Abstract

In our continuous wave cavity ring-down spectroscopy (CW-CRDS) experiments, we have often observed that the decay time constant drops to a lower value at some cavity lengths or some intercavity pressures. The resulting instabilities lead to a reduction in the sensitivity of our CRDS system. We have deduced that the cause of this noise is the coupling between the TEM00 mode that the laser excites, and the higher order transverse modes of the cavity. The coupling will cause anti-crossings as the modes tune with cavity length. A consequence is that the decay of light intensity leaving the cavity is no longer a single exponential decay, but the signal can be quantitatively fit to a two-mode beating model. With a 4mm diameter intra-cavity aperture, the higher order modes are suppressed and the stability of the system improved greatly. One coupling mechanism is scattering from the mirror surfaces. This can explain some features of our data including the strength of this coupling and the relative tuning rate of the coupled modes. Remarkably, a scattering intensity between modes of ~ 10-12 can produce observable changes in the cavity decay rate. However, the tuning rate between the TEM00 mode and the higher order modes in a cavity pressure scan is larger than predicted and is still not explained. Images of higher order transverse modes excited at certain cavity conditions were recorded by an Indium Gallium Arsenide (InGaAs) area camera.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. O’Keefe and D. A. G. Deacon, "Cavity Ring-Down Optical Spectrometer for absoption measurements using Pulsed Laser Sources," Rev. Sci. Instrum. 59, 2544 (1988).
    [CrossRef]
  2. D. Romanini and K. K. Lehmann, "Ring-down cavity absorption spectroscopy of the very weak HCN overtone bands with six, seven, and eight stretching quanta," J. Chem. Phys. 99, 6287-6301 (1993).
    [CrossRef]
  3. K. K. Lehmann, "Ring-down cavity spectroscopy cell using continuous wave excitation for trace species detection, U.S. Patent 5,528,040," (1996).
  4. J. Dudek, P. Rabinowitz, K. K. Lehmann, and A. Velasquez, "Trace gas detection with cw cavity ring-down laser absorption spectroscopy," in 52nd Ohio State University International Symposium on Molecular Spectroscopy, p. 36 WG05 (Columbus OH, June 1997), http://molspect.chemistry.ohio-state.edu/symposium 52/Abstracts/p346.pdf.
  5. D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stoeckel, "CW cavity ring down spectroscopy," Chem. Phys. Lett. 264, 316-322 (1997).
    [CrossRef]
  6. J. B. Dudek, P. B. Tarsa, A. Velasquez, M. Wladyslawski, P. Rabinowitz, and K. K. Lehmann, "Trace moisture detection using continuous-wave cavity ring-down spectroscopy," Anal. Chem. 75, 4599-4605 (2003).
    [CrossRef] [PubMed]
  7. P. R. Bevington and D. K. Robinson, Data reduction and error analysis for the Physical Sciences, 2nd ed. (McGraw-Hill Inc., 1992). pp 96, 141 and 69.
  8. A. E. Siegman, Lasers (University Science Books, Mill Valley, California, 1986). Pp. 691 and 762.
  9. P. Horowitz and W. Hill, The Art of Electronics, 2nd ed. (Cambridge University Press, 1989). Pp. 430.
  10. K. K. Lehmann and D. Romanini, "The superposition principle and cavity ring-down spectroscopy," J. Chem. Phys. 105, 10,263-10,277 (1996).
    [CrossRef]
  11. C. Cohen-Tannoudji, B. Diu, and F. Laloe, Quantum Mechanics, (John Wiley & Sons, 1977) Vol. 1, pp. 405.
  12. J. C. Stover, Optical Scattering, Measurement, and Analysis (McGraw-Hill Inc., 1990).
  13. T. Klaassen, J. D. Jong, M. V. Exter, and J. P. Woerdman, "Transverse mode coupling in an optical resonator," Opt. Lett. 30, 1959-1961 (2005).
    [CrossRef] [PubMed]

2005 (1)

2003 (1)

J. B. Dudek, P. B. Tarsa, A. Velasquez, M. Wladyslawski, P. Rabinowitz, and K. K. Lehmann, "Trace moisture detection using continuous-wave cavity ring-down spectroscopy," Anal. Chem. 75, 4599-4605 (2003).
[CrossRef] [PubMed]

1997 (1)

D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stoeckel, "CW cavity ring down spectroscopy," Chem. Phys. Lett. 264, 316-322 (1997).
[CrossRef]

1996 (1)

K. K. Lehmann and D. Romanini, "The superposition principle and cavity ring-down spectroscopy," J. Chem. Phys. 105, 10,263-10,277 (1996).
[CrossRef]

1993 (1)

D. Romanini and K. K. Lehmann, "Ring-down cavity absorption spectroscopy of the very weak HCN overtone bands with six, seven, and eight stretching quanta," J. Chem. Phys. 99, 6287-6301 (1993).
[CrossRef]

1988 (1)

A. O’Keefe and D. A. G. Deacon, "Cavity Ring-Down Optical Spectrometer for absoption measurements using Pulsed Laser Sources," Rev. Sci. Instrum. 59, 2544 (1988).
[CrossRef]

Deacon, D. A. G.

A. O’Keefe and D. A. G. Deacon, "Cavity Ring-Down Optical Spectrometer for absoption measurements using Pulsed Laser Sources," Rev. Sci. Instrum. 59, 2544 (1988).
[CrossRef]

Dudek, J. B.

J. B. Dudek, P. B. Tarsa, A. Velasquez, M. Wladyslawski, P. Rabinowitz, and K. K. Lehmann, "Trace moisture detection using continuous-wave cavity ring-down spectroscopy," Anal. Chem. 75, 4599-4605 (2003).
[CrossRef] [PubMed]

Exter, M. V.

Jong, J. D.

Kachanov, A. A.

D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stoeckel, "CW cavity ring down spectroscopy," Chem. Phys. Lett. 264, 316-322 (1997).
[CrossRef]

Klaassen, T.

Lehmann, K. K.

J. B. Dudek, P. B. Tarsa, A. Velasquez, M. Wladyslawski, P. Rabinowitz, and K. K. Lehmann, "Trace moisture detection using continuous-wave cavity ring-down spectroscopy," Anal. Chem. 75, 4599-4605 (2003).
[CrossRef] [PubMed]

K. K. Lehmann and D. Romanini, "The superposition principle and cavity ring-down spectroscopy," J. Chem. Phys. 105, 10,263-10,277 (1996).
[CrossRef]

D. Romanini and K. K. Lehmann, "Ring-down cavity absorption spectroscopy of the very weak HCN overtone bands with six, seven, and eight stretching quanta," J. Chem. Phys. 99, 6287-6301 (1993).
[CrossRef]

O’Keefe, A.

A. O’Keefe and D. A. G. Deacon, "Cavity Ring-Down Optical Spectrometer for absoption measurements using Pulsed Laser Sources," Rev. Sci. Instrum. 59, 2544 (1988).
[CrossRef]

Rabinowitz, P.

J. B. Dudek, P. B. Tarsa, A. Velasquez, M. Wladyslawski, P. Rabinowitz, and K. K. Lehmann, "Trace moisture detection using continuous-wave cavity ring-down spectroscopy," Anal. Chem. 75, 4599-4605 (2003).
[CrossRef] [PubMed]

Romanini, D.

D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stoeckel, "CW cavity ring down spectroscopy," Chem. Phys. Lett. 264, 316-322 (1997).
[CrossRef]

K. K. Lehmann and D. Romanini, "The superposition principle and cavity ring-down spectroscopy," J. Chem. Phys. 105, 10,263-10,277 (1996).
[CrossRef]

D. Romanini and K. K. Lehmann, "Ring-down cavity absorption spectroscopy of the very weak HCN overtone bands with six, seven, and eight stretching quanta," J. Chem. Phys. 99, 6287-6301 (1993).
[CrossRef]

Sadeghi, N.

D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stoeckel, "CW cavity ring down spectroscopy," Chem. Phys. Lett. 264, 316-322 (1997).
[CrossRef]

Stoeckel, F.

D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stoeckel, "CW cavity ring down spectroscopy," Chem. Phys. Lett. 264, 316-322 (1997).
[CrossRef]

Tarsa, P. B.

J. B. Dudek, P. B. Tarsa, A. Velasquez, M. Wladyslawski, P. Rabinowitz, and K. K. Lehmann, "Trace moisture detection using continuous-wave cavity ring-down spectroscopy," Anal. Chem. 75, 4599-4605 (2003).
[CrossRef] [PubMed]

Velasquez, A.

J. B. Dudek, P. B. Tarsa, A. Velasquez, M. Wladyslawski, P. Rabinowitz, and K. K. Lehmann, "Trace moisture detection using continuous-wave cavity ring-down spectroscopy," Anal. Chem. 75, 4599-4605 (2003).
[CrossRef] [PubMed]

Wladyslawski, M.

J. B. Dudek, P. B. Tarsa, A. Velasquez, M. Wladyslawski, P. Rabinowitz, and K. K. Lehmann, "Trace moisture detection using continuous-wave cavity ring-down spectroscopy," Anal. Chem. 75, 4599-4605 (2003).
[CrossRef] [PubMed]

Woerdman, J. P.

Anal. Chem. (1)

J. B. Dudek, P. B. Tarsa, A. Velasquez, M. Wladyslawski, P. Rabinowitz, and K. K. Lehmann, "Trace moisture detection using continuous-wave cavity ring-down spectroscopy," Anal. Chem. 75, 4599-4605 (2003).
[CrossRef] [PubMed]

Chem. Phys. Lett. (1)

D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stoeckel, "CW cavity ring down spectroscopy," Chem. Phys. Lett. 264, 316-322 (1997).
[CrossRef]

J. Chem. Phys. (2)

D. Romanini and K. K. Lehmann, "Ring-down cavity absorption spectroscopy of the very weak HCN overtone bands with six, seven, and eight stretching quanta," J. Chem. Phys. 99, 6287-6301 (1993).
[CrossRef]

K. K. Lehmann and D. Romanini, "The superposition principle and cavity ring-down spectroscopy," J. Chem. Phys. 105, 10,263-10,277 (1996).
[CrossRef]

Opt. Lett. (1)

Rev. Sci. Instrum. (1)

A. O’Keefe and D. A. G. Deacon, "Cavity Ring-Down Optical Spectrometer for absoption measurements using Pulsed Laser Sources," Rev. Sci. Instrum. 59, 2544 (1988).
[CrossRef]

Other (7)

K. K. Lehmann, "Ring-down cavity spectroscopy cell using continuous wave excitation for trace species detection, U.S. Patent 5,528,040," (1996).

J. Dudek, P. Rabinowitz, K. K. Lehmann, and A. Velasquez, "Trace gas detection with cw cavity ring-down laser absorption spectroscopy," in 52nd Ohio State University International Symposium on Molecular Spectroscopy, p. 36 WG05 (Columbus OH, June 1997), http://molspect.chemistry.ohio-state.edu/symposium 52/Abstracts/p346.pdf.

P. R. Bevington and D. K. Robinson, Data reduction and error analysis for the Physical Sciences, 2nd ed. (McGraw-Hill Inc., 1992). pp 96, 141 and 69.

A. E. Siegman, Lasers (University Science Books, Mill Valley, California, 1986). Pp. 691 and 762.

P. Horowitz and W. Hill, The Art of Electronics, 2nd ed. (Cambridge University Press, 1989). Pp. 430.

C. Cohen-Tannoudji, B. Diu, and F. Laloe, Quantum Mechanics, (John Wiley & Sons, 1977) Vol. 1, pp. 405.

J. C. Stover, Optical Scattering, Measurement, and Analysis (McGraw-Hill Inc., 1990).

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 (11)

Fig. 1.
Fig. 1.

Mode structure of the CRDS cavity. The length of the cavity was scanned by PZT at intracavity pressure ~ 30mtorr. Both signals were averages of 128 ramps. The calculated FSR and transverse mode spacing are 379.5MHz and 82.1MHz respectively. The energy coupling efficiency of the three labeled transverse modes are 94.1%, 2.6%, and 3.3% respectively. We believe the three small peaks labeled with * correspond to the unshifted laser frequency. The measured beam waist of the incident laser beam at the flat mirror is 0.517 mm, which is very close to the calculated beam size of TEM00, 0.507 mm. This suggests the resonator is well described by the model.

Fig. 2.
Fig. 2.

Cavity length scan by PZT. About 50V change of Vpzt corresponds to one FSR. Cavity was filled with 4.43 torr Nitrogen gas but similar results were observed for an empty cavity (pressure ~ 30mtorr).

Fig. 3.
Fig. 3.

Cavity pressure scan with Xenon gas. About 1.83 torr pressure change corresponds to one FSR. Laser current was modulated at 10 Hz by about 1.1 FSR.

Fig. 4.
Fig. 4.

Cavity pressure scan with Nitrogen gas. About 3.26 torr pressure change corresponds to one FSR. PZTs were modulated at 12 Hz by about 1.1 FSR and the laser wavelength was fixed.

Fig. 5.
Fig. 5.

One example of noisy decay signals. The first 10 points of each decay signal are always skipped in the fitting. After fitted to the two-mode beating model (Equation (3)), the reduced χ2 is very close to one.

Fig. 6.
Fig. 6.

A is the residuals of the fit to a single exponential decay and C is the noise spectrum of it; B is the residuals of the fit to two-mode beating model and D is the noise spectrum of it. A and B have the same horizontal axis. C and D have the same horizontal axis. The peak ~ 175 kHz in C and D is from the computer system. The time zero point has been shifted because the first 10 points of each decay are always skipped in the fitting.

Fig. 7.
Fig. 7.

Analysis of one of the noisy peaks in Fig. 2. The cavity was filled with 4.43 torr Nitrogen gas. The slope of Δv changing with Vpzt is ≈120 Hz/V, or 7.215 kHz/μm.

Fig. 8.
Fig. 8.

Analysis of one of the noisy peaks in Fig. 3. The slope of Δv changing with Xenon pressure is ≈30.7 kHz/torr.

Fig. 9.
Fig. 9.

Pressure scan and cavity length scan with 4mm diameter intracavity aperture. Laser current was modulated for the PZT scan and PZTs were modulated for the pressure scan.

Fig. 10.
Fig. 10.

Images of higher order transverse modes captured by InGaAs camera. Modes like the one in image A were found in both PZT scans and pressure scans and the mode in image B was only found in pressure scans. Each pixel corresponds to ~ 1mm by calibration. The size of the mode in image A is ~ 4mm and that in image B ~ 3.6 mm. When n+m = 60, the size of TEM nm is ~ 3.9mm at the input mirror of the cavity. All these modes have size less than the limiting aperture size near the output mirror. With a 4mm diameter intracavity aperture, this transverse mode excitation was no longer observed.

Fig. 11.
Fig. 11.

Image of damaged spots on one of the old supermirror surfaces. The picture represents an area of 146(H)×100(V)μm near the center of the HR surface of the mirror. The three black dots are damaged spots. The size of the spots is ~ 1μm. The nonuniform background is because the objective lens is dirty. This type of damaged spots were not observed for new mirrors.

Equations (6)

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

y ( t ) = A + B exp ( kt ) + detector noise
χ 2 = 1 ( N 3 ) σ 2 i = 0 n 1 ( y ( i ) A B exp ( ki ) ) 2
y ( t ) = A + B 1 exp ( k 1 t ) + B 2 exp ( k 2 t ) + 2 B 1 B 2 exp ( k 1 t 2 ) exp ( k 2 t 2 ) cos ( 2 πΔv t + Δ ϕ ) .
v qnm = c 2 n 0 L ( q + ( m + n + 1 ) cos 1 ( 1 L R c ) π + δφ )
dv qnm dL = v qnm L + c 2 n 0 L n + m + 1 2 π L ( R c L )
dv qnm d R c = c 2 n 0 L n + m + 1 2 π R c L ( R c L )

Metrics