Abstract

A theoretical model based on the ray-transfer matrix is developed for the pulsed cavity ring-down (CRD) technique to numerically investigate the influence of the geometric parameters of the pulsed-CRD arrangement on the CRD signal. By fitting the spatial distribution of the pulsed laser beam to that of the TEM00 cavity mode, the geometric parameters are optimized to obtain perfect matching between the laser beam and the ring-down cavity. It is indicated by the numerical simulations that as long as the laser power exiting the ring-down cavity is fully collected, a single exponential-decay signal, identical to the perfectly-matched CRD signal, is obtained in the mismatching case to determine accurately the cavity decay time. Intensity fluctuations appear in the mismatched CRD signal if the laser power exiting the ring-down cavity is not fully collected. Both the conventional exponential decay fitting approach and a linear fitting procedure are employed to analyze these mismatched CRD signals and the latter is recommended to make an accurate pulsed-CRD measurement.

© 2008 Optical Society of America

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References

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  1. G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: experimental schemes and applications,” Int. Rev. Phys. Chem. 19, 565-607 (2000).
    [CrossRef]
  2. J. M. Herbelin, J. A. McKay, M. A. Kwok, R. H. Uenten, D. S. Urevig, D. J. Spencer, and D. J. Bernard, “Sensitive measurement of photon lifetime and true reflectances in an optical cavity by a phase-shift method,” Appl. Opt. 19, 144-147 (1980).
    [CrossRef] [PubMed]
  3. D. Z. Anderson, J. C. Frisch, and C. S. Masser, “Mirror reflectometer based on optical cavity decay time,” Appl. Opt. 23, 1238-1245 (1984).
    [CrossRef] [PubMed]
  4. Y. Le Grand and A. Le Floch, “Sensitive dichroism measurement using eigenstate decay times,” Appl. Opt. 29, 1244-1248(1990).
    [CrossRef]
  5. G. Rempe, R. J. Thompson, H. J. Kimble, and R. Lalezari, “Measurement of ultralow losses in an optical interferometer,” Opt. Lett. 17, 363-365 (1992).
    [CrossRef] [PubMed]
  6. D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stoeckel, “CW cavity ring down spectroscopy,” Chem. Phys. Lett. 264, 316-322 (1997).
    [CrossRef]
  7. J. Morville, D. Romanini, M. Chenevier, and A. Kachanov, “Effects of laser phase noise on the injection of a high-finesse cavity,” Appl. Opt. 41, 6980-6990 (2002).
    [CrossRef] [PubMed]
  8. I. Debecker, A. K. Mohamed, and D. Romanini, “High-speed cavity ringdown spectroscopy with increased spectral resolution by simultaneous laser and cavity tuning,” Opt. Express 13, 2906-2915 (2005).
    [CrossRef] [PubMed]
  9. A. O'Keefe and D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 2544-2551 (1988).
    [CrossRef]
  10. A. P. Yalin, V. Surla, M. Butweiller, and J. D. Williams, “Detection of sputtered metals with cavity ring-down spectroscopy,” Appl. Opt. 44, 6496-6505 (2005).
    [CrossRef] [PubMed]
  11. A. Schocker, K. K-Hoinghaus, and A. Brockhinke, “Quantitative determination of combustion intermediates with cavity ring-down spectroscopy: systematic study in propene flames near the soot-formation limit,” Appl. Opt. 44, 6660-6672(2005).
    [CrossRef] [PubMed]
  12. R. D. van Zee, J. T. Hodges, and J. P. Looney, “Pulsed, single-mode cavity ringdown spectroscopy,” Appl. Opt. 38, 3951-3960(1999).
    [CrossRef]
  13. H. Naus, I. H. M. van Stokkum, W. Hogervorst, and W. Ubachs, “Quantitative analysis of decay transients applied to multimode pulsed cavity ringdown experiment,” Appl. Opt. 40, 4416-4426 (2001).
    [CrossRef]
  14. D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, “Optimization of the mode matching in pulsed cavity ringdown spectroscopy by monitoring non-degenerate transverse mode beating,” Appl. Phys. B 74, 435-440 (2002).
    [CrossRef]
  15. S. Spuler and M. Linne, “Numerical analysis of beam propagation in pulsed cavity ring-down spectroscopy,” Appl. Opt. 41, 2858-2868 (2002).
    [CrossRef] [PubMed]
  16. Y. He and B. J. Orr, “Detection of trace gases by rapidly-swept continuous-wave cavity ringdown spectroscopy: pushing the limits of sensitivity,” Appl. Phys. B 85, 355-364 (2006).
    [CrossRef]
  17. P. Maddaloni, G. Gagliardi, P. Malara, and P. De Natale, “Off-axis integrated-cavity-output spectroscopy for trace-gas concentration measurements: modeling and performance,” J. Opt. Soc. Am. B 23, 1938-1945 (2006).
    [CrossRef]
  18. B. A. Richman, A. A. Kachanov, and B. A. Paldus, “Novel detection of aerosols: combined cavity ring-down and fluorescence spectroscopy,” Opt. Express 13, 3376-3387 (2005).
    [CrossRef] [PubMed]
  19. J. J. Scherer, “Ringdown spectral photography,” Chem. Phys. Lett. 292, 143-153 (1998).
    [CrossRef]
  20. H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550-1567 (1966).
    [CrossRef] [PubMed]
  21. Y. Gong and B. C. Li, “Effect of instrumental response time in exponential-decay based cavity ring-down techniques for high reflectivity measurement,” Proc. SPIE 6720, 67201E-1-67201E-8 (2007).
  22. A. A. Tovar and L. W. Casperson, “Generalized beam matrices: Gaussian beam propagation in misaligned complex optical systems,” J. Opt. Soc. Am. A 12, 1522-1533 (1995).
    [CrossRef]
  23. A. A. Tovar and L. W. Casperson, “Generalized beam matrices. II. Mode selection in lasers and periodic misaligned complex optical systems,” J. Opt. Soc. Am. A 13, 90-96 (1996).
    [CrossRef]
  24. R. Hauck, H. P. Kortz, and H. Weber, “Misalignment sensitivity of optical resonators,” Appl. Opt. 19, 598-601 (1980).
    [CrossRef] [PubMed]
  25. J. T. Hodges, J. P. Looney, and R. D. van Zee, “Response of a ring-down cavity to an arbitrary excitation,” J. Chem. Phys. 105, 10278-10288 (1996).
    [CrossRef]

2007 (1)

Y. Gong and B. C. Li, “Effect of instrumental response time in exponential-decay based cavity ring-down techniques for high reflectivity measurement,” Proc. SPIE 6720, 67201E-1-67201E-8 (2007).

2006 (2)

Y. He and B. J. Orr, “Detection of trace gases by rapidly-swept continuous-wave cavity ringdown spectroscopy: pushing the limits of sensitivity,” Appl. Phys. B 85, 355-364 (2006).
[CrossRef]

P. Maddaloni, G. Gagliardi, P. Malara, and P. De Natale, “Off-axis integrated-cavity-output spectroscopy for trace-gas concentration measurements: modeling and performance,” J. Opt. Soc. Am. B 23, 1938-1945 (2006).
[CrossRef]

2005 (4)

2002 (3)

2001 (1)

2000 (1)

G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: experimental schemes and applications,” Int. Rev. Phys. Chem. 19, 565-607 (2000).
[CrossRef]

1999 (1)

1998 (1)

J. J. Scherer, “Ringdown spectral photography,” Chem. Phys. Lett. 292, 143-153 (1998).
[CrossRef]

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 (2)

J. T. Hodges, J. P. Looney, and R. D. van Zee, “Response of a ring-down cavity to an arbitrary excitation,” J. Chem. Phys. 105, 10278-10288 (1996).
[CrossRef]

A. A. Tovar and L. W. Casperson, “Generalized beam matrices. II. Mode selection in lasers and periodic misaligned complex optical systems,” J. Opt. Soc. Am. A 13, 90-96 (1996).
[CrossRef]

1995 (1)

1992 (1)

1990 (1)

1988 (1)

A. O'Keefe and D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 2544-2551 (1988).
[CrossRef]

1984 (1)

1980 (2)

1966 (1)

Anderson, D. Z.

Berden, G.

G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: experimental schemes and applications,” Int. Rev. Phys. Chem. 19, 565-607 (2000).
[CrossRef]

Bernard, D. J.

Brockhinke, A.

Butweiller, M.

Casperson, L. W.

Chenevier, M.

De Natale, P.

Deacon, D. A. G.

A. O'Keefe and D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 2544-2551 (1988).
[CrossRef]

Debecker, I.

Frisch, J. C.

Gagliardi, G.

Gong, Y.

Y. Gong and B. C. Li, “Effect of instrumental response time in exponential-decay based cavity ring-down techniques for high reflectivity measurement,” Proc. SPIE 6720, 67201E-1-67201E-8 (2007).

Hahn, J. W.

D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, “Optimization of the mode matching in pulsed cavity ringdown spectroscopy by monitoring non-degenerate transverse mode beating,” Appl. Phys. B 74, 435-440 (2002).
[CrossRef]

Hauck, R.

He, Y.

Y. He and B. J. Orr, “Detection of trace gases by rapidly-swept continuous-wave cavity ringdown spectroscopy: pushing the limits of sensitivity,” Appl. Phys. B 85, 355-364 (2006).
[CrossRef]

Herbelin, J. M.

Hodges, J. T.

R. D. van Zee, J. T. Hodges, and J. P. Looney, “Pulsed, single-mode cavity ringdown spectroscopy,” Appl. Opt. 38, 3951-3960(1999).
[CrossRef]

J. T. Hodges, J. P. Looney, and R. D. van Zee, “Response of a ring-down cavity to an arbitrary excitation,” J. Chem. Phys. 105, 10278-10288 (1996).
[CrossRef]

Hogervorst, W.

Kachanov, A.

Kachanov, A. A.

B. A. Richman, A. A. Kachanov, and B. A. Paldus, “Novel detection of aerosols: combined cavity ring-down and fluorescence spectroscopy,” Opt. Express 13, 3376-3387 (2005).
[CrossRef] [PubMed]

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

K-Hoinghaus, K.

Kim, B.

D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, “Optimization of the mode matching in pulsed cavity ringdown spectroscopy by monitoring non-degenerate transverse mode beating,” Appl. Phys. B 74, 435-440 (2002).
[CrossRef]

Kimble, H. J.

Kogelnik, H.

Kortz, H. P.

Kwok, M. A.

Lalezari, R.

Le Floch, A.

Le Grand, Y.

Lee, D.-H.

D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, “Optimization of the mode matching in pulsed cavity ringdown spectroscopy by monitoring non-degenerate transverse mode beating,” Appl. Phys. B 74, 435-440 (2002).
[CrossRef]

Lee, J. Y.

D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, “Optimization of the mode matching in pulsed cavity ringdown spectroscopy by monitoring non-degenerate transverse mode beating,” Appl. Phys. B 74, 435-440 (2002).
[CrossRef]

Li, B. C.

Y. Gong and B. C. Li, “Effect of instrumental response time in exponential-decay based cavity ring-down techniques for high reflectivity measurement,” Proc. SPIE 6720, 67201E-1-67201E-8 (2007).

Li, T.

Linne, M.

Looney, J. P.

R. D. van Zee, J. T. Hodges, and J. P. Looney, “Pulsed, single-mode cavity ringdown spectroscopy,” Appl. Opt. 38, 3951-3960(1999).
[CrossRef]

J. T. Hodges, J. P. Looney, and R. D. van Zee, “Response of a ring-down cavity to an arbitrary excitation,” J. Chem. Phys. 105, 10278-10288 (1996).
[CrossRef]

Maddaloni, P.

Malara, P.

Masser, C. S.

McKay, J. A.

Meijer, G.

G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: experimental schemes and applications,” Int. Rev. Phys. Chem. 19, 565-607 (2000).
[CrossRef]

Mohamed, A. K.

Morville, J.

Naus, H.

O'Keefe, A.

A. O'Keefe and D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 2544-2551 (1988).
[CrossRef]

Orr, B. J.

Y. He and B. J. Orr, “Detection of trace gases by rapidly-swept continuous-wave cavity ringdown spectroscopy: pushing the limits of sensitivity,” Appl. Phys. B 85, 355-364 (2006).
[CrossRef]

Paldus, B. A.

Peeters, R.

G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: experimental schemes and applications,” Int. Rev. Phys. Chem. 19, 565-607 (2000).
[CrossRef]

Rempe, G.

Richman, B. A.

Romanini, D.

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]

Scherer, J. J.

J. J. Scherer, “Ringdown spectral photography,” Chem. Phys. Lett. 292, 143-153 (1998).
[CrossRef]

Schocker, A.

Spencer, D. J.

Spuler, S.

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]

Surla, V.

Thompson, R. J.

Tovar, A. A.

Ubachs, W.

Uenten, R. H.

Urevig, D. S.

van Stokkum, I. H. M.

van Zee, R. D.

R. D. van Zee, J. T. Hodges, and J. P. Looney, “Pulsed, single-mode cavity ringdown spectroscopy,” Appl. Opt. 38, 3951-3960(1999).
[CrossRef]

J. T. Hodges, J. P. Looney, and R. D. van Zee, “Response of a ring-down cavity to an arbitrary excitation,” J. Chem. Phys. 105, 10278-10288 (1996).
[CrossRef]

Weber, H.

Williams, J. D.

Yalin, A. P.

Yoo, Y. S.

D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, “Optimization of the mode matching in pulsed cavity ringdown spectroscopy by monitoring non-degenerate transverse mode beating,” Appl. Phys. B 74, 435-440 (2002).
[CrossRef]

Yoon, Y.

D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, “Optimization of the mode matching in pulsed cavity ringdown spectroscopy by monitoring non-degenerate transverse mode beating,” Appl. Phys. B 74, 435-440 (2002).
[CrossRef]

Appl. Opt. (11)

J. M. Herbelin, J. A. McKay, M. A. Kwok, R. H. Uenten, D. S. Urevig, D. J. Spencer, and D. J. Bernard, “Sensitive measurement of photon lifetime and true reflectances in an optical cavity by a phase-shift method,” Appl. Opt. 19, 144-147 (1980).
[CrossRef] [PubMed]

D. Z. Anderson, J. C. Frisch, and C. S. Masser, “Mirror reflectometer based on optical cavity decay time,” Appl. Opt. 23, 1238-1245 (1984).
[CrossRef] [PubMed]

Y. Le Grand and A. Le Floch, “Sensitive dichroism measurement using eigenstate decay times,” Appl. Opt. 29, 1244-1248(1990).
[CrossRef]

J. Morville, D. Romanini, M. Chenevier, and A. Kachanov, “Effects of laser phase noise on the injection of a high-finesse cavity,” Appl. Opt. 41, 6980-6990 (2002).
[CrossRef] [PubMed]

A. P. Yalin, V. Surla, M. Butweiller, and J. D. Williams, “Detection of sputtered metals with cavity ring-down spectroscopy,” Appl. Opt. 44, 6496-6505 (2005).
[CrossRef] [PubMed]

A. Schocker, K. K-Hoinghaus, and A. Brockhinke, “Quantitative determination of combustion intermediates with cavity ring-down spectroscopy: systematic study in propene flames near the soot-formation limit,” Appl. Opt. 44, 6660-6672(2005).
[CrossRef] [PubMed]

R. D. van Zee, J. T. Hodges, and J. P. Looney, “Pulsed, single-mode cavity ringdown spectroscopy,” Appl. Opt. 38, 3951-3960(1999).
[CrossRef]

H. Naus, I. H. M. van Stokkum, W. Hogervorst, and W. Ubachs, “Quantitative analysis of decay transients applied to multimode pulsed cavity ringdown experiment,” Appl. Opt. 40, 4416-4426 (2001).
[CrossRef]

S. Spuler and M. Linne, “Numerical analysis of beam propagation in pulsed cavity ring-down spectroscopy,” Appl. Opt. 41, 2858-2868 (2002).
[CrossRef] [PubMed]

H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550-1567 (1966).
[CrossRef] [PubMed]

R. Hauck, H. P. Kortz, and H. Weber, “Misalignment sensitivity of optical resonators,” Appl. Opt. 19, 598-601 (1980).
[CrossRef] [PubMed]

Appl. Phys. B (2)

Y. He and B. J. Orr, “Detection of trace gases by rapidly-swept continuous-wave cavity ringdown spectroscopy: pushing the limits of sensitivity,” Appl. Phys. B 85, 355-364 (2006).
[CrossRef]

D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, “Optimization of the mode matching in pulsed cavity ringdown spectroscopy by monitoring non-degenerate transverse mode beating,” Appl. Phys. B 74, 435-440 (2002).
[CrossRef]

Chem. Phys. Lett. (2)

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

J. J. Scherer, “Ringdown spectral photography,” Chem. Phys. Lett. 292, 143-153 (1998).
[CrossRef]

Int. Rev. Phys. Chem. (1)

G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: experimental schemes and applications,” Int. Rev. Phys. Chem. 19, 565-607 (2000).
[CrossRef]

J. Chem. Phys. (1)

J. T. Hodges, J. P. Looney, and R. D. van Zee, “Response of a ring-down cavity to an arbitrary excitation,” J. Chem. Phys. 105, 10278-10288 (1996).
[CrossRef]

J. Opt. Soc. Am. A (2)

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

Opt. Express (2)

Opt. Lett. (1)

Proc. SPIE (1)

Y. Gong and B. C. Li, “Effect of instrumental response time in exponential-decay based cavity ring-down techniques for high reflectivity measurement,” Proc. SPIE 6720, 67201E-1-67201E-8 (2007).

Rev. Sci. Instrum. (1)

A. O'Keefe and D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 2544-2551 (1988).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of a typical pulsed-CRD setup. BS: beam splitter; M: reflective mirror; L1, L2: matching lenses; M1, M2: cavity mirrors; PD: photodetector.

Fig. 2
Fig. 2

Sensitivity of the mean square variance to the free parameters, (a)  d 2 and (b)  d 3 . The corresponding fitted (a)  d 3 and (b)  d 2 are also presented.

Fig. 3
Fig. 3

(a) Normalized matched (solid line) and mismatched (empty circles) pulsed-CRD signal in the case of full collection of the laser power exiting the output cavity mirror and (b) corresponding beam size on the output cavity mirror after each round-trip.

Fig. 4
Fig. 4

Influence of the geometric parameters, (a)  d 2 , (b)  d 3 , and (c)  w 0 , on the pulsed-CRD signals (upper plot) and the beam size on the output cavity mirror (lower plot). The deviation of the mismatched CRD signals from the matched CRD signal is also shown in each middle plot.

Fig. 5
Fig. 5

(a) Mismatched CRD signal I ( t ) and (b) its natural- logarithm value ln [ I ( t ) ] calculated with w 0 = 3 mm . The corresponding best-fit curves are also shown in (a) and (b), respectively.

Fig. 6
Fig. 6

The fitted reflectivity of the cavity mirror as a function of (a)  d 2 , (b)  d 3 , and (c)  w 0 obtained with the linear fitting (empty circles) and the conventional exponential decay fitting (solid circles). The input reflectivity of R = 99.5 % is also shown with a dashed line in each plot.

Tables (1)

Tables Icon

Table 1 Values of the Parameters Used in the Ray-Transfer-Matrix-Based Numerical Simulations

Equations (11)

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E ( r , z ) = E 0 w 0 w z exp ( i k z i k r 2 2 q ) .
1 q = 1 R c i λ π w z 2 .
M 1 = [ A 1 B 1 C 1 D 1 ] = M d 0 M f 3 M d 3 M f 2 M d 2 M f 1 M d 1 ,
M d m = [ 1 d m 0 1 ] ,
M f m = [ 1 0 1 / f m 1 ] ,
M = [ A B C D ] = M d 0 M f 0 M d 0 M f 0 ,
M j = [ A j B j C j D j ] = M j .
I ( t ) = T E 0 { Σ j = 0 R 2 j P ( t j t r ) w j 2 0 r 0 exp ( 2 r 2 / w j 2 ) r d r } .
Var = 1 N Σ k = 1 N ( 1 w z 1 0 k w z 1 k ) 2 + Σ k = 1 N ( R c z 1 0 k R c z 1 k ) 2 Σ k = 1 N R c z 1 0 k ,
Var 2 = Σ i = 1 N [ I S ( t i ) I F ( t i ) ] 2 Σ i = 1 N [ I S ( t i ) ] 2 .
Var 3 = Σ i = 1 N [ ln I S ( t i ) ln I F ( t i ) ] 2 Σ i = 1 N [ ln I S ( t i ) ] 2 .

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