Abstract

A new technique to improve the sensitivity of frequency-modulation laser absorption spectroscopy is reported. Theoretical analysis and experimental demonstration show that the application of two harmonically related, appropriately phase-shifted rf waves to the electro-optic modulator can reduce the residual amplitude-modulation background signal in the photodetector output current without reducing the absorption-induced signal. When the new method was used, the residual amplitude-modulation background was reduced by a factor of 4. Our results suggest that shot-noise-limited detection sensitivity may eventually be achieved without using dual-beam compensation or dc-biased modulators.

© 1988 Optical Society of America

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References

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  1. G. C. Bjorklund, Opt. Lett. 5, 15 (1980).
    [CrossRef]
  2. E. A. Whittaker, M. Gehrtz, G. C. Bjorklund, J. Opt. Soc. Am. B 2, 1320 (1985).
    [CrossRef]
  3. M. D. Levenson, W. E. Moernor, D. E. Horne, Opt. Lett. 8, 108 (1983).
    [CrossRef] [PubMed]
  4. E. A. Whittaker, B. J. Sullivan, G. C. Bjorklund, H. R. Wendt, H. E. Hunziker, J. Chem Phys. 80, 961 (1984).
    [CrossRef]
  5. L. Hollberg, M. Long-sheng, M. Hohenstatt, J. L. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 426, 91 (1983).
  6. M. Gehrtz, G. C. Bjorklund, E. A. Whittaker, J. Opt. Soc. Am. B 2, 1510 (1985).
    [CrossRef]
  7. N. C. Wong, J. L. Hall, J. Opt. Soc. Am. B 2, 1527 (1985).
    [CrossRef]
  8. G. R. Janik, C. B. Carlisle, T. F. Gallagher, J. Opt. Soc. Am. B 3, 1070 (1986).
    [CrossRef]
  9. R. G. DeVoe, R. G. Brewer, Phys. Rev. A 30, 2827 (1984).
    [CrossRef]
  10. See, for example J. L. Hall, H. G. Robinson, T. Baer, L. Hollberg, in NATO Advanced Study Institute, Series B, F. T. Arecchi, F. Strumia, H. Walther, eds. (Plenum, New York, 1983), Vol. 95, p. 99.
  11. For construction details, see D. J. Bernays, IBM Research Rep. RJ4166 RJ4166 (IBM, San Jose, Calif., 1984).

1986

1985

1984

E. A. Whittaker, B. J. Sullivan, G. C. Bjorklund, H. R. Wendt, H. E. Hunziker, J. Chem Phys. 80, 961 (1984).
[CrossRef]

R. G. DeVoe, R. G. Brewer, Phys. Rev. A 30, 2827 (1984).
[CrossRef]

1983

L. Hollberg, M. Long-sheng, M. Hohenstatt, J. L. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 426, 91 (1983).

M. D. Levenson, W. E. Moernor, D. E. Horne, Opt. Lett. 8, 108 (1983).
[CrossRef] [PubMed]

1980

Baer, T.

See, for example J. L. Hall, H. G. Robinson, T. Baer, L. Hollberg, in NATO Advanced Study Institute, Series B, F. T. Arecchi, F. Strumia, H. Walther, eds. (Plenum, New York, 1983), Vol. 95, p. 99.

Bernays, D. J.

For construction details, see D. J. Bernays, IBM Research Rep. RJ4166 RJ4166 (IBM, San Jose, Calif., 1984).

Bjorklund, G. C.

Brewer, R. G.

R. G. DeVoe, R. G. Brewer, Phys. Rev. A 30, 2827 (1984).
[CrossRef]

Carlisle, C. B.

DeVoe, R. G.

R. G. DeVoe, R. G. Brewer, Phys. Rev. A 30, 2827 (1984).
[CrossRef]

Gallagher, T. F.

Gehrtz, M.

Hall, J. L.

N. C. Wong, J. L. Hall, J. Opt. Soc. Am. B 2, 1527 (1985).
[CrossRef]

L. Hollberg, M. Long-sheng, M. Hohenstatt, J. L. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 426, 91 (1983).

See, for example J. L. Hall, H. G. Robinson, T. Baer, L. Hollberg, in NATO Advanced Study Institute, Series B, F. T. Arecchi, F. Strumia, H. Walther, eds. (Plenum, New York, 1983), Vol. 95, p. 99.

Hohenstatt, M.

L. Hollberg, M. Long-sheng, M. Hohenstatt, J. L. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 426, 91 (1983).

Hollberg, L.

L. Hollberg, M. Long-sheng, M. Hohenstatt, J. L. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 426, 91 (1983).

See, for example J. L. Hall, H. G. Robinson, T. Baer, L. Hollberg, in NATO Advanced Study Institute, Series B, F. T. Arecchi, F. Strumia, H. Walther, eds. (Plenum, New York, 1983), Vol. 95, p. 99.

Horne, D. E.

Hunziker, H. E.

E. A. Whittaker, B. J. Sullivan, G. C. Bjorklund, H. R. Wendt, H. E. Hunziker, J. Chem Phys. 80, 961 (1984).
[CrossRef]

Janik, G. R.

Levenson, M. D.

Long-sheng, M.

L. Hollberg, M. Long-sheng, M. Hohenstatt, J. L. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 426, 91 (1983).

Moernor, W. E.

Robinson, H. G.

See, for example J. L. Hall, H. G. Robinson, T. Baer, L. Hollberg, in NATO Advanced Study Institute, Series B, F. T. Arecchi, F. Strumia, H. Walther, eds. (Plenum, New York, 1983), Vol. 95, p. 99.

Sullivan, B. J.

E. A. Whittaker, B. J. Sullivan, G. C. Bjorklund, H. R. Wendt, H. E. Hunziker, J. Chem Phys. 80, 961 (1984).
[CrossRef]

Wendt, H. R.

E. A. Whittaker, B. J. Sullivan, G. C. Bjorklund, H. R. Wendt, H. E. Hunziker, J. Chem Phys. 80, 961 (1984).
[CrossRef]

Whittaker, E. A.

Wong, N. C.

J. Chem Phys.

E. A. Whittaker, B. J. Sullivan, G. C. Bjorklund, H. R. Wendt, H. E. Hunziker, J. Chem Phys. 80, 961 (1984).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. A

R. G. DeVoe, R. G. Brewer, Phys. Rev. A 30, 2827 (1984).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

L. Hollberg, M. Long-sheng, M. Hohenstatt, J. L. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 426, 91 (1983).

Other

See, for example J. L. Hall, H. G. Robinson, T. Baer, L. Hollberg, in NATO Advanced Study Institute, Series B, F. T. Arecchi, F. Strumia, H. Walther, eds. (Plenum, New York, 1983), Vol. 95, p. 99.

For construction details, see D. J. Bernays, IBM Research Rep. RJ4166 RJ4166 (IBM, San Jose, Calif., 1984).

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Figures (3)

Fig. 1
Fig. 1

Circuit used to generate the ω + 2ω waveform. The 80-MHz oscillator is doubled and quadrupled, then amplified, split, and filtered to produce phase-coherent signals at 160 MHz (ω) and 320 MHz (2ω). Approximately 2 W of power was applied at 160 MHz, and approximately 20 mW was applied at 360 MHz.

Fig. 2
Fig. 2

Data gathered by detecting the signal induced at 2ω. The column on the left shows FMS signals from a 1.5-GHz scan of a voltage-swept reflection-mode FP interferometer. The column on the right shows the FMS signal versus time with the FP tuned off resonance and with light on the detector and with light off. The difference between these two is the net RAM background signal. The sensitivity for these curves is ten times higher than for the FM resonance line signals. The horizontal scale corresponds to approximately a 250-msec observation time. There is an arbitrary but fixed dc offset present with the light off because of the detection electronics: (a) ω modulation only, (b) 2ω modulation only (c) ω + 2ω modulation.

Fig. 3
Fig. 3

Output from the FP in scanned transmission mode showing the modulated laser spectrum with (a) ω modulation only and (b) 2ω modulation only. The vertical scales were expanded to highlight the sidebands. The carrier in both cases is off scale. In (a) the arrows point to the weak 2ω sidebands induced by the relatively strong ω modulation. The arrows in (b) show the 2ω sidebands.

Equations (9)

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E ( t ) = E 0 exp ( i ω 0 t ) A FM [ 1 + A 1 sin ( ω t + ϕ ω ) + A 2 sin ( 2 ω t ) ] + c . c . ,
A FM = exp { i [ M 1 sin ( ω t + ϕ ω ) + M 2 sin ( 2 ω t ) ] }
I = I 0 [ 1 + A 1 sin ( ω t + ϕ ω ) + A 2 sin ( 2 ω t ) ] 2 = I 0 [ 2 A 1 sin ( ω t + ϕ ω ) + 2 A 2 sin ( 2 ω t ) + A 1 2 2 sin ( 2 ω t + 2 ϕ ω π 2 ) ] + dc terms and higher harmonics .
A 2 = ¼ A 1 2 ,
2 ϕ ω = π 2 mod 2 π ,
A FM = n , n T n + 2 n J n ( M 1 ) J n ( M 2 ) exp { i [ ( n + 2 n ) ω t + n ϕ ω ] } ,
T n + 2 n = exp ( δ n + 2 n + i ϕ n + 2 n ) .
T n + 2 n 1 δ n + 2 n + i ϕ n + 2 n .
| A FM | 2 = M 2 [ ( δ 2 δ 2 ) cos 2 ω t ( ϕ 2 + ϕ 2 2 ϕ 0 ) sin 2 ω t ] + M 1 2 4 { [ ( 2 δ 2 δ 2 ) e δ 0 + 2 ( δ 1 + δ 1 1 ) ] × cos ( 2 ω t + 2 ϕ ω ) + [ ( ϕ 2 ϕ 2 ) e δ 0 + 2 ( ϕ 1 ϕ 1 ) ] × sin ( 2 ω t + 2 ϕ ω ) } .

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