symposium on Frequency Standards & Metrology, J. C. Bergquist, ed. (World Scientific, Singapore, 1995), pp. 267–276.

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 (17)

Fig. 1
Fig. 1

Conversion of incident power into reflected, built-up, and transmitted powers. Tin, Tout and Lin, Lout, transmissions and losses of input and output coupling mirrors, respectively. Pin, Pr, Pt, cavity input and reflected and transmitted light powers, respectively. Pc, one-way circulating light power.

Fig. 2
Fig. 2

NICE-OHMS detection scheme. Sidebands at δ are used for reflection lock to the cavity; sidebands at Δ, matching the cavity FSR, are used to probe the molecular saturated absorption in cavity transmission. Other abbreviations defined in text.

Fig. 3
Fig. 3

(a) Optical frequency amplitude spectrum showing cavity resonances and two sets of rf sidebands in the input spectrum. (b) Three contributions to the servo error signal from the output of a balanced mixer demodulated at δ. (c) Transmitted amplitude spectrum, no molecular resonance, laser and sidebands precisely locked onto cavity resonances. (d) Transmitted amplitudes, showing a +νm shift of the central cavity resonance owing to molecular resonance. If only the carrier contributes to the servo, the laser still locks onto the cavity resonance center, which has been shifted. (e) Actually three components contribute to the servo, so the laser lock frequency is shifted relative to cavity resonances by a reduced amount x=2νmJ1(β)2.

Fig. 4
Fig. 4

Calculation of molecular signal size and its discrimination curve slope with respect to intracavity gas pressure. Input optical power is fixed at 14.5 mW. The molecular parameters are for P(11) of the C2H2 (ν1+3ν3) band at 790 nm. Assumed cavity finesse, 1.7×104; input and output coupling coefficients, 48 and 8 ppm, respectively; the total absorption and scatter loss, 310 ppm.

Fig. 5
Fig. 5

Experimental configuration for NICE-OHMS. An external stabilizer (AOM–EOM) is employed to widen the frequency servo bandwidth. Sidebands at δ/2π=4 MHz are used for reflection lock to cavity; sidebands at Δ=cavity FSR are used in transmitted light as local oscillators for heterodyne detection of saturated gas absorption inside the cavity. DBM’s, double-balanced mixers; PD’s, photodiodes; R, concave reflector; other abbreviations defined in text.

Fig. 6
Fig. 6

Precision scanning NPRO–HCCD spectrometer, referenced to an I2-stabilized NPRO. rf offset between the two laser systems is implemented by a phase-locked loop. PD’s, photodiodes; APD, avalanche photodiode.

Fig. 7
Fig. 7

(a) Experimental scheme for tracking sideband Δ produced by EOM1 to the cavity FSR. The frequency of the low-noise VCXO needs to be shifted by synthesizer f2 to make f1+f2=Δ match the FSR. (b) Optical spectrum of the input beam. (c) Resultant servo error signal after phase-sensitive detection at Ω. PD1, photodiode, PBS, polarizing beam splitter; other abbreviations defined in text.

Fig. 8
Fig. 8

(a) Triplet spectrum of FM spectroscopy for the P(11) line of the C2H2 (ν1+3ν3) band at 790.7 nm with the NICE-OHMS setup and dither lock-in detection of the first-harmonic signal. Free spectral range, 422 MHz. Distortion of the frequency axis was produced by PZT nonlinearity in these early data: resonances really occur at ±211 MHz. (b) Reduced laser frequency scanning range. (c) Second-harmonic detection signal with the same scanning range as for (b).

Fig. 9
Fig. 9

Frequency scan of C2HD overtone transitions for the ν2+3ν3 band at 1064 nm and overlaid theoretical fit based on the explanation in Ref. 18.

Fig. 10
Fig. 10

Comparison of dc and NICE-OHMS detected molecular resonances under the two experimental conditions of tight and loose laser–cavity locks. The apparent line-center shift between top and bottom traces is an artifact of the data processing.

Fig. 11
Fig. 11

Estimation of noise-equivalent sensitivity based on the S/N obtained by the NICE-OHMS technique and the saturated absorption level measured by dc detection.

Fig. 12
Fig. 12

Pressure-broadening measurement of the overtone transitions. (a) P(11) line in the (ν1+3ν3) overtone band of C2H2 at 790 nm. (b) P(5) line in the (ν2+3ν3) band of C2HD at 1064 nm.

Fig. 13
Fig. 13

Molecular signal slope versus gas pressure. Filled circles, experimental data; solid curves, fitted curves. (a) P(11) line, (b) P(5) line.

Fig. 14
Fig. 14

Signal line shape of intracavity Doppler molecular resonance detected by sideband tracking of the cavity FSR. (a) Theoretical line shape. (b) Experimental data (with integrated time of 1 s and rms noise of 0.1 Hz in each point) and their overlaid fit.

Fig. 15
Fig. 15

(a) NICE OHMS signal used for locking the NPRO–cavity system onto the C2HD resonance. (b) Experimental setup for heterodyne beat between the two MISER systems, one locked on the C2HD resonance and the other frequency doubled and locked onto an I2 reference at 532 nm. Abbreviations defined in text and previous figure captions.

Fig. 16
Fig. 16

Time record of the beat frequency between the two NPRO’s. The frequency offset of 5252.2254±0.0026 MHz in the beat is suppressed. The Allan variance is calculated from these data.

Fig. 17
Fig. 17

Observation of slow molecules in our buildup cavity with low optical power and pressure (1-mW input, 1.8 mTorr). The linewidth is narrowed 13-fold below the transit limit.

Tables (2)

Tables Icon

Table 1 Strengths of C2H2 and C2HD Vibration Overtone Bands at Five Selected Wavelengths

Tables Icon

Table 2 Differences in Experimental Realization of the C2H2 and C2HD Spectrometers

Equations (25)

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

F=2πTout+Tin+Lin+Lout+2αL,
R=PrPin=Tout-Tin+Lin+Lout+2αLTout+Tin+Lin+Lout+2αL2,
T=PtPin=4TinTout(Tout+Tin+Lin+Lout+2αL)2,
E=PcPin=4Tin(Tout+Tin+Lin+Lout+2αL)2.
G=2F/π.
E=E0J0 exp[-i(ωt-ϕx)]+E0J1×exp{-i[(ω+Δ)t+ϕm-ϕx]}-E0J1×exp{-i[(ω-Δ)t+ϕm-ϕx]}.
is=g4J0(β)J1(β)sin(Δt)sin(ϕm),
Signal=2-(Y/D),
Tout=T/(1-T)(Lin+Lout+2αL),
Tin=Tout/T.
Δα=α01+S-α01+2S.
i¯signal2=8eηP0J0(β)J1(β)sin(ϕm)hν2,
i¯noise2=2eB eηhνP0,
(S/N)2=i¯signal2i¯noise2=4ηP0[J0(β)J1(β)sin(ϕm)]2hνB,
ΔαL=πFhνBηP0 1J0(β)J1(β),
exp{i[ωt+β sin(Δt+M sin Ω t)]}=exp(iωt){-J1(β)J1(M)exp[i(-Δ-Ω)t]-J1(β)J0(M)exp(-iΔt)+J1(β)J1(M)exp[i(-Δ+Ω)t)]+J0(β)-J1(β)J1(M)exp[i(Δ-Ω)t]+J1(β)J0(M)exp(iΔt)+J1(β)J1(M)exp[i(Δ+Ω)t]},
Ir=J1(β)2J0(M)J1(M)Re[+Er*(ω+Δ)×Er(ω+Δ+Ω)-Er*(ω-Δ)×Er(ω-Δ+Ω)-Er(ω+Δ)×Er*(ω+Δ-Ω)+Er(ω-Δ)×Er*(ω-Δ-Ω)],
Ir=J1(β)2J0(M)J1(M)Re[+Er*(Δ)×Er(Δ+Ω)-Er*(-Δ)×Er(-Δ+Ω)-Er(Δ)×Er*(Δ-Ω)+Er(-Δ)Er*(-Δ-Ω)].
Isat=1.2×103(Γt/2π+29.8×P)2 W/mm2
(forC2H2at790 nm),
Isat=6.1×103(Γt/2π+34.7×P)2 W/mm2
(forC2HDat1064 nm),
Δn±1=-απ1ΔνDλ2π(d±Δ)exp-(d±Δ)ΔνD2.
Δf±1=-(ν0+d±Δ)Δn±,
Δf=(Δf+1-Δf-1)/2.

Metrics