Abstract

Strong self-locking phenomena are observed when laser power is converted into heat by a weakly absorbing medium within a high-finesse cavity. Deposited heat leads to increased temperature and, for the case of weakly absorbing intracavity gases studied here, to an associated reduction of density and refractive index. This thermal change in refractive index provides self-acting cavity tuning near resonant conditions. In the experiments reported here a Fabry–Perot cavity of finesse 274 was filled with acetylene gas and illuminated with a titanium:sapphire laser tuned to the P(11) line of the ν1 + 3ν3 overtone band near 790 nm. The dependencies of maximum frequency-locking range on gas pressure, laser power, and laser frequency sweep rate and direction were measured and could be well unified by analysis based on the thermal model. In the domain of strong self-tuning an interesting self-sustained oscillation was observed, with its several sharp frequencies directly and quantitatively linked to the acoustic boundary conditions in our cylindrical cell geometry. The differences between the behavior of acetylene near 790 nm and molecular oxygen with electronic transition near 763 nm are instructive; whereas the absorbed powers were similar, they differed strongly in their rates for internal to translational energy conversion by collisional relaxation.

© 1996 Optical Society of America

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References

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  1. 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]
  2. K. Nakagawa, M. de Labachelerie, Y. Awaji, M. Kourogi, T. Enami, and M. Ohtsu, “Highly precise 1-THz optical frequency-difference measurement of 1.5-µm molecular absorption lines,” Opt. Lett. 20, 410–412 (1995).
    [CrossRef]
  3. L.-S. Ma, P. Dubé, P. Jungner, J. Ye, and J. L. Hall, “Saturation spectroscopy of molecular overtones for laser frequency standards in visible and near-visible domains,” 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.
  4. T. N. C. Venkatesan, H. M. Gibbs, S. L. McCall, A. Passner, A. C. Gossard, and W. W. Wiegman, “Optical pulse tailoring and termination by self-sweeping of a Fabry-Pérot cavity,” Opt. Commun. 31, 228–230 (1979).
    [CrossRef]
  5. K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de Labachelerie, and M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
    [CrossRef]
  6. 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]
  7. D. E. Burch and D. A. Gryvnak, “Strengths, widths, and shapes of the oxygen lines near 13,100 cm-1 (7620 Å),” Appl. Opt. 8, 1493–1499 (1969).
    [CrossRef] [PubMed]
  8. J. H. Miller, R. W. Boese, and L. P. Giver, “Intensity measurements and rotational intensity distribution for the oxygen A-band,” J. Quant. Spectrosc. Radiat. Transfer 9, 1507–1517 (1969).
    [CrossRef]
  9. Oscilloscope, LeCroy Model 9410; FFT spectrum analyzer, Stanford Research Systems SR760. This information is provided for the purpose of technical completeness and not as a product or company endorsement.
  10. B. H. Armstrong, “Spectrum line profiles: the Voigt function,” J. Quant. Spectrosc. Radiat. Transfer 7, 61–88 (1967).
    [CrossRef]
  11. P. M. Morse and F. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), parts I and II.
  12. L’Air Liquide, Division Scientifique, Encyclopédie des Gaz (Elsevier/North-Holland, New York, 1976).
  13. A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif.1986).
  14. C. P. Rinsland, A. Baldacci, and K. N. Rao, “Acetylene bands observed in carbon stars: a laboratory study and an illustrative example of its application to IRC+10216,” Astrophys. J. Suppl. Ser. 49, 487–513 (1982).
    [CrossRef]
  15. J. D. Lambert and R. Salter, “Vibrational relaxation in gases,” Proc. R. Soc. London Ser. A 253, 277–288 (1959).
    [CrossRef]
  16. H. Gröber, S. Erk, and U. Grigull, Fundamentals of Heat Transfer (McGraw-Hill, New York, 1961), Chap. 14, p. 317.
  17. D. R. Lide, ed., CRC Handbook of Chemistry and Physics, 74th ed. (CRC, Boca Raton, Fla., 1993–1994).
  18. The self-diffusion coefficient of C2H2 at room temperature was calculated based on the average cross section obtained from thermal conductivity and viscosity. Numerical values for these properties were taken from Ref. 17.
  19. L. R. Martin, R. B. Cohen, and J. F. Schatz, “Quenching of laser induced fluorescence of O2 (b1Σg+) by O2 and N2,” Chem. Phys. Lett. 41, 394–396 (1976).
    [CrossRef]
  20. H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966).
    [CrossRef] [PubMed]
  21. R. T. Bailey, F. R. Cruickshank, R. Guthrie, D. Pugh, and I. J. M. Weir, “Short time-scale effects in the pulsed source thermal lens,” Mol. Phys. 48, 81–95 (1983); M.-C. Gagné and S. L. Chin, “Energy relaxation time in a gas mixture measured by a photothermal probe beam deflection technique,” Appl. Phys. B 52, 352–358 (1991).
    [CrossRef]

1995 (1)

1994 (2)

K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de Labachelerie, and M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
[CrossRef]

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]

1993 (1)

1983 (1)

R. T. Bailey, F. R. Cruickshank, R. Guthrie, D. Pugh, and I. J. M. Weir, “Short time-scale effects in the pulsed source thermal lens,” Mol. Phys. 48, 81–95 (1983); M.-C. Gagné and S. L. Chin, “Energy relaxation time in a gas mixture measured by a photothermal probe beam deflection technique,” Appl. Phys. B 52, 352–358 (1991).
[CrossRef]

1982 (1)

C. P. Rinsland, A. Baldacci, and K. N. Rao, “Acetylene bands observed in carbon stars: a laboratory study and an illustrative example of its application to IRC+10216,” Astrophys. J. Suppl. Ser. 49, 487–513 (1982).
[CrossRef]

1979 (1)

T. N. C. Venkatesan, H. M. Gibbs, S. L. McCall, A. Passner, A. C. Gossard, and W. W. Wiegman, “Optical pulse tailoring and termination by self-sweeping of a Fabry-Pérot cavity,” Opt. Commun. 31, 228–230 (1979).
[CrossRef]

1976 (1)

L. R. Martin, R. B. Cohen, and J. F. Schatz, “Quenching of laser induced fluorescence of O2 (b1Σg+) by O2 and N2,” Chem. Phys. Lett. 41, 394–396 (1976).
[CrossRef]

1969 (2)

D. E. Burch and D. A. Gryvnak, “Strengths, widths, and shapes of the oxygen lines near 13,100 cm-1 (7620 Å),” Appl. Opt. 8, 1493–1499 (1969).
[CrossRef] [PubMed]

J. H. Miller, R. W. Boese, and L. P. Giver, “Intensity measurements and rotational intensity distribution for the oxygen A-band,” J. Quant. Spectrosc. Radiat. Transfer 9, 1507–1517 (1969).
[CrossRef]

1967 (1)

B. H. Armstrong, “Spectrum line profiles: the Voigt function,” J. Quant. Spectrosc. Radiat. Transfer 7, 61–88 (1967).
[CrossRef]

1966 (1)

1959 (1)

J. D. Lambert and R. Salter, “Vibrational relaxation in gases,” Proc. R. Soc. London Ser. A 253, 277–288 (1959).
[CrossRef]

Armstrong, B. H.

B. H. Armstrong, “Spectrum line profiles: the Voigt function,” J. Quant. Spectrosc. Radiat. Transfer 7, 61–88 (1967).
[CrossRef]

Awaji, Y.

Bailey, R. T.

R. T. Bailey, F. R. Cruickshank, R. Guthrie, D. Pugh, and I. J. M. Weir, “Short time-scale effects in the pulsed source thermal lens,” Mol. Phys. 48, 81–95 (1983); M.-C. Gagné and S. L. Chin, “Energy relaxation time in a gas mixture measured by a photothermal probe beam deflection technique,” Appl. Phys. B 52, 352–358 (1991).
[CrossRef]

Baldacci, A.

C. P. Rinsland, A. Baldacci, and K. N. Rao, “Acetylene bands observed in carbon stars: a laboratory study and an illustrative example of its application to IRC+10216,” Astrophys. J. Suppl. Ser. 49, 487–513 (1982).
[CrossRef]

Boese, R. W.

J. H. Miller, R. W. Boese, and L. P. Giver, “Intensity measurements and rotational intensity distribution for the oxygen A-band,” J. Quant. Spectrosc. Radiat. Transfer 9, 1507–1517 (1969).
[CrossRef]

Burch, D. E.

Cohen, R. B.

L. R. Martin, R. B. Cohen, and J. F. Schatz, “Quenching of laser induced fluorescence of O2 (b1Σg+) by O2 and N2,” Chem. Phys. Lett. 41, 394–396 (1976).
[CrossRef]

Cruickshank, F. R.

R. T. Bailey, F. R. Cruickshank, R. Guthrie, D. Pugh, and I. J. M. Weir, “Short time-scale effects in the pulsed source thermal lens,” Mol. Phys. 48, 81–95 (1983); M.-C. Gagné and S. L. Chin, “Energy relaxation time in a gas mixture measured by a photothermal probe beam deflection technique,” Appl. Phys. B 52, 352–358 (1991).
[CrossRef]

de Labachelerie, M.

Di Lonardo, G.

Dubé, P.

L.-S. Ma, P. Dubé, P. Jungner, J. Ye, and J. L. Hall, “Saturation spectroscopy of molecular overtones for laser frequency standards in visible and near-visible domains,” 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.

Enami, T.

Erk, S.

H. Gröber, S. Erk, and U. Grigull, Fundamentals of Heat Transfer (McGraw-Hill, New York, 1961), Chap. 14, p. 317.

Ernst, K.

Feshbach, F.

P. M. Morse and F. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), parts I and II.

Gibbs, H. M.

T. N. C. Venkatesan, H. M. Gibbs, S. L. McCall, A. Passner, A. C. Gossard, and W. W. Wiegman, “Optical pulse tailoring and termination by self-sweeping of a Fabry-Pérot cavity,” Opt. Commun. 31, 228–230 (1979).
[CrossRef]

Giver, L. P.

J. H. Miller, R. W. Boese, and L. P. Giver, “Intensity measurements and rotational intensity distribution for the oxygen A-band,” J. Quant. Spectrosc. Radiat. Transfer 9, 1507–1517 (1969).
[CrossRef]

Gossard, A. C.

T. N. C. Venkatesan, H. M. Gibbs, S. L. McCall, A. Passner, A. C. Gossard, and W. W. Wiegman, “Optical pulse tailoring and termination by self-sweeping of a Fabry-Pérot cavity,” Opt. Commun. 31, 228–230 (1979).
[CrossRef]

Grigull, U.

H. Gröber, S. Erk, and U. Grigull, Fundamentals of Heat Transfer (McGraw-Hill, New York, 1961), Chap. 14, p. 317.

Gröber, H.

H. Gröber, S. Erk, and U. Grigull, Fundamentals of Heat Transfer (McGraw-Hill, New York, 1961), Chap. 14, p. 317.

Gryvnak, D. A.

Guthrie, R.

R. T. Bailey, F. R. Cruickshank, R. Guthrie, D. Pugh, and I. J. M. Weir, “Short time-scale effects in the pulsed source thermal lens,” Mol. Phys. 48, 81–95 (1983); M.-C. Gagné and S. L. Chin, “Energy relaxation time in a gas mixture measured by a photothermal probe beam deflection technique,” Appl. Phys. B 52, 352–358 (1991).
[CrossRef]

Hall, J. L.

L.-S. Ma, P. Dubé, P. Jungner, J. Ye, and J. L. Hall, “Saturation spectroscopy of molecular overtones for laser frequency standards in visible and near-visible domains,” 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.

Inguscio, M.

Jungner, P.

L.-S. Ma, P. Dubé, P. Jungner, J. Ye, and J. L. Hall, “Saturation spectroscopy of molecular overtones for laser frequency standards in visible and near-visible domains,” 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.

Katsuda, T.

K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de Labachelerie, and M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
[CrossRef]

Kogelnik, H.

Kourogi, M.

Lambert, J. D.

J. D. Lambert and R. Salter, “Vibrational relaxation in gases,” Proc. R. Soc. London Ser. A 253, 277–288 (1959).
[CrossRef]

Li, T.

Ma, L.-S.

L.-S. Ma, P. Dubé, P. Jungner, J. Ye, and J. L. Hall, “Saturation spectroscopy of molecular overtones for laser frequency standards in visible and near-visible domains,” 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.

Marin, F.

Martin, L. R.

L. R. Martin, R. B. Cohen, and J. F. Schatz, “Quenching of laser induced fluorescence of O2 (b1Σg+) by O2 and N2,” Chem. Phys. Lett. 41, 394–396 (1976).
[CrossRef]

McCall, S. L.

T. N. C. Venkatesan, H. M. Gibbs, S. L. McCall, A. Passner, A. C. Gossard, and W. W. Wiegman, “Optical pulse tailoring and termination by self-sweeping of a Fabry-Pérot cavity,” Opt. Commun. 31, 228–230 (1979).
[CrossRef]

Miller, J. H.

J. H. Miller, R. W. Boese, and L. P. Giver, “Intensity measurements and rotational intensity distribution for the oxygen A-band,” J. Quant. Spectrosc. Radiat. Transfer 9, 1507–1517 (1969).
[CrossRef]

Morse, P. M.

P. M. Morse and F. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), parts I and II.

Nakagawa, K.

Ohtsu, M.

Passner, A.

T. N. C. Venkatesan, H. M. Gibbs, S. L. McCall, A. Passner, A. C. Gossard, and W. W. Wiegman, “Optical pulse tailoring and termination by self-sweeping of a Fabry-Pérot cavity,” Opt. Commun. 31, 228–230 (1979).
[CrossRef]

Pavone, F. S.

Pugh, D.

R. T. Bailey, F. R. Cruickshank, R. Guthrie, D. Pugh, and I. J. M. Weir, “Short time-scale effects in the pulsed source thermal lens,” Mol. Phys. 48, 81–95 (1983); M.-C. Gagné and S. L. Chin, “Energy relaxation time in a gas mixture measured by a photothermal probe beam deflection technique,” Appl. Phys. B 52, 352–358 (1991).
[CrossRef]

Rao, K. N.

C. P. Rinsland, A. Baldacci, and K. N. Rao, “Acetylene bands observed in carbon stars: a laboratory study and an illustrative example of its application to IRC+10216,” Astrophys. J. Suppl. Ser. 49, 487–513 (1982).
[CrossRef]

Rinsland, C. P.

C. P. Rinsland, A. Baldacci, and K. N. Rao, “Acetylene bands observed in carbon stars: a laboratory study and an illustrative example of its application to IRC+10216,” Astrophys. J. Suppl. Ser. 49, 487–513 (1982).
[CrossRef]

Salter, R.

J. D. Lambert and R. Salter, “Vibrational relaxation in gases,” Proc. R. Soc. London Ser. A 253, 277–288 (1959).
[CrossRef]

Schatz, J. F.

L. R. Martin, R. B. Cohen, and J. F. Schatz, “Quenching of laser induced fluorescence of O2 (b1Σg+) by O2 and N2,” Chem. Phys. Lett. 41, 394–396 (1976).
[CrossRef]

Shelkovnikov, A. S.

K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de Labachelerie, and M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif.1986).

Venkatesan, T. N. C.

T. N. C. Venkatesan, H. M. Gibbs, S. L. McCall, A. Passner, A. C. Gossard, and W. W. Wiegman, “Optical pulse tailoring and termination by self-sweeping of a Fabry-Pérot cavity,” Opt. Commun. 31, 228–230 (1979).
[CrossRef]

Weir, I. J. M.

R. T. Bailey, F. R. Cruickshank, R. Guthrie, D. Pugh, and I. J. M. Weir, “Short time-scale effects in the pulsed source thermal lens,” Mol. Phys. 48, 81–95 (1983); M.-C. Gagné and S. L. Chin, “Energy relaxation time in a gas mixture measured by a photothermal probe beam deflection technique,” Appl. Phys. B 52, 352–358 (1991).
[CrossRef]

Wiegman, W. W.

T. N. C. Venkatesan, H. M. Gibbs, S. L. McCall, A. Passner, A. C. Gossard, and W. W. Wiegman, “Optical pulse tailoring and termination by self-sweeping of a Fabry-Pérot cavity,” Opt. Commun. 31, 228–230 (1979).
[CrossRef]

Ye, J.

L.-S. Ma, P. Dubé, P. Jungner, J. Ye, and J. L. Hall, “Saturation spectroscopy of molecular overtones for laser frequency standards in visible and near-visible domains,” 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.

Appl. Opt. (3)

Astrophys. J. Suppl. Ser. (1)

C. P. Rinsland, A. Baldacci, and K. N. Rao, “Acetylene bands observed in carbon stars: a laboratory study and an illustrative example of its application to IRC+10216,” Astrophys. J. Suppl. Ser. 49, 487–513 (1982).
[CrossRef]

Chem. Phys. Lett. (1)

L. R. Martin, R. B. Cohen, and J. F. Schatz, “Quenching of laser induced fluorescence of O2 (b1Σg+) by O2 and N2,” Chem. Phys. Lett. 41, 394–396 (1976).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (2)

B. H. Armstrong, “Spectrum line profiles: the Voigt function,” J. Quant. Spectrosc. Radiat. Transfer 7, 61–88 (1967).
[CrossRef]

J. H. Miller, R. W. Boese, and L. P. Giver, “Intensity measurements and rotational intensity distribution for the oxygen A-band,” J. Quant. Spectrosc. Radiat. Transfer 9, 1507–1517 (1969).
[CrossRef]

Mol. Phys. (1)

R. T. Bailey, F. R. Cruickshank, R. Guthrie, D. Pugh, and I. J. M. Weir, “Short time-scale effects in the pulsed source thermal lens,” Mol. Phys. 48, 81–95 (1983); M.-C. Gagné and S. L. Chin, “Energy relaxation time in a gas mixture measured by a photothermal probe beam deflection technique,” Appl. Phys. B 52, 352–358 (1991).
[CrossRef]

Opt. Commun. (2)

T. N. C. Venkatesan, H. M. Gibbs, S. L. McCall, A. Passner, A. C. Gossard, and W. W. Wiegman, “Optical pulse tailoring and termination by self-sweeping of a Fabry-Pérot cavity,” Opt. Commun. 31, 228–230 (1979).
[CrossRef]

K. Nakagawa, T. Katsuda, A. S. Shelkovnikov, M. de Labachelerie, and M. Ohtsu, “Highly sensitive detection of molecular absorption using a high finesse optical cavity,” Opt. Commun. 107, 369–372 (1994).
[CrossRef]

Opt. Lett. (2)

Proc. R. Soc. London Ser. A (1)

J. D. Lambert and R. Salter, “Vibrational relaxation in gases,” Proc. R. Soc. London Ser. A 253, 277–288 (1959).
[CrossRef]

Other (8)

H. Gröber, S. Erk, and U. Grigull, Fundamentals of Heat Transfer (McGraw-Hill, New York, 1961), Chap. 14, p. 317.

D. R. Lide, ed., CRC Handbook of Chemistry and Physics, 74th ed. (CRC, Boca Raton, Fla., 1993–1994).

The self-diffusion coefficient of C2H2 at room temperature was calculated based on the average cross section obtained from thermal conductivity and viscosity. Numerical values for these properties were taken from Ref. 17.

P. M. Morse and F. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), parts I and II.

L’Air Liquide, Division Scientifique, Encyclopédie des Gaz (Elsevier/North-Holland, New York, 1976).

A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif.1986).

L.-S. Ma, P. Dubé, P. Jungner, J. Ye, and J. L. Hall, “Saturation spectroscopy of molecular overtones for laser frequency standards in visible and near-visible domains,” 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.

Oscilloscope, LeCroy Model 9410; FFT spectrum analyzer, Stanford Research Systems SR760. This information is provided for the purpose of technical completeness and not as a product or company endorsement.

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Figures (10)

Fig. 1
Fig. 1

Demonstration of cavity self-locking to the laser frequency obtained by shining 140 mW of power from a free-running titanium: sapphire laser onto a Fabry–Perot cavity of finesse 274 filled with 20 Torr of acetylene gas. The laser was tuned near the P(11) line center of the ν1+3ν3 overtone band of acetylene at 790.7 nm. The slow, upward trend indicates a frequency drift of the laser toward higher frequencies.

Fig. 2
Fig. 2

Experimental configuration. The laser was intensity stabilized, and its free-running noise linewidth was ⩽1 MHz. Sweep rates were adjustable. With 140 mW of incident laser radiation the Fabry–Perot cavity built up 10 W of circulating power when there was no gas absorption. Cavity transmission was monitored with photodiode PD1, and the signals were recorded with a digital oscilloscope. FFT, fast Fourier transform; L1–L3, lenses; P.B.S., polarizing beam splitter. Photodiode PD2 monitored the laser output for intensity stabilization.

Fig. 3
Fig. 3

(a) Cavity transmission as a function of laser frequency over 11 consecutive cavity resonance modes. In this blue scan the P(11) absorption line shape for an acetylene pressure of 20 Torr is outlined by the reduced transmission maxima. Note that the effective absorption path length (2FL/π, where L is the cavity length) decreases with gas absorption, resulting in a broader observed linewidth. (b) Close-up of two cavity modes illustrating the change in the transmission widths caused by molecular absorption. For these figures the laser power was 140 mW and the sweeping rate was ∼10 GHz/s. The cavity transmission given in this figure and the following ones (unless otherwise specified) gives the ratio of transmission with and without gas absorption. It should not be confused with overall cavity transmission, which is limited to 51% at 790 nm for the present cavity when empty.

Fig. 4
Fig. 4

Cavity transmission for laser sweeping toward a resonance with (a) increasing frequency and (b) decreasing frequency. These scans were obtained near P(11) line center with a laser power of 165 mW, a sweeping rate of 100 MHz/s, and an acetylene pressure of 20 Torr. For comparison, a 3.1-MHz FWHM Lorentzian profile is given in (a). Its width was computed based on round-trip gas absorption at line center (Ag = 0.020) and cavity losses. In (b) the recorded sharp transmission peak is indicated by a dashed line because it was not properly sampled by the oscilloscope. The horizontal 10.8-MHz line gives the calculated position of the transmission spike from the cold cavity line center (cf. Subsection 4.A).

Fig. 5
Fig. 5

Blue scans for different acetylene pressures. The laser was tuned near P(11) line center and swept at a rate of 100 MHz/s. Laser powers were 145, 165, and 150 mW for, respectively, pressures of 4, 20, and 90 Torr. The asterisks are computed cavity transmissions for the laser tuned in simultaneous coincidence with P(11) line center and a cavity resonance.

Fig. 6
Fig. 6

Blue and red scans across a cavity resonance for three sweeping rates. The laser was tuned near P(11) line center and delivered ∼140 mW of power on the cavity filled with 90 Torr of acetylene.

Fig. 7
Fig. 7

Comparison of self-locking behavior obtained with 90 Torr of oxygen or acetylene in the Fabry–Perot cavity. For oxygen, laser power near 763 nm was 120 mW; for acetylene, near 790 nm, the power was 150 mW. In both cases the sweeping rates were 100 MHz/s. As discussed in the text, absorption properties are very similar. The large difference in self-locking arises from slow electronic-to-translational energy conversion in the oxygen gas. See Fig. 10 below for the resulting spatial temperature profiles.

Fig. 8
Fig. 8

(a) Blue scan taken with 400 Torr of acetylene and 140 mW of laser power. This scan covered 12 cavity modes. The first ramp coincides with P(11) line center, located at zero detuning. (b) Scan across two cavity modes taken with the laser tuned ∼12 FSR’s from line center. It shows the region on the transmission ramps where oscillations occurred. (c) Time-resolved record of the 42.5-kHz oscillations observed ∼6.5 GHz to the blue from line center.

Fig. 9
Fig. 9

Frequency spectrum of acoustic resonances in the cavity self-tuning experiment. The experimental conditions were identical to those of Fig. 8. (a) Power above threshold for 42.5-kHz oscillation, showing some second harmonic. One feature at 11.25 kHz and the sidebands arise from intensity AM produced by the laser intracavity Mach–Zehnder servo dither. (b) Spectrum obtained with laser tuned further to the red for near-threshold conditions [cf. Fig. 8(b)]. Lines identified with asterisks are from the étalon dither. (c) Vertical bars show six calculated acoustic eigenmode frequencies based uniquely on the room-temperature speed of sound in acetylene (341 m/s) and the 0.978-cm bore diameter of our cell (cf. Subsection 3.F). In order of increasing frequencies, these eigenmodes are (m, n) = (1,1), (2, 1), (0, 2), (1, 2), (0, 3), (1, 3). (d) Density plots, representing the pressure amplitude across the cavity bore, are given for some of these resonances. Pressure nodes appear as middle gray values, and maxima appear as either light or dark values.

Fig. 10
Fig. 10

Calculated excited-state population densities of oxygen and acetylene molecules as a function of distance, from center r/a = 0 to wall (a is the bore radius). (b) Temperature profiles for driven heat-diffusion equations, with spatially distributed heat input from (a) above. The relevant parameters are summarized in Table 1.

Tables (1)

Tables Icon

Table 1 Physical Parameters for the Diffusion and Heat Equations

Equations (26)

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ν=c2nl(q+κ),
n-1=KGDρ,
Δν=νc-ν0=-ν0nKGDΔρ,
Pg=AgPc=(Ag/t)Pt.
Pto=4tt(F/2π)2P0,
F=2πAc+Ag.
Δν=ν0KGDnTwρΔT,
Pg0=4tAg(Ac+Ag)2P0.
Pg0(νc-ν0)max(νc-ν0)=Pg01+νL-νcΔ2,
ΔT=B(Δν/P),
Dd2n*dr2+Drdn*dr-n*τ+f(r)=0,
n*(a)=0,dn*dr(0)=0,
f(r)=Pghν1V00exp(-2r2/w02),
λcd2θdr2+λcrdθdr+hντn*(r)=0,
θ(a)=0, dθdr(0)=0.
Tm-Tw=θm=4w020ξθ(r)rdr.
n(r)-n(0)=KGDρwθ(0)-θ(r)Tw,
n(r)-n(0)=1/2n2r2.
n2=5.4×10-4ΔT cm-2.
n2=βΔTKGDρwTw.
Δν=(ν0/β)n2,
tδn*hντt(δPg),
δν(t)ν0=-KGDδρa sin(ωt).
δPg(t)=Pg0dL(x)dxδν(t)=-983Pg0δν(t)Δ,
tδPg=ω983ν0KGDPg0Δδρa cos ωt.
Pg0Δ=16πtFSRP0Ag(Ac+Ag)3.

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