Abstract

A new method for performing high-frequency, visible FM spectroscopy by using low-frequency detection is demonstrated. By using this technique, a detection limit of 323 μTorr m (path length) has been established for atmospheric-pressure-broadened NO2. This corresponds to a differential absorption of 1.0 × 10−5.

© 1986 Optical Society of America

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References

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  1. G. C. Bjorklund, “Frequency modulation spectroscopy,” Opt. Lett. 5, 15 (1980).
    [CrossRef]
  2. N. H. Tran, R. Kachru, P. Pillet, H. B. Van Linden, Vanden Huevell, T. F. Gallagher, and J. P. Watjen, “Frequency modulation spectroscopy with a pulsed dye laser: experimental investigations of sensitivity and useful features,” Appl. Opt. 23, 1353 (1984).
    [CrossRef]
  3. G. Janik, C. B. Carlisle, and T. F. Gallagher, “Frequency modulation spectroscopy with second harmonic detection,” Appl. Opt. 24, 3318 (1985).
    [CrossRef] [PubMed]
  4. D. E. Cooper and T. F. Gallagher, “Frequency modulation spectroscopy with a multimode laser,” Opt. Lett. 9, 451 (1984).
    [CrossRef] [PubMed]
  5. S. Y. Wang, D. M. Bloom, and D. M. Collins, “20-GHz bandwidth GaAs photodiode,” Appl. Phys. Lett. 42, 190 (1983).
    [CrossRef]
  6. D. E. Cooper and T. F. Gallagher, “Double frequency modulation spectroscopy: high modulation frequency with low-bandwidth detectors,” Appl. Opt. 24, 1327 (1985).
    [CrossRef] [PubMed]
  7. H. E. Warner, W. T. Conner, and R. C. Woods, “The lowest rotational transition of several isotopic forms of KrD+,” J. Chem. Phys. 81, 5413 (1984).
    [CrossRef]
  8. C. S. Gudeman, M. H. Begemann, J. Pfaff, and R. J. Saykally, “Tone-burst modulated color-center laser spectroscopy,” Opt. Lett. 8, 310 (1983),
    [CrossRef] [PubMed]
  9. D. T. Cassidy and J. Reid, “Harmonic detection with tunable diode lasers—two-tone modulation,” Appl. Phys. B 29, 279 (1982).
    [CrossRef]
  10. N. H. Tran, T. F. Gallagher, J. P. Watjen, G. Janik, and C. B. Carlisle, “A high-efficiency resonant cavity microwave modulator,” Appl. Opt. 24, 4282 (1985).
    [CrossRef] [PubMed]
  11. L. S. Andrews, Department of Chemistry, University of Virginia, Charlottesville, Va. 22901 (personal communication).
  12. E. A. Whittaker, M. Gehrtz, and G. C. Bjorklund, “Residual amplitude modulation in laser electro-optic phase modulation,” J. Opt. Soc. Am. B 2, 1320 (1985).
    [CrossRef]
  13. M. Gehrtz, G. C. Bjorklund, and E. A. Whittaker, “Quantum-limited laser frequency-modulation spectroscopy,” J. Opt. Soc. Am. B 2, 1510 (1985).
    [CrossRef]
  14. G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy: theory of line-shapes and signal-to-noise analysis,” Appl. Phys. B 32, 145 (1983).
    [CrossRef]
  15. G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B 32, 145 (1983).
    [CrossRef]

1985 (5)

1984 (3)

1983 (4)

S. Y. Wang, D. M. Bloom, and D. M. Collins, “20-GHz bandwidth GaAs photodiode,” Appl. Phys. Lett. 42, 190 (1983).
[CrossRef]

C. S. Gudeman, M. H. Begemann, J. Pfaff, and R. J. Saykally, “Tone-burst modulated color-center laser spectroscopy,” Opt. Lett. 8, 310 (1983),
[CrossRef] [PubMed]

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

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B 32, 145 (1983).
[CrossRef]

1982 (1)

D. T. Cassidy and J. Reid, “Harmonic detection with tunable diode lasers—two-tone modulation,” Appl. Phys. B 29, 279 (1982).
[CrossRef]

1980 (1)

Andrews, L. S.

L. S. Andrews, Department of Chemistry, University of Virginia, Charlottesville, Va. 22901 (personal communication).

Begemann, M. H.

Bjorklund, G. C.

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

M. Gehrtz, G. C. Bjorklund, and E. A. Whittaker, “Quantum-limited laser frequency-modulation spectroscopy,” J. Opt. Soc. Am. B 2, 1510 (1985).
[CrossRef]

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

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B 32, 145 (1983).
[CrossRef]

G. C. Bjorklund, “Frequency modulation spectroscopy,” Opt. Lett. 5, 15 (1980).
[CrossRef]

Bloom, D. M.

S. Y. Wang, D. M. Bloom, and D. M. Collins, “20-GHz bandwidth GaAs photodiode,” Appl. Phys. Lett. 42, 190 (1983).
[CrossRef]

Carlisle, C. B.

Cassidy, D. T.

D. T. Cassidy and J. Reid, “Harmonic detection with tunable diode lasers—two-tone modulation,” Appl. Phys. B 29, 279 (1982).
[CrossRef]

Collins, D. M.

S. Y. Wang, D. M. Bloom, and D. M. Collins, “20-GHz bandwidth GaAs photodiode,” Appl. Phys. Lett. 42, 190 (1983).
[CrossRef]

Conner, W. T.

H. E. Warner, W. T. Conner, and R. C. Woods, “The lowest rotational transition of several isotopic forms of KrD+,” J. Chem. Phys. 81, 5413 (1984).
[CrossRef]

Cooper, D. E.

Gallagher, T. F.

Gehrtz, M.

Gudeman, C. S.

Huevell, Vanden

Janik, G.

Kachru, R.

Lenth, W.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B 32, 145 (1983).
[CrossRef]

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

Levenson, M. D.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B 32, 145 (1983).
[CrossRef]

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

Ortiz, C.

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

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B 32, 145 (1983).
[CrossRef]

Pfaff, J.

Pillet, P.

Reid, J.

D. T. Cassidy and J. Reid, “Harmonic detection with tunable diode lasers—two-tone modulation,” Appl. Phys. B 29, 279 (1982).
[CrossRef]

Saykally, R. J.

Tran, N. H.

Van Linden, H. B.

Wang, S. Y.

S. Y. Wang, D. M. Bloom, and D. M. Collins, “20-GHz bandwidth GaAs photodiode,” Appl. Phys. Lett. 42, 190 (1983).
[CrossRef]

Warner, H. E.

H. E. Warner, W. T. Conner, and R. C. Woods, “The lowest rotational transition of several isotopic forms of KrD+,” J. Chem. Phys. 81, 5413 (1984).
[CrossRef]

Watjen, J. P.

Whittaker, E. A.

Woods, R. C.

H. E. Warner, W. T. Conner, and R. C. Woods, “The lowest rotational transition of several isotopic forms of KrD+,” J. Chem. Phys. 81, 5413 (1984).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. B (3)

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

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B 32, 145 (1983).
[CrossRef]

D. T. Cassidy and J. Reid, “Harmonic detection with tunable diode lasers—two-tone modulation,” Appl. Phys. B 29, 279 (1982).
[CrossRef]

Appl. Phys. Lett. (1)

S. Y. Wang, D. M. Bloom, and D. M. Collins, “20-GHz bandwidth GaAs photodiode,” Appl. Phys. Lett. 42, 190 (1983).
[CrossRef]

J. Chem. Phys. (1)

H. E. Warner, W. T. Conner, and R. C. Woods, “The lowest rotational transition of several isotopic forms of KrD+,” J. Chem. Phys. 81, 5413 (1984).
[CrossRef]

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

Opt. Lett. (3)

Other (1)

L. S. Andrews, Department of Chemistry, University of Virginia, Charlottesville, Va. 22901 (personal communication).

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Figures (4)

Fig. 1
Fig. 1

Spectral components of the laser after two-tone modulation.

Fig. 2
Fig. 2

Comparison of direct and two-tone FM absorption signals of the Na D lines, with 2% absorption in the D2 line. (a) FM signal with β = 0.25 at 17 GHz. (b) Direct absorption signal. The D2 line is barely visible and the D1 line cannot be seen.

Fig. 3
Fig. 3

Schematic of the experimental setup.

Fig. 4
Fig. 4

Two-tone FM scans with modulator frequency = 16 GHz, β = 0.35. Note that the attenuation refers to electronic attenuation (in power), i.e., 40 dB = × 100 in voltage (also decibels). (a) FM signal from 1 Torr of NO2 gas near 590 nm with a scan range of about 25 cm−1. (b) Same scan as in (a) but with 1-atm N2 added to the cell. (c) FM signal from 1.7 mTorr of NO2 with 1-atm N2 added to the cell. (d) FM signal from empty absorption cell.

Equations (14)

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E 2 ( t ) = E 0 exp ( i ω 0 t ) n = J n ( β 1 ) exp ( i n ω 1 t ) ,
E 2 ( t ) = E 0 exp ( i ω 0 t ) n = J n ( β 1 ) exp ( i n ω 1 t ) × m = m = J m ( β 2 ) exp ( i m ω 2 t ) = E 0 exp ( i ω 0 t ) n , m J n ( β 1 ) J m ( β 2 ) exp ( n ω 1 + m ω 2 ) t .
E 2 ( t ) E 0 exp ( i ω 0 t ) [ 1 + β 2 exp ( i ω 1 t ) β 2 exp ( i ω 1 t ) ] × [ 1 + β 2 exp ( i ω 2 t ) β 2 exp ( i ω 2 t ) ] .
ω 1 = ω m + Ω 2 , ω 2 = ω m Ω 2 , Ω ω m < 10 3 ,
E 3 ( t ) = E 0 { exp ( i ω 0 t ) β 2 4 exp [ i ( ω 0 + Ω ) t ] β 2 4 exp [ i ( ω 0 Ω ) t ] + β 2 exp [ i ( ω 0 + ω m + Ω 2 ) t ] + β 2 exp [ i ( ω 0 + ω m Ω 2 ) t ] β 2 exp [ i ( ω 0 ω m Ω 2 ) t ] β 2 exp [ i ( ω 0 ω m + ω 2 ) t ] } .
E 3 ( t ) = E 0 ( T 0 { exp ( i ω 0 t ) β 2 4 exp [ i ( ω 0 + Ω ) t ] β 2 4 exp [ i ( ω 0 Ω ) t ] + T + 1 { β 2 exp [ i ( ω 0 + ω m + Ω 2 ) t ] + β 2 exp [ i ( ω 0 + ω m Ω 2 ) t ] } + T 1 { β 2 exp [ i ( ω 0 ω m Ω 2 ) t ] β 2 exp [ i ( ω 0 ω m + Ω 2 ) t ] } .
I 3 ( at Ω ) = c E 0 2 β 2 16 π [ exp ( 2 δ 1 ) + exp ( 2 δ 1 ) ] 2 exp ( 2 δ 0 ) ] cos ( Ω t ) ,
I 3 ( at Ω ) = c E 0 2 β 2 8 ( 2 δ 0 δ 1 δ 1 ) cos ( Ω t ) .
DL 323 μ Torr m ,
δ 1 = δ 1 1 + [ 2 ( ω 1 ω 1 ) γ ] 2 = δ , δ 1 = δ 1 1 + [ 2 ( ω 1 ω 1 ) γ ] 2 = δ 1 1 + 16 f m 2 γ 2 ,
δ 1 δ 1 = δ [ 1 1 1 + 16 ( f m γ 2 ) 2 ]
δ 1 δ 1 = δ [ 1 1 1 + 0.01 ] = δ 101 .
Δ δ min = 2 β [ Δ f ћ ω 0 I 0 ] 1 / 2 ,
Δ δ min = 2.6 × 10 7 .

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